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Sample records for bessel functions

  1. Unified Bessel, Modified Bessel, Spherical Bessel and Bessel-Clifford Functions

    OpenAIRE

    Yaşar, Banu Yılmaz; Özarslan, Mehmet Ali

    2016-01-01

    In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K{\\i}ymaz O. A certain generalized Pochhammer symbol and its applications to hypergeometric functions. Applied Mathematics and Computation, 2014, 226 : 484-491] is defined. Several potentially useful properties of the unified family such as generating function, integral representation, Laplace transform and Mellin tran...

  2. Theory of Bessel Functions of High Rank - I: Fundamental Bessel Functions

    OpenAIRE

    Qi, Zhi

    2014-01-01

    In this article we introduce a new category of special functions called fundamental Bessel functions arising from the Voronoi summation formula for $\\mathrm{GL}_n (\\mathbb{R})$. The fundamental Bessel functions of rank one and two are the oscillatory exponential functions $e^{\\pm i x}$ and the classical Bessel functions respectively. The main implements and subjects of our study of fundamental Bessel functions are their formal integral representations and Bessel equations.

  3. Conformable Fractional Bessel Equation and Bessel Functions

    OpenAIRE

    Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

    2015-01-01

    In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary solutions. In addition, we present certain property of fractional Bessel functions.

  4. Symmetric q-Bessel functions

    Directory of Open Access Journals (Sweden)

    Giuseppe Dattoli

    1996-05-01

    Full Text Available q analog of bessel functions, symmetric under the interchange of q and q^ −1 are introduced. The definition is based on the generating function realized as product of symmetric q-exponential functions with appropriate arguments. Symmetric q-Bessel function are shown to satisfy various identities as well as second-order q-differential equations, which in the limit q → 1 reproduce those obeyed by the usual cylindrical Bessel functions. A brief discussion on the possible algebraic setting for symmetric q-Bessel functions is also provided.

  5. Bessel functions

    CERN Document Server

    Nambudiripad, K B M

    2014-01-01

    After presenting the theory in engineers' language without the unfriendly abstraction of pure mathematics, several illustrative examples are discussed in great detail to see how the various functions of the Bessel family enter into the solution of technically important problems. Axisymmetric vibrations of a circular membrane, oscillations of a uniform chain, heat transfer in circular fins, buckling of columns of varying cross-section, vibrations of a circular plate and current density in a conductor of circular cross-section are considered. The problems are formulated purely from physical considerations (using, for example, Newton's law of motion, Fourier's law of heat conduction electromagnetic field equations, etc.) Infinite series expansions, recurrence relations, manipulation of expressions involving Bessel functions, orthogonality and expansion in Fourier-Bessel series are also covered in some detail. Some important topics such as asymptotic expansions, generating function and Sturm-Lioville theory are r...

  6. Integrals of Bessel functions

    OpenAIRE

    Babusci, D.; Dattoli, G.; Germano, B.; Martinelli, M. R.; Ricci, P. E.

    2011-01-01

    We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.

  7. Inequalities for the Modified k-Bessel Function

    Directory of Open Access Journals (Sweden)

    Saiful Rahman Mondal

    2017-07-01

    Full Text Available The article considers the generalized k-Bessel functions and represents it as Wright functions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel functions, and the ratio of the k-Bessel and the k-Bessel functions. The log-convexity with respect to the order of the k-Bessel also given. An investigation regarding the monotonicity of the ratio of the k-Bessel and k-confluent hypergeometric functions are discussed.

  8. Spherical Bessel transform via exponential sum approximation of spherical Bessel function

    Science.gov (United States)

    Ikeno, Hidekazu

    2018-02-01

    A new algorithm for numerical evaluation of spherical Bessel transform is proposed in this paper. In this method, the spherical Bessel function is approximately represented as an exponential sum with complex parameters. This is obtained by expressing an integral representation of spherical Bessel function in complex plane, and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double-exponential transformation. The number of terms in the expression is reduced using the modified balanced truncation method. The residual part of integrand is also expanded by exponential functions using Prony-like method. The spherical Bessel transform can be evaluated analytically on arbitrary points in half-open interval.

  9. Topological setting of Bessel functions

    International Nuclear Information System (INIS)

    Mekhfi, M.

    1995-11-01

    We start from the topology of the punctured plane encoded within its homotopy group which is isomorphic to the set of integers Z. We then realize group elements Π(n), n is an element of Z as differential operators on the space of analytic functions. Using plausible physical arguments we select a subset of functions which we identify with integer orders reduced Bessel functions. On the other hand we propose a unifying new formula of topological origin, generating real orders Bessel functions out of integers orders ones, the generator being an operator built entirely out of the Π s . We thus have shown that the topology (of the puntured plane) is underlying the inner structure of Bessel functions, in addition it unifies them independently of the orders being integers or reals. (author). 4 refs

  10. Bessel functions: parallel display and processing.

    Science.gov (United States)

    Lohmann, A W; Ojeda-Castañeda, J; Serrano-Heredia, A

    1994-01-01

    We present an optical setup that converts planar binary curves into two-dimensional amplitude distributions, which are proportional, along one axis, to the Bessel function of order n, whereas along the other axis the order n increases. This Bessel displayer can be used for parallel Bessel transformation of a signal. Experimental verifications are included.

  11. Theory of generalized Bessel functions

    International Nuclear Information System (INIS)

    Dattoli, G.; Giannessi, L.; Mezi, L.; Torre, A.

    1990-01-01

    In this paper it is discussed the theory of generalized Bessel functions which are of noticeable importance in the analysis of scattering processes for which the dipole approximation cannot be used. These functions have been introduced in their standard form and their modified version. The relevant generating functions and Graf-type addition theorems have been stated. The usefulness of the results to construct a fast algorithm for their quantitative computation is also devised. It is commented on the possibility of getting two-index generalized Bessel functions in e.g. the study of sum rules of the type Σ n=-∞ ∞ t n J n 3 (x), where J n is the cylindrical Bessel function of the first kind. The usefulness of the results for problems of practical interest is finally commented on. It is shown that a modified Anger function can be advantageously introduced to get an almost straightforward computation of the Bernstein sum rule in the theory of ion waves

  12. Extension of Oppenheim's Problem to Bessel Functions

    Directory of Open Access Journals (Sweden)

    Zhu Ling

    2007-01-01

    Full Text Available Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we deduce the hyperbolic analogue of these trigonometric inequalities, and we extend these inequalities to modified Bessel functions.

  13. Zernike vs. Bessel circular functions in visual optics.

    Science.gov (United States)

    Trevino, Juan P; Gómez-Correa, Jesus E; Iskander, D Robert; Chávez-Cerda, Sabino

    2013-07-01

    We propose the Bessel Circular Functions as alternatives of the Zernike Circle Polynomials to represent relevant circular ophthalmic surfaces. We assess the fitting capabilities of the orthogonal Bessel Circular Functions by comparing them to Zernike Circle Polynomials for approximating a variety of computationally generated surfaces which can represent ophthalmic surfaces. The Bessel Circular Functions showed better modelling capabilities for surfaces with abrupt variations such as the anterior eye surface at the limbus region, and influence functions. From our studies we find that the Bessel Circular Functions can be more suitable for studying particular features of post surgical corneal surfaces. We show that given their boundary conditions and free oscillating properties, the Bessel Circular Functions are an alternative for representing specific wavefronts and can be better than the Zernike Circle Polynomials for some important cases of corneal surfaces, influence functions and the complete anterior corneal surface. © 2013 The Authors Ophthalmic & Physiological Optics © 2013 The College of Optometrists.

  14. Computation of hyperspherical Bessel functions

    OpenAIRE

    Tram, Thomas

    2013-01-01

    In this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of large order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed so far due to the lack of a backwards recurrence. We solved this problem by establishing a relation to Gegenbauer polynomials. All our algorithms are written in C and are publicly available at Github [https://github.com/lesgourg/class_public]. A Python wrapp...

  15. Bessel-like beams modulated by arbitrary radial functions

    Science.gov (United States)

    Herman; Wiggins

    2000-06-01

    An approximate method for determining the radial and axial intensity of a Bessel-like beam is presented for the general case in which a radial Bessel distribution of any order is modulated by an arbitrary function. For Bessel-Gauss, generalized Bessel-Gauss, and Bessel-super-Gauss beams, this simple approximation yields results that are very close to the exact values, while they are exact for Bessel beams. A practical beam that can be generated with a combination of simple lenses is also analyzed and illustrated.

  16. FUNPACK-2, Subroutine Library, Bessel Function, Elliptical Integrals, Min-max Approximation

    International Nuclear Information System (INIS)

    Cody, W.J.; Garbow, Burton S.

    1975-01-01

    1 - Description of problem or function: FUNPACK is a collection of FORTRAN subroutines to evaluate certain special functions. The individual subroutines are (Identification/Description): NATSI0 F2I0 Bessel function I 0 ; NATSI1 F2I1 Bessel function I 1 ; NATSJ0 F2J0 Bessel function J 0 ; NATSJ1 F2J1 Bessel function J 1 ; NATSK0 F2K0 Bessel function K 0 ; NATSK1 F2K1 Bessel function K 1 ; NATSBESY F2BY Bessel function Y ν ; DAW F1DW Dawson's integral; DELIPK F1EK Complete elliptic integral of the first kind; DELIPE F1EE Complete elliptic integral of the second kind; DEI F1EI Exponential integrals; NATSPSI F2PS Psi (logarithmic derivative of gamma function); MONERR F1MO Error monitoring package . 2 - Method of solution: FUNPACK uses evaluation of min-max approximations

  17. Generating bessel functions in mie scattering calculations using continued fractions.

    Science.gov (United States)

    Lentz, W J

    1976-03-01

    A new method of generating the Bessel functions and ratios of Bessel functions necessary for Mie calculations is presented. Accuracy is improved while eliminating the need for extended precision word lengths or large storage capability. The algorithm uses a new technique of evaluating continued fractions that starts at the beginning rather than the tail and has a built-in error check. The continued fraction representations for both spherical Bessel functions and ratios of Bessel functions of consecutive order are presented.

  18. Poisson processes and a Bessel function integral

    NARCIS (Netherlands)

    Steutel, F.W.

    1985-01-01

    The probability of winning a simple game of competing Poisson processes turns out to be equal to the well-known Bessel function integral J(x, y) (cf. Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill, New York, 1962). Several properties of J, some of which seem to be new, follow quite easily

  19. Series of Bessel and Kummer-type functions

    CERN Document Server

    Baricz, Arpad; Pogány, Tibor K

    2017-01-01

    This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.

  20. Approximation of Analytic Functions by Bessel's Functions of Fractional Order

    Directory of Open Access Journals (Sweden)

    Soon-Mo Jung

    2011-01-01

    Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.

  1. Computer program for Bessel and Hankel functions

    Science.gov (United States)

    Kreider, Kevin L.; Saule, Arthur V.; Rice, Edward J.; Clark, Bruce J.

    1991-01-01

    A set of FORTRAN subroutines for calculating Bessel and Hankel functions is presented. The routines calculate Bessel and Hankel functions of the first and second kinds, as well as their derivatives, for wide ranges of integer order and real or complex argument in single or double precision. Depending on the order and argument, one of three evaluation methods is used: the power series definition, an Airy function expansion, or an asymptotic expansion. Routines to calculate Airy functions and their derivatives are also included.

  2. Generalized Bessel functions in tunnelling ionization

    International Nuclear Information System (INIS)

    Reiss, H R; Krainov, V P

    2003-01-01

    We develop two new approximations for the generalized Bessel function that frequently arises in the analytical treatment of strong-field processes, especially in non-perturbative multiphoton ionization theories. Both these new forms are applicable to the tunnelling environment in atomic ionization, and are analytically much simpler than the currently used low-frequency asymptotic approximation for the generalized Bessel function. The second of the new forms is an approximation to the first, and it is the second new form that exhibits the well-known tunnelling exponential

  3. Bessel functions for root systems via the trigonometric setting

    DEFF Research Database (Denmark)

    Ørsted, Bent; Said, S.B.

    2005-01-01

    In this paper, we study generalized Bessel functions related to root systems and give explicit formulas in several cases.......In this paper, we study generalized Bessel functions related to root systems and give explicit formulas in several cases....

  4. The Bessel functions J0 and J1 of complex argument

    International Nuclear Information System (INIS)

    Ardill, R.W.B.; Moriarty, K.J.M.

    1977-01-01

    The Bessel function appears in a wide range of physical applications. The package Bessel contains complex function routines to calculate J 0 (z) and J 1 (z) for complex z. Bessel functions of higher order n 0 (z) and J 1 (z) for all values of mod(z) up to machine overflow. For mod(z) 10, the results diverge quite rapidly from their actual values. The accuracy for mod(z)<=10 is sufficient for most physical applications, and the polynomial approximations provide a quicker calculation of Bessel functions than the use of the ascending series formula used previously, particularly for values of mod(z) near 10. (Auth.)

  5. q-Sumudu transforms of q-analogues of Bessel functions.

    Science.gov (United States)

    Uçar, Faruk

    2014-01-01

    The main purpose of this paper is to evaluate q-Sumudu transforms of a product of q-Bessel functions. Interesting special cases of theorems are also discussed. Further, the results proved in this paper may find certain applications of q-Sumudu transforms to the solutions of the q-integrodifferential equations involving q-Bessel functions. The results may help to extend the q-theory of orthogonal functions.

  6. Bessel harmonic analysis and approximation of functions on the half-line

    International Nuclear Information System (INIS)

    Platonov, Sergei S

    2007-01-01

    We study problems of approximation of functions on [0,+∞) in the metric of L p with power weight using generalized Bessel shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Bessel shifts. We establish the equivalence of the modulus of smoothness and the K-functional. We define function spaces of Nikol'skii-Besov type and describe them in terms of best approximations. As a tool for approximation, we use a certain class of entire functions of exponential type. In this class, we prove analogues of Bernstein's inequality and others for the Bessel differential operator and its fractional powers. The main tool we use to solve these problems is Bessel harmonic analysis

  7. Fourier expansions and multivariable Bessel functions concerning radiation programmes

    International Nuclear Information System (INIS)

    Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.

    1996-01-01

    The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)

  8. Numerical model of the influence function of deformable mirrors based on Bessel Fourier orthogonal functions

    International Nuclear Information System (INIS)

    Li Shun; Zhang Sijiong

    2014-01-01

    A numerical model is presented to simulate the influence function of deformable mirror actuators. The numerical model is formed by Bessel Fourier orthogonal functions, which are constituted of Bessel orthogonal functions and a Fourier basis. A detailed comparison is presented between the new Bessel Fourier model, the Zernike model, the Gaussian influence function and the modified Gaussian influence function. Numerical experiments indicate that the new numerical model is easy to use and more accurate compared with other numerical models. The new numerical model can be used for describing deformable mirror performances and numerical simulations of adaptive optics systems. (research papers)

  9. On numerical Bessel transformation

    International Nuclear Information System (INIS)

    Sommer, B.; Zabolitzky, J.G.

    1979-01-01

    The authors present a computer program to calculate the three dimensional Fourier or Bessel transforms and definite integrals with Bessel functions. Numerical integration of systems containing Bessel functions occurs in many physical problems, e.g. electromagnetic form factor of nuclei, all transitions involving multipole expansions at high momenta. Filon's integration rule is extended to spherical Bessel functions. The numerical error is of the order of the Simpson error term of the function which has to be transformed. Thus one gets a stable integral even at large arguments of the transformed function. (Auth.)

  10. Optimized Kaiser-Bessel Window Functions for Computed Tomography.

    Science.gov (United States)

    Nilchian, Masih; Ward, John Paul; Vonesch, Cedric; Unser, Michael

    2015-11-01

    Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform independent of the direction. In this paper, we aim at optimizing the parameters of these basis functions. We present a formalism based on the theory of approximation and point out the importance of the partition-of-unity condition. While we prove that, for compact-support functions, this condition is incompatible with isotropy, we show that minimizing the deviation from the partition of unity condition is highly beneficial. The numerical results confirm that the proposed tuning of the Kaiser-Bessel window functions yields the best performance.

  11. A Limit Relation for Dunkl-Bessel Functions of Type A and B

    Directory of Open Access Journals (Sweden)

    Margit Rösler

    2008-12-01

    Full Text Available We prove a limit relation for the Dunkl-Bessel function of type BN with multiplicity parameters k_1 on the roots ±ei and k_2 on ±e_i±e_j where k_1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkl-type Bessel function of type A_{N−1} with multiplicity k_2. For certain values of k_2 an improved estimate is obtained from a corresponding limit relation for Bessel functions on matrix cones.

  12. The Bessel-Struve intertwining operator on ℂ and mean-periodic functions

    Directory of Open Access Journals (Sweden)

    A. Gasmi

    2004-01-01

    Full Text Available We give a description of all transmutation operators from the Bessel-Struve operator to the second-derivative operator. Next we define and characterize the mean-periodic functions on the space ℋ of entire functions and we characterize the continuous linear mappings from ℋ into itself which commute with Bessel-Struve operator.

  13. Symbolic methods for the evaluation of sum rules of Bessel functions

    International Nuclear Information System (INIS)

    Babusci, D.; Dattoli, G.; Górska, K.; Penson, K. A.

    2013-01-01

    The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics

  14. Bessel functions in mass action modeling of memories and remembrances

    Energy Technology Data Exchange (ETDEWEB)

    Freeman, Walter J. [Department of Molecular and Cell Biology, University of California, Berkeley, CA 94720-3206 (United States); Capolupo, Antonio [Dipartimento di Fisica, E.R. Caianiello Universitá di Salerno, and INFN Gruppo collegato di Salerno, Fisciano 84084 (Italy); Kozma, Robert [Department of Mathematics, Memphis University, Memphis, TN 38152 (United States); Olivares del Campo, Andrés [The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BZ (United Kingdom); Vitiello, Giuseppe, E-mail: vitiello@sa.infn.it [Dipartimento di Fisica, E.R. Caianiello Universitá di Salerno, and INFN Gruppo collegato di Salerno, Fisciano 84084 (Italy)

    2015-10-02

    Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which provide time dependent representation of Bessel equation. The root loci of poles and zeros conform to solutions of K-sets. Some light is shed on the problem of filling the gap between the cellular level dynamics and the brain functional activity. Breakdown of time-reversal symmetry is related with the cortex thermodynamic features. This provides a possible mechanism to deduce lifetime of recorded memory. - Highlights: • We consider data from observations of impulse responses of cortex to electric shocks. • These data are fitted by Bessel functions which may be represented by couples of damped/amplified oscillators. • We study the data by using couples of damped/amplified oscillators. • We discuss lifetime and other properties of the considered brain processes.

  15. Bessel-function analysis of the optimized star coupler for uniform power splitting.

    Science.gov (United States)

    Song, G Hugh; Park, Mahn Yong

    2004-08-01

    An optimized N x N planar optic star coupler that utilizes directional coupling of arrayed waveguides for uniform power splitting is analyzed on the basis of special properties of the involved Bessel-function series. The analysis has provided a remarkably simple, novel basic design formula for such a device with much needed physical insights into the unique diffraction properties. For the analysis of diffraction from the end of directionally coupled arrayed waveguides, many useful formulas around the Bessel functions, such as the addition theorem and the Kepler-Bessel series, have been given in new forms.

  16. Comment on 'Analytical results for a Bessel function times Legendre polynomials class integrals'

    International Nuclear Information System (INIS)

    Cregg, P J; Svedlindh, P

    2007-01-01

    A result is obtained, stemming from Gegenbauer, where the products of certain Bessel functions and exponentials are expressed in terms of an infinite series of spherical Bessel functions and products of associated Legendre functions. Closed form solutions for integrals involving Bessel functions times associated Legendre functions times exponentials, recently elucidated by Neves et al (J. Phys. A: Math. Gen. 39 L293), are then shown to result directly from the orthogonality properties of the associated Legendre functions. This result offers greater flexibility in the treatment of classical Heisenberg chains and may do so in other problems such as occur in electromagnetic diffraction theory. (comment)

  17. K-Bessel functions associated to a 3-rank Jordan algebra

    Directory of Open Access Journals (Sweden)

    Hacen Dib

    2005-01-01

    Full Text Available Using the Bessel-Muirhead system, we can express the K-Bessel function defined on a Jordan algebra as a linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a reduction to the rank two. The main tools are some algebraic identities developed for this occasion.

  18. On functions defined by sums of products of Bessel functions

    International Nuclear Information System (INIS)

    Martin, P A

    2008-01-01

    Various functions, defined as infinite series of products of Bessel functions of the first kind, are studied. Integral representations are obtained, and then used to deduce asymptotic approximations. Although several methods have been investigated (including power series expansions and integral transforms), methods based on Fourier series emerge as the most useful

  19. Monotonicity and bounds on Bessel functions

    Directory of Open Access Journals (Sweden)

    Larry Landau

    2000-07-01

    Full Text Available survey my recent results on monotonicity with respect to order of general Bessel functions, which follow from a new identity and lead to best possible uniform bounds. Application may be made to the "spreading of the wave packet" for a free quantum particle on a lattice and to estimates for perturbative expansions.

  20. General description of transverse mode Bessel beams and construction of basis Bessel fields

    Science.gov (United States)

    Wang, Jia Jie; Wriedt, Thomas; Lock, James A.; Jiao, Yong Chang

    2017-07-01

    Based on an analysis of polarized Bessel beams using the Hertz vector potentials and the angular spectrum representation (ASR), a general description of transverse mode Bessel beams is proposed. As opposed to the cases of linearly and circularly polarized Bessel beams, the magnetic and electric fields of a Bessel beam in a transverse mode are orthogonal to each other. Both sets of fields together form a complete set of basis Bessel fields, in terms of which an arbitrary Bessel beam can be regarded as a linear combination. The completeness of the basis Bessel fields is analyzed from the perspectives of waveguide theory and vector wave functions. Decompositions of linearly polarized, circularly polarized, and circularly symmetric n-order Bessel beams in terms of basis Bessel fields are given. The results presented in this paper provide a fresh perspective on the description of Bessel beams, which are useful in casting insights into the experimental generation of Bessel beams and the interpretation of light scattering-related problems in practice.

  1. A linear combination of modified Bessel functions

    Science.gov (United States)

    Shitzer, A.; Chato, J. C.

    1971-01-01

    A linear combination of modified Bessel functions is defined, discussed briefly, and tabulated. This combination was found to recur in the analysis of various heat transfer problems and in the analysis of the thermal behavior of living tissue when modeled by cylindrical shells.

  2. Quasi-fractional approximation to the Bessel functions

    International Nuclear Information System (INIS)

    Guerrero, P.M.L.

    1989-01-01

    In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions J ν (x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4

  3. Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions.

    Science.gov (United States)

    Ziener, Christian H; Kurz, Felix T; Buschle, Lukas R; Kampf, Thomas

    2015-01-01

    The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval [Formula: see text] with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function [Formula: see text] or linear combinations of the spherical Bessel functions [Formula: see text]. The orthogonality relations with analytical expressions for the normalization constant are given. Explicit expressions for the Lommel integrals in terms of Lommel functions are derived. The cross product zeros [Formula: see text] and [Formula: see text] are considered in the complex plane for real as well as complex values of the index [Formula: see text] and approximations for the exceptional zero [Formula: see text] are obtained. A numerical scheme based on the discretization of the two-dimensional and three-dimensional Laplace operator with Neumann boundary conditions is presented. Explicit representations of the radial part of the Laplace operator in form of a tridiagonal matrix allow the simple computation of the cross product zeros.

  4. Multidimensional digital image representations using generalized Kaiser-Bessel window functions.

    Science.gov (United States)

    Lewitt, R M

    1990-10-01

    Inverse problems that require the solution of integral equations are inherent in a number of indirect imaging applications, such as computerized tomography. Numerical solutions based on discretization of the mathematical model of the imaging process, or on discretization of analytic formulas for iterative inversion of the integral equations, require a discrete representation of an underlying continuous image. This paper describes discrete image representations, in n-dimensional space, that are constructed by the superposition of shifted copies of a rotationally symmetric basis function. The basis function is constructed using a generalization of the Kaiser-Bessel window function of digital signal processing. The generalization of the window function involves going from one dimension to a rotationally symmetric function in n dimensions and going from the zero-order modified Bessel function of the standard window to a function involving the modified Bessel function of order m. Three methods are given for the construction, in n-dimensional space, of basis functions having a specified (finite) number of continuous derivatives, and formulas are derived for the Fourier transform, the x-ray transform, the gradient, and the Laplacian of these basis functions. Properties of the new image representations using these basis functions are discussed, primarily in the context of two-dimensional and three-dimensional image reconstruction from line-integral data by iterative inversion of the x-ray transform. Potential applications to three-dimensional image display are also mentioned.

  5. Nonparaxial Bessel and Bessel-Gauss pincers light-sheets

    Science.gov (United States)

    Mitri, F. G.

    2017-01-01

    Nonparaxial optical Bessel and Bessel-Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.

  6. On the Computation and Applications of Bessel Functions with Pure Imaginary Indices

    OpenAIRE

    Matyshev, A. A.; Fohtung, E.

    2009-01-01

    Bessel functions with pure imaginary index (order) play an important role in corpuscular optics where they govern the dynamics of charged particles in isotrajectory quadrupoles. Recently they were found to be of great importance in semiconductor material characterization as they are manifested in the strain state of crystalline material. A new algorithm which can be used for the computation of the normal and modifed Bessel functions with pure imaginary index is proposed. The developed algorit...

  7. Further properties of the zeros of Bessel functions

    Directory of Open Access Journals (Sweden)

    Carla Giordano

    1987-11-01

    Full Text Available New monotonicity and convexity properties for the zeros cνk  (k=1,2,... of the Bessel functions are proved. New inequalities for cνk are also given. These inequalities are useful for small values of ν.

  8. Bessel Weighted Asymmetries

    Energy Technology Data Exchange (ETDEWEB)

    Avakian, Harut [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Gamberg, Leonard [Pennsylvania State Univ., University Park, PA (United States); Rossi, Patrizia [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Prokudin, Alexei [Pennsylvania State Univ., University Park, PA (United States)

    2016-05-01

    We review the concept of Bessel weighted asymmetries for semi-inclusive deep inelastic scattering and focus on the cross section in Fourier space, conjugate to the outgoing hadron’s transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. The procedure is applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations, which is due to the limitations imposed by the energy and momentum conservation at the given energy and hard scale Q2. We find that the Bessel weighting technique provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs.

  9. Generalized coherent states related to the associated Bessel functions and Morse potential

    International Nuclear Information System (INIS)

    Mojaveri, B; Amiri Faseghandis, S

    2014-01-01

    Using the associated Bessel functions, a shape-invariant Lie algebra spanned by ladder operators plus the identity operator, is realized. The Hilbert space of the associated Bessel functions, representing the Lie algebra, are established and two kinds of generalized coherent states as an appropriate superposition of these functions are constructed. By implying appropriate similarity transformation on the constructed coherent states, the generalized coherent states for the Morse potential are obtained. By considering some statistical characteristics, it is revealed that the constructed coherent states indeed possess nonclassical features, such as squeezing and sub-Poissonian statistics. (paper)

  10. Superiority of Bessel function over Zernicke polynomial as base ...

    Indian Academy of Sciences (India)

    Abstract. Here we describe the superiority of Bessel function as base function for radial expan- sion over Zernicke polynomial in the tomographic reconstruction technique. The causes for the superiority have been described in detail. The superiority has been shown both with simulated data for Kadomtsev's model for ...

  11. Expansion of infinite series containing modified Bessel functions of the second kind

    International Nuclear Information System (INIS)

    Fucci, Guglielmo; Kirsten, Klaus

    2015-01-01

    The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the parameters in the argument of the modified Bessel function of the second kind is small compared to the others. We apply the results obtained for the asymptotic expansion to specific problems that arise in the ambit of quantum field theory. (paper)

  12. Studies on the Zeroes of Bessel Functions and Methods for Their Computation: IV. Inequalities, Estimates, Expansions, etc., for Zeros of Bessel Functions

    Science.gov (United States)

    Kerimov, M. K.

    2018-01-01

    This paper is the fourth in a series of survey articles concerning zeros of Bessel functions and methods for their computation. Various inequalities, estimates, expansions, etc. for positive zeros are analyzed, and some results are described in detail with proofs.

  13. A simple derivation of new sum rules of Bessel functions

    International Nuclear Information System (INIS)

    Ciocci, F.; Dattoli, G.; Dipace, A.

    1985-01-01

    In this note it is exploited a recently suggested technique to get simple expressions for a class of sum rules of Bessel functions appearing in plasma physics; their relevance to the numerical evaluation of the Turkin function is also discussed

  14. Studies on the zeros of Bessel functions and methods for their computation

    Science.gov (United States)

    Kerimov, M. K.

    2014-09-01

    The zeros of Bessel functions play an important role in computational mathematics, mathematical physics, and other areas of natural sciences. Studies addressing these zeros (their properties, computational methods) can be found in various sources. This paper offers a detailed overview of the results concerning the real zeros of the Bessel functions of the first and second kinds and general cylinder functions. The author intends to publish several overviews on this subject. In this first publication, works dealing with real zeros are analyzed. Primary emphasis is placed on classical results, which are still important. Some of the most recent publications are also discussed.

  15. Further 'comment on 'Generalized Bessel functions in tunnelling ionization''

    International Nuclear Information System (INIS)

    Reiss, H R; Krainov, V P

    2005-01-01

    J Bauer, in commenting on our tunnelling approximation for the generalized Bessel function, points out that when the approximation is applied to strong-field ionization, it is suitable only for the lowest-energy part of an ionization spectrum. We do not disagree. We point out several things: the results of Bauer are to be expected; linear polarization results are dominated by the lowest part of the multiphoton spectrum; and we do not recommend practical use of this tunnelling approximation, since the asymptotic approximation is so much better. We show comparisons of momentum distributions calculated with the tunnelling approximation and those with the complete strong-field approximation, which show in more detail than spectrum comparisons that the tunnelling approximation to the generalized Bessel function is applicable only to the low-momentum part of the distribution, and neglects altogether the high-momentum portion. (reply)

  16. On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind

    Directory of Open Access Journals (Sweden)

    Dinesh Kumar

    2015-01-01

    Full Text Available We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably new results.

  17. Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions.

    Science.gov (United States)

    Lötstedt, Erik; Jentschura, Ulrich D

    2009-02-01

    In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.

  18. The generalized Laguerre polynomials, the associated Bessel functions and application to propagation problems

    International Nuclear Information System (INIS)

    Dattoli, G.; Torre, A.; Mancho, A.M.

    2000-01-01

    The theory of generalized Bessel functions has found significant applications in the analysis of radiation phenomena, associated with charges moving in magnetic devices. In this paper we exploit the monomiality principle to discuss the theory of two-variable Laguerre polynomials and introduce the associated Laguerre-Bessel functions. We study their properties (addition and multiplication theorems, generating function, recurrence relations and so on) and discuss the link with the ordinary case. The usefulness of the obtained results to treat problems relevant to the paraxial propagation of electromagnetic waves is also discussed.

  19. Algorithm 831: modified Bessel functions of imaginary order and positive argument

    NARCIS (Netherlands)

    A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

    2004-01-01

    textabstract77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions Kia (x), Lia (x) and their derivatives for real a and positive x; these functions are independent solutions of the differential equation x2w'' + xw' + (a2

  20. Stability of cylindrical plasma in the Bessel function model

    International Nuclear Information System (INIS)

    Yamagishi, T.; Gimblett, C.G.

    1988-01-01

    The stability of free boundary ideal and tearing modes in a cylindrical plasma is studied by examining the discontinuity (Δ') of the helical flux function given by the force free Bessel function model at the singular surface. The m = O and m = 1 free boundary tearing modes become strongly unstable when the singular surface is just inside the plasma boundary for a wide range of longitudinal wave numbers. (author)

  1. Theory of generalized Bessel functions: Pt. 2

    International Nuclear Information System (INIS)

    Dattoli, G.; Torre, A.; Chiccoli, C.

    1991-01-01

    In this paper the systematic study of the generalized Bessel functions (GBF), recently introduced and often encountered in problems of scattering for which the dipole approximation is inadequate, is continuated. The relations among different GBF are analysed and their importance for the solution of differential finite-difference equation of the Raman-Nath type is discussed. Numerical results for the first-kind cylinder GBF in the preasymptotic region and also a preliminary analysis of the asymptotic properties of the modified GBF are presented

  2. On a new class of integrals involving Bessel functions of the first kind

    Directory of Open Access Journals (Sweden)

    P. Agarwal

    2014-06-01

    Full Text Available In recent years, several integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas containing the Bessel function $J_\

  3. On a family of Bessel type functions: Estimations, series, overconvergence

    Science.gov (United States)

    Paneva-Konovska, Jordanka

    2017-12-01

    A family of the Bessel-Maitland functions are considered in this paper and some useful estimations are obtained for them. Series defined by means of these functions are considered and their behaviour on the boundaries of the convergence domains is discussed. Using the obtained estimations, necessary and sufficient conditions for the series overconvergence, as well as Hadamard type theorem are proposed.

  4. Computation of bessel functions in light scattering studies.

    Science.gov (United States)

    Ross, W D

    1972-09-01

    Computations of light scattering require finding Bessel functions of a series of orders. These are found most easily by recurrence, but excessive rounding errors may accumulate. Satisfactory procedures for cylinder and sphere functions are described. If argument z is real, find Y(n)(z) by recurrence to high orders. From two high orders of Y(n)(z) estimate J(n)(z). Use backward recurrence to maximum J(n)(z). Correct by forward recurrence to maximum. If z is complex, estimate high orders of J(n)(z) without Y(n)(z) and use backward recurrence.

  5. A symmetric integral identity for Bessel functions with applications to integral geometry

    Science.gov (United States)

    Salman, Yehonatan

    2017-12-01

    In the article of Kunyansky (Inverse Probl 23(1):373-383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in Rn . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in R2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates.

  6. Asymptotic formulae for the Lommel and Bessel functions and their derivatives.

    Science.gov (United States)

    Aleksandrova, N I

    2014-10-01

    We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for what values of the parameters our representations have reasonable accuracy.

  7. Sobre la inversión de los potenciales de Bessel-Riesz Sobre la inversión de los potenciales de Bessel-Riesz

    Directory of Open Access Journals (Sweden)

    Ruben Alejandro Cerutti

    2010-02-01

    Full Text Available En este trabajo se obtiene la inversión de un operador del tipo convolución usando técnicas de integrales hipersingulares. El operador de Bessel-Riesz de una función ϕ perteneciente a S , el espacio de funciones de prueba de Schwartz, es definido por la convolución con las funciones generalizadas (fórmula expresables en términos de la función de Bessel de primera especie (formula es también una combinación lineal infinita del núcleo ultrahiperbólico de Riesz de diferentes ordenes. Este hecho nos permite invertir los potenciales de Bessel-Riesz de un modo análogo a lo αhecho en el caso de los potenciales ultrahiperbólicos de Bessel (cf. [01] y los potenciales causales de Riesz (cf. [2].In this paper the inversion of a convolution type operator is obtained by using hypersingular integral technics. The Bessel-Riesz operator of a function ϕ belonging to S , the space of test functions of Schwartz, is definied by the convolution with the generalized functions  (formula expressible in terms of the Bessel function of first kind (formula . γ is also an infinite linear combination of the ultrahyperbolic Riesz kernel of differents orders. This fact allows us to invert the Bessel-Riesz potential in an analogue manner of the ultrahyperbolic Bessel potentials (cf. [01] and causal Riesz potentials (cf. [2].

  8. Analysis of optical vortices with suppressed sidelobes using modified Bessel-like function and trapezoid annulus modulation structures.

    Science.gov (United States)

    Guo, Jian; Wei, Zhongchao; Liu, Yuebo; Huang, Aili

    2015-02-01

    Two amplitude modulation methods, including modified Bessel-like function modulation structure and trapezoid annulus structure, for suppressing sidelobes of optical vortices are studied. In the former approach, we propose that the order of the Bessel-like function can be an additional parameter to modulate diffraction patterns of optical vortices motivated by the idea of conventional annulus structures. Furthermore, new Bessel-like modulation functions are introduced to solve the problem of low diffraction efficiency of the original one. Trapezoid annulus structure is proposed as a compromise structure between the modified Bessel-like modulation structure and the conventional annulus one, and has advantages of both. It is demonstrated that these two approaches can achieve high-quality optical vortices with suppressed sidelobes effectively, and the relative structures behave as more flexible and applicable structures for producing optical vortices with large coverage of topological charges, which suggests great potential in simplifying the structure designing procedure. These reliable and generalized structures for generating high-quality optical vortices will help to promote the development of future optical communication and optical manipulation significantly.

  9. Reciprocal expansion of modified Bessel function in simple fractions and obtaining general summation relationships containing its zeros

    Science.gov (United States)

    Sherstyukov, V. B.; Sumin, E. V.

    2017-12-01

    Modified Bessel functions of the first kind Iv (z) (Infeld functions) where v > -1 are considered. Due to the constraint on the parameter v, all zeros of the function Iv (z) except z = 0 are simple, located on the imaginary axis by symmetric pairs and form an infinite countable set. On the basis on previous research of the authors dealing with general Bessel functions of the first kind Jv (z), a question about reciprocal expansion 1/Iv (z) in series of simple fractions of a certain structure (Krein’s series) is studied. The general formulas to calculate of special infinite sums containing degrees of Infeld function zeros are an important consequence of obtained expansion in simple fractions of the value 1/Iv (z) with any v > -1. The possibility of concrete definition of established summation relationships at different values of parameters and their connection with analogous relationships for the Bessel functions of the first kind Jv (z) is discussed.

  10. Physical Applications of a Simple Approximation of Bessel Functions of Integer Order

    Science.gov (United States)

    Barsan, V.; Cojocaru, S.

    2007-01-01

    Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…

  11. Semi-Inclusive Deep Inelastic Scattering and Bessel-Weighted Asymmetries

    International Nuclear Information System (INIS)

    Gamberg, Leonard; Boer, Daniel; Musch, Bernhard; Prokudin, Alexei

    2012-01-01

    We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

  12. A generalization for the infinite integral over three spherical Bessel functions

    International Nuclear Information System (INIS)

    Mehrem, R; Hohenegger, A

    2010-01-01

    A new formula is derived that generalizes an earlier result for the infinite integral over three spherical Bessel functions. The analytical result involves a finite sum over associated Legendre functions, P m l (x) of degree l and order m. The sum allows for the values of |m| that are greater than l. A generalization for the associated Legendre functions to allow for any rational m for a specific l is also shown.

  13. Factorization of products of discontinuous functions applied to Fourier-Bessel basis.

    Science.gov (United States)

    Popov, Evgeny; Nevière, Michel; Bonod, Nicolas

    2004-01-01

    The factorization rules of Li [J. Opt. Soc. Am. A 13, 1870 (1996)] are generalized to a cylindrical geometry requiring the use of a Bessel function basis. A theoretical study confirms the validity of the Laurent rule when a product of two continuous functions or of one continuous and one discontinuous function is factorized. The necessity of applying the so-called inverse rule in factorizing a continuous product of two discontinuous functions in a truncated basis is demonstrated theoretically and numerically.

  14. Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering

    International Nuclear Information System (INIS)

    Boer, D.; Gamberg, L.; Musch, B.U.; Prokudin, A.

    2011-01-01

    The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

  15. Generation of Nondiffracting Electron Bessel Beams

    Directory of Open Access Journals (Sweden)

    Vincenzo Grillo

    2014-01-01

    Full Text Available Almost 30 years ago, Durnin discovered that an optical beam with a transverse intensity profile in the form of a Bessel function of the first order is immune to the effects of diffraction. Unlike most laser beams, which spread upon propagation, the transverse distribution of these Bessel beams remains constant. Electrons also obey a wave equation (the Schrödinger equation, and therefore Bessel beams also exist for electron waves. We generate an electron Bessel beam by diffracting electrons from a nanoscale phase hologram. The hologram imposes a conical phase structure on the electron wave-packet spectrum, thus transforming it into a conical superposition of infinite plane waves, that is, a Bessel beam. We verify experimentally that these beams can propagate for 0.6 m without measurable spreading and can also reconstruct their intensity distributions after being partially obstructed by an obstacle. Finally, we show by numerical calculations that the performance of an electron microscope can be increased dramatically through use of these beams.

  16. Certain new unified integrals associated with the product of generalized Bessel functions

    Directory of Open Access Journals (Sweden)

    Praveen Agarwal

    2016-02-01

    Full Text Available Our focus to presenting two very general integral formulas whose integrands are the integrand given in the Oberhettinger's integral formula and a finite product of the generalized Bessel function of the first kind, which are expressed in terms of the generalized Lauricella functions. Among a large number of interesting and potentially useful special cases of our main results, some integral formulas involving such elementary functions are also considered.

  17. Analytic approximation for the modified Bessel function I -2/3(x)

    Science.gov (United States)

    Martin, Pablo; Olivares, Jorge; Maass, Fernando

    2017-12-01

    In the present work an analytic approximation to modified Bessel function of negative fractional order I -2/3(x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and assymptotic expansions are simultaneously used to obtain the approximation.

  18. Numerical evaluation of integrals containing a spherical Bessel function by product integration

    International Nuclear Information System (INIS)

    Lehman, D.R.; Parke, W.C.; Maximon, L.C.

    1981-01-01

    A method is developed for numerical evaluation of integrals with k-integration range from 0 to infinity that contain a spherical Bessel function j/sub l/(kr) explicitly. The required quadrature weights are easily calculated and the rate of convergence is rapid: only a relatively small number of quadrature points is needed: for an accurate evaluation even when r is large. The quadrature rule is obtained by the method of product integration. With the abscissas chosen to be those of Clenshaw--Curtis and the Chebyshev polynomials as the interpolating polynomials, quadrature weights are obtained that depend on the spherical Bessel function. An inhomogenous recurrence relation is derived from which the weights can be calculated without accumulation of roundoff error. The procedure is summarized as an easily implementable algorithm. Questions of convergence are discussed and the rate of convergence demonstrated for several test integrals. Alternative procedures are given for generating the integration weights and an error analysis of the method is presented

  19. Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

    Science.gov (United States)

    Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

    2017-07-10

    This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

  20. Studies on the zeros of Bessel functions and methods for their computation: 2. Monotonicity, convexity, concavity, and other properties

    Science.gov (United States)

    Kerimov, M. K.

    2016-07-01

    This work continues the study of real zeros of first- and second-kind Bessel functions and Bessel general functions with real variables and orders begun in the first part of this paper (see M.K. Kerimov, Comput. Math. Math. Phys. 54 (9), 1337-1388 (2014)). Some new results concerning such zeros are described and analyzed. Special attention is given to the monotonicity, convexity, and concavity of zeros with respect to their ranks and other parameters.

  1. Multipole expansion of acoustical Bessel beams with arbitrary order and location.

    Science.gov (United States)

    Gong, Zhixiong; Marston, Philip L; Li, Wei; Chai, Yingbin

    2017-06-01

    An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.

  2. An exactly solvable model of an oscillator with nonlinear coupling and zeros of Bessel functions

    Science.gov (United States)

    Dodonov, V. V.; Klimov, A. B.

    1993-01-01

    We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.

  3. Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

    International Nuclear Information System (INIS)

    Doha, E H; Ahmed, H M

    2004-01-01

    A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed

  4. Scattering of a high-order Bessel beam by a spheroidal particle

    Science.gov (United States)

    Han, Lu

    2018-05-01

    Within the framework of generalized Lorenz-Mie theory (GLMT), scattering from a homogeneous spheroidal particle illuminated by a high-order Bessel beam is formulated analytically. The high-order Bessel beam is expanded in terms of spheroidal vector wave functions, where the spheroidal beam shape coefficients (BSCs) are computed conveniently using an intrinsic method. Numerical results concerning scattered field in the far zone are displayed for various parameters of the incident Bessel beam and of the scatter. These results are expected to provide useful insights into the scattering of a Bessel beam by nonspherical particles and particle manipulation applications using Bessel beams.

  5. Three-dimensional Bessel light bullets in self-focusing Kerr media

    International Nuclear Information System (INIS)

    Zhong Weiping; Belic, Milivoj; Huang Tingwen

    2010-01-01

    We study three-dimensional (3D) Bessel light-bullet solutions of the nonlinear Schroedinger equation with a photonic lattice potential in the form of squared Bessel functions in polar coordinates, both analytically and numerically. Analytical solutions are obtained by the Hartree approximation, and numerical simulations are performed, to compare with the analytical solutions and to confirm the stability of localized solutions. The 3D spatial wave packets are built by the products of hyperbolic secant and Bessel functions. These solitons appear in different forms, such as 3D vortex solitons and multipole solitons.

  6. Certain fractional integral formulas involving the product of generalized Bessel functions.

    Science.gov (United States)

    Baleanu, D; Agarwal, P; Purohit, S D

    2013-01-01

    We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

  7. Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

    Science.gov (United States)

    Baleanu, D.; Agarwal, P.; Purohit, S. D.

    2013-01-01

    We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions. PMID:24379745

  8. Mean intensity of the fundamental Bessel-Gaussian beam in turbulent atmosphere

    Science.gov (United States)

    Lukin, Igor P.

    2017-11-01

    In the given article mean intensity of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is studied. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian beam of optical radiation. Distributions of mean intensity of a fundamental Bessel- Gaussian beam optical beam in longitudinal and transverse to a direction of propagation of optical radiation are investigated in detail. Influence of atmospheric turbulence on change of radius of the central part of a Bessel optical beam is estimated. Values of parameters at which it is possible to generate in turbulent atmosphere a nondiffracting pseudo-Bessel optical beam by means of a fundamental Bessel-Gaussian optical beam are established.

  9. Spherical Bessel functions jsub(n) and ysub(n) of integer order and real argument

    International Nuclear Information System (INIS)

    Ardill, R.W.B.; Moriarty, K.J.M.

    1978-01-01

    The spherical Bessel function appears in a variety of physical applications, and especially in phase shift analysis. The package SPHBES contains a subroutine to calculate jsub(n)(x) and ysub(n)(x) for any integer order n and real argument x. The functions jsub(n)(x) and ysub(n)(x) are produced simultaneously and efficiently. (Auth.)

  10. Roots of two transcendental equations involving spherical bessel functions

    International Nuclear Information System (INIS)

    Pexton, R.L.; Steiger, A.D.

    1977-01-01

    Roots of the transcendental equations j/sub l/(αlambda) y/sub l/(lambda) =j/sub l/(lambda) y/sub l/(αlambda) and [xj/sub l/(x)]'/sub x alphaeta yl-italic/(x)]'/sub x eta/=xj/sub l/(x)]'/sub x eta yl-italic/(x)]'/sub x alphaeta/for the spherical Bessel functions of the first and second kind, j/sub l/(z) and y/sub l/(z), have been computed. The ranges for the parameter α, the order l and the root index n are: α=0.1(0.1)0.7,l=1(1)15,n=1(1)30

  11. Scattering of linearly polarized Bessel beams by dielectric spheres

    Science.gov (United States)

    Shoorian, Hamed

    2017-09-01

    The scattering of a Linearly Polarized Bessel Beam (LPBB) by an isotropic and homogenous dielectric sphere is investigated. Using analytical relation between the cylindrical and the spherical vector wave functions, all the closed- form analytical expressions, in terms of spherical wave-functions expansions, are derived for the scattered field. It is shown that in the case of conical angle of incident Bessel beam is equal to zero, the Linearly Polarized Bessel Beam becomes a plane wave and its scattering coefficients become the same as the expansion coefficients of plane wave in Mie theory. The transverse Cartesian and spherical components of the electric field, scattered by a sphere are shown in the z-plane for different cases, moreover the intensity of the incident Bessel beam and the effects of its conical angle on the scattered field and the field inside the sphere are investigated. To quantitatively study the scattering phenomenon and the variations of the fields inside and outside of the sphere, the scattering and absorption efficiencies are obtained for the scattering of the linearly-polarized Bessel beam, and are compared with those of the plane wave scattering.

  12. Studies on the zeros of Bessel functions and methods for their computation: 3. Some new works on monotonicity, convexity, and other properties

    Science.gov (United States)

    Kerimov, M. K.

    2016-12-01

    This paper continues the study of real zeros of Bessel functions begun in the previous parts of this work (see M. K. Kerimov, Comput. Math. Math. Phys. 54 (9), 1337-1388 (2014); 56 (7), 1175-1208 (2016)). Some new results regarding the monotonicity, convexity, concavity, and other properties of zeros are described. Additionally, the zeros of q-Bessel functions are investigated.

  13. Dispersion relation for Bernstein waves using a new transformation for the modified Bessel function

    International Nuclear Information System (INIS)

    Sato, Masumi

    1985-01-01

    Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves. (author)

  14. Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions

    CERN Document Server

    Farrell, Orin J

    2013-01-01

    Nearly 200 problems, each with a detailed, worked-out solution, deal with the properties and applications of the gamma and beta functions, Legendre polynomials, and Bessel functions. The first two chapters examine gamma and beta functions, including applications to certain geometrical and physical problems such as heat-flow in a straight wire. The following two chapters treat Legendre polynomials, addressing applications to specific series expansions, steady-state heat-flow temperature distribution, gravitational potential of a circular lamina, and application of Gauss's mechanical quadrature

  15. Terahertz plasmonic Bessel beamformer

    International Nuclear Information System (INIS)

    Monnai, Yasuaki; Shinoda, Hiroyuki; Jahn, David; Koch, Martin; Withayachumnankul, Withawat

    2015-01-01

    We experimentally demonstrate terahertz Bessel beamforming based on the concept of plasmonics. The proposed planar structure is made of concentric metallic grooves with a subwavelength spacing that couple to a point source to create tightly confined surface waves or spoof surface plasmon polaritons. Concentric scatterers periodically incorporated at a wavelength scale allow for launching the surface waves into free space to define a Bessel beam. The Bessel beam defined at 0.29 THz has been characterized through terahertz time-domain spectroscopy. This approach is capable of generating Bessel beams with planar structures as opposed to bulky axicon lenses and can be readily integrated with solid-state terahertz sources

  16. Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere

    Science.gov (United States)

    Lukin, Igor P.

    2017-11-01

    In this paper the theoretical research of coherent properties of the vortex Bessel-Gaussian optical beams propagating in turbulent atmosphere are developed. The approach to the analysis of this problem is based on the analytical solution of the equation for the transverse second-order mutual coherence function of a field of optical radiation. The behavior of integral scale of coherence degree of vortex Bessel-Gaussian optical beams depending on parameters of an optical beam and characteristics of turbulent atmosphere is particularly considered. It is shown that the integral scale of coherence degree of a vortex Bessel-Gaussian optical beam essentially depends on value of a topological charge of a vortex optical beam. With increase in a topological charge of a vortex Bessel-Gaussian optical beam the value of integral scale of coherence degree of a vortex Bessel-Gaussian optical beam are decreased.

  17. Generating Generalized Bessel Equations by Virtue of Bose Operator Algebra and Entangled State Representations

    International Nuclear Information System (INIS)

    Fan Hongyi; Wang Yong

    2006-01-01

    With the help of Bose operator identities and entangled state representation and based on our previous work [Phys. Lett. A 325 (2004) 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.

  18. On the evaluation of modified Bessel functions of the second kind and fractional order for synchrotron radiation calculations

    International Nuclear Information System (INIS)

    Rutt, H.N.

    2003-01-01

    The modified Bessel functions of the second kind and fractional order K 1/3 (x) and K 2/3 (x) are of importance in the calculation of the frequency spectrum of synchrotron radiation. The parameter range of interest is typically 10 -6 x10. Recently, there has been particular interest in the generation of 'terahertz' radiation, which can be coherently enhanced by many orders of magnitude when the electron bunch length is shorter than the terahertz wavelength. This requires evaluation of the Bessel functions for small values of the argument. It is shown that the series commonly used to evaluate these functions has poor convergence properties under these conditions. An alternative series is derived which has much better convergence for x1

  19. Amos-type bounds for modified Bessel function ratios☆

    Science.gov (United States)

    Hornik, Kurt; Grün, Bettina

    2013-01-01

    We systematically investigate lower and upper bounds for the modified Bessel function ratio Rν=Iν+1/Iν by functions of the form Gα,β(t)=t/(α+t2+β2) in case Rν is positive for all t>0, or equivalently, where ν≥−1 or ν is a negative integer. For ν≥−1, we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If ν≥−1/2, the minimal elements are tangent to Rν in exactly one point 0≤t≤∞, and have Rν as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if ν is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively. PMID:24926105

  20. Amos-type bounds for modified Bessel function ratios.

    Science.gov (United States)

    Hornik, Kurt; Grün, Bettina

    2013-12-01

    We systematically investigate lower and upper bounds for the modified Bessel function ratio [Formula: see text] by functions of the form [Formula: see text] in case [Formula: see text] is positive for all [Formula: see text], or equivalently, where [Formula: see text] or [Formula: see text] is a negative integer. For [Formula: see text], we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If [Formula: see text], the minimal elements are tangent to [Formula: see text] in exactly one point [Formula: see text], and have [Formula: see text] as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if [Formula: see text] is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively.

  1. Evaluating the Financial Flows of Bessel Processes by Using Spectral Analysis

    Directory of Open Access Journals (Sweden)

    Burtnyak Ivan V.

    2017-07-01

    Full Text Available The article solves the two-parameter task of evaluating the intensity of diffuse Bessel processes by the methods of spectral theory. In particular, barriers for cost of options, where the derivative of financial flows turns into zero, have been considered, and a task for the two-barrier option has been solved, which corresponds to Bessel process. A Green’s function has been built for the diffusion Bessel process of the two-barrier option, decomposed according to the first-type system of Bessel functions. The barriers are taken in such a way that the derivative of financial flow in terms of price is turned to zero, i.e. there are the points where flow can acquire extreme values. On the basis of Green’s function, the value of securities has been calculated. It is handier to use similar barriers when monitoring a stock market. The Green’s function for this task, which represents the probability of spreading the option price, is represented through the Fourier series. This provides an opportunity to evaluate the intensity of financial flows in stock markets.

  2. Bessel collocation approach for approximate solutions of Hantavirus infection model

    Directory of Open Access Journals (Sweden)

    Suayip Yuzbasi

    2017-11-01

    Full Text Available In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.

  3. Generalized approach to modifying optical vortices with suppressed sidelobes using Bessel-like functions.

    Science.gov (United States)

    Chen, J; Yuan, X-C; Zhao, X; Fang, Z L; Zhu, S W

    2009-11-01

    We propose a generalized approach to producing optical vortices with suppressed sidelobes using a variable Bessel-like function added to the conventional spiral phase plate. Experimental verifications are implemented by a phase-only spatial light modulator. It is demonstrated that the method is valid for optical vortex beams with arbitrary topological charges and without changing the primary ring size as a unique property among the existing techniques.

  4. Generation of an elliptic hollow beam using Mathieu and Bessel functions.

    Science.gov (United States)

    Chakraborty, Rijuparna; Ghosh, Ajay

    2006-09-01

    A new (to our knowledge) technique for the generation of a propagation-invariant elliptic hollow beam is reported. It avoids the use of the radial Mathieu function and hence is mathematically simpler. Bessel functions with their arguments having elliptic locus are used to generate the mask, which is then recorded using holographic technique. To generate such an elliptic beam, both the angular Mathieu function, i.e., elliptic vortex term, and the expression for the circular vortex are used separately. The resultant mask is illuminated with a plane beam, and the proper filtering of its Fourier transform generates the expected elliptic beam. Results with both vortex terms are satisfactory. It has been observed that even for higher ellipticity the vortices do not separate.

  5. Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere

    Science.gov (United States)

    Lukin, Igor P.

    2017-11-01

    In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.

  6. Accurate Bessel functions Jsub(n)(z), Ysub(n)(z), Hsub(n)sup((1))(z) and Hsub(n)sup((2))(z) of integer order and complex argument

    International Nuclear Information System (INIS)

    Ardill, R.W.B.; Moriarty, K.J.M.

    1979-01-01

    The Bessel function appears in a wide range of physical applications, and in particular where there is axial symmetry. The package contains complex function routines to calculate Jsub(n)(z), Ysub(n)(z), Hsub(n)sup((1))(z) and Hsub(n)sup((2))(z) for integer n and complex z. The method of solution is based on the ascending series representations and asymptotic forms of the Bessel functions Jsub(n)(z) and Ysub(n)(z) and asymptotic forms of the modified Bessel functions Isub(n)(z) and Ksub(n)(z). The program will return results for all values of mod(z) up to machine overflows in the Bessel functions. The size of the order should not be too large (say, mod(n) -11 . For the asymptotic region, the accuracy EPS may not always be achieved (since the asymptotic series may have to be truncated at their lower terms), in which case the output parameter ISET will indicate this and an estimation of the relative error is also produced. The functions Ysub(n)(z), Hsub(n)sup((1))(z) and Hsub(n)sup((2))(z) have a branch point at the origin, together with a cut along the negative real axis. (Auth.)

  7. Precise analytic approximations for the Bessel function J1 (x)

    Science.gov (United States)

    Maass, Fernando; Martin, Pablo

    2018-03-01

    Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.

  8. Application of a non-integer Bessel uniform approximation to inelastic molecular collisions

    International Nuclear Information System (INIS)

    Connor, J.N.L.; Mayne, H.R.

    1979-01-01

    A non-integer Bessel uniform approximation has been used to calculate transition probabilities for collinear atom-oscillator collisions. The collision systems used are a harmonic oscillator interacting via a Lennard-Jones potential and a Morse oscillator interacting via an exponential potential. Both classically allowed and classically forbidden transitions have been treated. The order of the Bessel function is chosen by a physical argument that makes use of information contained in the final-action initial-angle plot. Limitations of this procedure are discussed. It is shown that the non-integer Bessel approximation is accurate for elastic 0 → 0 collisions at high collision energies, where the integer Bessel approximation is inaccurate or inapplicable. (author)

  9. Theory of third-harmonic generation using Bessel beams, and self-phase-matching

    International Nuclear Information System (INIS)

    Tewari, S.P.; Huang, H.; Boyd, R.W.

    1996-01-01

    Taking Bessel beams (J 0 beam) as a representation of a conical beam, and a slowly varying envelope approximation (SVEA) we obtain the results for the theory of third-harmonic generation from an atomic medium. We demonstrate how the phenomenon of self-phase-matching is contained in the transverse-phase-matching integral of the theory. A method to calculate the transverse-phase-matching integral containing four Bessel functions is described which avoids the computer calculations of the Bessel functions. In order to consolidate the SVEA result an alternate method is used to obtain the exact result for the third-harmonic generation. The conditions are identified in which the exact result goes over to the result of the SVEA. The theory for multiple Bessel beams is also discussed which has been shown to be the source of the wide width of the efficiency curve of the third-harmonic generation observed in experiments. copyright 1996 The American Physical Society

  10. On sharp estimates of the convergence of double Fourier-Bessel series

    Science.gov (United States)

    Abilov, V. A.; Abilova, F. V.; Kerimov, M. K.

    2017-11-01

    The problem of approximation of a differentiable function of two variables by partial sums of a double Fourier-Bessel series is considered. Sharp estimates of the rate of convergence of the double Fourier-Bessel series on the class of differentiable functions of two variables characterized by a generalized modulus of continuity are obtained. The proofs of four theorems on this issue, which can be directly applied to solving particular problems of mathematical physics, approximation theory, etc., are presented.

  11. Filtered Bessel functions in computerized tomography

    International Nuclear Information System (INIS)

    Rathore, R.K.S.; Munshi, P.; Bhatia, V.K.; Pandimani, S.

    1988-01-01

    Computer Aided Tomography (CAT) is widely used in the medical imaging area for the detection of cancerous tissues. It has also proved to be a good technique for measuring point-density (void-fraction) in two-phase flow systems. The present day CAT-scanners employ alogorithms which are essentially a discrete implementation of the Radon Inversion Formulae. These methods of reconstructing density distributions are fast and easy to implement. The present work is an attempt to simplify (and consequently to speed-up) the existing algorithms for the cases of radially symmetric density distribution. The method uses Radon Inversion Formulae and involves Bessels's Function of Fourier frequency. The algorithm was tested on some known distributions and the reconstruction is excellent. Data for bubbly-flow was also processed to obtain a point density distribution. The range of investigation was 0.6 ≤ ≤ 0.9 g/cm 3 , where ' ' denotes average cross-sectional value. The values of CT > are within ±0.03 g/cm 3 of the true values , for the data sets considered. The results are comparable with another simple method involving radial polynominals. It is observed that the simplified Radon Inversion Formulae for the radially symmetric case gives good results and can be implemented with ease. (orig.)

  12. On the validity of localized approximations for Bessel beams: All N-Bessel beams are identically equal to zero

    International Nuclear Information System (INIS)

    Gouesbet, Gérard

    2016-01-01

    Localized approximation procedures are efficient ways to evaluate beam shape coefficients of a laser beam. They are particularly useful when other methods are ineffective or inefficient. Several papers in the literature have reported the use of such procedures to evaluate the beam shape coefficients of Bessel beams. Relying on the concept of N-beams, it is demonstrated that care must be taken when constructing a localized approximation for a Bessel beam, namely a localized Bessel beam is satisfactorily close enough to the intended beam only when the axicon angle is small enough. - Highlights: • Localized approximation has been used to evaluate BSCs of Bessel beams. • N-beam procedure fails to provide a localized approximation for Bessel beams. • Localized approximation should be used only for small axicon angles.

  13. Harmonic Analysis Associated with the Generalized q-Bessel Operator

    Directory of Open Access Journals (Sweden)

    Ahmed Abouelaz

    2016-01-01

    Full Text Available In this article, we give a new harmonic analysis associated with the generalized q-Bessel operator. We introduce the generalized $q$-Bessel transform, the generalized q-Bessel translation and the generalized $q$-Bessel convolution product.

  14. Optical breakdown of helium in Bessel laser radiation beams

    International Nuclear Information System (INIS)

    Andreev, N E; Pleshanov, I V; Margolin, L Ya; Pyatnitskii, Lev N

    1998-01-01

    Numerical simulation is used to investigate the dynamics of formation of a helium plasma in Bessel beams, shaped by an axicon and a phase converter from a laser radiation pulse with Gaussian temporal and radial intensity profiles. The beam intensities at the breakdown threshold are determined as a function of the pulse duration for various radial field distributions in a beam characterised by Bessel functions of order m (m = 0 - 5). It is shown that in the investigated range of parameters the threshold intensity is independent of m. The temporal and spatial evolution of the resultant plasma, and the dependence of the plasma characteristics on the pulse parameters are considered. Conditions are found for the formation of tubular plasma channels in beams of orders m≥1. The adopted model of the optical breakdown of helium is shown to be satisfactory because of a good agreement between the results of calculations of the moment of breakdown in a zeroth-order Bessel beam and experimental results. (interaction of laser radiation with matter. laser plasma)

  15. Nonparaxial Bessel and Bessel–Gauss pincers light-sheets

    Energy Technology Data Exchange (ETDEWEB)

    Mitri, F.G., E-mail: F.G.Mitri@ieee.org

    2017-01-23

    Highlights: • Bessel and Bessel–Gauss autofocusing light sheets (i.e. beams in 2D) are developed. • The light-sheets are synthesized based on the angular spectrum decomposition method. • Computations of the scattering, radiation force and torque benefit from the solutions. - Abstract: Nonparaxial optical Bessel and Bessel–Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.

  16. Nonparaxial Bessel and Bessel–Gauss pincers light-sheets

    International Nuclear Information System (INIS)

    Mitri, F.G.

    2017-01-01

    Highlights: • Bessel and Bessel–Gauss autofocusing light sheets (i.e. beams in 2D) are developed. • The light-sheets are synthesized based on the angular spectrum decomposition method. • Computations of the scattering, radiation force and torque benefit from the solutions. - Abstract: Nonparaxial optical Bessel and Bessel–Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.

  17. Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations

    International Nuclear Information System (INIS)

    Poquerusse, A.; Alexiou, S.

    1999-01-01

    In this work we review the status of the standard line broadening theory for plasmas and fill in the existing gap, i.e., the partially overlapping case for ions lines, by deriving expressions as well as fast and accurate numerical approximations for the relevant functions, namely the modified Bessel function of imaginary order and its derivative with respect to argument. These functions also arise in the context of the theory of Coulomb excitation. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

  18. Materials processing with superposed Bessel beams

    Energy Technology Data Exchange (ETDEWEB)

    Yu, Xiaoming [Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66506 (United States); Trallero-Herrero, Carlos A. [J. R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506 (United States); Lei, Shuting, E-mail: lei@ksu.edu [Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66506 (United States)

    2016-01-01

    Graphical abstract: - Highlights: • Superpositions of Bessel beams can be generated with >50% efficiency using an SLM and an axicon. • These beams have orders-of-magnitude increase in depth-of-focus compared to Gaussian beams. • Multiple craters can be fabricated on glass with single-shot exposure. • The 1+(−1) superposition can reduce collateral damage caused by the rings in the zero-order Bessel beams. - Abstract: We report experimental results of femtosecond laser processing on the surface of glass and metal thin film using superposed Bessel beams. These beams are generated by a combination of a spatial light modulator (SLM) and an axicon with >50% efficiency, and they possess the long depth-of-focus (propagation-invariant) property as found in ordinary Bessel beams. Through micromachining experiments using femtosecond laser pulses, we show that multiple craters can be fabricated on glass with single-shot exposure, and the 1+(−1) superposed beam can reduce collateral damage caused by the rings in zero-order Bessel beams in the scribing of metal thin film.

  19. On the evaluation of the integral over the product of two spherical Bessel functions

    International Nuclear Information System (INIS)

    Maximon, L.C.

    1991-01-01

    The integral I l,l' (k,k')=∫ ∞ 0 j l (kr)j l' (k'r)r 2 dr, in which the spherical Bessel functions j l (kr) are the radial eigenfunctions of the three-dimensional wave equation in spherical coordinates, is evaluated in terms of distributions, in particular, step functions and delta functions. It will be shown that the behavior of I l,l' is very different in the cases l-l' even (0, ±2, ±4, ...) and l-l' odd (±1, ±3, ...). For l-l' even it is expressed in terms of the delta function, step functions, and Legendre polynomials. For l-l' odd it is expressed in terms of Legendre functions of the second kind and step functions; no delta functions appear

  20. BESSEL FILTER AND CHAOS: THREE-IN-ONE ACTION

    DEFF Research Database (Denmark)

    Tamaševicius, Arunas; Mykolaitis, Gytis; Bumeliene, Skaidra

    2006-01-01

    Low-pass active Bessel filters are proposed to be used in a chaotic oscillator. The Bessel unit plays the role of three-in-one: the delay line, the amplifier, and the filter. Results of Spice simulations and hardware experiments are presented.......Low-pass active Bessel filters are proposed to be used in a chaotic oscillator. The Bessel unit plays the role of three-in-one: the delay line, the amplifier, and the filter. Results of Spice simulations and hardware experiments are presented....

  1. Laser-driven acceleration with Bessel beam

    International Nuclear Information System (INIS)

    Imasaki, Kazuo; Li, Dazhi

    2005-01-01

    A new approach of laser-driven acceleration with Bessel beam is described. Bessel beam, in contrast to the Gaussian beam, shows diffraction-free'' characteristics in its propagation, which implies potential in laser-driven acceleration. But a normal laser, even if the Bessel beam, laser can not accelerate charged particle efficiently because the difference of velocity between the particle and photon makes cyclic acceleration and deceleration phase. We proposed a Bessel beam truncated by a set of annular slits those makes several special regions in its travelling path, where the laser field becomes very weak and the accelerated particles are possible to receive no deceleration as they undergo decelerating phase. Thus, multistage acceleration is realizable with high gradient. In a numerical computation, we have shown the potential of multistage acceleration based on a three-stage model. (author)

  2. On q-analogues of the Mangontarum transform for certain q-Bessel functions and some application

    Directory of Open Access Journals (Sweden)

    S.K.Q. Al-Omari

    2016-10-01

    Full Text Available Several q-analogues of certain integral transforms have been recently investigated by many authors in the recent past. In this paper, we introduce certain analogues of the so-called q-Mangontarum transform and implement the proposed variants to given classes of q-Bessel functions. The results of this paper are new and complement the previously known results of Mangontarum (2014. Some results related to q-Laplace transforms are also obtained.

  3. Bessel beam CARS of axially structured samples

    Science.gov (United States)

    Heuke, Sandro; Zheng, Juanjuan; Akimov, Denis; Heintzmann, Rainer; Schmitt, Michael; Popp, Jürgen

    2015-06-01

    We report about a Bessel beam CARS approach for axial profiling of multi-layer structures. This study presents an experimental implementation for the generation of CARS by Bessel beam excitation using only passive optical elements. Furthermore, an analytical expression is provided describing the generated anti-Stokes field by a homogeneous sample. Based on the concept of coherent transfer functions, the underling resolving power of axially structured geometries is investigated. It is found that through the non-linearity of the CARS process in combination with the folded illumination geometry continuous phase-matching is achieved starting from homogeneous samples up to spatial sample frequencies at twice of the pumping electric field wave. The experimental and analytical findings are modeled by the implementation of the Debye Integral and scalar Green function approach. Finally, the goal of reconstructing an axially layered sample is demonstrated on the basis of the numerically simulated modulus and phase of the anti-Stokes far-field radiation pattern.

  4. A Determinant Expression for the Generalized Bessel Polynomials

    Directory of Open Access Journals (Sweden)

    Sheng-liang Yang

    2013-01-01

    Full Text Available Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented as determinant the entries of which involve Catalan numbers.

  5. Computation of the modified Bessel function of the third kind of imaginary orders: uniform Airy-type asymptotic expansion

    NARCIS (Netherlands)

    A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

    2002-01-01

    textabstractThe use of a uniform Airy-type asymptotic expansion for the computation of the modified Bessel functions of the third kind of imaginary orders ($K_{ia}(x)$) near the transition point $x=a$, is discussed. In [2], an algorithm for the evaluation of $K_{ia}(x)$ was presented, which made use

  6. Large degree asymptotics of generalized Bessel polynomials

    NARCIS (Netherlands)

    J.L. López; N.M. Temme (Nico)

    2011-01-01

    textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the

  7. Construction of normal-regular decisions of Bessel typed special system

    Science.gov (United States)

    Tasmambetov, Zhaksylyk N.; Talipova, Meiramgul Zh.

    2017-09-01

    Studying a special system of differential equations in the separate production of the second order is solved by the degenerate hypergeometric function reducing to the Bessel functions of two variables. To construct a solution of this system near regular and irregular singularities, we use the method of Frobenius-Latysheva applying the concepts of rank and antirank. There is proved the basic theorem that establishes the existence of four linearly independent solutions of studying system type of Bessel. To prove the existence of normal-regular solutions we establish necessary conditions for the existence of such solutions. The existence and convergence of a normally regular solution are shown using the notion of rank and antirank.

  8. Vectorial diffraction properties of THz vortex Bessel beams.

    Science.gov (United States)

    Wu, Zhen; Wang, Xinke; Sun, Wenfeng; Feng, Shengfei; Han, Peng; Ye, Jiasheng; Yu, Yue; Zhang, Yan

    2018-01-22

    A vortex Bessel beam combines the merits of an optical vortex and a Bessel beam, including a spiral wave front and a non-diffractive feature, which has immense application potentials in optical trapping, optical fabrication, optical communications, and so on. Here, linearly and circularly polarized vortex Bessel beams in the terahertz (THz) frequency range are generated by utilizing a THz quarter wave plate, a spiral phase plate, and Teflon axicons with different opening angles. Taking advantage of a THz focal-plane imaging system, vectorial diffraction properties of the THz vortex Bessel beams are comprehensively characterized and discussed, including the transverse (Ex, Ey) and longitudinal (Ez) polarization components. The experimental phenomena are accurately simulated by adopting the vectorial Rayleigh diffraction integral. By varying the opening angle of the axicon, the characteristic parameters of these THz vortex Bessel beams are exhibited and compared, including the light spot size, the diffraction-free range, and the phase evolution process. This work provides the precise experimental and theoretical bases for the comprehension and application of a THz vortex Bessel beam.

  9. Pupil filter design by using a Bessel functions basis at the image plane.

    Science.gov (United States)

    Canales, Vidal F; Cagigal, Manuel P

    2006-10-30

    Many applications can benefit from the use of pupil filters for controlling the light intensity distribution near the focus of an optical system. Most of the design methods for such filters are based on a second-order expansion of the Point Spread Function (PSF). Here, we present a new procedure for designing radially-symmetric pupil filters. It is more precise than previous procedures as it considers the exact expression of the PSF, expanded as a function of first-order Bessel functions. Furthermore, this new method presents other advantages: the height of the side lobes can be easily controlled, it allows the design of amplitude-only, phase-only or hybrid filters, and the coefficients of the PSF expansion can be directly related to filter parameters. Finally, our procedure allows the design of filters with very different behaviours and optimal performance.

  10. Modified Bessel P-integrals and P-derivatives and their properties

    International Nuclear Information System (INIS)

    Volosivets, S S

    2014-01-01

    We study the modified Bessel P-integral, whose properties are similar to those of the Bessel potential, and the modified Bessel P-derivative. These operators are inverse to each other. We prove analogues of the embedding theorems of Hardy, Littlewood, Stein, Zygmund and Lizorkin concerning the images of L p (R) under the action of Bessel potentials. We give applications of the Bessel integral and derivative to the integrability of the P-adic Fourier transform and to approximation theory (an embedding theorem of Ul'yanov type)

  11. Materials processing with superposed Bessel beams

    Science.gov (United States)

    Yu, Xiaoming; Trallero-Herrero, Carlos A.; Lei, Shuting

    2016-01-01

    We report experimental results of femtosecond laser processing on the surface of glass and metal thin film using superposed Bessel beams. These beams are generated by a combination of a spatial light modulator (SLM) and an axicon with >50% efficiency, and they possess the long depth-of-focus (propagation-invariant) property as found in ordinary Bessel beams. Through micromachining experiments using femtosecond laser pulses, we show that multiple craters can be fabricated on glass with single-shot exposure, and the 1+(⿿1) superposed beam can reduce collateral damage caused by the rings in zero-order Bessel beams in the scribing of metal thin film.

  12. Low-frequency acousto-optic backscattering of Bessel light beams

    Science.gov (United States)

    Khilo, Nikolai A.; Belyi, Vladimir N.; Khilo, Petr A.; Kazak, Nikolai S.

    2018-05-01

    The use of Bessel light beams, as well as Bessel acoustic beams, substantially enhances the capabilities of acousto-optic methods for control of optical field. We present a theoretical study of the process of optical Bessel beams conversion by means of backward acousto-optic scattering on a Bessel acoustic field in a transversely isotropic crystal. It is shown that, with an appropriate choice of Bessel beams parameters, the backscattering in visible spectral range can be realized at relatively low acoustic frequencies less than one gigahertz. Under conditions of phase matching and transverse spatial synchronism, the efficiency of backscattering is sufficiently high, which is interesting, for example, for construction of acousto-optic spectral analyzers.

  13. Calculating the Price for Derivative Financial Assets of Bessel Processes Using the Sturm-Liouville Theory

    Directory of Open Access Journals (Sweden)

    Burtnyak Ivan V.

    2017-06-01

    Full Text Available In the paper we apply the spectral theory to find the price for derivatives of financial assets assuming that the processes described are Markov processes and such that can be considered in the Hilbert space L^2 using the Sturm-Liouville theory. Bessel diffusion processes are used in studying Asian options. We consider the financial flows generated by the Bessel diffusions by expressing them in terms of the system of Bessel functions of the first kind, provided that they take into account the linear combination of the flow and its spatial derivative. Such expression enables calculating the size of the market portfolio and provides a measure of the amount of internal volatility in the market at any given moment, allows investigating the dynamics of the equity market. The expansion of the Green function in terms of the system of Bessel functions is expressed by an analytic formula that is convenient in calculating the volume of financial flows. All assumptions are natural, result in analytic formulas that are consistent with the empirical data and, when applied in practice, adequately reflect the processes in equity markets.

  14. Electromagnetic scattering by a uniaxial anisotropic sphere located in an off-axis Bessel beam.

    Science.gov (United States)

    Qu, Tan; Wu, Zhen-Sen; Shang, Qing-Chao; Li, Zheng-Jun; Bai, Lu

    2013-08-01

    Electromagnetic scattering of a zero-order Bessel beam by an anisotropic spherical particle in the off-axis configuration is investigated. Based on the spherical vector wave functions, the expansion expression of the zero-order Bessel beam is derived, and its convergence is numerically discussed in detail. Utilizing the tangential continuity of the electromagnetic fields, the expressions of scattering coefficients are given. The effects of the conical angle of the wave vector components of the zero-order Bessel beam, the ratio of the radius of the sphere to the central spot radius of the zero-order Bessel beam, the shift of the beam waist center position along both the x and y axes, the permittivity and permeability tensor elements, and the loss of the sphere on the radar cross section (RCS) are numerically analyzed. It is revealed that the maximum RCS appears in the conical direction or neighboring direction when the sphere is illuminated by a zero-order Bessel beam. Furthermore, the RCS will decrease and the symmetry is broken with the shift of the beam waist center.

  15. Analytical study on the self-healing property of Bessel beam

    Science.gov (United States)

    Chu, X.

    2012-10-01

    With the help of Babinet principle, an analytical expression for the self-healing of Bessel beam is derived by using the Gaussian absorption function to describe the obstacle. Based on the analytical expression, the self-healing properties of Bessel beam are studied. It shows that Bessel beam has the ability to reconstruct its beam shape disturbed by an obstacle. However, during the self-healing process, not only the intensity of the beam behind the obstacle but also the other part will be affected by the obstruction. Meanwhile, the highlight spot, which intensity is larger than that without the obstacle will appear, and the size and strength of the highlight spot is determined by the size of the obstacle. From the change of Poynting vector and Babinet principle, the physical interpretations for the self-healing ability, the effects of the obstruction on the other part and the appearance of highlight spot are given.

  16. Spatial-temporal dynamics of broadband terahertz Bessel beam propagation

    International Nuclear Information System (INIS)

    Semenova, V A; Kulya, M S; Bespalov, V G

    2016-01-01

    The unique properties of narrowband and broadband terahertz Bessel beams have led to a number of their applications in different fields, for example, for the depth of focusing and resolution enhancement in terahertz imaging. However, broadband terahertz Bessel beams can probably be also used for the diffraction minimization in the short-range broadband terahertz communications. For this purpose, the study of spatial-temporal dynamics of the broadband terahertz Bessel beams is needed. Here we present a simulation-based study of the propagating in non-dispersive medium broadband Bessel beams generated by a conical axicon lens. The algorithm based on scalar diffraction theory was used to obtain the spatial amplitude and phase distributions of the Bessel beam in the frequency range from 0.1 to 3 THz at the distances 10-200 mm from the axicon. Bessel beam field is studied for the different spectral components of the initial pulse. The simulation results show that for the given parameters of the axicon lens one can obtain the Gauss-Bessel beam generation in the spectral range from 0.1 to 3 THz. The length of non-diffraction propagation for a different spectral components was measured, and it was shown that for all spectral components of the initial pulse this length is about 130 mm. (paper)

  17. A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions

    International Nuclear Information System (INIS)

    Qin Hong; Phillips, Cynthia K.; Davidson, Ronald C.

    2007-01-01

    The susceptibility tensor of a hot, magnetized plasma is conventionally expressed in terms of infinite sums of products of Bessel functions. For applications where the particle's gyroradius is larger than the wavelength, such as alpha particle dynamics interacting with lower-hybrid waves, and the focusing of charged particle beams using a solenoidal field, the infinite sums converge slowly. In this paper, a new derivation of the plasma susceptibility tensor is presented which exploits a symmetry in the particle's orbit to simplify the integration along the unperturbed trajectories. As a consequence, the infinite sums appearing in the conventional expression are replaced by definite double integrals over one gyroperiod, and the cyclotron resonances of all orders are captured by a single term. Furthermore, the double integrals can be carried out and expressed in terms of Bessel functions of complex order, in agreement with expressions deduced previously using the Newburger sum rule. From this new formulation, it is straightforward to derive the asymptotic form of the full hot plasma susceptibility tensor for a gyrotropic but otherwise arbitrary plasma distribution in the large gyroradius limit. These results are of more general importance in the numerical evaluation of the plasma susceptibility tensor. Instead of using the infinite sums occurring in the conventional expression, it is only necessary to evaluate the Bessel functions once according to the new expression, which has significant advantages, especially when the particle's gyroradius is large and the conventional infinite sums converge slowly. Depending on the size of the gyroradius, the computational saving enabled by this representation can be several orders-of-magnitude

  18. Generation and application of Bessel beam in alignment works

    International Nuclear Information System (INIS)

    Gale, D. M.

    2009-01-01

    The divergence of a Gaussian laser beam is a limiting factor for optical alignment tasks at large distances. Bessel beams have almost zero divergence but are still not widely used. We discuss the construction of an alignment telescope based on Bessel beam generation using a commercial laser diode module. The Bessel beam is generated with conical or plano-convex lenses, and projected using a commercial CCD camera lens to extend the useful range of the beam. Our Bessel beams have diameters of between 0.5 - 1mm over beam lengths of 15m, representing a six-fold improvement compared to Gaussian beams, while the transverse beam structure (Bessel pattern) provides an excellent alignment aid for use with beam target. Another advantage of Bessel beams is their self-regeneration property, which allows the use of multiple beam targets with minimum beam degradation. We are using our crosshair targets with crosshair targets to align optical components in a large astronomical telescope, and can achieve precisions of tens of microns over distances of 20m using purely visual methods. (Author)

  19. Behavior of obliquely incident vector Bessel beams at planar interfaces

    KAUST Repository

    Salem, Mohamed; Bagci, Hakan

    2013-01-01

    We investigate the behavior of full-vector electromagnetic Bessel beams obliquely incident at an interface between two electrically different media. We employ a Fourier transform domain representation of Bessel beams to determine their behavior upon reflection and transmission. This transform, which is geometric in nature, consists of elliptical support curves with complex weighting associated with them. The behavior of the scattered field at an interface is highly complex, owing to its full-vector nature; nevertheless, this behavior has a straightforward representation in the transform domain geometry. The analysis shows that the reflected field forms a different vector Bessel beam, but in general, the transmitted field cannot be represented as a Bessel beam. Nevertheless, using this approach, we demonstrate a method to propagate a Bessel beam in the refractive medium by launching a non- Bessel beam at the interface. Several interesting phenomena related to the behavior of Bessel beams are illustrated, such as polarized reflection at Brewster's angle incidence, and the Goos-Hänchen and Imbert-Federov shifts in the case of total reflection. © 2013 Optical Society of America.

  20. Behavior of obliquely incident vector Bessel beams at planar interfaces

    KAUST Repository

    Salem, Mohamed

    2013-01-01

    We investigate the behavior of full-vector electromagnetic Bessel beams obliquely incident at an interface between two electrically different media. We employ a Fourier transform domain representation of Bessel beams to determine their behavior upon reflection and transmission. This transform, which is geometric in nature, consists of elliptical support curves with complex weighting associated with them. The behavior of the scattered field at an interface is highly complex, owing to its full-vector nature; nevertheless, this behavior has a straightforward representation in the transform domain geometry. The analysis shows that the reflected field forms a different vector Bessel beam, but in general, the transmitted field cannot be represented as a Bessel beam. Nevertheless, using this approach, we demonstrate a method to propagate a Bessel beam in the refractive medium by launching a non- Bessel beam at the interface. Several interesting phenomena related to the behavior of Bessel beams are illustrated, such as polarized reflection at Brewster\\'s angle incidence, and the Goos-Hänchen and Imbert-Federov shifts in the case of total reflection. © 2013 Optical Society of America.

  1. Second-harmonic generation of practical Bessel beams

    Science.gov (United States)

    Huang, Jin H.; Ding, Desheng; Hsu, Yin-Sung

    2009-11-01

    A fast Gaussian expansion approach is used to investigate fundamental and second-harmonic generation in practical Bessel beams of finite aperture. The analysis is based on the integral solutions of the KZK equation under the quasilinear approximation. The influence of the medium's attenuation on the beam profile is considered. Analysis results show that the absorption parameter has a significant effect on the far-field beam profile of the second harmonic. Under certain circumstances, the second harmonic of a practical Bessel beam still has the main properties of an ideal Bessel beam of infinite aperture when it propagates within its depth of field.

  2. Creation of matter wave Bessel beams and observation of quantized circulation in a Bose–Einstein condensate

    International Nuclear Information System (INIS)

    Ryu, C; Henderson, K C; Boshier, M G

    2014-01-01

    Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because they propagate ‘diffraction-free’ and because they can carry orbital angular momentum. Here we report the creation of a Bessel beam of de Broglie matter waves. The Bessel beam is produced by the free evolution of a thin toroidal atomic Bose–Einstein condensate (BEC) which has been set into rotational motion. By attempting to stir it at different rotation rates, we show that the toroidal BEC can only be made to rotate at discrete, equally spaced frequencies, demonstrating that circulation is quantized in atomic BECs. The method used here can be viewed as a form of wavefunction engineering which might be developed to implement cold atom matter wave holography. (paper)

  3. Probing the longitudinal electric field of Bessel beams using second-harmonic generation from nano-objects

    Science.gov (United States)

    Turquet, Léo; Kakko, Joona-Pekko; Karvonen, Lasse; Jiang, Hua; Kauppinen, Esko; Lipsanen, Harri; Kauranen, Martti; Bautista, Godofredo

    2017-08-01

    Non-diffractive Bessel beams are receiving significant interest in optical microscopy due to their remarkably large depth of field. For example, studies have shown the superiority of Bessel beams over Gaussian beams for volumetric imaging of three-dimensionally thick or extended samples. However, the vectorial aspects of the focal fields of Bessel beams are generally obscured when traditional methods are used to characterize their three-dimensional point-spread function in space, which contains contributions from all optical field components. Here, we show experimentally the three-dimensional spatial distribution and enhanced depth of field of the longitudinal electric field components of a focused linearly-polarized Bessel beam. This is done through second-harmonic generation from well-defined vertically-aligned gallium-arsenide nanowires, whose second-order response is primarily driven by the longitudinal fields at the beam focus.

  4. Experimental generation of two-index Bessel-Gauss beams by engineering their angular spectrum functions

    Science.gov (United States)

    Yao, Hainan; Wang, Fei; Cai, Yangjian

    2018-01-01

    Two-index Bessel beams (TIBBs) was introduced by Ornigotti and Aiello (2014) theoretically. In this paper, we propose a simple experimental scheme for generation of two-index Bessel-Gauss beams (TIBGBs), as an extension of the TIBBs. The scheme is based on manipulating the amplitude and phase in the Fourier plane with the use of a spatial light modulator and a spiral phase plate. Furthermore, we experimentally report the generation of the several examples of the TIBGBs based on the proposed optical system. The focusing properties of the TIBGB with indices p = 1 and l = 2 passing through a single lens are investigated both theoretically and experimentally. The experimental results agree well with theoretical predictions.

  5. Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid

    Science.gov (United States)

    Mitri, F. G.

    2015-12-01

    Partial-wave series representation of the acoustic scattering field of high-order Bessel vortex beams by rigid oblate and prolate spheroids using the modal matching method is developed. The method, which is applicable to slightly elongated objects at low-to-moderate frequencies, requires solving a system of linear equations which depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated partial-wave series expansions (PWSEs), and satisfying the Neumann boundary condition for a rigid immovable surface in the least-squares sense. This original semi-analytical approach developed for Bessel vortex beams is demonstrated for finite oblate and prolate spheroids, where the mathematical functions describing the spheroidal geometry are written in a form involving single angular (polar) integrals that are numerically computed. The transverse (θ = π / 2) and 3D scattering directivity patterns are evaluated in the far-field for both prolate and oblate spheroids, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid) not exceeding 3:1, the half-cone angle β and order m of the Bessel vortex beam, as well as the dimensionless size parameter kr0. Periodic oscillations in the magnitude plots of the far-field scattering form function are observed, which result from the interference of the reflected waves with the circumferential (Franz') waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the far-field scattering from the spheroid, that vanishes in the forward (θ = 0) and backward (θ = π) directions. Particular applications in underwater acoustics and scattering, acoustic levitation and the detection of submerged elongated objects using Bessel vortex waves to name a few, would benefit from the results of the present investigation.

  6. Rapid volumetric imaging with Bessel-Beam three-photon microscopy

    Science.gov (United States)

    Chen, Bingying; Huang, Xiaoshuai; Gou, Dongzhou; Zeng, Jianzhi; Chen, Guoqing; Pang, Meijun; Hu, Yanhui; Zhao, Zhe; Zhang, Yunfeng; Zhou, Zhuan; Wu, Haitao; Cheng, Heping; Zhang, Zhigang; Xu, Chris; Li, Yulong; Chen, Liangyi; Wang, Aimin

    2018-01-01

    Owing to its tissue-penetration ability, multi-photon fluorescence microscopy allows for the high-resolution, non-invasive imaging of deep tissue in vivo; the recently developed three-photon microscopy (3PM) has extended the depth of high-resolution, non-invasive functional imaging of mouse brains to beyond 1.0 mm. However, the low repetition rate of femtosecond lasers that are normally used in 3PM limits the temporal resolution of point-scanning three-photon microscopy. To increase the volumetric imaging speed of 3PM, we propose a combination of an axially elongated needle-like Bessel-beam with three-photon excitation (3PE) to image biological samples with an extended depth of focus. We demonstrate the higher signal-to-background ratio (SBR) of the Bessel-beam 3PM compared to the two-photon version both theoretically and experimentally. Finally, we perform simultaneous calcium imaging of brain regions at different axial locations in live fruit flies and rapid volumetric imaging of neuronal structures in live mouse brains. These results highlight the unique advantage of conducting rapid volumetric imaging with a high SBR in the deep brain in vivo using scanning Bessel-3PM.

  7. Occupation times and exact asymptotics of small deviations of Bessel processes for Lp-norms with p>0

    International Nuclear Information System (INIS)

    Fatalov, V R

    2007-01-01

    We prove theorems on exact asymptotics of the distributions of integral functionals of the occupation time of Bessel processes. Using these results, we obtain exact asymptotics of small deviations for Bessel processes in the L p -norm. We use Laplace's method for the occupation times of Markov processes with continuous time. Computations are carried out for p=2 and p=1. We also solve extremal problems for the action functional

  8. A theorem regarding roots of the zero-order Bessel function of the first kind

    Science.gov (United States)

    Lin, X.-A.; Agrawal, O. P.

    1993-01-01

    This paper investigates a problem on the steady-state, conduction-convection heat transfer process in cylindrical porous heat exchangers. The governing partial differential equations for the system are obtained using the energy conservation law. Solution of these equations and the concept of enthalpy lead to a new approach to prove a theorem that the sum of inverse squares of all the positive roots of the zero order Bessel function of the first kind equals to one-forth. As a corollary, it is shown that the sum of one over pth power (p greater than or equal to 2) of the roots converges to some constant.

  9. Higher-order Bessel like beams with z-dependent cone angles

    CSIR Research Space (South Africa)

    Ismail, Y

    2010-08-01

    Full Text Available .64.81.22. Terms of Use: http://spiedl.org/terms Fig.5: Optical design to generate z-dependent Bessel-like beams 4. CONSIDERING A MATHEMATICAL APPROACH TO EXPLAINING Z-DEPENDENT BLB?S The stationary phase method is implemented in order to confirm... on higher-order z-dependent BLB?s [6]. 5. EXPERIMENTALLY GENERATED Z-DEPENDENT BESSEL-LIKE BEAMS From the above in can be deduced that these beams are Bessel-like hence they are so named z-dependent Bessel-like beams. These beams are produced however...

  10. The Bessel polynomials and their differential operators

    International Nuclear Information System (INIS)

    Onyango Otieno, V.P.

    1987-10-01

    Differential operators associated with the ordinary and the generalized Bessel polynomials are defined. In each case the commutator bracket is constructed and shows that the differential operators associated with the Bessel polynomials and their generalized form are not commutative. Some applications of these operators to linear differential equations are also discussed. (author). 4 refs

  11. Generating and measuring non-diffracting vector Bessel beams

    CSIR Research Space (South Africa)

    Dudley, Angela L

    2014-03-01

    Full Text Available We demonstrate how to create non-diffracting vector Bessel beams by implementing a spatial light modulator (SLM) to generate scalar Bessel beams which are then converted into vector fields by the use of an azimuthally-varying birefringent plate...

  12. Generation and application of bessel beams in electron microscopy

    Energy Technology Data Exchange (ETDEWEB)

    Grillo, Vincenzo, E-mail: vincenzo.grillo@cnr.it [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); CNR-IMEM, Parco Area delle Scienze 37/A, I-43124 Parma (Italy); Harris, Jérémie [Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5 (Canada); Gazzadi, Gian Carlo [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); Balboni, Roberto [CNR-IMM Bologna, Via P. Gobetti 101, 40129 Bologna (Italy); Mafakheri, Erfan [Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena (Italy); Dennis, Mark R. [H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL (United Kingdom); Frabboni, Stefano [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena (Italy); Boyd, Robert W.; Karimi, Ebrahim [Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5 (Canada)

    2016-07-15

    We report a systematic treatment of the holographic generation of electron Bessel beams, with a view to applications in electron microscopy. We describe in detail the theory underlying hologram patterning, as well as the actual electron-optical configuration used experimentally. We show that by optimizing our nanofabrication recipe, electron Bessel beams can be generated with relative efficiencies reaching 37±3%. We also demonstrate by tuning various hologram parameters that electron Bessel beams can be produced with many visible rings, making them ideal for interferometric applications, or in more highly localized forms with fewer rings, more suitable for imaging. We describe the settings required to tune beam localization in this way, and explore beam and hologram configurations that allow the convergences and topological charges of electron Bessel beams to be controlled. We also characterize the phase structure of the Bessel beams generated with our technique, using a simulation procedure that accounts for imperfections in the hologram manufacturing process. - Highlights: • Bessel beams with different convergence, topological charge, visible fringes are demonstrated. • The relation between the Fresnel hologram and the probe shape is explained by detailed calculations and experiments. • Among the holograms here presented the highest relative efficiency is 37%, the best result ever reached for blazed holograms.

  13. Generation and application of bessel beams in electron microscopy

    International Nuclear Information System (INIS)

    Grillo, Vincenzo; Harris, Jérémie; Gazzadi, Gian Carlo; Balboni, Roberto; Mafakheri, Erfan; Dennis, Mark R.; Frabboni, Stefano; Boyd, Robert W.; Karimi, Ebrahim

    2016-01-01

    We report a systematic treatment of the holographic generation of electron Bessel beams, with a view to applications in electron microscopy. We describe in detail the theory underlying hologram patterning, as well as the actual electron-optical configuration used experimentally. We show that by optimizing our nanofabrication recipe, electron Bessel beams can be generated with relative efficiencies reaching 37±3%. We also demonstrate by tuning various hologram parameters that electron Bessel beams can be produced with many visible rings, making them ideal for interferometric applications, or in more highly localized forms with fewer rings, more suitable for imaging. We describe the settings required to tune beam localization in this way, and explore beam and hologram configurations that allow the convergences and topological charges of electron Bessel beams to be controlled. We also characterize the phase structure of the Bessel beams generated with our technique, using a simulation procedure that accounts for imperfections in the hologram manufacturing process. - Highlights: • Bessel beams with different convergence, topological charge, visible fringes are demonstrated. • The relation between the Fresnel hologram and the probe shape is explained by detailed calculations and experiments. • Among the holograms here presented the highest relative efficiency is 37%, the best result ever reached for blazed holograms.

  14. Approximate solutions of the hyperchaotic Rössler system by using the Bessel collocation scheme

    Directory of Open Access Journals (Sweden)

    Şuayip Yüzbaşı

    2015-02-01

    Full Text Available The purpose of this study is to give a Bessel polynomial approximation for the solutions of the hyperchaotic Rössler system. For this purpose, the Bessel collocation method applied to different problems is developed for the mentioned system. This method is based on taking the truncated Bessel expansions of the functions in the hyperchaotic Rössler systems. The suggested secheme converts the problem into a system of nonlinear algebraic equations by means of the matrix operations and collocation points, The accuracy and efficiency of the proposed approach are demonstrated by numerical applications and performed with the help of a computer code written in Maple. Also, comparison between our method and the differential transformation method is made with the accuracy of solutions.

  15. F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements

    Science.gov (United States)

    Karney, C. F. F.; Deakin, R. E.

    2010-08-01

    Issue No. 86 (1825 October) of the Astronomische Nachrichten was largely devoted to a single paper by F. W. Bessel on the solution of the direct geodesic problem (see the first sentences of the paper). For the most part, the paper stands on its own and needs little introduction. However, a few words are in order to place this paper in its historical context. First of all, it should be no surprise that a paper on this subject appeared in an astronomical journal. At the time, the disciplines of astronomy, navigation, and surveying were inextricably linked -- the methods and, in many cases, the practitioners (in particular, Bessel) were the same. Prior to Bessel's paper, the solution of the geodesic problem had been the subject of several studies by Clairaut, Euler, du Séjour, Legendre, Oriani, and others. The interest in the subject was twofold. It combined several new fields of mathematics: the calculus of variations, the theory of elliptic functions, and the differential geometry of curved surfaces. It also addressed very practical needs: the determination of the figure of the earth, the requirements of large scale surveys, and the construction of map projections. With the papers of Legendre and of Oriani in 1806, the framework for the mathematical solution for an ellipsoid of revolution had been established. However, Bessel was firmly in the practical camp; he carried out the East Prussian survey that connected the West European and Russian triangulation networks and later he made the first accurate estimate of the figure of the Earth, the ``Bessel ellipsoid''. He lays out his goal for this paper in its first section: to simplify the numerical solution of the geodesic problem. In Sects. \\ref{sec2}--\\ref{sec4}, Bessel gives a clear and concise summary of the previous work on the problem. In the remaining sections, he develops series for the distance and longitude integrals and constructs the tables which allow geodesics to be calculated to an accuracy of about 3

  16. Higher-order harmonics of general limited diffraction Bessel beams

    International Nuclear Information System (INIS)

    Ding De-Sheng; Huang Jin-Huang

    2016-01-01

    In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m -th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. (special topic)

  17. Heat kernel analysis for Bessel operators on symmetric cones

    DEFF Research Database (Denmark)

    Möllers, Jan

    2014-01-01

    . The heat kernel is explicitly given in terms of a multivariable $I$-Bessel function on $Ω$. Its corresponding heat kernel transform defines a continuous linear operator between $L^p$-spaces. The unitary image of the $L^2$-space under the heat kernel transform is characterized as a weighted Bergmann space...

  18. Monotonicity of the ratio of modified Bessel functions of the first kind with applications.

    Science.gov (United States)

    Yang, Zhen-Hang; Zheng, Shen-Zhou

    2018-01-01

    Let [Formula: see text] with [Formula: see text] be the modified Bessel functions of the first kind of order v . In this paper, we prove the monotonicity of the function [Formula: see text] on [Formula: see text] for different values of parameter p with [Formula: see text]. As applications, we deduce some new Simpson-Spector-type inequalities for [Formula: see text] and derive a new type of bounds [Formula: see text] ([Formula: see text]) for [Formula: see text]. In particular, we show that the upper bound [Formula: see text] for [Formula: see text] is the minimum over all upper bounds [Formula: see text], where [Formula: see text] and is not comparable with other sharpest upper bounds. We also find such type of upper bounds for [Formula: see text] with [Formula: see text] and for [Formula: see text] with [Formula: see text].

  19. A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

    Science.gov (United States)

    Parand, K.; Nikarya, M.

    2017-11-01

    In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

  20. Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.

    Science.gov (United States)

    Lukin, Igor P

    2016-04-20

    The orbital angular momentum of vortex Bessel-Gaussian beams propagating in turbulent atmosphere is studied theoretically. The field of an optical beam is determined through the solution of the paraxial wave equation for a randomly inhomogeneous medium with fluctuations of the refraction index of the turbulent atmosphere. Peculiarities in the behavior of the total power of the vortex Bessel-Gaussian beam at the receiver (or transmitter) are examined. The dependence of the total power of the vortex Bessel-Gaussian beam on optical beam parameters, namely, the transverse wave number of optical radiation, amplitude factor radius, and, especially, topological charge of the optical beam, is analyzed in detail. It turns out that the mean value of the orbital angular momentum of the vortex Bessel-Gaussian beam remains constant during propagation in the turbulent atmosphere. It is shown that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam propagating in turbulent atmosphere calculated with the "mean-intensity" approximation is equal to zero identically. Thus, it is possible to declare confidently that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam in turbulent atmosphere is not very large.

  1. Higher-order chaotic oscillator using active bessel filter

    DEFF Research Database (Denmark)

    Lindberg, Erik; Mykolaitis, Gytis; Bumelien, Skaidra

    2010-01-01

    A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending...

  2. On computing special functions in marine engineering

    Science.gov (United States)

    Constantinescu, E.; Bogdan, M.

    2015-11-01

    Important modeling applications in marine engineering conduct us to a special class of solutions for difficult differential equations with variable coefficients. In order to be able to solve and implement such models (in wave theory, in acoustics, in hydrodynamics, in electromagnetic waves, but also in many other engineering fields), it is necessary to compute so called special functions: Bessel functions, modified Bessel functions, spherical Bessel functions, Hankel functions. The aim of this paper is to develop numerical solutions in Matlab for the above mentioned special functions. Taking into account the main properties for Bessel and modified Bessel functions, we shortly present analytically solutions (where possible) in the form of series. Especially it is studied the behavior of these special functions using Matlab facilities: numerical solutions and plotting. Finally, it will be compared the behavior of the special functions and point out other directions for investigating properties of Bessel and spherical Bessel functions. The asymptotic forms of Bessel functions and modified Bessel functions allow determination of important properties of these functions. The modified Bessel functions tend to look more like decaying and growing exponentials.

  3. Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio

    Science.gov (United States)

    Gong, Zhixiong; Li, Wei; Mitri, Farid G.; Chai, Yingbin; Zhao, Yao

    2016-11-01

    In this paper, the T-matrix (null-field) method is applied to investigate the acoustic scattering by a large-aspect-ratio rigid spheroid immersed in a non-viscous fluid under the illumination of an unbounded zeroth-order Bessel beam with arbitrary orientation. Based on the proposed method, a MATLAB software package is constructed accordingly, and then verified and validated to compute the acoustic scattering by a rigid oblate or prolate spheroid in the Bessel beam. Several numerical examples are carried out to investigate the novel phenomenon of acoustic scattering by spheroids in Bessel beams with arbitrary incidence, with particular emphasis on the aspect ratio (i.e. the ratio of the polar radius over the equatorial radius of the spheroid), the half-cone angle of Bessel beam, the dimensionless frequency, as well as the angle of incidence. The quasi-periodic oscillations are observed in the plots of the far-field backscattering form function modulus versus the dimensionless frequency, owing to the interference between the specular reflection and the Franz wave circumnavigating the spheroid in the surrounding fluid. Furthermore, the 3D far-field scattering directivity patterns at end-on incidence and 2D polar plots at arbitrary angles of incidence are exhibited, which could provide new insights into the physical mechanisms of Bessel beam scattering by flat or elongated spheroid. This research work may provide an impetus for the application of acoustic Bessel beam in engineering practices.

  4. Compact and continuous embeddings of logarithmic Bessel potential spaces

    Czech Academy of Sciences Publication Activity Database

    Edmunds, D. E.; Gurka, P.; Opic, Bohumír

    2005-01-01

    Roč. 168, č. 3 (2005), s. 229-250 ISSN 0039-3223 R&D Projects: GA ČR(CZ) GA201/01/0333 Institutional research plan: CEZ:AV0Z10190503 Keywords : Bessel potential spaces * spaces of Hölder-continuous functions * Lorentz-Zygmund spaces Subject RIV: BA - General Mathematics Impact factor: 0.538, year: 2005

  5. Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model

    Science.gov (United States)

    Wang, Jia Jie; Han, Yi Ping; Chang, Jiao Yong; Chen, Zhu Yang

    2018-02-01

    Within the framework of generalized Lorenz-Mie theory (GLMT), an eccentrically stratified dielectric sphere model illuminated by an arbitrarily incident Bessel beam is applied to investigate the scattering characteristics of a single nucleated biological cell. The Bessel beam propagating in an arbitrary direction is expanded in terms of vector spherical wave functions (VSWFs), where the beam shape coefficients (BSCs) are calculated rigorously in a closed analytical form. The effects of the half-cone angle of Bessel beam, the location of the particle in the beam, the size ratio of nucleus to cell, and the location of the nucleus inside the cell on the scattering properties of a nucleated cell are analyzed. The results provide useful references for optical diagnostic and imaging of particle having nucleated structure.

  6. Ultrafast Bessel beams: advanced tools for laser materials processing

    Science.gov (United States)

    Stoian, Razvan; Bhuyan, Manoj K.; Zhang, Guodong; Cheng, Guanghua; Meyer, Remy; Courvoisier, Francois

    2018-05-01

    Ultrafast Bessel beams demonstrate a significant capacity of structuring transparent materials with a high degree of accuracy and exceptional aspect ratio. The ability to localize energy on the nanometer scale (bypassing the 100-nm milestone) makes them ideal tools for advanced laser nanoscale processing on surfaces and in the bulk. This allows to generate and combine micron and nano-sized features into hybrid structures that show novel functionalities. Their high aspect ratio and the accurate location can equally drive an efficient material modification and processing strategy on large dimensions. We review, here, the main concepts of generating and using Bessel non-diffractive beams and their remarkable features, discuss general characteristics of their interaction with matter in ablation and material modification regimes, and advocate their use for obtaining hybrid micro and nanoscale structures in two and three dimensions (2D and 3D) performing complex functions. High-throughput applications are indicated. The example list ranges from surface nanostructuring and laser cutting to ultrafast laser welding and the fabrication of 3D photonic systems embedded in the volume.

  7. The nonlocal problem for a hyperbolic equation with Bessel operator in a rectangular domain

    Directory of Open Access Journals (Sweden)

    Natalya V. Zaitseva

    2016-12-01

    Full Text Available We consider a boundary value problem for a hyperbolic equation with Bessel differential operator in a rectangular domain with integral nonlocal boundary value condition of the first kind. The equivalence between boundary value problem with integral nonlocal condition of the first kind and a local boundary value problem with mixed boundary conditions of the first and third kinds is proved. The existence and uniqueness of solution of the equivalent problem are established by means of the spectral method. At the uniqueness proof the completeness of the eigenfunction system of the spectral problem is used . At the existence proof the assessment of coefficients of series, the asymptotic formula for Bessel function of the first kind and asymptotic formula for eigenvalues are used. Sufficient conditions on the functions defining initial data of the problem are received. The solution of the problem is obtained in explicit form. The solution is obtained in the form of the Fourier–Bessel series. Its convergence is proved in the class of regular solutions.

  8. Higher-order harmonics of general limited diffraction Bessel beams

    Science.gov (United States)

    Ding, De-Sheng; Huang, Jin-Huang

    2016-12-01

    In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).

  9. Study of graphitic microstructure formation in diamond bulk by pulsed Bessel beam laser writing

    Science.gov (United States)

    Kumar, S.; Sotillo, B.; Chiappini, A.; Ramponi, R.; Di Trapani, P.; Eaton, S. M.; Jedrkiewicz, O.

    2017-11-01

    The advantages of using Bessel beams for the generation of graphitic structures in diamond bulk are presented. We show that by irradiating the sample with a pulsed Bessel beam whose non-diffracting zone is of the same order of the sample thickness, it is possible to produce without any sample translation straight graphitic through-microstructures, whose size depends on the input pulse energy. The microstructure growth is investigated as a function of the number of irradiating pulses, and the femtosecond and picosecond regimes are contrasted.

  10. A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Nash, Patrick L.

    2008-01-01

    Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation Δ perpendicular FDA of 1/r (∂)/(∂r) r(∂)/(∂r) that possesses an associated exact unitary representation of e i/2λΔ perpendicular FDA . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium

  11. Self-healing of Bessel-like beams with longitudinally dependent cone angles

    International Nuclear Information System (INIS)

    Litvin, I; Burger, L; Forbes, A

    2015-01-01

    Bessel beams have been extensively studied, but to date have been created over a finite region inside the laboratory. Recently Bessel-like beams with longitudinally dependent cone angles have been introduced allowing for a potentially infinite quasi non-diffracting propagation region. Here we show that such beams can self-heal. Moreover, in contrast to Bessel beams where the self-healing distance is constant, here the self-healing distance is dependent on where the obstruction is placed in the field, with the distance increasing as the Bessel-like beam propagates farther. We outline the theoretical concept for this self-healing and confirm it experimentally. (paper)

  12. Higher-order harmonics of limited diffraction Bessel beams

    Science.gov (United States)

    Ding; Lu

    2000-03-01

    We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.

  13. The generalized Abel-Plana formula. Applications to Bessel functions and Casimir effect

    International Nuclear Information System (INIS)

    Saharian, A.A.; Institute of Applied Problems in Physics NAS RA, Yerevan; Abdus Salam International Centre for Theoretical Physics, Trieste

    2000-02-01

    One of the most efficient methods to obtain the vacuum expectation values for the physical observables in the Casimir effect is based on using the Abel-Plana summation formula. This allows us to derive the regularized quantities in a manifestly cutoff independent way and present them in the form of strongly convergent integrals. However, the application of Abel-Plana formula, in its usual form, is restricted by simple geometries when the eigenmodes have a simple dependence on quantum numbers. The author generalized the Abel-Plana formula which essentially enlarges its application range. Based on this generalization, formulae have been obtained for various types of series over the zeros of some combinations of Bessel functions and for integrals involving these functions. It has been shown that these results generalize the special cases existing in literature. Further, the derived summation formulae have been used to summarize series arising in the mode summation approach to the Casimir effect for spherically and cylindrically symmetric boundaries. This allows us to extract the divergent parts from the vacuum expectation values for the local physical observables in a manifestly cutoff independent way. The present paper reviews these results. Some new considerations are also added. (author)

  14. On the product and ratio of Bessel random variables

    Directory of Open Access Journals (Sweden)

    Saralees Nadarajah

    2005-01-01

    Full Text Available The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.

  15. On the Operator ⨁Bk Related to Bessel Heat Equation

    Directory of Open Access Journals (Sweden)

    Wanchak Satsanit

    2010-01-01

    Full Text Available We study the equation (∂/∂tu(x,t=c2⊕Bku(x,t with the initial condition u(x,0=f(x for x∈Rn+. The operator ⊕Bk is the operator iterated k-times and is defined by ⊕Bk=((∑i=1pBxi4-(∑j=p+1p+qBxi4k, where p+q=n is the dimension of the Rn+, Bxi=∂2/∂xi2+(2vi/xi(∂/∂xi, 2vi=2αi+1, αi>-1/2, i=1,2,3,…,n, and k is a nonnegative integer, u(x,t is an unknown function for (x,t=(x1,x2,…,xn,t∈Rn+×(0,∞, f(x is a given generalized function, and c is a positive constant. We obtain the solution of such equation, which is related to the spectrum and the kernel, which is so called Bessel heat kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.

  16. Laser-driven acceleration with Bessel and Gaussian beams

    International Nuclear Information System (INIS)

    Hafizi, B.; Esarey, E.; Sprangle, P.

    1997-01-01

    The possibility of enhancing the energy gain in laser-driven accelerators by using Bessel laser beams is examined. Scaling laws are derived for the propagation length, acceleration gradient, and energy gain in various accelerators for both Gaussian and Bessel beam drivers. For equal beam powers, the energy gain can be increased by a factor of N 1/2 by utilizing a Bessel beam with N lobes, provided that the acceleration gradient is linearly proportional to the laser field. This is the case in the inverse free electron laser and the inverse Cherenkov accelerators. If the acceleration gradient is proportional to the square of the laser field (e.g., the laser wakefield, plasma beat wave, and vacuum beat wave accelerators), the energy gain is comparable with either beam profile. copyright 1997 American Institute of Physics

  17. The Generation Mechanism of Airy—Bessel Wave Packets in Free Space

    International Nuclear Information System (INIS)

    Ren Zhi-Jun; Ying Chao-Fu; Fan Chang-Jiang; Wu Qiong

    2012-01-01

    Localized optical Airy—Bessel configuration wave packets were first generated on the basis of a grating-telescope combination [Nat. Photon. 4(2010) 103]. By studying the spatially induced group velocity dispersion effect of ultrashort pulsed Bessel beams during propagation, we find the universal physical foundation of generating Airy—Bessel wave packets (ABWs) in free space. The research results are expected to open up more common channels for generating stable linear localized ABWs

  18. CMB in a box: Causal structure and the Fourier-Bessel expansion

    International Nuclear Information System (INIS)

    Abramo, L. Raul; Reimberg, Paulo H.; Xavier, Henrique S.

    2010-01-01

    This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility γ=e -μ , where μ is the optical depth to Thomson scattering. We show that the contributions of order γ N to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z>>10 3 , effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position x-vector=0 and time t 0 . Hence, for each multipole l there is a discrete tower of momenta k il (not a continuum) which can affect physical observables, with the smallest momenta being k 1l ∼l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

  19. High-power Bessel beams with orbital angular momentum in the terahertz range

    Science.gov (United States)

    Choporova, Yu. Yu.; Knyazev, B. A.; Kulipanov, G. N.; Pavelyev, V. S.; Scheglov, M. A.; Vinokurov, N. A.; Volodkin, B. O.; Zhabin, V. N.

    2017-08-01

    In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of ±1 and ±2 formed by silicon binary phase axicons (BPAs) with spiral zone structures. The axicons were illuminated with the Novosibirsk free electron laser radiation (a continuous stream of 100-ps pulses at f =5.6 MHz). The cw power of the beams produced reached 30 W and can by doubled via antireflection coating of the axicons. The intensity distribution in the beam cross sections was in good agreement with the Bessel functions and was kept constant within a distance of about L /r ≈190 and 100, where the first ring radii of the beams r were 0.9 and 1.5 mm for the Bessel beams of the first and second orders, respectively. Although the characteristics of the beams (Bessel cross section, "diffraction-free" propagation, self-recovery after passing obstacles, and randomly inhomogeneous media) corresponded to the properties of ideal Bessel beams, their spatial Fourier spectrum (the image in the focal plane of the lens) was, instead of an ideal ring, intertwined segments of arcs with phases shifted by π , the number of which was equal to the double value of the topological charge. This feature can be used, for example, in a demultiplexing unit of a free vortex-wave communication system or for identification of beam topological charge. We also revisited Young's double-slit diffraction and rotation of beams obstructed by a half-plane, previously applied to Laguerre-Gaussian beam characterization, in the case of the Bessel beams. The Young diffraction pattern demonstrated in this case a complicated intensity-phase distribution. It was shown that the Bessel beams formed by BPAs have two important advantages, which can be used in applications, in comparison with other methods of generation, e.g., a combination of an axicon lens with a spiral phase plate. Although the phase jumps of the axicons are designed for a determined wavelength (141 μ m in our case

  20. Optical tractor Bessel polarized beams

    International Nuclear Information System (INIS)

    Mitri, F.G.; Li, R.X.; Guo, L.X.; Ding, C.Y.

    2017-01-01

    Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α_0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications. - Highlights: • Optical tractor Bessel polarized beams are

  1. Microwave bessel beams generation using guided modes

    KAUST Repository

    Salem, Mohamed

    2011-06-01

    A novel method is devised for Bessel beams generation in the microwave regime. The beam is decomposed in terms of a number of guided transverse electric modes of a metallic waveguide. Modal expansion coefficients are computed from the modal power orthogonality relation. Excitation is achieved by means of a number of inserted coaxial loop antennas, whose currents are calculated from the excitation coefficients of the guided modes. The efficiency of the method is evaluated and its feasibility is discussed. Obtained results can be utilized to practically realize microwave Bessel beam launchers. © 2006 IEEE.

  2. Microwave bessel beams generation using guided modes

    KAUST Repository

    Salem, Mohamed; Kamel, Aladin Hassan; Niver, Edip

    2011-01-01

    A novel method is devised for Bessel beams generation in the microwave regime. The beam is decomposed in terms of a number of guided transverse electric modes of a metallic waveguide. Modal expansion coefficients are computed from the modal power orthogonality relation. Excitation is achieved by means of a number of inserted coaxial loop antennas, whose currents are calculated from the excitation coefficients of the guided modes. The efficiency of the method is evaluated and its feasibility is discussed. Obtained results can be utilized to practically realize microwave Bessel beam launchers. © 2006 IEEE.

  3. Engineering the on-axis intensity of Bessel beam by a feedback tuning loop

    Science.gov (United States)

    Li, Runze; Yu, Xianghua; Yang, Yanlong; Peng, Tong; Yao, Baoli; Zhang, Chunmin; Ye, Tong

    2018-02-01

    The Bessel beam belongs to a typical class of non-diffractive optical fields that are characterized by their invariant focal profiles along the propagation direction. However, ideal Bessel beams only rigorously exist in theory; Bessel beams generated in the lab are quasi-Bessel beams with finite focal extensions and varying intensity profiles along the propagation axis. The ability to engineer the on-axis intensity profile to the desired shape is essential for many applications. Here we demonstrate an iterative optimization-based approach to engineering the on-axis intensity of Bessel beams. The genetic algorithm is used to demonstrate this approach. Starting with a traditional axicon phase mask, in the design process, the computed on-axis beam profile is fed into a feedback tuning loop of an iterative optimization process, which searches for an optimal radial phase distribution that can generate a generalized Bessel beam with the desired onaxis intensity profile. The experimental implementation involves a fine-tuning process that adjusts the originally targeted profile so that the optimization process can optimize the phase mask to yield an improved on-axis profile. Our proposed method has been demonstrated in engineering several zeroth-order Bessel beams with customized on-axis profiles. High accuracy and high energy throughput merit its use in many applications.

  4. Optical trapping with Bessel beams generated from semiconductor lasers

    International Nuclear Information System (INIS)

    Sokolovskii, G S; Dudelev, V V; Losev, S N; Soboleva, K K; Deryagin, A G; Kuchinskii, V I; Sibbett, W; Rafailov, E U

    2014-01-01

    In this paper, we study generation of Bessel beams from semiconductor lasers with high beam propagation parameter M 2 and their utilization for optical trapping and manipulation of microscopic particles including living cells. The demonstrated optical tweezing with diodegenerated Bessel beams paves the way to replace their vibronic-generated counterparts for a range of applications towards novel lab-on-a-chip configurations

  5. Acoustic manipulation: Bessel beams and active carriers

    Science.gov (United States)

    Rajabi, Majid; Mojahed, Alireza

    2017-10-01

    In this paper, we address the interaction of zero-order acoustic Bessel beams as an acoustic manipulation tool, with an active spherical shell, as a carrier in drug, agent, or material delivery systems, in order to investigate the controllability of exerted acoustic radiation force as the driver. The active body is comprised of a spherical elastic shell stimulated in its monopole mode of vibrations with the same frequency as the incident wave field via an internally bonded and spatially uniformly excited piezoelectric actuator. The main aim of this work is to examine the performance of a nondiffracting and self-reconstructing zero-order Bessel beam to obtain the full manipulability condition of active carriers in comparison with the case of a plane wave field. The results unveil some unique potentials of the Bessel beams in the company of active carriers, with emphasis on the consumed power of the actuation system. This paper will widen the path toward the single-beam robust acoustic manipulation techniques and may lead to the prospect of combined tweezers and fields, with applications in delivery systems, microswimmers, and trapper designs.

  6. Talbot self-imaging phenomenon under Bessel beam illumination

    Science.gov (United States)

    Chakraborty, Rijuparna; Chowdhury, Subhajit Dutta; Chakraborty, Ajoy Kumar

    2018-06-01

    In this paper, we report the results of our theoretical studies on the phenomenon of self-imaging of periodic object under the illumination of zero-order Bessel beam. Our theoretical analysis indicates that the self-images are visible only after the walk-off distance of the Bessel beam used. It is also observed that the self-images bend around the optical axis of the setup. Besides, the present study justifies the importance of the conditions stipulated by Montgomery.

  7. Bessel beam fluorescence lifetime tomography of live embryos (Conference Presentation)

    Science.gov (United States)

    Xu, Dongli; Peng, Leilei

    2016-03-01

    Optical tomography allows isotropic 3D imaging of embryos. Scanning-laser optical tomography (SLOT) has superior light collecting efficiency than wide-field optical tomography, making it ideal for fluorescence imaging of live embryos. We previously reported an imaging system that combines SLOT with a novel Fourier-multiplexed fluorescence lifetime imaging (FmFLIM) technique named FmFLIM-SLOT. FmFLIM-SLOT performs multiplexed FLIM-FRET readout of multiple FRET sensors in live embryos. Here we report a recent effort on improving the spatial resolution of the FmFLIM-SLOT system in order to image complex biochemical processes in live embryos at the cellular level. Optical tomography has to compromise between resolution and the depth of view. In SLOT, the commonly-used focused Gaussian beam diverges quickly from the focal plane, making it impossible to achieve high resolution imaging in a large volume specimen. We thus introduce Bessel beam laser-scanning tomography, which illuminates the sample with a spatial-light-modulator-generated Bessel beam that has an extended focal depth. The Bessel beam is scanned across the whole specimen. Fluorescence projection images are acquired at equal angular intervals as the sample rotates. Reconstruction artifacts due to annular-rings of the Bessel beam are removed by a modified 3D filtered back projection algorithm. Furthermore, in combination of Fourier-multiplexing fluorescence lifetime imaging (FmFLIM) method, the Bessel FmFLIM-SLOT system is capable of perform 3D lifetime imaging of live embryos at cellular resolution. The system is applied to in-vivo imaging of transgenic Zebrafish embryos. Results prove that Bessel FmFLIM-SLOT is a promising imaging method in development biology research.

  8. Techniques to sort Bessel beams

    CSIR Research Space (South Africa)

    Dudley, Angela L

    2013-09-01

    Full Text Available -polar coordinate transformation, translating helically phased beams into a transverse phase gradient. By introducing two cylindrical lenses we can focus each of the azimuthal modes associated with each Bessel beam to a different lateral position in the Fourier...

  9. Optimality of embeddings of Bessel-potential-type spaces into Lorentz-Karamata spaces

    Czech Academy of Sciences Publication Activity Database

    Gogatishvili, Amiran; Opic, Bohumír; Neves, J. S.

    2004-01-01

    Roč. 134, č. 6 (2004), s. 1127-1147 ISSN 0308-2105 R&D Projects: GA ČR GA201/01/0333 Institutional research plan: CEZ:AV0Z1019905 Keywords : slowly varying functions * Lorentz-Karamata spaces * Bessel potentials Subject RIV: BA - General Mathematics Impact factor: 0.487, year: 2004

  10. Simple numerical evaluation of modified Bessel functions Ksub(ν)(x) of fractional order and the integral ∫sup(infinitely)sub(x)Ksub(ν)(eta)d eta

    International Nuclear Information System (INIS)

    Kostroun, V.O.

    1980-01-01

    Theoretical expressions for the angular and spectral distributions of synchrotron radiation involve modified Bessel functions of fractional order and the integral ∫sup(infinitely)sub(x)Ksub(ν)(eta)d eta. A simple series expression for these quantities which can be evaluated numerically with hand-held programmable calculators is presented. (orig.)

  11. Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid.

    Science.gov (United States)

    Mitri, Farid G

    2015-10-01

    Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (θ = π) in the near field and the backscattering form function in the far field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) because of the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3-D directivity patterns illustrate the near- and far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.

  12. Optical force exerted on a Rayleigh particle by a vector arbitrary-order Bessel beam

    International Nuclear Information System (INIS)

    Yang, Ruiping; Li, Renxian

    2016-01-01

    An analytical description of optical force on a Rayleigh particle by a vector Bessel beam is investigated. Linearly, radially, azimuthally, and circularly polarized Bessel beams are considered. The radial, azimuthal, and axial forces by a vector Bessel beam are numerically simulated. The effect of polarization, order of beams, and half-cone angle to the optical force are mainly discussed. For Bessel beams of larger half-cone angle, the non-paraxiality of beams plays an important role in optical forces. Numerical calculations show that optical forces, especially azimuthal forces, are very sensitive to the polarization of beams. - Highlights: • Optical force exerted on a Rayleigh particle by a vector Bessel beam is analytically derived. • Radial, azimuthal, and axial forces are numerically analyzed. • The effect of polarization, order of beam, and non-paraxiality is analyzed.

  13. Azimuthally matched interactions and azimuthal correlation of Bessel light beams

    International Nuclear Information System (INIS)

    Khilo, N A

    2000-01-01

    A theoretical investigation is reported of the regime of azimuthally matched interactions in the process of conversion of the frequency of Bessel light beams. It is shown that this nonlinear interaction regime is accompanied by the establishment of correlations of the mutual azimuthal orientations of plane-wave components of Bessel beams and by an increase in the overlap integral. (nonlinear optical phenomena)

  14. DRAMAtic transforms in magic angle spinning recoupling NMR: The Bessel function pathway.

    Science.gov (United States)

    Goodman, Russell; Hancock, Jason; Siemens, Mark; Jarrell, Harold; Siminovitch, David

    2005-07-01

    In magic angle spinning (MAS) NMR recoupling experiments, the extraction of multiple couplings or a coupling distribution from the observed dephasing signals remains a challenging problem. At least for REDOR experiments, the REDOR transform solves this problem, enabling the simultaneous measurement of multiple dipolar couplings. Focusing on the quadrupolar dephasing observed in QUADRAMA experiments as a representative example, we demonstrate that the same analytical form used for the mathematical description of REDOR dephasing also describes the dephasing observed in a wide variety of MAS NMR recoupling experiments. This fact immediately extends REDOR transform techniques to a much broader suite of recoupling experiments than had previously been realized, including those of DRAMA, MELODRAMA and QUADRAMA. As an illustration, we use the DRAMAtic transform to provide the first inversion of a QUADRAMA dephasing signal to extract the quadrupole coupling distribution. Using a complete elliptic integral of the first kind, we further develop a novel expression for the Pake-spun powder patterns of the corresponding recoupled lineshapes. Our methods and results reinforce the central role that Bessel functions can play in simplifying the integrals that define both the dephasing signals in the time domain, and their Fourier transforms in the frequency domain.

  15. Computational Diffusion Magnetic Resonance Imaging Based on Time-Dependent Bloch NMR Flow Equation and Bessel Functions.

    Science.gov (United States)

    Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I

    2016-04-01

    Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it

  16. Complex-scaling of screened Coulomb potentials for resonance calculations utilizing the modified Bessel functions

    Science.gov (United States)

    Jiao, Li-Guang; Ho, Yew Kam

    2014-05-01

    The screened Coulomb potential (SCP) has been extensively used in atomic physics, nuclear physics, quantum chemistry and plasma physics. However, an accurate calculation for atomic resonances under SCP is still a challenging task for various methods. Within the complex-scaling computational scheme, we have developed a method utilizing the modified Bessel functions to calculate doubly-excited resonances in two-electron atomic systems with configuration interaction-type basis. To test the validity of our method, we have calculated S- and P-wave resonance states of the helium atom with various screening strengths, and have found good agreement with earlier calculations using different methods. Our present method can be applied to calculate high-lying resonances associated with high excitation thresholds of the He+ ion, and with high-angular-momentum states. The derivation and calculation details of our present investigation together with new results of high-angular-momentum states will be presented at the meeting. Supported by NSC of Taiwan.

  17. On the validity of localized approximation for an on-axis zeroth-order Bessel beam

    International Nuclear Information System (INIS)

    Gouesbet, Gérard; Lock, J.A.; Ambrosio, L.A.; Wang, J.J.

    2017-01-01

    Localized approximation procedures are efficient ways to evaluate beam shape coefficients of laser beams, and are particularly useful when other methods are ineffective or inefficient. Several papers in the literature have reported the use of such procedures to evaluate the beam shape coefficients of Bessel beams. Examining the specific case of an on-axis zeroth-order Bessel beam, we demonstrate that localized approximation procedures are valid only for small axicon angles. - Highlights: • The localized approximation has been widely used to evaluate the Beam Shape Coefficients (BSCs) of Bessel beams. • The validity of this approximation is examined in the case of an on-axis zeroth-order Bessel beam. • It is demonstrated, in this specific example, that the localized approximation is efficient only for small enough axicon angles. • It is easily argued that this result must remain true for any kind of Bessel beams.

  18. Practical realization of a microwave Bessel beam launcher

    KAUST Repository

    Manzhura, Oksana

    2011-08-01

    An experimental setup is realized to practically generate Bessel beams in the microwave regime. The setup, which consists of a series of circular loop antennas inserted coaxially inside a circular metallic waveguide, excites the waveguide\\'s transverse-electric modes such that their superposition forms a Bessel beam at the open-end of the waveguide. The excitation currents are calculated from the needed excitation coefficients of each guided mode, which, in turn, are calculated from the modal decomposition of the beam. The efficiency of the setup is evaluated and the obtained experimental results are compared to the theoretical estimates. © 2011 IEEE.

  19. Bessel equation as an operator identity's matrix element in quantum mechanics

    International Nuclear Information System (INIS)

    Fan Hongyi; Li Chao

    2004-01-01

    We study the well-known Bessel equation itself in the framework of quantum mechanics. We show that the Bessel equation is a spontaneous result of an operator identity's matrix element in some definite entangled state representations, which is a fresh look. Application of this operator formalism in the Hankel transform of Laplace equation is presented

  20. Expansion of a zero-order Bessel beam in spheroidal coordinates by generalized Lorenz–Mie theory

    International Nuclear Information System (INIS)

    Han, L.; Han, Y.P.; Cui, Z.W.; Wang, J.J.

    2014-01-01

    An analytic solution to the scattering of the zero-order Bessel beam by a spheroidal particle is constructed on the basis of the generalized Lorenz–Mie theory (GLMT). The spheroidal beam shape coefficients (BSCs) of the zero-order Bessel beam are directly expressed in spheroidal coordinates and computed conveniently using an intrinsic method. Utilizing the tangential continuity of the electromagnetic fields, the expression coefficients of scattered and internal fields are determined. Numerical results concerning scattered field in the far zone are displayed for various parameters of the incident electromagnetic beam and of the scatter. These results are expected to provide useful insights into the scattering of a Bessel beam by spheroidal particles and particle manipulation applications using Bessel beams. - Highlights: • The scattering of zero-order Bessel beam by dielectric spheroid is investigated. • The analytic solution is constructed within the framework of the GLMT. • The spheroidal beam shape coefficients of the zero-order Bessel beam are computed by use an intrinsic method. • Numerical results concerning scattered field are displayed for various parameters

  1. Controlled acceleration of superimposed Bessel beams

    CSIR Research Space (South Africa)

    Dudley, Angela L

    2013-06-01

    Full Text Available spatial light modulator (SLM) to create superimposed, non-canonical, higher-order Bessel beams and a CCD camera to investigate the propagation of the resulting field. It is already known that the intensity profile of the resulting field experiences...

  2. Optimal condition for employing an axicon-generated Bessel beam to fabricate cylindrical microlens arrays

    Science.gov (United States)

    Luo, Zhi; Yin, Kai; Dong, Xinran; Duan, Ji’an

    2018-05-01

    A numerical algorithm, modelling the transformation from a Gaussian beam to a Bessel beam, is presented for the purpose to study the optimal condition for employing an axicon-generated Bessel beam to fabricate cylindrical microlens arrays (CMLAs). By applying the numerical algorithm to simulate the spatial intensity distribution behind the axicon under different defects of a rotund-apex and different diameter ratios of an incident beam to the axicon, we find that the diffraction effects formed by the axicon edge can be almost eliminated when the diameter ratio is less than 1:2, but the spatial intensity distribution is disturbed dramatically even a few tens of microns deviation of the apex, especially for the front part of the axicon-generated Bessel beam. Fortunately, the lateral intensity profile in the rear part still maintains a desirable Bessel curve. Therefore, the rear part of the Bessel area and the less than 1:2 diameter ratio are the optimal choice for employing an axicon-generated Bessel beam to implement surface microstructures fabrication. Furthermore, by applying the optimal conditions to direct writing microstructures on fused silica with a femtosecond (fs) laser, a large area close-packed CMLA is fabricated. The CMLA presents high quality and uniformity and its optical performance is also demonstrated.

  3. Optical tractor Bessel polarized beams

    Science.gov (United States)

    Mitri, F. G.; Li, R. X.; Guo, L. X.; Ding, C. Y.

    2017-01-01

    Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications.

  4. Bessel light sheet structured illumination microscopy

    Science.gov (United States)

    Noshirvani Allahabadi, Golchehr

    Biomedical study researchers using animals to model disease and treatment need fast, deep, noninvasive, and inexpensive multi-channel imaging methods. Traditional fluorescence microscopy meets those criteria to an extent. Specifically, two-photon and confocal microscopy, the two most commonly used methods, are limited in penetration depth, cost, resolution, and field of view. In addition, two-photon microscopy has limited ability in multi-channel imaging. Light sheet microscopy, a fast developing 3D fluorescence imaging method, offers attractive advantages over traditional two-photon and confocal microscopy. Light sheet microscopy is much more applicable for in vivo 3D time-lapsed imaging, owing to its selective illumination of tissue layer, superior speed, low light exposure, high penetration depth, and low levels of photobleaching. However, standard light sheet microscopy using Gaussian beam excitation has two main disadvantages: 1) the field of view (FOV) of light sheet microscopy is limited by the depth of focus of the Gaussian beam. 2) Light-sheet images can be degraded by scattering, which limits the penetration of the excitation beam and blurs emission images in deep tissue layers. While two-sided sheet illumination, which doubles the field of view by illuminating the sample from opposite sides, offers a potential solution, the technique adds complexity and cost to the imaging system. We investigate a new technique to address these limitations: Bessel light sheet microscopy in combination with incoherent nonlinear Structured Illumination Microscopy (SIM). Results demonstrate that, at visible wavelengths, Bessel excitation penetrates up to 250 microns deep in the scattering media with single-side illumination. Bessel light sheet microscope achieves confocal level resolution at a lateral resolution of 0.3 micron and an axial resolution of 1 micron. Incoherent nonlinear SIM further reduces the diffused background in Bessel light sheet images, resulting in

  5. Generation of the second harmonics of Bessel light beams in a KTP crystal

    International Nuclear Information System (INIS)

    Belyi, V N; Kazak, N S; Kondratyuk, N V; Khilo, N A; Shagov, A A

    1998-01-01

    Theoretical and experimental investigations were made of the characteristic features of doubling the frequency of Bessel light beams by the oe - e interaction in a KTP crystal. All possible and scalar interactions of plane-wave components of Bessel beams were observed experimentally. The spatial structure of the second harmonic in the far zone consisted of a central spot and a concentric ring. The diffraction divergence of the central beam was weak ( ∼ 1.7 mrad). The energy conversion efficiency was ∼ 21% for a Bessel beam, which was three times higher than the efficiency of conversion of the initial laser beam. A theoretical model was based on representation of the field of the second harmonic as a superposition of Bessel beams, which provided a correct description of the observed spatial and energy characteristics of the second harmonic. (nonlinear optical phenomena and devices)

  6. Elliptic integral evaluations of Bessel moments and applications

    International Nuclear Information System (INIS)

    Bailey, David H; Borwein, Jonathan M; Broadhurst, David; Glasser, M L

    2008-01-01

    We record and substantially extend what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. In particular, we develop formulae for integrals of products of six or fewer Bessel functions. In consequence, we are able to discover and prove closed forms for c n,k := ∫ ∞ 0 t k K n 0 (t) dt with integers n 1, 2, 3, 4 and k ≥ 0, obtaining new results for the even moments c 3,2k and c 4,2k . We also derive new closed forms for the odd moments s n,2k+1 := ∫ ∞ 0 t 2k+1 I 0 (t)K n-1 0 (t) dt with n = 3, 4 and for t n,2k+1 :∫ ∞ 0 t 2k+1 I 2 0 (t)K n-2 0 (t) dt with n = 5, relating the latter to Green functions on hexagonal, diamond and cubic lattices. We conjecture the values of s 5,2k+1 , make substantial progress on the evaluation of c 5,2k+1 , s 6,2k+1 and t 6,2k+1 and report more limited progress regarding c 5,2k , c 6,2k+1 and c 6,2k . In the process, we obtain eight conjectural evaluations, each of which has been checked to 1200 decimal places. One of these lies deep in four-dimensional quantum field theory and two are probably provable by delicate combinatorics. There remains a hard core of five conjectures whose proofs would be most instructive, to mathematicians and physicists alike

  7. Transverse characterization of focused Bessel beams with angular momentum applied to study degree of coherence

    International Nuclear Information System (INIS)

    He, Xi; Wu, Fengtie; Chen, Ziyang; Pu, Jixiong; Chavez-Cerda, Sabino

    2016-01-01

    The transverse focusing properties at the ‘pseudo-focal’ plane of coherent Bessel beams with angular momentum are analyzed in detail. The transverse magnification of the central dark region of Bessel beams at this pseudo-focal plane is derived for the first time by calculating the ratio of the magnitude of the transverse components of the corresponding wave vectors before and after the focusing lens. We test our results experimentally with coherent laser Bessel beams and excellent agreement is observed. Then, an LED light source is used to generate Bessel beams. By modifying the coherence of the LED light source, we observe that by reducing coherence a smaller and shallower central dark region of Bessel beams with angular momentum is produced at the pseudo-focal plane. This technique can be used as a method to characterize the degree of coherence of vortex beams. (paper)

  8. Spatial characterization of Bessel-like beams for strong-field physics.

    Science.gov (United States)

    Summers, Adam M; Yu, Xiaoming; Wang, Xinya; Raoul, Maxime; Nelson, Josh; Todd, Daniel; Zigo, Stefan; Lei, Shuting; Trallero-Herrero, Carlos A

    2017-02-06

    We present a compact, simple design for the generation and tuning of both the spot size and effective focal length of Bessel-like beams. In particular, this setup provides an important tool for the use of Bessel-like beams with high-power, femtosecond laser systems. Using a shallow angle axicon in conjunction with a spherical lens, we show that it is possible to focus Bessel-like modes to comparable focal spot sizes to sharp axicons while maintaining a long effective focal length. The resulting focal profiles are characterized in detail using an accurate high dynamic range imaging technique. Quantitatively, we introduce a metric (R0.8) which defines the spot-size containing 80% of the total energy. Our setup overcomes the typical compromise between long working distances and small spot sizes. This is particularly relevant for strong-field physics where most experiments must operate in vacuum.

  9. Two-color above-threshold ionization of atoms and ions in XUV Bessel beams and intense laser light

    Science.gov (United States)

    Seipt, D.; Müller, R. A.; Surzhykov, A.; Fritzsche, S.

    2016-11-01

    The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultraviolet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target atoms with regard to the beam axis. In addition, analog to the circular dichroism in typical two-color ATI experiments with circularly polarized light, we define and discuss seven different dichroism signals for such vortex Bessel beams that arise from the various combinations of the orbital and spin angular momenta of the two light fields. For localized targets, it is found that these dichroism signals strongly depend on the size and position of the atoms relative to the beam. For macroscopically extended targets, in contrast, three of these dichroism signals tend to zero, while the other four just coincide with the standard circular dichroism, similar as for Bessel beams with a small opening angle. Detailed computations of the dichroism are performed and discussed for the 4 s valence-shell photoionization of Ca+ ions.

  10. Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves.

    Science.gov (United States)

    Mitri, F G

    2017-02-01

    The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto

  11. THz computed tomography system with zero-order Bessel beam

    Science.gov (United States)

    Niu, Liting; Wu, Qiao; Wang, Kejia; Liu, Jinsong; Yang, Zhengang

    2018-01-01

    Terahertz (THz) waves can penetrate many optically opaque dielectric materials such as plastics, ceramics and colorants. It is effective to reveal the internal structures of these materials. We have built a THz Computed Tomography (CT) system with 0.3 THz zero-order Bessel beam to improve the depth of focus of this imaging system for the non-diffraction property of Bessel beam. The THz CT system has been used to detect a paper cup with a metal rod inside. Finally, the acquired projection data have been processed by the filtered back-projection algorithm and the reconstructed image of the sample has been obtained.

  12. Propagation of high-order circularly polarized Bessel beams and vortex generation in uniaxial crystals

    CSIR Research Space (South Africa)

    Belyi, VN

    2011-05-01

    Full Text Available The authors investigate the generation and transformation of Bessel beams through linear and nonlinear optical crystals. They outline the generation of high-order vortices due to propagation of Bessel beams along the optical axis of uniaxial...

  13. A note on a hyper-cubic Mahler measure and associated Bessel integral

    International Nuclear Information System (INIS)

    Glasser, M L

    2012-01-01

    The Mahler measure for the n-variable polynomial k + ∑(x j + 1/x j ) is reduced to a single integral of the n-th power of the modified Bessel function I 0 . Several special cases are examined in detail. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday. (paper)

  14. On the propagation of transient waves in a viscoelastic Bessel medium

    Science.gov (United States)

    Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco

    2017-06-01

    In this paper, we discuss the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium. First, we provide the analytic expression for the response function of the material as we approach the wave front. To do so, we take profit of a revisited version of the so called Buchen-Mainardi algorithm. Secondly, we provide an analytic expression for the long-time behavior of the response function of the material. This result is obtained by means of the Tauberian theorems for the Laplace transform. Finally, we relate the obtained results to a peculiar model for fluid-filled elastic tubes.

  15. Two-photon optics of Bessel-Gaussian modes

    CSIR Research Space (South Africa)

    McLaren, M

    2013-09-01

    Full Text Available In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum...

  16. Spin polarisation with electron Bessel beams

    Energy Technology Data Exchange (ETDEWEB)

    Schattschneider, P., E-mail: schattschneider@ifp.tuwien.ac.at [Institut für Festkörperphysik, Technische Universität Wien, A-1040 Wien (Austria); USTEM, Technische Universität Wien, A-1040 Wien (Austria); Grillo, V. [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); CNR-IMEM, Parco delle Scienze 37a, I-43100 Parma (Italy); Aubry, D. [Centrale Supelec, MSSMast CNRS 8579, F-92295 Châtenay-Malabry (France)

    2017-05-15

    The theoretical possibility to use an electron microscope as a spin polarizer is studied. It turns out that a Bessel beam passing a standard magnetic objective lens is intrinsically spin polarized when post-selected on-axis. In the limit of infinitely small detectors, the spin polarisation tends to 100 %. Increasing the detector size, the polarisation decreases rapidly, dropping below 10{sup −4} for standard settings of medium voltage microscopes. For extremely low voltages, the Figure of Merit increases by two orders of magnitude, approaching that of existing Mott detectors. Our findings may lead to new desings of spin filters, an attractive option in view of its inherent combination with the electron microscope, especially at low voltage. - Highlights: • TEM round magnetic lenses can act as spin polarizers when a Bessel beam is sent through. • This is found on theoretical grounds and demonstrated numerically for a few cases. • The effect is small, but can reach a Figure of Merit similar to existing Mott detectors. • This opens the possibility to construct nanometer-sized spin filters or detectors.

  17. Non-Compact and Sharp Embeddings of Logarithmic Bessel Potential Spaces into Hölder-Type Spaces

    Czech Academy of Sciences Publication Activity Database

    Edmunds, D. E.; Gurka, P.; Opic, Bohumír

    2006-01-01

    Roč. 25, č. 1 (2006), s. 73-80 ISSN 0232-2064 R&D Projects: GA ČR(CZ) GA201/01/0333 Institutional research plan: CEZ:AV0Z10190503 Keywords : generalized Lorentz-Zygmund spaces * logarithmic Bessel potential spaces * Hölder-continuous functions Subject RIV: BA - General Mathematics Impact factor: 0.360, year: 2006

  18. Multiple scattering of a zero-order Bessel beam with arbitrary incidence by an aggregate of uniaxial anisotropic spheres

    International Nuclear Information System (INIS)

    Li, Z.J.; Wu, Z.S.; Qu, T.; Shang, Q.C.; Bai, L.

    2016-01-01

    Based on the generalized multiparticle Mie theory, multiple scattering of an aggregate of uniaxial anisotropic spheres illuminated by a zero-order Bessel beam (ZOBB) with arbitrary propagation direction is investigated. The particle size and configuration are arbitrary. The arbitrary incident Bessel beam is expanded in terms of spherical vector wave functions (SVWFs). Utilizing the vector addition theorem of SVWFs, interactive and total scattering coefficients are derived through the continuous boundary conditions on which the interaction of the particles is considered. The accuracy of the theory and codes are verified by comparing results with those obtained for arbitrary plane wave incidence by CST simulation, and for ZOBB incidence by a numerical method. The effects of angle of incidence, pseudo-polarization angle, half-conical angle, beam center position, and permittivity tensor elements on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres, such as a linear chain, a 4×4×4 cube-shaped array, and other periodical structures consisting of massive spheres, are numerically analyzed. Selected results on the properties of typical particles such as TiO 2 , SiO 2 , or other particle lattices are calculated. This investigation could provide an effective test for further research on the scattering characteristics of an aggregate of anisotropic spheres by a high-order Bessel vortex beam. The results have important application in optical tweezers and particle manipulation. - Highlights: • Scattering of Bessel beam by an aggregate of uniaxial anisotropic spheres is studied. • The zero-order Bessel beam propagates and polarizes along arbitrary direction. • The accuracy of expansion coefficients, the scattering theory and codes is verified. • Effects of various parameters on scattering properties are numerically discussed. • Scattering properties of several type of periodical array are numerically analyzed.

  19. Revisiting the orthogonality of Bessel functions of the first kind on an infinite interval

    International Nuclear Information System (INIS)

    Leon, J Ponce de

    2015-01-01

    The rigorous proof of the orthogonality integral ∫ 0 ∞ ρ J ν (kρ)J ν (k ′ ρ) dρ=((δ(k−k ′ ))/k), for ν>=−1, is laborious and requires the use of mathematical techniques that, probably, are unfamiliar to most physics students, even at the graduate level. In physics, we are used to the argument that it may be proved by the use of Hankel transforms. However, the logic of the matter is the opposite, i.e., the existence of the inverse Hankel transform is a consequence of the orthogonality integral. The goal of this work is to prove this integral without circular reasoning. In this paper, using elementary properties of Bessel functions, we give a simple analytical derivation of this integral for the case where ν is an integer, zero, or half-integer not less than −1/2. Then, using the asymptotic behaviour of J ν (x), we extend the result to any ν>=−1. This work is of a pedagogical nature. Therefore, to add educational value to the discussion, we do not skip the details of the calculations. (paper)

  20. Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams

    CSIR Research Space (South Africa)

    Milione, G

    2015-02-01

    Full Text Available be simply understood via geometric optics [3]. When a portion of a Bessel beam is obstructed in one plane, the unobstructed conical rays interfere in its shadow region in another plane, as shown in Fig. 1(e). Due to this property, Bessel beams have been... extensively studied and have been used for a number of applications; for comprehensive reviews see [4–7]. For example, when using a Bessel beam for optical trapping, it is possible to simultaneously trap multiple particles in well separated planes [8...

  1. Extension of filament propagation in water with Bessel-Gaussian beams

    Energy Technology Data Exchange (ETDEWEB)

    Kaya, G.; Sayrac, M.; Boran, Y.; Kolomenskii, A. A. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Kaya, N.; Schuessler, H. A. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Science and Petroleum, Texas A& M University at Qatar, Doha 23874 (Qatar); Strohaber, J. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Department of Physics, Florida A& M University, Tallahassee, Florida 32307 (United States); Amani, M. [Science and Petroleum, Texas A& M University at Qatar, Doha 23874 (Qatar)

    2016-03-15

    We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.

  2. Two-photon polymerization of cylinder microstructures by femtosecond Bessel beams

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Liang [Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026 (China); Laser Zentrum Hannover e.V., 30419 Hannover (Germany); El-Tamer, Ayman; Hinze, Ulf; Chichkov, Boris N [Laser Zentrum Hannover e.V., 30419 Hannover (Germany); Li, Jiawen, E-mail: jwl@ustc.edu.cn; Hu, Yanlei; Huang, Wenhao; Chu, Jiaru [Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026 (China)

    2014-07-28

    In this work, we present an approach to modulate femtosecond laser beams into Bessel beams with a spatial light modulator (SLM) for two-photon polymerization applications. Bessel beams with different parameters are generated and annular optical fields are produced at the focal plane of the objective. Uniform cylinder microstructures are fabricated by a single illumination during a few seconds without stage translation. By modulating the holograms encoded on the SLM, the diameters of the fabricated annular structures can be flexibly controlled in a wide range with no need of changing the optical elements and realignment of the optical path.

  3. Polarization properties of linearly polarized parabolic scaling Bessel beams

    Energy Technology Data Exchange (ETDEWEB)

    Guo, Mengwen; Zhao, Daomu, E-mail: zhaodaomu@yahoo.com

    2016-10-07

    The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge. - Highlights: • We investigated the polarization properties of modified parabolic scaling Bessel beams with linear polarization. • We studied the evolution of transverse intensity profiles for the three components of these beams. • The intensity patterns of the cross polarization and longitudinal components can reflect the sign of the topological charge.

  4. Interaction of a high-order Bessel beam with a submerged spherical ultrasound contrast agent shell - Scattering theory.

    Science.gov (United States)

    Mitri, F G

    2010-03-01

    Acoustic scattering properties of ultrasound contrast agents are useful in extending existing or developing new techniques for biomedical imaging applications. A useful first step in this direction is to investigate the acoustic scattering of a new class of acoustic beams, known as helicoidal high-order Bessel beams, to improve the understanding of their scattering characteristics by an ultrasound contrast agent, which at present is very limited. The transverse acoustic scattering of a commercially available albuminoidal ultrasound contrast agent shell filled with air or a denser gas such as perfluoropropane and placed in a helicoidal Bessel beam of any order is examined numerically. The shell is assumed to possess an outer radius a=3.5 microns and a thickness of approximately 105 nm. Moduli of the total and resonance transverse acoustic scattering form functions are numerically evaluated in the bandwidth 0scattering of a helicoidal Bessel beam of order m1 so that the dynamics of contrast agents would be significantly altered. The main finding of the present theory is the suppression or enhancement for a particular resonance that may be used to advantage in imaging with ultrasound contrast agents for clinical applications. 2009 Elsevier B.V. All rights reserved.

  5. Experiments with BECs in a Painted Potential: Atom SQUID, Matter Wave Bessel Beams, and Matter Wave Circuits

    Science.gov (United States)

    Boshier, Malcolm; Ryu, Changhyun; Blackburn, Paul; Blinova, Alina; Henderson, Kevin

    2014-05-01

    The painted potential is a time-averaged optical dipole potential which is able to create arbitrary and dynamic two dimensional potentials for Bose Einstein condensates (BECs). This poster reports three recent experiments using this technique. First, we have realized the dc atom SQUID geometry of a BEC in a toroidal trap with two Josephson junctions. We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. Second, we have used free expansion of a rotating toroidal BEC to create matter wave Bessel beams, which are of interest because perfect Bessel beams (plane waves with amplitude profiles described by Bessel functions) propagate without diffraction. Third, we have realized the basic circuit elements necessary to create complex matter wave circuits. We launch BECs at arbitrary velocity along straight waveguides, propagate them around curved waveguides and stadium-shaped waveguide traps, and split them coherently at y-junctions that can also act as switches. Supported by LANL/LDRD.

  6. Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers

    International Nuclear Information System (INIS)

    Mitri, F.G.

    2008-01-01

    Starting from the exact acoustic scattering from a sphere immersed in an ideal fluid and centered along the propagation axis of a standing or quasi-standing zero-order Bessel beam, explicit partial-wave representations for the radiation force are derived. A standing or a quasi-standing acoustic field is the result of propagating two equal or unequal amplitude zero-order Bessel beams, respectively, along the same axis but in opposite sense. The Bessel beam is characterized by the half-cone angle β of its plane wave components, such that β = 0 represents a plane wave. It is assumed here that the half-cone angle β for each of the counter-propagating acoustic Bessel beams is equal. Fluid, elastic and viscoelastic spheres immersed in water are treated as examples. Results indicate the capability of manipulating spherical targets based on their mechanical and acoustical properties. This condition provides an impetus for further designing acoustic tweezers operating with standing or quasi-standing Bessel acoustic waves. Potential applications include particle manipulation in micro-fluidic lab-on-chips as well as in reduced gravity environments

  7. Photorefractive Axicon: Study of Light-induced Effect by Bessel Beam in Photorefractive Crystal

    International Nuclear Information System (INIS)

    Vieira, T A; Gesualdi, M R R; Zamboni-Rached, M; Muramatsu, M

    2011-01-01

    In this work, we present the theoretical and computational study of the original analysis of the light-induced effects by Bessel beams in photorefractive crystals. Modern applications of these beams as: metrological, alignment of optical systems, optical tweezers, non linear optics, optical communication, and others, becoming a very interesting substitute for a Gaussian beam when this is subject to diffraction and dispersion effects to large distance propagation. On the other hand, the photorefractive crystals are very important materials for applications in non-linear optics, holographic storage, interferometry and optical information processing. We perform an analysis of the index refraction modulation generated by Bessel beam in photorefractive medium discussing the possibility this optical material to control and generation of Bessel beam properties.

  8. Fourier Bessel transform method for efficiently calculating the magnetic field of solenoids

    International Nuclear Information System (INIS)

    Nachamkin, J.; Maggiore, C.J.

    1980-01-01

    A numerical procedure for calculating the magnetic field of a selenoid is derived. Based on the properties of Bessel functions, the procedure is shown to be convergent everywhere, including within the windings of the solenoid. The most critical part of the procedure is detailed in the main text. A simple method is used to ensure numerical significance while allowing economical computational times. In the appendix the procedure is generalized to universal convergence by appropriate partitioning of the solenoid windings

  9. Improved fixation quality provided by a Bessel beacon in an adaptive optics system.

    Science.gov (United States)

    Lambert, Andrew J; Daly, Elizabeth M; Dainty, Christopher J

    2013-07-01

    We investigate whether a structured probe beam that creates the beacon for use in a retinal imaging adaptive optics system can provide useful side effects. In particular we investigate whether a Bessel beam that is seen by the subject as a set of concentric rings has a dampening effect on fixation variations of the subject under observation. This calming effect would allow longer periods of observation, particularly for patients with abnormal fixation. An experimental adaptive optics system developed for retinal imaging is used to monitor the fluctuations in aberrations for artificial and human subjects. The probe beam is alternated between a traditional beacon and one provided by a Bessel beam created by SLM. Time-frequency analysis is used to indicate the differences in power and time variation during fixation depending on whether the Bessel beam or the traditional beacon is employed. Comparison is made with the response for an artificial eye to discount systemic variations. Significant evidence is accrued to indicate the reduced fluctuations in fixation when the Bessel beam is employed to create the beacon. © 2013 The Authors Ophthalmic & Physiological Optics © 2013 The College of Optometrists.

  10. Orbital angular momentum of a high-order Bessel light beam

    International Nuclear Information System (INIS)

    Volke-Sepulveda, K; Garces-Chavez, V; Chavez-Cerda, S; Arlt, J; Dholakia, K

    2002-01-01

    The orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment. This allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams. Furthermore, we demonstrate experimentally the mechanical transfer of orbital angular momentum to trapped particles in optical tweezers using a high-order Bessel beam. We set transparent particles of known dimensions into rotation, where the sense of rotation can be reversed by changing the sign of the singularity. Quantitative results are obtained for rotation rates. This paper's animations are available from the Multimedia Enhancements page

  11. Extension of filament propagation in water with Bessel-Gaussian beams

    Directory of Open Access Journals (Sweden)

    G. Kaya

    2016-03-01

    Full Text Available We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.

  12. Cauchy problem for a parabolic equation with Bessel operator and Riemann–Liouville partial derivative

    Directory of Open Access Journals (Sweden)

    Fatima G. Khushtova

    2016-03-01

    Full Text Available In this paper Cauchy problem for a parabolic equation with Bessel operator and with Riemann–Liouville partial derivative is considered. The representation of the solution is obtained in terms of integral transform with Wright function in the kernel. It is shown that when this equation becomes the fractional diffusion equation, obtained solution becomes the solution of Cauchy problem for the corresponding equation. The uniqueness of the solution in the class of functions that satisfy the analogue of Tikhonov condition is proved.

  13. Gaussian vs. Bessel light-sheets: performance analysis in live large sample imaging

    Science.gov (United States)

    Reidt, Sascha L.; Correia, Ricardo B. C.; Donnachie, Mark; Weijer, Cornelis J.; MacDonald, Michael P.

    2017-08-01

    Lightsheet fluorescence microscopy (LSFM) has rapidly progressed in the past decade from an emerging technology into an established methodology. This progress has largely been driven by its suitability to developmental biology, where it is able to give excellent spatial-temporal resolution over relatively large fields of view with good contrast and low phototoxicity. In many respects it is superseding confocal microscopy. However, it is no magic bullet and still struggles to image deeply in more highly scattering samples. Many solutions to this challenge have been presented, including, Airy and Bessel illumination, 2-photon operation and deconvolution techniques. In this work, we show a comparison between a simple but effective Gaussian beam illumination and Bessel illumination for imaging in chicken embryos. Whilst Bessel illumination is shown to be of benefit when a greater depth of field is required, it is not possible to see any benefits for imaging into the highly scattering tissue of the chick embryo.

  14. The generalized Abel-Plana formula with applications to Bessel functions and casimir effect

    International Nuclear Information System (INIS)

    Saharian, Aram A.

    2007-08-01

    One of the most efficient methods for the evaluation of the vacuum expectation values for physical observables in the Casimir effect is based on using the Abel-Plana summation formula. This enables to derive the renormalized quantities in a manifestly cutoff independent way and to present them in the form of strongly convergent integrals. However, applications of the Abel- Plana formula, in its usual form, are restricted by simple geometries when the eigenmodes have a simple dependence on quantum numbers. The author generalized the Abel-Plana formula which essentially enlarges its application range. Based on this generalization, formulae have been obtained for various types of series over the zeros of combinations of Bessel functions and for integrals involving these functions. It has been shown that these results generalize the special cases existing in literature. Further, the derived summation formulae have been used to summarize series arising in the direct mode summation approach to the Casimir effect for spherically and cylindrically symmetric boundaries, for boundaries moving with uniform proper acceleration, and in various braneworld scenarios. This allows to extract from the vacuum expectation values of local physical observables the parts corresponding to the geometry without boundaries and to present the boundary-induced parts in terms of integrals strongly convergent for the points away from the boundaries. As a result, the renormalization procedure for these observables is reduced to the corresponding procedure for bulks without boundaries. The present paper reviews these results. We also aim to collect the results on vacuum expectation values for local physical observables such as the field square and the energy-momentum tensor in manifolds with boundaries for various bulk and boundary geometries. (author)

  15. Experimental generation and application of the superposition of higher-order Bessel beams

    CSIR Research Space (South Africa)

    Dudley, Angela L

    2009-07-01

    Full Text Available Academy of Sciences of Belarus 4 School of Physics, University of Stellenbosch Presented at the 2009 South African Institute of Physics Annual Conference University of KwaZulu-Natal Durban, South Africa 6-10 July 2009 Page 2 © CSIR 2008... www.csir.co.za Generation of Bessel Fields: • METHOD 1: Ring Slit Aperture • METHOD 2: Axicon Adaptation of method 1 to produce superpositions of higher-order Bessel beams: J. Durnin, J.J. Miceli and J.H. Eberly, Phys. Rev. Lett. 58 1499...

  16. Fast and accurate computation of projected two-point functions

    Science.gov (United States)

    Grasshorn Gebhardt, Henry S.; Jeong, Donghui

    2018-01-01

    We present the two-point function from the fast and accurate spherical Bessel transformation (2-FAST) algorithm1Our code is available at https://github.com/hsgg/twoFAST. for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when projecting the galaxy power spectrum P (k ) onto the configuration space, ξℓν(r ), or spherical harmonic space, Cℓ(χ ,χ'). First, we employ the FFTLog transformation of the power spectrum to divide the calculation into P (k )-dependent coefficients and P (k )-independent integrations of basis functions multiplied by spherical Bessel functions. We find analytical expressions for the latter integrals in terms of special functions, for which recursion provides a fast and accurate evaluation. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.

  17. Optical pulling force on a magneto-dielectric Rayleigh sphere in Bessel tractor polarized beams

    International Nuclear Information System (INIS)

    Mitri, F.G.; Li, R.X.; Yang, R.P.; Guo, L.X.; Ding, C.Y.

    2016-01-01

    The optical radiation force induced by Bessel (vortex) beams on a magneto-dielectric subwavelength sphere is investigated with particular emphasis on the beam polarization and order l (or topological charge). The analysis is focused on identifying the regions and some of the conditions to achieve retrograde motion of the sphere centered on the axis of wave propagation of the incident beam, or shifted off-axially. Exact non-paraxial analytical solutions are established, and computations for linear, circular, radial, azimuthal and mixed polarizations of the individual plane wave components forming the Bessel (vortex) beams by means of the angular spectrum decomposition method (ASDM) illustrate the theory with particular emphasis on the tractor (i.e. reversal) behavior of the force. This effect results in the pulling of the magneto-dielectric sphere against the forward linear momentum density flux associated with the incoming waves. Should some conditions related to the choice of the beam parameters as well as the permittivity and permeability of the sphere be met, the optical force vanishes and reverses sign. Moreover, the beam polarization is shown to affect differently the axial negative pulling force for either the zeroth- or the first-order Bessel beam. When the sphere is centered on the beam′s axis, the axial force component is always negative for the zeroth-order Bessel beam except for the radial and azimuthal polarization configurations. Nonetheless, for the first-order Bessel beam, the axial force is negative for the radial polarization case only. Additional tractor beam effects arise when the sphere departs from the center of the beam. It is also demonstrated that the tractor beam effect arises from the force component originating from the cross-interaction between the electric and magnetic dipoles. Potential applications are in particle manipulation, optical levitation, tractor beam tweezers, and other emergent technologies using polarized Bessel beams on

  18. Particle confinement by a radially polarized laser Bessel beam

    Science.gov (United States)

    Laredo, Gilad; Kimura, Wayne D.; Schächter, Levi

    2017-03-01

    The stable trajectory of a charged particle in an external guiding field is an essential condition for its acceleration or for forcing it to generate radiation. Examples of possible guiding devices include a solenoidal magnetic field or permanent periodic magnet in klystrons, a wiggler in free-electron lasers, the lattice of any accelerator, and finally the crystal lattice for the case of channeling radiation. We demonstrate that the trajectory of a point-charge in a radially polarized laser Bessel beam may be stable similarly to the case of a positron that bounces back and forth in the potential well generated by two adjacent atomic planes. While in the case of channeling radiation, the transverse motion is controlled by a harmonic oscillator equation, for a Bessel beam the transverse motion is controlled by the Mathieu equation. Some characteristics of the motion are presented.

  19. The application of a Bessel transform to the determination of stellar rotational velocities

    International Nuclear Information System (INIS)

    Deeming, T.J.

    1977-01-01

    A method for analysing line profiles by means of a transform using Bessel functions is described. This yields the stellar rotational velocity γ sin i, to an accuracy of about +-1 km s -1 for rotational velocities greater than about 5 km s -1 , provided that rotation is the major source of line broadening. The theory of the method is a special case of a general theory of linear transforms in data analysis, which is outlined in an appendix. (Auth.)

  20. Generating superpositions of higher order bessel beams [Conference paper

    CSIR Research Space (South Africa)

    Vasilyeu, R

    2009-10-01

    Full Text Available An experimental setup to generate a superposition of higher-order Bessel beams by means of a spatial light modulator and ring aperture is presented. The experimentally produced fields are in good agreement with those calculated theoretically....

  1. Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series

    International Nuclear Information System (INIS)

    Li, Renxian; Ren, Kuan Fang; Han, Xiang'e; Wu, Zhensen; Guo, Lixin; Gong, Shuxi

    2013-01-01

    Debye series expansion (DSE) is employed to the analysis of radiation pressure force (RPF) exerted on biological cells induced by high-order Bessel beams (BB). The beam shape coefficients (BSCs) for high-order Bessel beams are calculated using analytical expressions obtained by the integral localized approximation (ILA). Different types of cells, including a real Chinese Hamster Ovary (CHO) cell and a lymphocyte which are respectively modeled by a coated and five-layered sphere, are considered. The RPF induced by high-order Bessel beams is compared with that by Gaussian beams and zeroth-order Bessel beams, and the effect of different scattering processes on RPF is studied. Numerical calculations show that high-order Bessel beams with zero central intensity can also transversely trap particle in the beam center, and some scattering processes can provide longitudinal pulling force. -- Highlights: ► BSCs for high-order Bessel beam (HOBB) is derived using ILA. ► DSE is employed to study the RPF induced by HOBB exerted on multilayered cells. ► RPF is decided by radius relative to the interval of peaks in intensity profile. ► HOBB can also transversely trap high-index particle in the vicinity of beam axis. ► RPF for some scattering processes can longitudinally pull particles back

  2. Effective and efficient method of calculating Bessel beam fields

    CSIR Research Space (South Africa)

    Litvin, IA

    2005-01-01

    Full Text Available Bessel beams have gathered much interest of late due to their properties of near diffraction free propagation and self reconstruction after obstacles. Such laser beams have already found applications in fields such as optical tweezers and as pump...

  3. Limitations to laser machining of silicon using femtosecond micro-Bessel beams in the infrared

    International Nuclear Information System (INIS)

    Grojo, David; Mouskeftaras, Alexandros; Delaporte, Philippe; Lei, Shuting

    2015-01-01

    We produce and characterize high-angle femtosecond Bessel beams at 1300-nm wavelength leading to nonlinearly ionized plasma micro-channels in both glass and silicon. With microjoule pulse energy, we demonstrate controlled through-modifications in 150-μm glass substrates. In silicon, strong two-photon absorption leads to larger damages at the front surface but also a clamping of the intensity inside the bulk at a level of ≈4 × 10 11  W cm −2 which is below the threshold for volume and rear surface modification. We show that the intensity clamping is associated with a strong degradation of the Bessel-like profile. The observations highlight that the inherent limitation to ultrafast energy deposition inside semiconductors with Gaussian focusing [Mouskeftaras et al., Appl. Phys. Lett. 105, 191103 (2014)] applies also for high-angle Bessel beams

  4. Generation of high-order Bessel vortex beam carrying orbital angular momentum using multilayer amplitude-phase-modulated surfaces in radiofrequency domain

    Science.gov (United States)

    Kou, Na; Yu, Shixing; Li, Long

    2017-01-01

    A high-order Bessel vortex beam carrying orbital angular momentum (OAM) is generated by using multilayer amplitude-phase-modulated surfaces (APMSs) at 10 GHz. The APMS transmitarray is composed of four-layer conformal square-loop (FCSL) surfaces with both amplitude and phase modulation. The APMS can transform a quasi-spherical wave emitted from the feeding source into a pseudo non-diffractive high-order Bessel vortex beam with OAM. The APMS for a second-order Bessel beam carrying OAM in the n = 2 mode is designed, fabricated, and measured. Full-wave simulation and measurement results confirm that Bessel vortex beams with OAM can be effectively generated using the proposed APMS transmitarray.

  5. Generating superpositions of higher–order Bessel beams [Journal article

    CSIR Research Space (South Africa)

    Vasilyeu, R

    2009-12-01

    Full Text Available The authors report the first experimental generation of the superposition of higher-order Bessel beams, by means of a spatial light modulator (SLM) and a ring slit aperture. They present illuminating a ring slit aperture with light which has...

  6. Exponential and Bessel fitting methods for the numerical solution of the Schroedinger equation

    International Nuclear Information System (INIS)

    Raptis, A.D.; Cash, J.R.

    1987-01-01

    A new method is developed for the numerical integration of the one dimensional radial Schroedinger equation. This method involves using different integration formulae in different parts of the range of integration rather than using the same integration formula throughout. Two new integration formulae are derived, one which integrates Bessel and Neumann functions exactly and another which exactly integrates certain exponential functions. It is shown that, for large r, these new formulae are much more accurate than standard integration methods for the Schroedinger equation. The benefit of using this new approach is demonstrated by considering some numerical examples based on the Lennard-Jones potential. (orig.)

  7. Asymmetric skew Bessel processes and their applications to finance

    NARCIS (Netherlands)

    Decamps, M.; Goovaerts, M.J.; Schoutens, W.

    2006-01-01

    In this paper, we extend the Harrison and Shepp's construction of the skew Brownian motion (1981) and we obtain a diffusion similar to the two-dimensional Bessel process with speed and scale densities discontinuous at one point. Natural generalizations to multi-dimensional and fractional order

  8. Resonant Self-Trapping and Absorption of Intense Bessel Beams

    International Nuclear Information System (INIS)

    Fan, J.; Parra, E.; Milchberg, H. M.

    2000-01-01

    We report the observation of resonant self-trapping and enhanced laser-plasma heating resulting from propagation of high intensity Bessel beams in neutral gas. The enhancement in absorption and plasma heating is directly correlated to the spatial trapping of laser radiation. (c) 2000 The American Physical Society

  9. Generating millimeter-wave Bessel beam with orbital angular momentum using reflective-type metasurface inherently integrated with source

    Science.gov (United States)

    Shen, Yizhu; Yang, Jiawei; Meng, Hongfu; Dou, Wenbin; Hu, Sanming

    2018-04-01

    Metasurfaces, orbital angular momenta (OAM), and non-diffractive Bessel beams have been attracting worldwide research. Combining the benefits of these three promising techniques, this paper proposes a metasurface-based reflective-type approach to generate a first-order Bessel beam carrying OAM. To validate this approach, a millimeter-wave metasurface is analyzed, designed, fabricated, and measured. Experimental results agree well with simulation. Moreover, this reflective-type metasurface, generating a Bessel beam with OAM, is inherently integrated with a planar feeding source in the same single-layer printed circuit board. Therefore, the proposed design features low profile, low cost, easy integration with front-end active circuits, and no alignment error between the feeding source and the metasurface.

  10. ON WEIGHTED GENERALIZED FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS

    Directory of Open Access Journals (Sweden)

    E. L. Shishkina

    2016-12-01

    Full Text Available In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with the Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with the Bessel operator.

  11. Optimal Embeddings of Bessel-Potential-Type Spaces into Generalized Hölder Spaces Involving k-Modulus of Smoothness

    Czech Academy of Sciences Publication Activity Database

    Gogatishvili, Amiran; Neves, J. S.; Opic, Bohumír

    2010-01-01

    Roč. 32, č. 3 (2010), s. 201-228 ISSN 0926-2601 R&D Projects: GA ČR GA201/05/2033; GA ČR GA201/08/0383 Institutional research plan: CEZ:AV0Z10190503 Keywords : slowly varying functions * Lorentz-Karamata spaces * Rearrangement-invariant Banach function spaces * Bessel potentials * (fractional) Sobolev-type spaces * Hölder-type spaces * Zygmund-type spaces Subject RIV: BA - General Mathematics Impact factor: 0.853, year: 2010 http://link.springer.com/article/10.1007%2Fs11118-009-9148-2

  12. Spherical space Bessel-Legendre-Fourier mode solver for Maxwell's wave equations

    Science.gov (United States)

    Alzahrani, Mohammed A.; Gauthier, Robert C.

    2015-02-01

    For spherically symmetric dielectric structures, a basis set composed of Bessel, Legendre and Fourier functions, BLF, are used to cast Maxwell's wave equations into an eigenvalue problem from which the localized modes can be determined. The steps leading to the eigenmatrix are reviewed and techniques used to reduce the order of matrix and tune the computations for particular mode types are detailed. The BLF basis functions are used to expand the electric and magnetic fields as well as the inverse relative dielectric profile. Similar to the common plane wave expansion technique, the BLF matrix returns the eigen-frequencies and eigenvectors, but in BLF only steady states, non-propagated, are obtained. The technique is first applied to a air filled spherical structure with perfectly conducting outer surface and then to a spherical microsphere located in air. Results are compared published values were possible.

  13. Axial and transverse acoustic radiation forces on a fluid sphere placed arbitrarily in Bessel beam standing wave tweezers

    International Nuclear Information System (INIS)

    Mitri, F.G.

    2014-01-01

    The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to an equilibrium position depending on the chosen size parameter ka (where k is the wave-number and a the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study. -- Highlights: •The axial and transverse forces on a fluid sphere in acoustical Bessel beams tweezers are evaluated. •The attraction or repulsion to an equilibrium position in the standing wave field is examined. •Potential applications are in particle manipulation using standing waves

  14. Axial and transverse acoustic radiation forces on a fluid sphere placed arbitrarily in Bessel beam standing wave tweezers

    Energy Technology Data Exchange (ETDEWEB)

    Mitri, F.G., E-mail: mitri@chevron.com

    2014-03-15

    The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to an equilibrium position depending on the chosen size parameter ka (where k is the wave-number and a the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study. -- Highlights: •The axial and transverse forces on a fluid sphere in acoustical Bessel beams tweezers are evaluated. •The attraction or repulsion to an equilibrium position in the standing wave field is examined. •Potential applications are in particle manipulation using standing waves.

  15. A proposal of Fourier-Bessel expansion with optimized ensembles of bases to analyse two dimensional image

    Science.gov (United States)

    Yamasaki, K.; Fujisawa, A.; Nagashima, Y.

    2017-09-01

    It is a critical issue to find the best set of fitting function bases in mode structural analysis of two dimensional images like plasma emission profiles. The paper proposes a method to optimize a set of the bases in the case of Fourier-Bessel function series, using their orthonormal property, for more efficient and precise analysis. The method is applied on a tomography image of plasma emission obtained with the Maximum-likelihood expectation maximization method in a linear cylindrical device. The result demonstrates the excellency of the method that realizes the smaller residual error and minimum Akaike information criterion using smaller number of fitting function bases.

  16. Special features of local spatial spectrum of Bessel light beams

    CSIR Research Space (South Africa)

    Belyi, VN

    2011-11-01

    Full Text Available In this paper the authors consider the angular spectrum of an apertured Bessel beam when the aperture is circular and shifted laterally with respect to the optical axis. Since the perturbation of the resulting angular spectrum is due to a spatially...

  17. Efficient second-harmonic imaging of collagen in histological slides using Bessel beam excitation

    Science.gov (United States)

    Vuillemin, Nelly; Mahou, Pierre; Débarre, Delphine; Gacoin, Thierry; Tharaux, Pierre-Louis; Schanne-Klein, Marie-Claire; Supatto, Willy; Beaurepaire, Emmanuel

    2016-07-01

    Second-harmonic generation (SHG) is the most specific label-free indicator of collagen accumulation in widespread pathologies such as fibrosis, and SHG-based measurements hold important potential for biomedical analyses. However, efficient collagen SHG scoring in histological slides is hampered by the limited depth-of-field of usual nonlinear microscopes relying on focused Gaussian beam excitation. In this work we analyze theoretically and experimentally the use of Bessel beam excitation to address this issue. Focused Bessel beams can provide an axially extended excitation volume for nonlinear microscopy while preserving lateral resolution. We show that shaping the focal volume has consequences on signal level and scattering directionality in the case of coherent signals (such as SHG) which significantly differ from the case of incoherent signals (two-photon excited fluorescence, 2PEF). We demonstrate extended-depth SHG-2PEF imaging of fibrotic mouse kidney histological slides. Finally, we show that Bessel beam excitation combined with spatial filtering of the harmonic light in wave vector space can be used to probe collagen accumulation more efficiently than the usual Gaussian excitation scheme. These results open the way to SHG-based histological diagnoses.

  18. Superpositions of higher-order bessel beams and nondiffracting speckle fields

    CSIR Research Space (South Africa)

    Dudley, Angela L

    2009-08-01

    Full Text Available speckle fields. The paper reports on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light...

  19. Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

    Science.gov (United States)

    Tang, Bin; Jiang, Chun; Zhu, Haibin

    2012-08-01

    Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

  20. Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone

    KAUST Repository

    Salem, Mohamed

    2013-07-01

    The electromagnetic field scattering of a vector Bessel beam in the presence of an infinite circular cone with an impedance boundary on its surface is considered. The impinging field is normal to the tip of the cone and is expanded in terms of vector spherical wave functions; a Kontorovich-Lebedev (KL) transform is employed to expand the scattered fields. The problem is reduced to a singular integral equation with a variable coefficient of the non-convolution type. The singularities of the spectral function are deduced and representations for the field at the tip of the cone as well as other regions are given together with the conditions of validity of these representations. © 2013 IEEE.

  1. Efficient sorting of Bessel beams [Conference paper

    CSIR Research Space (South Africa)

    Mhlanga, T

    2013-02-01

    Full Text Available measured in entanglement and shown an increased spiral bandwidth17. Exploiting these properties of Bessel beams will make them very useful in the field of long-range, broad bandwidth communication systems. However, in order for these fields to be a... success in the area of optical communication, efficient techniques for extracting the information they carry (i.e. their azimuthal mode indices) need to exist. The ‘fork’ diffraction grating can be used to couple light of a particular OAM state into a...

  2. Self-healing of Bessel-like beams with longitudinally dependent cone angles

    CSIR Research Space (South Africa)

    Litvin, I

    2015-09-01

    Full Text Available non-diffracting propagation region. Here we show that such beams can self-heal. Moreover, in contrast to Bessel beams where the self-healing distance is constant, here the self-healing distance is dependent on where the obstruction is placed...

  3. Bessel beam transformation in c-cuts of uniaxial crystals by varying the source wavelength

    Energy Technology Data Exchange (ETDEWEB)

    Paranin, V. D. [Samara State Aerospace University, 34, Moskovskoe shosse, Samara, 443086 (Russian Federation)

    2016-04-13

    Transformation of Bessel beam of a zero order to Bessel beam of the second order in c-cut of CaCO{sub 3} crystal is experimentally investigated. Possibility of output beam control at changing of wavelength and using of a diffraction axicon is shown. Full transformation of beams at changing of wavelength Δλ=1.5 nanometers is received at initial wavelength λ=637.5 nanometers for a crystal of CaCO{sub 3} with 15 mm long and a diffraction axicon with period of 2 microns. The theoretical value of necessary wavelength changing is Δλ=1.7 nanometers that is according with experimental results.

  4. On the MAF solution of the uniformly lengthening pendulum via change of independent variable in the Bessel’s equation

    Directory of Open Access Journals (Sweden)

    Coşkun Deniz

    Full Text Available Common recipe for the Lengthening Pendulum (LP involves some change of variables to give a relationship with the Bessel’s equation. In this work, semiclassical MAF (Modified Airy Function solution of the LP is being obtained by first transforming the related Bessel’s equation into the normal form via the suggested change of independent variable just as one of our recent work regarding the JWKB solution of the LP in (Deniz, 2017. MAF approximation of the first order Bessel Functions (ν = 1 of both type along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders (ν = 0 and 2 by the recursion relations. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is small, MAF solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined via the use of MAF applicability criterion given in the literature. As a result, the semiclassical MAF method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully just as our previous work regarding the JWKB solution of the LP. Interestingly, we have very accurate results in the entire domain except for x≈0. PACS: 02.30.Hq, 02.30.Mv, 03.65.Sq, 03.65.-w, 45.05.+x, 45.10.-b, Keywords: Method of Modified Airy Function (MAF, Semiclassical approximation, Linear differential equations, Initial value problems, The lengthening pendulum

  5. On a novel iterative method to compute polynomial approximations to Bessel functions of the first kind and its connection to the solution of fractional diffusion/diffusion-wave problems

    International Nuclear Information System (INIS)

    Yuste, Santos Bravo; Abad, Enrique

    2011-01-01

    We present an iterative method to obtain approximations to Bessel functions of the first kind J p (x) (p > -1) via the repeated application of an integral operator to an initial seed function f 0 (x). The class of seed functions f 0 (x) leading to sets of increasingly accurate approximations f n (x) is considerably large and includes any polynomial. When the operator is applied once to a polynomial of degree s, it yields a polynomial of degree s + 2, and so the iteration of this operator generates sets of increasingly better polynomial approximations of increasing degree. We focus on the set of polynomial approximations generated from the seed function f 0 (x) = 1. This set of polynomials is useful not only for the computation of J p (x) but also from a physical point of view, as it describes the long-time decay modes of certain fractional diffusion and diffusion-wave problems.

  6. Extensions of Bessel sequences to dual pairs of frames

    DEFF Research Database (Denmark)

    Christensen, Ole; Kim, Hong Oh; Kim, Rae Young

    2013-01-01

    Tight frames in Hilbert spaces have been studied intensively for the past years. In this paper we demonstrate that it often is an advantage to use pairs of dual frames rather than tight frames. We show that in any separable Hilbert space, any pairs of Bessel sequences can be extended to a pair of...... be extended to a pair of dual frames. © 2012 Elsevier Inc. All rights reserved....

  7. Elliptic integral evaluations of Bessel moments

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Glasser, M.L.

    2008-01-06

    We record what is known about the closed forms for variousBessel function moments arising in quantum field theory, condensed mattertheory and other parts of mathematical physics. More generally, wedevelop formulae for integrals of products of six or fewer Besselfunctions. In consequence, we are able to discover and prove closed formsfor c(n,k) := Int_0 inf tk K_0 n(t) dt, with integers n = 1, 2, 3, 4 andk greater than or equal to 0, obtaining new results for the even momentsc3,2k and c4,2k . We also derive new closed forms for the odd momentss(n,2k+1) := Int_0 inf t(2k+1) I_0(t) K_0n(t) dt,with n = 3, 4 and fort(n,2k+1) := Int_0 inf t(2k+1) I_02(t) K_0(n-2) dt, with n = 5, relatingthe latter to Green functions on hexagonal, diamond and cubic lattices.We conjecture the values of s(5,2k+1), make substantial progress on theevaluation of c(5,2k+1), s(6,2k+1) and t(6,2k+1) and report more limitedprogress regarding c(5,2k), c(6,2k+1) and c(6,2k). In the process, weobtain 8 conjectural evaluations, each of which has been checked to 1200decimal places. One of these lies deep in 4-dimensional quantum fieldtheory and two are probably provable by delicate combinatorics. Thereremains a hard core of five conjectures whose proofs would be mostinstructive, to mathematicians and physicists alike.

  8. Stored polarized beams: MILES, LIMES, SMILE, sine-Bessels and SODOM2 too

    International Nuclear Information System (INIS)

    Mane, S.R.

    2008-01-01

    The fundamental theory underlying several computational algorithms for the spin dynamics of stored polarized beams is analyzed. Particular attention is paid to the consequences of the use of finite-dimensional matrices and/or Fourier series. The single resonance model with a pair of diametrically opposed nonorthogonal pointlike Siberian Snakes is analyzed in detail to clarify several points pertaining to the above algorithms, and more generally to the spin dynamics of stored polarized beams in rings with Snakes. New analytical results are also presented, e.g. for the spin tune shift in the nonorthogonal Snakes model, and the sine-Bessel functions for the orthogonal Snakes model. Many results are derived using multiple algorithms, which serves as a check on their mutual consistency

  9. Shape invariant higher-order Bessel-like beams carrying orbital angular momentum

    CSIR Research Space (South Africa)

    Ismail, Y

    2012-09-01

    Full Text Available -1 Journal of Optics September 2012/ Vol. 14 Shape invariant higher-order Bessel-like beams carrying orbital angular momentum Y Ismail1,2, N Khilo3, V Belyi3 and A Forbes1,2 1 School of Physics, University of KwaZulu-Natal, Private Bag X54001...

  10. Mathieu functions and its useful approximation for elliptical waveguides

    Science.gov (United States)

    Pillay, Shamini; Kumar, Deepak

    2017-11-01

    The standard form of the Mathieu differential equation is where a and q are real parameters and q > 0. In this paper we obtain closed formula for the generic term of expansions of modified Mathieu functions in terms of Bessel and modified Bessel functions in the following cases: Let ξ0 = ξ0, where i can take the values 1 and 2 corresponding to the first and the second boundary. These approximations also provide alternative methods for numerical evaluation of Mathieu functions.

  11. On a method for generating inequalities for the zeros of certain functions

    Science.gov (United States)

    Gatteschi, Luigi; Giordano, Carla

    2007-10-01

    In this paper we describe a general procedure which yields inequalities satisfied by the zeros of a given function. The method requires the knowledge of a two-term approximation of the function with bound for the error term. The method was successfully applied many years ago [L. Gatteschi, On the zeros of certain functions with application to Bessel functions, Nederl. Akad. Wetensch. Proc. Ser. 55(3)(1952), Indag. Math. 14(1952) 224-229] and more recently too [L. Gatteschi and C. Giordano, Error bounds for McMahon's asymptotic approximations of the zeros of the Bessel functions, Integral Transform Special Functions, 10(2000) 41-56], to the zeros of the Bessel functions of the first kind. Here, we present the results of the application of the method to get inequalities satisfied by the zeros of the derivative of the function . This function plays an important role in the asymptotic study of the stationary points of the solutions of certain differential equations.

  12. Superpositions of higher-order bessel beams and nondiffracting speckle fields - (SAIP 2009)

    CSIR Research Space (South Africa)

    Dudley, Angela L

    2009-07-01

    Full Text Available speckle fields. The paper reports on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light...

  13. Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam

    International Nuclear Information System (INIS)

    Mitri, F.G.

    2016-01-01

    An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas. - Highlights: • Optical nondiffracting nonparaxial fractional Bessel vortex beam is considered. • Negative spin torque on an absorptive dielectric Rayleigh sphere is predicted numerically. • Negative spin torque occurs as the sphere departs from the center of the beam.

  14. Improved WKB radial wave functions in several bases

    International Nuclear Information System (INIS)

    Durand, B.; Durand, L.; Department of Physics, University of Wisconsin, Madison, Wisconsin 53706)

    1986-01-01

    We develop approximate WKB-like solutions to the radial Schroedinger equation for problems with an angular momentum barrier using Riccati-Bessel, Coulomb, and harmonic-oscillator functions as basis functions. The solutions treat the angular momentum singularity near the origin more accurately in leading approximation than the standard WKB solutions based on sine waves. The solutions based on Riccati-Bessel and free Coulomb wave functions continue smoothly through the inner turning point and are appropriate for scattering problems. The solutions based on oscillator and bound Coulomb wave functions incorporate both turning points smoothly and are particularly appropriate for bound-state problems; no matching of piecewise solutions using Airy functions is necessary

  15. Completeness, special functions and uncertainty principles over q-linear grids

    International Nuclear Information System (INIS)

    Abreu, LuIs Daniel

    2006-01-01

    We derive completeness criteria for sequences of functions of the form f(xλ n ), where λ n is the nth zero of a suitably chosen entire function. Using these criteria, we construct complete nonorthogonal systems of Fourier-Bessel functions and their q-analogues, as well as other complete sets of q-special functions. We discuss connections with uncertainty principles over q-linear grids and the completeness of certain sets of q-Bessel functions is used to prove that, if a function f and its q-Hankel transform both vanish at the points {q -n } ∞ n=1 , 0 n } ∞ n=-∞

  16. Momentum autocorrelation function of a classic diatomic chain

    Energy Technology Data Exchange (ETDEWEB)

    Yu, Ming B., E-mail: mingbyu@gmail.com

    2016-10-23

    A classical harmonic diatomic chain is studied using the recurrence relations method. The momentum autocorrelation function results from contributions of acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical contributions are derived as even-order Bessel function expansions with coefficients given in terms of integrals of elliptic functions in real axis and a contour parallel to the imaginary axis, respectively. - Highlights: • Momentum autocorrelation function of a classic diatomic chain is studied. • It is derived as even-order Bessel function expansion using the convolution theorem. • The expansion coefficients are integrals of elliptic functions. • Addition theorem is used to reduce complex elliptic function to complex sum of real ones.

  17. Radiophotoluminescence of alkali-halide crystals stimulated by Bessel laser beam

    CERN Document Server

    Lyakh, V V; Kochubey, D I; Gyunsburg, K E; Zvezdova, N P; Kochubey, D I; Sedova, Y G; Koronkevich, V P; Poleschuk, A G; Sedukhin, A G

    2000-01-01

    A new approach to realization of optimal high-resolution reading of deep X-ray images in X-ray-sensitive materials on the base of alkali-halide crystals modified with admixtures has been suggested and investigated experimentally. A possibility to use diffraction axicons with ring aperture for forming micron bright light beams (spatially truncated Bessel beams) which can efficiently de-excite radiophotoluminescence centers lying at large depth in crystals is also presented.

  18. The compact converter of Bessel beams of zero and second orders on the basis of z-cut lithium niobate

    International Nuclear Information System (INIS)

    Paranin, V D; Karpeev, S V; Khonina, S N; Tukmakov, K N

    2016-01-01

    Transformation of zero-order Bessel beams into a second-order vortex beam in the process of propagation in a c-cut of lithium niobate LiNbO 3 crystal has been investigated experimentally. The possibility of controlling beam transformation by means of changing the curve radius of the illuminating beam is shown. The possibility of Bessel beam transforming by compact devices on the basis of thin c-cuts of uniaxial crystals with a diffraction mask formed on their surface is proved. (paper)

  19. Application for coordinate transformation between Gaus - Kruger projection: Bessel ellipsoid and UTM projection: WGS84 ellipsoid

    Directory of Open Access Journals (Sweden)

    Zoran Gojković

    2017-01-01

    Full Text Available The physical surface of the earth has irregular shape which is not mathematically defined, therefore the shape of the Earth is approximated with mathematically defined surfaces such as ellipsoid and sphere. The developing of a global positioning systems, thus and modern navigation systems, as effect produce large amounts of data which contain the problem of homogeneity. This problem could be exceed if all the data are store in the same coordinate system. Hence the need for data transformation from local coordinate systems to the global coordinate systems. Global level implies WGS84 ellipsoid and UTM projection while national coordinate system of Republic Serbia is Gauss-Kruger with Bessel ellipsoid. This coordinate system of Republic Serbia on a global level has a local character. Applying appropriate mathematical models and functions it is possible to transform coordinates from one system to another and vice versa. The paper describes coordinate transformations from Gauss-Kruger coordinate system ellipsoid Bessel to UTM projection WGS84 ellipsoid and vice versa, and also an application which provides transformation of its kind that is made using open source environment. Name of the application is TRANS7_GK_UTM_GK and it can be found and used on the web page of the faculty for Mining and Geology under the link http://gk2utm.rgf.bg.ac.rs with a user guide.

  20. Bessel smoothing filter for spectral-element mesh

    Science.gov (United States)

    Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.

    2017-06-01

    Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the

  1. Discrete imaging models for three-dimensional optoacoustic tomography using radially symmetric expansion functions.

    Science.gov (United States)

    Wang, Kun; Schoonover, Robert W; Su, Richard; Oraevsky, Alexander; Anastasio, Mark A

    2014-05-01

    Optoacoustic tomography (OAT), also known as photoacoustic tomography, is an emerging computed biomedical imaging modality that exploits optical contrast and ultrasonic detection principles. Iterative image reconstruction algorithms that are based on discrete imaging models are actively being developed for OAT due to their ability to improve image quality by incorporating accurate models of the imaging physics, instrument response, and measurement noise. In this work, we investigate the use of discrete imaging models based on Kaiser-Bessel window functions for iterative image reconstruction in OAT. A closed-form expression for the pressure produced by a Kaiser-Bessel function is calculated, which facilitates accurate computation of the system matrix. Computer-simulation and experimental studies are employed to demonstrate the potential advantages of Kaiser-Bessel function-based iterative image reconstruction in OAT.

  2. Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone

    KAUST Repository

    Salem, Mohamed; Bagci, Hakan

    2013-01-01

    The electromagnetic field scattering of a vector Bessel beam in the presence of an infinite circular cone with an impedance boundary on its surface is considered. The impinging field is normal to the tip of the cone and is expanded in terms

  3. Investigation of local spatial spectra of Bessel light beams

    CSIR Research Space (South Africa)

    Belyi, VN

    2009-08-01

    Full Text Available plane of lens and illuminated by plane wave. The superposition of plane waves in such scheme is proposed to be generated by point sources distributed within the circular diaphragm. In a case when diaphragm is placed outside of lens focus [2], Bessel... beam can be described as an image in lens of spherical waves superposition formed by some effective circular source in object plane of lens. In the scheme of BLB obtaining based on axicons, the appearance of superposition of plane waves can be studied...

  4. An optical tweezer in asymmetrical vortex Bessel-Gaussian beams

    Energy Technology Data Exchange (ETDEWEB)

    Kotlyar, V. V.; Kovalev, A. A., E-mail: alexeysmr@mail.ru; Porfirev, A. P. [Image Processing Systems Institute, 151 Molodogvardeiskaya St., 443001 Samara (Russian Federation); Department of Technical cybernetics, Samara State Aerospace University, Samara 443086 (Russian Federation)

    2016-07-14

    We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.

  5. Enhancement of photorefractive two wave mixing gain with a Bessel pump beam

    International Nuclear Information System (INIS)

    Biswas, Dhruba J.; Padma Nilaya, J.; Danailov, Miltcho, B.

    2001-07-01

    The performance of a photo-refractive amplifier has been shown to greatly improve when a diffraction free beam is employed as the pump source. It has been established experimentally that this behaviour owes primarily to the ability of this beam to propagate in the photo-refractive crystal will less fanning. A qualitative explanation for the reduction of fanning with Bessel beam is offered. (author)

  6. COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments

    International Nuclear Information System (INIS)

    Thompson, I.J.; Barnett, A.R.

    1985-01-01

    The routine COULCC calculates both the oscillating and the exponentially varying Coulomb wave functions, and their radial derivations, for complex eta(Sommerfeld parameter), complex energies and complex angular momenta. The functions for uncharged scattering (spherical Bessels) and cylindrical Bessel functions are special cases which are more easily solved. Two linearly independent solutions are found, in general, to the differential equation f''(x)+g(x)f(x)=0, where g(x) has x 0 , x -1 and x -2 terms, with coefficients 1, -2eta and -lambda(lambda+1), respectively. (orig.)

  7. Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces

    International Nuclear Information System (INIS)

    David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth

    2015-01-01

    We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape

  8. Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces

    Energy Technology Data Exchange (ETDEWEB)

    David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth, E-mail: rsignorell@ethz.ch [Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich (Switzerland)

    2015-04-21

    We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.

  9. Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces.

    Science.gov (United States)

    David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth

    2015-04-21

    We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.

  10. Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces

    Science.gov (United States)

    David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth

    2015-04-01

    We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.

  11. Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam

    Science.gov (United States)

    Mitri, F. G.

    2016-10-01

    An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas.

  12. All-optical 3D atomic loops generated with Bessel light fields

    International Nuclear Information System (INIS)

    Volke-Sepulveda, Karen; Jauregui, RocIo

    2009-01-01

    The propagation invariance of Bessel beams as well as their transversal structure is used to perform a comparative analysis of their effect on cold atoms for four different configurations and combinations thereof. We show that, even at temperatures for which the classical description of the atom's centre-of-mass motion is valid, the interchange of momentum, energy and orbital angular momentum between light and atoms yields efficient tools for all-optical trapping, transporting and, in general, manipulating the state of motion of cold atoms.

  13. Theory and experiment of Fourier-Bessel field calculation and tuning of a pulsed wave annular array

    DEFF Research Database (Denmark)

    Fox, Paul D.; Jiqi, Cheng; Jian-yu, Lu

    2003-01-01

    A one-dimensional (1D) Fourier-Bessel series method for computing and tuning (beamforming) the linear lossless field of flat pulsed wave annular arrays is developed and supported with both numerical simulation and experimental verification. The technique represents a new method for modeling and t...

  14. Measurement of the orbital angular momentum density of Bessel beams by projection into a Laguerre–Gaussian basis

    CSIR Research Space (South Africa)

    Schulze, C

    2014-09-01

    Full Text Available We present the measurement of the orbital angular momentum (OAM) density of Bessel beams and superpositions thereof by projection into a Laguerre–Gaussian basis. This projection is performed by an all-optical inner product measurement performed...

  15. Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid

    OpenAIRE

    Mitri, F. G.

    2015-01-01

    Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (\\theta = \\pi) in the near-field an...

  16. Photoacoustic transformation of Bessel light beams in magnetoactive superlattices

    Energy Technology Data Exchange (ETDEWEB)

    Mityurich, G. S., E-mail: George-mityurich@mail.ru [Belarusian Trade and Economics University of Consumer Cooperatives (Belarus); Chernenok, E. V.; Sviridova, V. V.; Serdyukov, A. N. [Gomel State University (Belarus)

    2015-03-15

    Photoacoustic transformation of the TE mode of a Bessel light beam (BLB) has been studied for piezoelectric detection in short-period superlattices formed by magnetoactive crystals of bismuth germanate (Bi{sub 12}GeO{sub 20}) and bismuth silicate (Bi{sub 12}SiO{sub 20}) types. It is shown that the resulting signal amplitude can be controlled using optical schemes of BLB formation with a tunable cone angle. A resonant increase in the signal amplitude has been found in the megahertz range of modulation frequencies and its dependences on the BLB modulation frequency, geometric sizes of the two-layer structure and piezoelectric transducer, radial coordinate of the polarization BLB mode, and dissipative superlattice parameters are analyzed.

  17. KLEIN: Coulomb functions for real lambda and positive energy to high accuracy

    International Nuclear Information System (INIS)

    Barnett, A.R.

    1981-01-01

    KLEIN computes relativistic Schroedinger (Klein-Gordon) equation solutions, i.e. Coulomb functions for real lambda > - 1, Fsub(lambda)(eta,x), Gsub(lambda)(eta,x), F'sub(lambda)(eta,x) and G'sub(lambda)(eta,x) for real kappa > 0 and real eta, - 10 4 4 . Hence it is also suitable for Bessel and spherical Bessel functions. Accuracies are in the range 10 -14 -10 -16 in oscillating region, and approx. equal to 10 -30 on an extended precision compiler. The program is suitable for generating Klein-Gordon wavefunctions for matching in pion and kaon physics. (orig.)

  18. Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map

    KAUST Repository

    San Roman Alerigi, Damian

    2012-07-01

    In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si1-yOy/Si1-x-yGexCy platform or by photo-refractive media. The proposed device is 200 ?m in length and 25 ?m in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers. © 2012 Optical Society of America.

  19. Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map

    KAUST Repository

    San Roman Alerigi, Damian; Alsunaidi, Mohammad; Ben Slimane, Ahmed; Ng, Tien Khee; Ooi, Boon S.; Zhang, Yaping

    2012-01-01

    In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si1-yOy/Si1-x-yGexCy platform or by photo-refractive media. The proposed device is 200 ?m in length and 25 ?m in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers. © 2012 Optical Society of America.

  20. Fractional Vector Calculus and Fractional Special Function

    OpenAIRE

    Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

    2010-01-01

    Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric functions.

  1. SPECFUN1, Portable Special FORTRAN Routines with Test Drivers

    International Nuclear Information System (INIS)

    Cody, W.J.

    1993-01-01

    1 - Description of program or function: SPECFUN is a collection of transportable FORTRAN subroutines and test drivers to evaluate certain special functions. The individual subroutines are - Name/Description: ALGAMA: Log gamma function, DAW: Dawson's integral, EI: Exponential integrals, ERF: Error function, ERFC: Complementary error function, GAMMA: Gamma function, I0: Bessel function I-sub-0, I1: Bessel function I-sub-1, J0Y0: Bessel functions J-sub-0 and Y-sub-0, J1Y1: Bessel functions J-sub-1 and Y-sub-1, K0: Bessel function K-sub-0, K1: Bessel function K-sub-1, PSI: Logarithmic derivative of the gamma function, REN: Random number generator, RIBESL: Bessel function I-sub-(N,ALPHA), RJBESL: Bessel function J-sub-(N,ALPHA), RKBESL: Bessel function K-sub-(N,ALPHA), RYBESL: Bessel function Y-sub-(N,ALPHA), MACHAR: Machine-dependent constants. 2 - Method of solution: SPECFUN generally uses rational mini-max approximations for functions of one variable and recurrence relations for functions of two or more variables. 3 - Restrictions on the complexity of the problem: Accuracy is targeted at between 18 and 20 significant decimal digits

  2. Wave-optics description of self-healing mechanism in Bessel beams.

    Science.gov (United States)

    Aiello, Andrea; Agarwal, Girish S

    2014-12-15

    Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work, we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.

  3. Geometric optical transfer function and tis computation method

    International Nuclear Information System (INIS)

    Wang Qi

    1992-01-01

    Geometric Optical Transfer Function formula is derived after expound some content to be easily ignored, and the computation method is given with Bessel function of order zero and numerical integration and Spline interpolation. The method is of advantage to ensure accuracy and to save calculation

  4. Walk-off reduction, using an external optical plate and Bessel-Gaussian interaction

    Science.gov (United States)

    Masoume, Mansouri; Mohsen, Askarbioki; Saeed Ghavami, Sabouri; Alireza, Khorsandi

    2015-02-01

    To reduce the walk-off angle of the extraordinary third-harmonic ultraviolet wave at 355 nm generated by type II KTiOPO4 and type I β-BaB2O4 optical crystals, and the Gaussian output beam of a Q-switched Nd:YAG laser, a simple theoretical model was developed based on a rotatable BK7 plate of variable thickness. By rotating the plate up to 35° along the beam direction, we reduced the walk-off angle up to ˜ 13%. The same phenomenon is predicted by the model, confirming the performance of the model. It is found that, due to the walk-off effect, the intensity profile of the third-harmonic generation beam is slightly degraded. To compensate for the observed phenomena and further reduce the walk-off, we used a combination of a convex lens and an axicon to transform the beam profile of the interacting fundamental and second-harmonic generation waves to the zero-order Bessel-Gaussian form. As a result, the walk-off is decreased to ˜48.81 mrad, providing ˜30% relative reduction. By using the same BK7 plate rotated up to 35° along the third-harmonic beam direction, the walk-off angle is further reduced to 38.9 mrad. Moreover, it is observed that the beam profile of the emerged Bessel-Gaussian third-harmonic generation beam remains unchanged with no degradation.

  5. High resolution multiplexed functional imaging in live embryos (Conference Presentation)

    Science.gov (United States)

    Xu, Dongli; Zhou, Weibin; Peng, Leilei

    2017-02-01

    Fourier multiplexed fluorescence lifetime imaging (FmFLIM) scanning laser optical tomography (FmFLIM-SLOT) combines FmFLIM and Scanning laser optical tomography (SLOT) to perform multiplexed 3D FLIM imaging of live embryos. The system had demonstrate multiplexed functional imaging of zebrafish embryos genetically express Foster Resonant Energy Transfer (FRET) sensors. However, previous system has a 20 micron resolution because the focused Gaussian beam diverges quickly from the focused plane, makes it difficult to achieve high resolution imaging over a long projection depth. Here, we present a high-resolution FmFLIM-SLOT system with achromatic Bessel beam, which achieves 3 micron resolution in 3D deep tissue imaging. In Bessel-FmFLIM-SLOT, multiple laser excitation lines are firstly intensity modulated by a Michelson interferometer with a spinning polygon mirror optical delay line, which enables Fourier multiplexed multi-channel lifetime measurements. Then, a spatial light modulator and a prism are used to transform the modulated Gaussian laser beam to an achromatic Bessel beam. The achromatic Bessel beam scans across the whole specimen with equal angular intervals as sample rotated. After tomography reconstruction and the frequency domain lifetime analysis method, both the 3D intensity and lifetime image of multiple excitation-emission can be obtained. Using Bessel-FmFLIM-SLOT system, we performed cellular-resolution FLIM tomography imaging of live zebrafish embryo. Genetically expressed FRET sensors in these embryo will allow non-invasive observation of multiple biochemical processes in vivo.

  6. Asymptotics with respect to the spectral parameter and Neumann series of Bessel functions for solutions of the one-dimensional Schrödinger equation

    Science.gov (United States)

    Kravchenko, Vladislav V.; Torba, Sergii M.

    2017-12-01

    A representation for a solution u(ω, x) of the equation -u″ + q(x)u = ω2u, satisfying the initial conditions u(ω, 0) = 1, u'(ω, 0) = iω, is derived in the form u (ω ,x ) = ei ω x(1 +u/1(x ) ω +u/2(x ) ω2 )+e/-iω xu3(x ) ω2 -1/ω2 ∑n=0 ∞inαn(x ) jn(ω x ) , where um(x), m = 1, 2, 3, are given in a closed form, jn stands for a spherical Bessel function of order n, and the coefficients αn are calculated by a recurrent integration procedure. The following estimate is proved |u (ω ,x ) -uN(ω ,x ) |≤1/|ω|2 ɛ N(x ) √{sinh(2/Imω x ) Imω } for any ω ∈C {0 } , where uN(ω, x) is an approximate solution given by truncating the series in the proposed representation for u(ω, x) and ɛN(x) is a non-negative function tending to zero for all x belonging to a finite interval of interest. In particular, for ω ∈R {0 } , the estimate has the form |u (ω ,x ) -uN(ω ,x ) |≤1/|ω|2 ɛ N(x ) . A numerical illustration of application of the new representation for computing the solution u(ω, x) on large sets of values of the spectral parameter ω with an accuracy nondeteriorating (and even improving) when ω → ±∞ is given.

  7. Inequalities for Humbert functions

    Directory of Open Access Journals (Sweden)

    Ayman Shehata

    2014-04-01

    Full Text Available This paper is motivated by an open problem of Luke’s theorem. We consider the problem of developing a unified point of view on the theory of inequalities of Humbert functions and of their general ratios are obtained. Some particular cases and refinements are given. Finally, we obtain some important results involving inequalities of Bessel and Whittaker’s functions as applications.

  8. Quasi-ideal dynamics of vortex solitons embedded in flattop nonlinear Bessel beams.

    Science.gov (United States)

    Porras, Miguel A; Ramos, Francisco

    2017-09-01

    The applications of vortex solitons are severely limited by the diffraction and self-defocusing spreading of the background beam where they are nested. Nonlinear Bessel beams in self-defocusing media are nondiffracting, flattop beams where the nested vortex solitons can survive for propagation distances that are one order of magnitude larger than in the Gaussian or super-Gaussian beams. The dynamics of the vortex solitons is studied numerically and found to approach that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.

  9. Orthogonal bases of radial functions for charge density refinements

    International Nuclear Information System (INIS)

    Restori, R.

    1990-01-01

    Charge density determination from X-ray measurements necessitates the evaluation of the Fourier-Bessel transforms of the radial functions used to expand the charge density. Analytical expressions are given here for four sets of orthogonal functions which can substitute for the 'traditional exponential functions' set in least-squares refinements. (orig.)

  10. Coulomb Green's function and image potential near a cylindrical diffuse interface

    Science.gov (United States)

    Xue, Changfeng; Huang, Qiongwei; Deng, Shaozhong

    2015-12-01

    In a preceding paper [Comput. Phys. Commun. 184 (1): 51-59, 2013], we revisited the problem of calculating Coulomb Green's function and image potential near a planar diffuse interface within which the dielectric permittivity of the inhomogeneous medium changes continuously along one Cartesian direction in a transition layer between two dissimilar dielectric materials. In the present paper, we consider a cylindrical diffuse interface within which the dielectric permittivity changes continuously along the radial direction instead. First we propose a specific cylindrical diffuse interface model, termed the quasi-harmonic diffuse interface model, that can admit analytical solution for the Green's function in terms of the modified Bessel functions. Then and more importantly we develop a robust numerical method for building Green's functions for any cylindrical diffuse interface models. The main idea of the numerical method is, after dividing a diffuse interface into multiple sublayers, to approximate the dielectric permittivity profile in each one of the sublayers by one of the quasi-harmonic functional form rather than simply by a constant value as one would normally do. Next we describe how to efficiently compute well-behaved ratios, products, and logarithmic derivatives of the modified Bessel functions so as to avoid direct evaluations of individual modified Bessel functions in our formulations. Finally we conduct numerical experiments to show the effectiveness of the quasi-harmonic diffuse interface model in overcoming the divergence of the image potential, to validate the numerical method in terms of its accuracy and convergence, and to demonstrate its capability for computing Green's functions for any cylindrical diffuse interface models.

  11. Transmission of a Bessel beam through a circular aperture in an impedance screen

    International Nuclear Information System (INIS)

    Umul, Yusuf Ziya

    2014-01-01

    The scattering effect of a circular aperture, located in an impedance plane, on a Bessel beam is investigated by decomposing the scattered wave into two subcomponents, namely the geometrical optics and diffracted fields. The diffracted waves are investigated with the aid of the geometrical theory of diffraction. The detour parameter is evaluated and the existence zones of the geometrical optics fields are determined. The various aspects of the reflected and transmitted scattered waves, including the self healing of the beam, are studied numerically. (letter)

  12. Polysheroidal periodic functions

    International Nuclear Information System (INIS)

    Truskova, N.F.

    1985-01-01

    Separation of variables in the Helmholtz N-dimensional (N≥4) equation in polyspheroidal coordinate systems leads to the necessity of solving equations going over into equations for polyspheroidal periodic functions used for solving the two-centre problem in quantum mechanics, the three-body problem with Coulomb interaction, etc. For these functions the expansions are derived in terms of the Jacobi polynomials and Bessel functions. Their basic properties, asymptotics are considered. The algorithm of their computer calculations is developed. The results of numerical calculations are given

  13. Higher order Riesz transforms associated with Bessel operators

    Science.gov (United States)

    Betancor, Jorge J.; Fariña, Juan C.; Martinez, Teresa; Rodríguez-Mesa, Lourdes

    2008-10-01

    In this paper we investigate Riesz transforms R μ ( k) of order k≥1 related to the Bessel operator Δμ f( x)=- f”( x)-((2μ+1)/ x) f’( x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We obtain that for every k≥1, R μ ( k) is a principal value operator of strong type ( p, p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ( x)= x 2μ+1 dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R μ ( k) maps L p (ω) into itself and L 1(ω) into L 1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class mathcal{A}p^μ of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman.

  14. A complexity analysis of the Gauss-Bessel quadrature as applied to the evaluation of multi-centre integrals over STFs

    International Nuclear Information System (INIS)

    Bouferguene, Ahmed; Safouhi, Hassan

    2006-01-01

    In a previous work (Bouferguene 2005 J. Phys. A: Math. Gen. 38 3923), we have shown that in the framework of the Gaussian integral transform, multi-centre integrals over Slater type functions can be evaluated to an acceptable accuracy using a tailored Gauss quadrature in which the weight function has the form W(σ, τ; z) = z ν exp(-σz - τ/z). To be considered a solution worth implementing within a software for routine use in ab initio molecular simulations, the method must also prove to be at least as efficient as those methods previously published in the literature. Two major results are provided in this paper. Firstly, an improvement of the procedure used to generate the roots and weights of the Gauss-Bessel quadrature is proposed. Secondly, a computational cost analysis of the present method and the SD-bar (Safouhi 2001 J. Phys. A: Math. Gen. 34 2801) based approach are compared, hence proving the equivalence of the two from a complexity point of view

  15. Asymptotics and Numerics of Polynomials Used in Tricomi and Buchholz Expansions of Kummer functions

    NARCIS (Netherlands)

    J.L. López; N.M. Temme (Nico)

    2010-01-01

    textabstractExpansions in terms of Bessel functions are considered of the Kummer function ${}_1F_1(a;c,z)$ (or confluent hypergeometric function) as given by Tricomi and Buchholz. The coefficients of these expansions are polynomials in the parameters of the Kummer function and the asymptotic

  16. Special functions for scientists and engineers

    CERN Document Server

    Bell, William Wallace

    1968-01-01

    Clear and comprehensive, this text provides undergraduates with a straightforward guide to special functions. It is equally suitable as a reference volume for professionals, and readers need no higher level of mathematical knowledge beyond elementary calculus. Topics include the solution of second-order differential equations in terms of power series; gamma and beta functions; Legendre polynomials and functions; Bessel functions; Hermite, Laguerre, and Chebyshev polynomials; Gegenbauer and Jacobi polynomials; and hypergeometric and other special functions. Three appendices offer convenient t

  17. Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel

    International Nuclear Information System (INIS)

    Tiwari, S K; Ram, S P; Jayabalan, J; Mishra, S R

    2010-01-01

    By scanning a charge-coupled device (CCD) camera transverse to the beam axis and observing the variation in counts on a marked pixel, we demonstrate that we can measure a laser beam spot size smaller than the size of the CCD-pixel. We find this method particularly attractive for measuring the size of central spot of a Bessel beam, for which the established scanning knife-edge method does not work appropriately because of the large contribution of the rings surrounding the central spot to the signal

  18. New Bessel-type function associated with SU(3) representation

    International Nuclear Information System (INIS)

    Tanimura, N.; Tanimura, O.

    1990-01-01

    A new set of functions that are given by the coefficients of the character expansion of the single-link action in the SU(3) lattice-gauge theory is studied. The function is specified by the indices λ and μ of the SU(3) representation of the Young tableau. From the Schwinger-Dyson variational method the recursion relations among the functions are derived. By combining the recursion relation and the relation of the differentiation, the linear differential equation of the sixth order for the function is derived. The properties of the function are discussed in detail in comparison with the functions in the SU(2) group

  19. Anisotropic resonator analysis using the Fourier-Bessel mode solver

    Science.gov (United States)

    Gauthier, Robert C.

    2018-03-01

    A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday's and Ampere's laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier-Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.

  20. Debye series analysis of internal and near-surface fields for a homogeneous sphere illuminated by an axicon-generated vector Bessel beam

    International Nuclear Information System (INIS)

    Qin, Shitong; Li, Renxian; Yang, Ruiping; Ding, Chunying

    2017-01-01

    The interaction of an axicon-generated vector Bessel beam (AGVBB) with a homogeneous sphere is investigated in the framework of generalized Lorenz-Mie theory (GLMT). An analytical expression of beam shape coefficients (BSCs) is derived using angular spectrum decomposition method (ASDM), and the scattering coefficients are expanded using Debye series (DSE) in order to isolate the contribution of single scattering process. The internal and near-surface electric fields are numerically analyzed, and the effect of beam location, polarization, order of beam, half-cone angle, and scattering process (namely Debye mode p) are mainly discussed. Numerical results show that a curve formed by extreme peaks can be observed, and the electric fields can be locally enhanced after the interaction of AGVBBs with the particle. Internal and near-surface fields, especially its local enhancement, are very sensitive to the beam parameters, including polarization, order, half-cone angle, etc. The internal fields can also be enhanced by various scattering process (or Debye mode p). Such results have important applications in various fields, including particle sizing, optical tweezers, etc. - Highlights: • Debye series is employed to the analysis of internal and near-surface fields for a sphere illuminated by a vector Bessel beam. • Analytical expressions of BSCs for vector Bessel beams with selected polarizations are derived using ASDM. • The local enhancement of internal and near-surface fields is investigated. • The polarization, order, half-cone angle of the beam affect the local enhancement. • The local enhancement of internal fields is sensitive to the scattering process.

  1. Marichev-Saigo-Maeda fractional integration operators of the Bassel functions

    Directory of Open Access Journals (Sweden)

    Sunil D. Purohit

    2012-05-01

    Full Text Available In this paper, we apply generalized operators of fractional integration involving Appell’s function F_3 (. due to Marichev-Saigo-Maeda, to the Bessel function of first kind. The results are expressed in terms of generalized Wright function and hypergeometric functions _pF_q . Special cases involving this function are mentioned. Results given recently by Kilbas and Sebastian follow as special cases of the theorems establish here.

  2. Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type

    International Nuclear Information System (INIS)

    Gorbachev, D V; Ivanov, V I

    2015-01-01

    Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles

  3. Generalised partition functions: inferences on phase space distributions

    Directory of Open Access Journals (Sweden)

    R. A. Treumann

    2016-06-01

    Full Text Available It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1∕|q − 1|, with κ, q ∈ R both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel–Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs–Boltzmann partition function is fundamental not only to Gibbs–Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the

  4. Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

    Energy Technology Data Exchange (ETDEWEB)

    Balakin, A. A., E-mail: balakin.alexey@yandex.ru; Mironov, V. A.; Skobelev, S. A., E-mail: sk.sa1981@gmail.com [Russian Academy of Sciences, Institute of Applied Physics (Russian Federation)

    2017-01-15

    The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.

  5. Bessel Plasmon-Polaritons at the Boundaries of Metamaterials with Near-Zero Dielectric Constants

    Science.gov (United States)

    Kurilkina, S. N.; Belyi, V. N.; Kazak, N. S.; Binhussain, M. A.

    2015-07-01

    The conditions for and features of the excitation of Bessel plasmon-polaritons (BPP) are examined at the boundary of a hyperbolic metamaterial with a near-zero dielectric constant made of a dielectric matrix with metal nanorods embedded in it normal to its surface. This material is compared with BPP that have traditional surface plasmons. The effect of the absorption of the metamaterial on the excitation of BPP is studied. The possibility of changes in the direction of the radial energy fl ows in BPP excited at the surface of an isotropic medium, a hyperbolic metamaterial, is demonstrated and the conditions for these changes are determined.

  6. Accurate and efficient computation of synchrotron radiation functions

    International Nuclear Information System (INIS)

    MacLeod, Allan J.

    2000-01-01

    We consider the computation of three functions which appear in the theory of synchrotron radiation. These are F(x)=x∫x∞K 5/3 (y) dy))F p (x)=xK 2/3 (x) and G p (x)=x 1/3 K 1/3 (x), where K ν denotes a modified Bessel function. Chebyshev series coefficients are given which enable the functions to be computed with an accuracy of up to 15 sig. figures

  7. Propagation-invariant vectorial Bessel beams by use of sub wavelength quantized Pancharatnam-Berry phase optics

    International Nuclear Information System (INIS)

    Niv, A.; Biener, G.; Kleiner, V.; Hasman, E.

    2004-01-01

    Full Text:Propagation-invariant scalar fields have been extensively studied both theoretically and experimentally, since they were proposed by Durnin et al. These fields were employed in applications such as optical tweezers and for transport and guiding of microspheres. Although there has recently been considerable theoretical interest in propagation-invariant vectorial beams, experimental studies of such beams have remained somewhat limited. One of the most interesting types of propagation-invariant vectorial beam is the linearly polarized axially symmetric beam (LPASB) [l]. Recently, we introduced and experimentally demonstrated propagation-invariant vectorial Bessel beams with linearly polarized axial symmetry based on quantized Pancharatnam-Berry phase optical elements (QPBOEs) [21 and an axicon. QP-BOEs utilize the geometric phase that accompanies space-variant polarization manipulations to achieve a desired phase modification [31. To test our approach we formed QPBOEs with different polarization orders as computer-generated space-variant sub wavelength gratings upon GaAs wafers for use with 10.6 micron laser radiation. The resultant beams were also transmitted through a polarizer that produced a unique propagation-invariant scalar beam. This beam has a propeller-shaped intensity pattern that can be rotated by simple rotation of the polarizer. We therefore have demonstrated the formation of a vectorial Bessel beam by using simple, lightweight thin elements and exploited that beam to perform a controlled rotation of a propeller-shaped intensity pattern that can be suitable for optical tweezers

  8. The Meijer transformation of generalized functions

    Directory of Open Access Journals (Sweden)

    E. L. Koh

    1987-01-01

    where f belongs to an appropriate function space, μ ϵ (−1,∞ and Kμ is the modified Bessel function of third kind of order μ, to certain generalized functions. A testing space is constructed so as to contain the Kernel, (ptμ/2Kμ(2pt, of the transformation. Some properties of the kernel, function space and its dual are derived. The generalized Meijer transform, M¯μf, is now defined on the dual space. This transform is shown to be analytic and an inversion theorem, in the distributional sense, is established.

  9. Transform analysis of generalized functions

    CERN Document Server

    Misra, O P

    1986-01-01

    Transform Analysis of Generalized Functions concentrates on finite parts of integrals, generalized functions and distributions. It gives a unified treatment of the distributional setting with transform analysis, i.e. Fourier, Laplace, Stieltjes, Mellin, Hankel and Bessel Series.Included are accounts of applications of the theory of integral transforms in a distributional setting to the solution of problems arising in mathematical physics. Information on distributional solutions of differential, partial differential equations and integral equations is conveniently collected here.The volume will

  10. A summary of numerical computation for special functions

    International Nuclear Information System (INIS)

    Zhang Shanjie

    1992-01-01

    In the paper, special functions frequently encountered in science and engineering calculations are introduced. The computation of the values of Bessel function and elliptic integrals are taken as the examples, and some common algorithms for computing most special functions, such as series expansion for small argument, asymptotic approximations for large argument, polynomial approximations, recurrence formulas and iteration method, are discussed. In addition, the determination of zeros of some special functions, and the other questions related to numerical computation are also discussed

  11. Laser-plasma interactions with a Fourier-Bessel particle-in-cell method

    Energy Technology Data Exchange (ETDEWEB)

    Andriyash, Igor A., E-mail: igor.andriyash@gmail.com [Synchrotron SOLEIL, L' Orme des Merisiers, Saint Aubin, 91192 Gif-sur-Yvette (France); LOA, ENSTA ParisTech, CNRS, Ecole polytechnique, Université Paris-Saclay, 828 bd des Maréchaux, 91762 Palaiseau cedex (France); Lehe, Remi [Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Lifschitz, Agustin [LOA, ENSTA ParisTech, CNRS, Ecole polytechnique, Université Paris-Saclay, 828 bd des Maréchaux, 91762 Palaiseau cedex (France)

    2016-03-15

    A new spectral particle-in-cell (PIC) method for plasma modeling is presented and discussed. In the proposed scheme, the Fourier-Bessel transform is used to translate the Maxwell equations to the quasi-cylindrical spectral domain. In this domain, the equations are solved analytically in time, and the spatial derivatives are approximated with high accuracy. In contrast to the finite-difference time domain (FDTD) methods, that are used commonly in PIC, the developed method does not produce numerical dispersion and does not involve grid staggering for the electric and magnetic fields. These features are especially valuable in modeling the wakefield acceleration of particles in plasmas. The proposed algorithm is implemented in the code PLARES-PIC, and the test simulations of laser plasma interactions are compared to the ones done with the quasi-cylindrical FDTD PIC code CALDER-CIRC.

  12. An integral transform of Green's function, off-shell Jost solution and T ...

    Indian Academy of Sciences (India)

    integral transform of the Green's function for motion in Coulomb–Yamaguchi potential is derived via the r-space ... use in the calculation of the corresponding off-shell quantities without the explicit use of two-potential theorem and ..... (x), spherical Bessel function and gli(βli,r)s, the form factors of the sep- arable potential the ...

  13. Using special functions to model the propagation of airborne diseases

    Science.gov (United States)

    Bolaños, Daniela

    2014-06-01

    Some special functions of the mathematical physics are using to obtain a mathematical model of the propagation of airborne diseases. In particular we study the propagation of tuberculosis in closed rooms and we model the propagation using the error function and the Bessel function. In the model, infected individual emit pathogens to the environment and this infect others individuals who absorb it. The evolution in time of the concentration of pathogens in the environment is computed in terms of error functions. The evolution in time of the number of susceptible individuals is expressed by a differential equation that contains the error function and it is solved numerically for different parametric simulations. The evolution in time of the number of infected individuals is plotted for each numerical simulation. On the other hand, the spatial distribution of the pathogen around the source of infection is represented by the Bessel function K0. The spatial and temporal distribution of the number of infected individuals is computed and plotted for some numerical simulations. All computations were made using software Computer algebra, specifically Maple. It is expected that the analytical results that we obtained allow the design of treatment rooms and ventilation systems that reduce the risk of spread of tuberculosis.

  14. [Research of dual-photoelastic-modulator-based beat frequency modulation and Fourier-Bessel transform imaging spectrometer].

    Science.gov (United States)

    Wang, Zhi-Bin; Zhang, Rui; Wang, Yao-Li; Huang, Yan-Fei; Chen, You-Hua; Wang, Li-Fu; Yang, Qiang

    2014-02-01

    As the existing photoelastic-modulator(PEM) modulating frequency in the tens of kHz to hundreds of kHz between, leading to frequency of modulated interference signal is higher, so ordinary array detector cannot effectively caprure interference signal..A new beat frequency modulation method based on dual-photoelastic-modulator (Dual-PEM) and Fourier-Bessel transform is proposed as an key component of dual-photoelastic-modulator-based imaging spectrometer (Dual-PEM-IS) combined with charge coupled device (CCD). The dual-PEM are operated as an electro-optic circular retardance modulator, Operating the PEMs at slightly different resonant frequencies w1 and w2 respectively, generates a differential signal at a much lower heterodyne frequency that modulates the incident light. This method not only retains the advantages of the existing PEM, but also the frequency of modulated photocurrent decreased by 2-3 orders of magnitude (10-500 Hz) and can be detected by common array detector, and the incident light spectra can be obtained by Fourier-Bessel transform of low frequency component in the modulated signal. The method makes the PEM has the dual capability of imaging and spectral measurement. The basic principle is introduced, the basic equations is derived, and the feasibility is verified through the corresponding numerical simulation and experiment. This method has' potential applications in imaging spectrometer technology, and analysis of the effect of deviation of the optical path difference. This work provides the necessary theoretical basis for remote sensing of new Dual-PEM-IS and for engineering implementation of spectra inversion.

  15. Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis.

    Science.gov (United States)

    Gutiérrez-Vega, Julio C; Rodríguez-Masegosa, Rodolfo; Chávez-Cerda, Sabino

    2003-11-01

    A detailed study of the axicon-based Bessel-Gauss resonator with concave output coupler is presented. We employ a technique to convert the Huygens-Fresnel integral self-consistency equation into a matrix equation and then find the eigenvalues and the eigenfields of the resonator at one time. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectories after one or two round trips. The fast-Fourier-transform-based Fox and Li algorithm is applied to describe the three-dimensional intracavity field distribution. Special attention was directed to the dependence of the output transverse profiles, the losses, and the modal-frequency changes on the curvature of the output coupler and the cavity length. The propagation of the output beam is discussed.

  16. Luigi Gatteschi's work on asymptotics of special functions and their zeros

    Science.gov (United States)

    Gautschi, Walter; Giordano, Carla

    2008-12-01

    A good portion of Gatteschi's research publications-about 65%-is devoted to asymptotics of special functions and their zeros. Most prominently among the special functions studied figure classical orthogonal polynomials, notably Jacobi polynomials and their special cases, Laguerre polynomials, and Hermite polynomials by implication. Other important classes of special functions dealt with are Bessel functions of the first and second kind, Airy functions, and confluent hypergeometric functions, both in Tricomi's and Whittaker's form. This work is reviewed here, and organized along methodological lines.

  17. The functions of mathematical physics

    CERN Document Server

    Hochstadt, Harry

    2012-01-01

    A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics.In the 18th and 19th centuries, the theorists who devoted themselves to this field - pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel - were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating

  18. Intrinsic cylindrical and spherical waves

    International Nuclear Information System (INIS)

    Ludlow, I K

    2008-01-01

    Intrinsic waveforms associated with cylindrical and spherical Bessel functions are obtained by eliminating the factors responsible for the inverse radius and inverse square radius laws of wave power per unit area of wavefront. The resulting expressions are Riccati-Bessel functions for both cases and these can be written in terms of amplitude and phase functions of order v and wave variable z. When z is real, it is shown that a spatial phase angle of the intrinsic wave can be defined and this, together with its amplitude function, is systematically investigated for a range of fixed orders and varying z. The derivatives of Riccati-Bessel functions are also examined. All the component functions exhibit different behaviour in the near field depending on the order being less than, equal to or greater than 1/2. Plots of the phase angle can be used to display the locations of the zeros of the general Riccati-Bessel functions and lead to new relations concerning the ordering of the real zeros of Bessel functions and the occurrence of multiple zeros when the argument of the Bessel function is fixed

  19. Accurate calculation of Green functions on the d-dimensional hypercubic lattice

    International Nuclear Information System (INIS)

    Loh, Yen Lee

    2011-01-01

    We write the Green function of the d-dimensional hypercubic lattice in a piecewise form covering the entire real frequency axis. Each piece is a single integral involving modified Bessel functions of the first and second kinds. The smoothness of the integrand allows both real and imaginary parts of the Green function to be computed quickly and accurately for any dimension d and any real frequency, and the computational time scales only linearly with d.

  20. Generation and propagation of high-order Bessel vortices in linear and non-linear crystals

    CSIR Research Space (South Africa)

    Belyi, VN

    2009-08-01

    Full Text Available E⊥ of the electric field for these beams are given by the following expressions: ( ))2exp()()( )( )exp( 20 1 10 ϕρρ iqJqJ qw zikA i zoo −+⊥ += eeE , (1) с Uniaxial crystal θs Bs2ω(ρ) Bsω(ρ) Figure 1: Geometry of SHG when wave vectors cone of Bessel... beam at fundamental )(ρωBs and second harmonic frequencies )(2 ρωBs coincides with phase-matching cone of uniaxial crystal. Proc. of SPIE Vol. 7430 74300F-2 ( ))2exp()()()cos( )( )exp( 20 1 1 ϕρργ iqJqJ qw zikA i e zee e −+⊥ −= ee...

  1. Acoustical radiation torque and force for spheres and Bessel beam extinction efficiency

    Science.gov (United States)

    Marston, Philip L.; Zhang, Likun

    2014-11-01

    The scattering of optical and acoustical beams is relevant to the levitation and manipulation of drops. Here we examine theoretical developments in the acoustical case. We previously showed how the optical theorem for extinction can be extended to invariant beams. The example of a sphere in a Bessel beam facilitates the direct comparison with a circular disc computed using Babinet's principle and the Kirchhoff approximation. In related work, by considering traveling or standing wave first-order vortex beams we previously showed that the radiation torque is the ratio of the absorbed power and the radian acoustic frequency. By modifying the scattering to account for the viscosity of the surrounding fluid in the analysis of the absorbed power, approximations for radiation torque and force are obtained at long wavelengths in special cases and these can be compared with results published elsewhere.

  2. Analysis of a multi-frequency electromagnetic imaging functional for thin, crack-like electromagnetic inclusions

    OpenAIRE

    Park, Won-Kwang

    2012-01-01

    Recently, a non-iterative multi-frequency subspace migration imaging algorithm was developed based on an asymptotic expansion formula for thin, curve-like electromagnetic inclusions and the structure of singular vectors in the Multi-Static Response (MSR) matrix. The present study examines the structure of subspace migration imaging functional and proposes an improved imaging functional weighted by the frequency. We identify the relationship between the imaging functional and Bessel functions ...

  3. Generating relations of multi-variable Tricomi functions of two indices using Lie algebra representation

    Directory of Open Access Journals (Sweden)

    Nader Ali Makboul Hassan

    2014-01-01

    Full Text Available This paper is an attempt to stress the usefulness of the multi-variable special functions. In this paper, we derive certain generating relations involving 2-indices 5-variables 5-parameters Tricomi functions (2I5V5PTF by using a Lie-algebraic method. Further, we derive certain new and known generating relations involving other forms of Tricomi and Bessel functions as applications.

  4. Foreign Object Detection by Sub-Terahertz Quasi-Bessel Beam Imaging

    Directory of Open Access Journals (Sweden)

    Hyang Sook Chun

    2012-12-01

    Full Text Available Food quality monitoring, particularly foreign object detection, has recently become a critical issue for the food industry. In contrast to X-ray imaging, terahertz imaging can provide a safe and ionizing-radiation-free nondestructive inspection method for foreign object sensing. In this work, a quasi-Bessel beam (QBB known to be nondiffracting was generated by a conical dielectric lens to detect foreign objects in food samples. Using numerical evaluation via the finite-difference time-domain (FDTD method, the beam profiles of a QBB were evaluated and compared with the results obtained via analytical calculation and experimental characterization (knife edge method, point scanning method. The FDTD method enables a more precise estimation of the beam profile. Foreign objects in food samples, namely crickets, were then detected with the QBB, which had a deep focus and a high spatial resolution at 210 GHz. Transmitted images using a Gaussian beam obtained with a conventional lens were compared in the sub-terahertz frequency experimentally with those using a QBB generated using an axicon.

  5. Optical reprogramming of human somatic cells using ultrashort Bessel-shaped near-infrared femtosecond laser pulses

    Science.gov (United States)

    Uchugonova, Aisada; Breunig, Hans Georg; Batista, Ana; König, Karsten

    2015-11-01

    We report a virus-free optical approach to human cell reprogramming into induced pluripotent stem cells with low-power nanoporation using ultrashort Bessel-shaped laser pulses. Picojoule near-infrared sub-20 fs laser pulses at a high 85 MHz repetition frequency are employed to generate transient nanopores in the membrane of dermal fibroblasts for the introduction of four transcription factors to induce the reprogramming process. In contrast to conventional approaches which utilize retro- or lentiviruses to deliver genes or transcription factors into the host genome, the laser method is virus-free; hence, the risk of virus-induced cancer generation limiting clinical application is avoided.

  6. Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime.

    Science.gov (United States)

    Ambrosio, Leonardo A; Hernández-Figueroa, Hugo E

    2010-11-08

    Gradient forces on double negative (DNG) spherical dielectric particles are theoretically evaluated for v-th Bessel beams supposing geometrical optics approximations based on momentum transfer. For the first time in the literature, comparisons between these forces for double positive (DPS) and DNG particles are reported. We conclude that, contrary to the conventional case of positive refractive index, the gradient forces acting on a DNG particle may not reverse sign when the relative refractive index n goes from |n|>1 to |n|<1, thus revealing new and interesting trapping properties.

  7. VizieR Online Data Catalog: Bessel (1825) calculation for geodesic measurements (Karney+, 2010)

    Science.gov (United States)

    Karney, C. F. F.; Deakin, R. E.

    2010-06-01

    The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. Included here are the tables that accompanied Bessel's paper (with corrections). The tables were crafted by Bessel to be minimize the labor of hand calculations. To this end, he adjusted the intervals in the tables, the number of terms included in the series, and the number of significant digits given so that the final results are accurate to about 8 places. For that reason, the most useful form of the tables is as the PDF file which provides the tables in a layout close to the original. Also provided is the LaTeX source file for the PDF file. Finally, the data has been put into a format so that it can be read easily by computer programs. All the logarithms are in base 10 (common logarithms). The characteristic and the mantissa should be read separately (indicated as x.c and x.m in the file description). Thus the first entry in the table, -4.4, should be parsed as "-4" (the characteristic) and ".4" (the mantissa); the anti-log for this entry is 10(-4+0.4)=2.5e-4. The "Delta" columns give the first difference of the preceding column, i.e., the difference of the preceding column in the next row and the preceding column in the current row. In the printed tables these are expressed as "units in the last place" and the differences are of the rounded representations in the preceding columns (to minimize interpolation errors). In table1.dat these are given scaled to a match the format used for the preceding column, as indicated by the units given for these columns. The unit log(") (in the description within square brackets [arcsec]) means the logarithm of a quantity expressed in arcseconds. (3 data files).

  8. A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d-Finite Functions

    Directory of Open Access Journals (Sweden)

    Agata Bezubik

    2006-03-01

    Full Text Available This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotational symmetry. The method used to derive the expansion formula is based entirely on differential methods and completely avoids the use of various integral identities commonly used in this context. Some new identities for the Fourier transform are derived and as a byproduct seemingly new recurrence relations for the classical Bessel functions are obtained.

  9. A Fortran program for the numerical integration of the one-dimensional Schroedinger equation using exponential and Bessel fitting methods

    International Nuclear Information System (INIS)

    Cash, J.R.; Raptis, A.D.; Simos, T.E.

    1990-01-01

    An efficient algorithm is described for the accurate numerical integration of the one-dimensional Schroedinger equation. This algorithm uses a high-order, variable step Runge-Kutta like method in the region where the potential term dominates, and an exponential or Bessel fitted method in the asymptotic region. This approach can be used to compute scattering phase shifts in an efficient and reliable manner. A Fortran program which implements this algorithm is provided and some test results are given. (orig.)

  10. Complexity of Gaussian-Radial-Basis Networks Approximating Smooth Functions

    Czech Academy of Sciences Publication Activity Database

    Kainen, P.C.; Kůrková, Věra; Sanguineti, M.

    2009-01-01

    Roč. 25, č. 1 (2009), s. 63-74 ISSN 0885-064X R&D Projects: GA ČR GA201/08/1744 Institutional research plan: CEZ:AV0Z10300504 Keywords : Gaussian-radial-basis-function networks * rates of approximation * model complexity * variation norms * Bessel and Sobolev norms * tractability of approximation Subject RIV: IN - Informatics, Computer Science Impact factor: 1.227, year: 2009

  11. Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions

    OpenAIRE

    Biane, P.; Pitman, J.; Yor, M.

    1999-01-01

    This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws.

  12. Generalized Airy functions for use in one-dimensional quantum mechanical problems

    Science.gov (United States)

    Eaves, J. O.

    1972-01-01

    The solution of the one dimensional, time independent, Schroedinger equation in which the energy minus the potential varies as the nth power of the distance is obtained from proper linear combinations of Bessel functions. The linear combinations called generalized Airy functions, reduce to the usual Airy functions Ai(x) and Bi(x) when n equals 1 and have the same type of simple asymptotic behavior. Expressions for the generalized Airy functions which can be evaluated by the method of generalized Gaussian quadrature are obtained.

  13. Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping.

    Science.gov (United States)

    Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan

    2012-02-15

    Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.

  14. Generalization of Bateman-Hillion progressive wave and Bessel-Gauss pulse solutions of the wave equation via a separation of variables

    CERN Document Server

    Kiselev, A

    2003-01-01

    Two new families of exact solutions of the wave equation u sub x sub x + u sub y sub y + u sub z sub z - c sup - sup 2 u sub t sub t = 0 generalizing Bessel-Gauss pulses and Bateman-Hillion relatively undistorted progressive waves, respectively are presented. In each of these families new simple solutions describing localized wave propagation are found. The approach is based on a kind of separation of variables. (letter to the editor)

  15. On an integral transform

    Directory of Open Access Journals (Sweden)

    D. Naylor

    1988-01-01

    Full Text Available A formula of inversion is established for an integral transform whose kernel is the Bessel function Ju(kr where r varies over the finite interval (0,a and the order u is taken to be the eigenvalue parameter. When this parameter is large the Bessel function behaves for varying r like the power function ru and by relating the Bessel functions to their corresponding power functions the proof of the inversion formula can be reduced to one depending on the Mellin inversion theorem.

  16. Acoustic radiation force on an air bubble and soft fluid spheres in ideal liquids: example of a high-order Bessel beam of quasi-standing waves.

    Science.gov (United States)

    Mitri, F G

    2009-04-01

    The partial wave series for the scattering of a high-order Bessel beam (HOBB) of acoustic quasi-standing waves by an air bubble and fluid spheres immersed in water and centered on the axis of the beam is applied to the calculation of the acoustic radiation force. A HOBB refers to a type of beam having an axial amplitude null and an azimuthal phase gradient. Radiation force examples obtained through numerical evaluation of the radiation force function are computed for an air bubble, a hexane, a red blood and mercury fluid spheres in water. The examples were selected to illustrate conditions having progressive, standing and quasi-standing waves with appropriate selection of the waves' amplitude ratio. An especially noteworthy result is the lack of a specific vibrational mode contribution to the radiation force determined by appropriate selection of the HOBB parameters.

  17. Acoustics of finite asymmetric exotic beams: Examples of Airy and fractional Bessel beams

    Science.gov (United States)

    Mitri, F. G.

    2017-12-01

    The purpose of this investigation is to examine the properties of finite asymmetric exotic scalar (acoustic) beams with unusual properties using the angular spectrum decomposition in plane waves. Such beams possess intrinsic uncommon characteristics that make them attractive from the standpoint of particle manipulation, handling and rotation, and possibly other applications in particle clearing and separation. Assuming a specific apodization function at the acoustic source, the angular spectrum function is calculated and used to synthesize the radiated pressure field (i.e., excluding evanescent waves that decay away from the source) in the forward direction of wave motion (i.e., away from the source). Moreover, a generalized hybrid method combining the angular spectrum approach with the multipole expansion formalism in spherical coordinates is developed, which is applicable to any finite beam of arbitrary wavefront. The improved approach allows adequate computation of the resonance scattering, radiation force, and spin torque components on an object of arbitrary shape, located on or off the axis of the incident beam in space. Considering the illustrative example of a viscous fluid sphere submerged in a non-viscous liquid and illuminated by finite asymmetric beams such as the Airy and the Bessel vortex beam with fractional order, numerical computations for the scattering, radiation force, and torque components are performed with an emphasis on the distance from the source, the arbitrary location of the particle ,and the asymmetric nature of the incident field. Moreover, beamforming calculations are presented with supplementary animations for the pressure field distribution in space, with an emphasis on the intrinsic properties of the selected beams. The numerical predictions illustrate the scattering, radiation force, and spin torque properties depending on the beam parameters and the distance separating the sphere from the source. This study provides a generalized

  18. Higher-order automatic differentiation of mathematical functions

    Science.gov (United States)

    Charpentier, Isabelle; Dal Cappello, Claude

    2015-04-01

    Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

  19. AMDLIBAE, IBM 360 Subroutine Library, Special Function, Polynomials, Differential Equation

    International Nuclear Information System (INIS)

    Wang, Jesse Y.

    1980-01-01

    Description of problem or function: AMDLIBAE is a subset of the IBM 360 Subroutine Library at the Applied Mathematics Division at Argonne National Laboratory. This subset includes library categories A-E: Identification/Description: A152S A MPA: Mult. prec. floating point arith. package; B156S A ARSIN: Arcsine, arccosine; B158S A DSIN/DCOS: DP sine, cosine; B159S A DTAN/DCOT: DP tangent, cotangent; B252S A SINH/COSH: Hyperbolic sine, cosine; B353S A ALOG: SP logarithm; B354S A DEXP: DP exponential; B355S A DLOG: DP logarithm; B456S A DCUBRT: DP cube root; B457S A ARGPOWER: X Y ; B458S A ARGFDXPD: DP X Y ; C150S F DQD: Q. D. algorithm applied to a power series; C151S F DCONF1: Eval. cont. fract. Q. D. of power series; C250S F CUBIC: Roots of cubic polynomial equation; C251S F QUARTIC: Roots of quartic polynomial equation; C252S F RSSR: All roots of poly eqs. with real coef.; C253S F POLDRV: Driver for C254S; C254S F CPOLY: Roots arb. poly. Jenkins-Traub algorithm; C353S F1 CLEBSH: Ang. mom. coef. - Clebsch, Racah, Wigner; C365S A ALGAMA: Logarithm of the gamma function; C366S A DGAMMA/DLGAMA: DP gamma and log(gamma) functions; C368S F EONE: Exponential integral E1; C370S F BESJY: Bessel functions J and Y; C371S F BESIK: Bessel functions I and K; C372S F CHIPRB: Chi-square integral; C380S F DRZETA: Long precision zeta, zeta-1 functions; C382S F DCGAM: Long precision complex gamma; C383S A DERF/DERFC: DP error function; C384S F BFJ1: Bessel function J1; C385S F COULMB: Regular Coulomb wave functions; C386S F1 DSGMAL: Coulomb phase shift; C387S F BFJYR: Bessel functions J0,J1,Y0,Y1; C388S F IRCOUL: LP irregular Coulomb wave functions; C389S F GAMIN: Incomplete gamma function; C390S F LQ: Assoc. Legendre functions of 2. kind; C392S A DAERF: Inverse error function; C393S F CDEONE: Modified complex exponential integral; D153S F DROMB: Two-dimensional Romberg quadrature; D153S P DROMBP: Two-dimensional Romberg quadrature; D158S F ANC4: Adap. quad. using 4. order Newton

  20. On Parameter Differentiation for Integral Representations of Associated Legendre Functions

    Directory of Open Access Journals (Sweden)

    Howard S. Cohl

    2011-05-01

    Full Text Available For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-half-integer degrees, for general complex-orders, and derivatives with respect to the order are evaluated at integer-orders, for general complex-degrees. We also discuss the properties of the complex function f: C{−1,1}→C given by f(z=z/((z+1^{1/2}(z−1^{1/2}.

  1. Characterization of microwave plasma in a multicusp using 2D emission based tomography: Bessel modes and wave absorption

    Science.gov (United States)

    Rathore, Kavita; Bhattacharjee, Sudeep; Munshi, Prabhat

    2017-06-01

    A tomographic method based on the Fourier transform is used for characterizing a microwave plasma in a multicusp (MC), in order to obtain 2D distribution of plasma emissions, plasma (electron) density (Ne) and temperature (Te). The microwave plasma in the MC is characterized as a function of microwave power, gas pressure, and axial distance. The experimentally obtained 2D emission profiles show that the plasma emissions are generated in a circular ring shape. There are usually two bright rings, one at the plasma core and another near the boundary. The experimental results are validated using a numerical code that solves Maxwell's equations inside a waveguide filled with a plasma in a magnetic field, with collisions included. It is inferred that the dark and bright circular ring patterns are a result of superposition of Bessel modes (TE11 and TE21) of the wave electric field inside the plasma filled MC, which are in reasonable agreement with the plasma emission profiles. The tomographically obtained Ne and Te profiles indicate higher densities in the plasma core (˜1010 cm-3) and enhanced electron temperature in the ECR region (˜13 eV), which are in agreement with earlier results using a Langmuir probe and optical emission spectroscopy (OES) diagnostics.

  2. On the constant-roll inflation

    Science.gov (United States)

    Yi, Zhu; Gong, Yungui

    2018-03-01

    The primordial power spectra of scalar and tensor perturbations during slow-roll inflation are usually calculated with the method of Bessel function approximation. For constant-roll or ultra slow-roll inflation, the method of Bessel function approximation may be invalid. We compare the numerical results with the analytical results derived from the Bessel function approximation, and we find that they differ significantly on super-horizon scales if the constant slow-roll parameter ηH is not small. More accurate method is needed for calculating the primordial power spectrum for constant-roll inflation.

  3. Instantaneous axial force of a high-order Bessel vortex beam of acoustic waves incident upon a rigid movable sphere.

    Science.gov (United States)

    Mitri, F G; Fellah, Z E A

    2011-08-01

    The present investigation examines the instantaneous force resulting from the interaction of an acoustical high-order Bessel vortex beam (HOBVB) with a rigid sphere. The rigid sphere case is important in fluid dynamics applications because it perfectly simulates the interaction of instantaneous sound waves in a reduced gravity environment with a levitated spherical liquid soft drop in air. Here, a closed-form solution for the instantaneous force involving the total pressure field as well as the Bessel beam parameters is obtained for the case of progressive, stationary and quasi-stationary waves. Instantaneous force examples for progressive waves are computed for both a fixed and a movable rigid sphere. The results show how the instantaneous force per unit cross-sectional surface and unit pressure varies versus the dimensionless frequency ka (k is the wave number in the fluid medium and a is the sphere's radius), the half-cone angle β and the order m of the HOBVB. It is demonstrated here that the instantaneous force is determined only for (m,n) = (0,1) (where n is the partial-wave number), and vanishes for m>0 because of symmetry. In addition, the instantaneous force and normalized amplitude velocity results are computed and compared with those of a rigid immovable (fixed) sphere. It is shown that they differ significantly for ka values below 5. The proposed analysis may be of interest in the analysis of instantaneous forces on spherical particles for particle manipulation, filtering, trapping and drug delivery. The presented solutions may also serve as a method for comparison to other solutions obtained by strictly numerical or asymptotic approaches. Copyright © 2011 Elsevier B.V. All rights reserved.

  4. Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media.

    Science.gov (United States)

    Fahrbach, Florian O; Rohrbach, Alexander

    2012-01-17

    Laser beams that can self-reconstruct their initial beam profile even in the presence of massive phase perturbations are able to propagate deeper into inhomogeneous media. This ability has crucial advantages for light sheet-based microscopy in thick media, such as cell clusters, embryos, skin or brain tissue or plants, as well as scattering synthetic materials. A ring system around the central intensity maximum of a Bessel beam enables its self-reconstruction, but at the same time illuminates out-of-focus regions and deteriorates image contrast. Here we present a detection method that minimizes the negative effect of the ring system. The beam's propagation stability along one straight line enables the use of a confocal line principle, resulting in a significant increase in image contrast. The axial resolution could be improved by nearly 100% relative to the standard light-sheet techniques using scanned Gaussian beams, while demonstrating self-reconstruction also for high propagation depths.

  5. Theory of function spaces

    CERN Document Server

    Triebel, Hans

    1983-01-01

    The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where -8Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rn in the framework of Fourier analysis, which is based on the technique of maximal functions, Fourier multipliers and interpolation assertions. These topics are treated in Chapter 2, which is the heart

  6. Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging.

    Science.gov (United States)

    Thériault, Gabrielle; Cottet, Martin; Castonguay, Annie; McCarthy, Nathalie; De Koninck, Yves

    2014-01-01

    Two-photon microscopy has revolutionized functional cellular imaging in tissue, but although the highly confined depth of field (DOF) of standard set-ups yields great optical sectioning, it also limits imaging speed in volume samples and ease of use. For this reason, we recently presented a simple and retrofittable modification to the two-photon laser-scanning microscope which extends the DOF through the use of an axicon (conical lens). Here we demonstrate three significant benefits of this technique using biological samples commonly employed in the field of neuroscience. First, we use a sample of neurons grown in culture and move it along the z-axis, showing that a more stable focus is achieved without compromise on transverse resolution. Second, we monitor 3D population dynamics in an acute slice of live mouse cortex, demonstrating that faster volumetric scans can be conducted. Third, we acquire a stereoscopic image of neurons and their dendrites in a fixed sample of mouse cortex, using only two scans instead of the complete stack and calculations required by standard systems. Taken together, these advantages, combined with the ease of integration into pre-existing systems, make the extended depth-of-field imaging based on Bessel beams a strong asset for the field of microscopy and life sciences in general.

  7. Assessment of an extended Nijboer-Zernike approach for the computation of optical point-spread functions.

    Science.gov (United States)

    Braat, Joseph; Dirksen, Peter; Janssen, Augustus J E M

    2002-05-01

    We assess the validity of an extended Nijboer-Zernike approach [J. Opt. Soc. Am. A 19, 849 (2002)], based on ecently found Bessel-series representations of diffraction integrals comprising an arbitrary aberration and a defocus part, for the computation of optical point-spread functions of circular, aberrated optical systems. These new series representations yield a flexible means to compute optical point-spread functions, both accurately and efficiently, under defocus and aberration conditions that seem to cover almost all cases of practical interest. Because of the analytical nature of the formulas, there are no discretization effects limiting the accuracy, as opposed to the more commonly used numerical packages based on strictly numerical integration methods. Instead, we have an easily managed criterion, expressed in the number of terms to be included in the Bessel-series representations, guaranteeing the desired accuracy. For this reason, the analytical method can also serve as a calibration tool for the numerically based methods. The analysis is not limited to pointlike objects but can also be used for extended objects under various illumination conditions. The calculation schemes are simple and permit one to trace the relative strength of the various interfering complex-amplitude terms that contribute to the final image intensity function.

  8. Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups

    DEFF Research Database (Denmark)

    Hilgert, Joachim; Kobayashi, Toshiyuki; Möllers, Jan

    2012-01-01

    For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K_C-orbit X in p_C and the L^2-inner product involves a K-Bessel function as density. Here K is a maximal compact subgroup of G, and g......_C=k_C+p_C is a complexified Cartan decomposition. In this realization the space of k-finite vectors consists of holomorphic polynomials on X. The reproducing kernel of the Fock space is calculated explicitly in terms of an I-Bessel function. We further find an explicit formula of a generalized Segal-Bargmann transform which...... intertwines the Schroedinger and Fock model. Its kernel involves the same I-Bessel function. Using the Segal--Bargmann transform we also determine the integral kernel of the unitary inversion operator in the Schroedinger model which is given by a J-Bessel function....

  9. Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm

    Science.gov (United States)

    Yang, Minglin; Wu, Yueqian; Sheng, Xinqing; Ren, Kuan Fang

    2017-12-01

    Computation of scattering of shaped beams by large nonspherical particles is a challenge in both optics and electromagnetics domains since it concerns many research fields. In this paper, we report our new progress in the numerical computation of the scattering diagrams. Our algorithm permits to calculate the scattering of a particle of size as large as 110 wavelengths or 700 in size parameter. The particle can be transparent or absorbing of arbitrary shape, smooth or with a sharp surface, such as the Chebyshev particles or ice crystals. To illustrate the capacity of the algorithm, a zero order Bessel beam is taken as the incident beam, and the scattering of ellipsoidal particles and Chebyshev particles are taken as examples. Some special phenomena have been revealed and examined. The scattering problem is formulated with the combined tangential formulation and solved iteratively with the aid of the multilevel fast multipole algorithm, which is well parallelized with the message passing interface on the distributed memory computer platform using the hybrid partitioning strategy. The numerical predictions are compared with the results of the rigorous method for a spherical particle to validate the accuracy of the approach. The scattering diagrams of large ellipsoidal particles with various parameters are examined. The effect of aspect ratios, as well as half-cone angle of the incident zero-order Bessel beam and the off-axis distance on scattered intensity, is studied. Scattering by asymmetry Chebyshev particle with size parameter larger than 700 is also given to show the capability of the method for computing scattering by arbitrary shaped particles.

  10. Analytical fits to the synchrotron functions

    Science.gov (United States)

    Fouka, Mourad; Ouichaoui, Saad

    2013-06-01

    Accurate fitting formulae to the synchrotron function, F(x), and its complementary function, G(x), are performed and presented. The corresponding relative errors are less than 0.26% and 0.035% for F(x) and G(x), respectively. To this end we have, first, fitted the modified Bessel functions, K5/3(x) and K2/3(x). For all the fitted functions, the general fit expression is the same, and is based on the well known asymptotic forms for low and large values of x for each function. It consists of multiplying each asymptotic form by a function that tends to unity or zero for low and large values of x. Simple formulae are suggested in this paper, depending on adjustable parameters. The latter have been determined by adopting the Levenberg-Marquardt algorithm. The proposed formulae should be of great utility and simplicity for computing spectral powers and the degree of polarization for synchrotron radiation, both for laboratory and astrophysical applications.

  11. Hybrid fast Hankel transform implementation for optics simulation

    Science.gov (United States)

    Davis, Paul K.

    2013-09-01

    The most compute intensive part of a full optics simulation, especially including diffraction effects, is the Fourier transform between pupil and image spaces. This is typically performed as a two dimensional fast discrete transform. For a nearly radially symmetric system there are advantages to using polar coordinates, in which case the radial transform becomes a Hankel transform, using Bessel functions instead of circular functions. However, there are special difficulties in calculating and handling Bessel functions. Several solutions have been proposed. We present a hybrid Hankel transform which divides the domain, calculating a portion using Bessel function approximations but converting most of the domain into a one dimensional Fourier transform which can be handled by standard methods.

  12. Bessel Fourier Orientation Reconstruction (BFOR): An Analytical Diffusion Propagator Reconstruction for Hybrid Diffusion Imaging and Computation of q-Space Indices

    Science.gov (United States)

    Hosseinbor, A. Pasha; Chung, Moo K.; Wu, Yu-Chien; Alexander, Andrew L.

    2012-01-01

    The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier orientation reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA). PMID:22963853

  13. Application of Fourier-Bessel technique for computing Eigen-states in a Bragg cylindrical space slot channel waveguide

    Science.gov (United States)

    Jafari, Seyed Hamed; Gauthier, Robert C.

    2015-02-01

    Maxwell's wave equations can be solved using different techniques in order to extract optical properties of a variety of dielectric structures. For structures that contain an extended axis which serve for the reference for cylindrical symmetry, we have shown that an expansion of the fields and inverse of the relative dielectric profile using a simplified and complete set of basis functions of Fourier-Bessel terms provide access to an eigenvalue formulation from which the eigen-states can be computed. We review the steps used to convert Maxwell's equation into an eigenvalue formulation, and then proceed to discuss several applications of the technique. For cylindrically symmetric structures, the computational technique provides a significantly reduced matrix order to be populated. New target structure for the presentation consists of cylindrical space slot channel waveguide in which the channel extends in azimuthal (ϕ) direction. The channel is provided by considering the etching of external side walls of "Bragg fiber". The configuration is similar to a structure that can support whispering-gallery modes, except that the modes highest field locations are within the ambient medium of the channel. Optical properties of this structure can be best examined through ?? field component which is discontinuous by ratio of relative dielectric constants when passing air-Bragg interfaces. The ability to select Bragg dielectric properties and to introduce non-uniformities in Bragg plane spacing provides access to tuning slot channel waveguide properties and design several novel configurations.

  14. Zeros of smallest modulus of functions resembling exp(z

    Directory of Open Access Journals (Sweden)

    Kenneth B. Stolarsky

    1982-01-01

    Full Text Available To determine (in various senses the zeros of the Laplace transform of a signed mass distribution is of great importance for many problems in classical analysis and number theory. For example, if the mass consists of finitely many atoms, the transform is an exponential polynomial. This survey studies what is known when the distribution is a probability density function of small variance, and examines in what sense the zeros must have large moduli. In particular, classical results on Bessel function zeros, of Szegö on zeros of partial sums of the exponential, of I. J. Schoenberg on k-times positive functions, and a result stemming from Graeffe's method, are all presented from a unified probabilistic point of view.

  15. Is relativistic quantum mechanics compatible with special relativity?

    International Nuclear Information System (INIS)

    Lavenda, B.H.

    2001-01-01

    The transformation from a time-dependent random walk to quantum mechanics converts a modified Bessel function into an ordinary one together with a phase factor e iπ/2 for each time the electron flips both direction and handedness. Causality requires the argument to be greater than the order of the Bessel function. Assuming equal probabilities for jumps ±1, the normalized modified Bessel function of an imaginary argument is the solution of the finite difference differential Schroedinger equation whereas the same function of a real argument satisfies the diffusion equation. In the nonrelativistic limit, the stability condition of the difference scheme contains the mass whereas in the ultrarelativistic limit only the velocity of light appears. Particle waves in the nonrelativistic limit become elastic waves in the ultrarelativistic limit with a phase shift in the frequency and wave number of π/2. The ordinary Bessel function satisfies a second order recurrence relation which is a finite difference differential wave equation, using non-nearest neighbors, whose solutions are the chirality components of a free-particle in the zero fermion mass limit. Reintroducing the mass by a phase transformation transforms the wave equation into the Klein-Gordon equation but does not admit a solution in terms of ordinary Bessel functions. However, a sign change of the mass term permits a solution in terms of a modified Bessel function whose recurrence formulas produce all the results of special relativity. The Lorentz transformation maximizes the integral of the modified Bessel function and determines the paths of steepest descent in the classical limit. If the definitions of frequency and wave number in terms of the phase were used in special relativity, the condition that the frame be inertial would equate the superluminal phase velocity with the particle velocity in violation of causality. In order to get surfaces of constant phase to move at the group velocity, an integrating

  16. ОБОБЩЕННЫЕ СДВИГИ БЕССЕЛЯ И НЕКОТОРЫЕ ОБРАТНЫЕ ТЕОРЕМЫ ТЕОРИИ ПРИБЛИЖЕНИЯ ФУНКЦИЙ НА ПОЛУПРЯМОЙ

    Directory of Open Access Journals (Sweden)

    ПЛАТОНОВ С. С.

    2007-01-01

    Full Text Available The generalized translations of Bessel and the harmonic analysis of Bessel may be used for study some problems of approximations of functions on the half-line [0, +?] in the weighted Lp spaces. Using generalized translations of Bessel we can de?ne generalized moduli of continuity and we can consider many natural analogs of classical problems of approximation. As aggregates of approximation we use certain class of entire functions of exponential type. In this paper we obtain some analogs of classical inverse approximation theorems due to S. B. Stechkin, A. F. Timan and M. F. Timan.

  17. Generalized fractional integration of the \\overline{H}-function

    Directory of Open Access Journals (Sweden)

    Praveen Agarwal

    2012-11-01

    Full Text Available A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera. In the present paper, we study and develop the generalized fractional integral operators given by Saigo. First, we establish two Theorems that give the images of the product of H-function and a general class of polynomials inSaigo operators. On account of the general nature of the Saigo operators, H-function and a general class of polynomials a large number of new and known Images involving Riemann-Liouville and Erdélyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, generalized Wright-Bessel function, the polylogarithm and Mittag-Leffler functions follow as special cases of our main findings.

  18. Implementation of Bessel's method for solar eclipses prediction in the WRF-ARW model

    Directory of Open Access Journals (Sweden)

    A. Montornès

    2016-05-01

    Full Text Available Solar eclipses are predictable astronomical events that abruptly reduce the incoming solar radiation into the Earth's atmosphere, which frequently results in non-negligible changes in meteorological fields. The meteorological impacts of these events have been analyzed in many studies since the late 1960s. The recent growth in the solar energy industry has greatly increased the interest in providing more detail in the modeling of solar radiation variations in numerical weather prediction (NWP models for the use in solar resource assessment and forecasting applications. The significant impact of the recent partial and total solar eclipses that occurred in the USA (23 October 2014 and Europe (20 March 2015 on solar power generation have provided additional motivation and interest for including these astronomical events in the current solar parameterizations.Although some studies added solar eclipse episodes within NWP codes in the 1990s and 2000s, they used eclipse parameterizations designed for a particular case study. In contrast to these earlier implementations, this paper documents a new package for the Weather Research and Forecasting–Advanced Research WRF (WRF-ARW model that can simulate any partial, total or hybrid solar eclipse for the period 1950 to 2050 and is also extensible to a longer period. The algorithm analytically computes the trajectory of the Moon's shadow and the degree of obscuration of the solar disk at each grid point of the domain based on Bessel's method and the Five Millennium Catalog of Solar Eclipses provided by NASA, with a negligible computational time. Then, the incoming radiation is modified accordingly at each grid point of the domain.This contribution is divided in three parts. First, the implementation of Bessel's method is validated for solar eclipses in the period 1950–2050, by comparing the shadow trajectory with values provided by NASA. Latitude and longitude are determined with a bias lower than 5

  19. Stability analysis of Hasegawa space-charge waves in a plasma waveguide with collisional ion beam

    Science.gov (United States)

    Lee, Myoung-Jae; Jung, Young-Dae

    2017-12-01

    The dispersion relation for the Hasegawa space-charge wave propagating in a cylindrical waveguide dusty plasma containing collision-dominated ion stream is derived by using the fluid equations and the Poisson equation which lead to a Bessel equation. The solution of Bessel equation is null at the boundary and then the roots of the Bessel function would characterize the property of space-charge wave propagation. We have found that the Hasegawa space-charge wave can be excited for a large axial wave number. The growth rate of excitation increases as the order of the roots of the Bessel function increases. The growth rate decreases with an increase of the radius of cylindrical waveguide as well as with an increase of the collision frequency. We found that the disturbance of wave can be damped only for small wave numbers.

  20. On the relation between Kaiser–Bessel blob and tube of response based modelling of the system matrix in iterative PET image reconstruction

    International Nuclear Information System (INIS)

    Lougovski, Alexandr; Hofheinz, Frank; Maus, Jens; Schramm, Georg; Van den Hoff, Jörg

    2015-01-01

    We investigate the question of how the blob approach is related to tube of response based modelling of the system matrix. In our model, the tube of response (TOR) is approximated as a cylinder with constant density (TOR-CD) and the cubic voxels are replaced by spheres. Here we investigate a modification of the TOR model that makes it effectively equivalent to the blob model, which models the intersection of lines of response (LORs) with radially variant basis functions (‘blobs’) replacing the cubic voxels. Implications of the achieved equivalence regarding the necessity of final resampling in blob-based reconstructions are considered. We extended TOR-CD to a variable density tube model (TOR-VD) that yields a weighting function (defining all system matrix elements) which is essentially identical to that of the blob model. The variable density of TOR-VD was modelled by a Gaussian and a Kaiser–Bessel function, respectively. The free parameters of both model functions were determined by fitting the corresponding weighting function to the weighting function of the blob model. TOR-CD and the best-fitting TOR-VD were compared to the blob model with a final resampling step (BLOB-RS) and without resampling (BLOB-NRS) in phantom studies. For three different contrast ratios and two different voxel sizes, resolution noise curves were generated. TOR-VD and BLOB-NRS lead to nearly identical images for all investigated contrast ratios and voxel sizes. Both models showed strong Gibbs artefacts at 4 mm voxel size, while at 2 mm voxel size there were no Gibbs artefacts visible. The spatial resolution was similar to the resolution with TOR-CD in all cases. The resampling step removed most of the Gibbs artefacts and reduced the noise level but also degraded the spatial resolution substantially. We conclude that the blob model can be considered just as a special case of a TOR-based reconstruction. The latter approach provides a more natural description of the detection process

  1. An alternative way of computation of amplitudes and intensities in time-dependent Moessbauer spectroscopy (TDMS)

    International Nuclear Information System (INIS)

    Christoskov, I.D.; Vapirev, E.I.

    1990-01-01

    An alternative way of presenting the time-dependent amplitudes and intensities of radiation, corresponding to resonant absorption and scattering experiments, is developed. Infinite series of Bessel functions with complex coefficients are replaced by simple for calculation definite integrals and the number of Bessel function calls is reduced to one per a tabulation point. Thus the calculational effort for experimental data processing becomes smaller

  2. Proceedings (Mathematical Sciences) SUBJECT INDEX

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    On some congruence with application to exponential sums. 1. Congruence groups. The congruence ... flag varieties. 123. Diamond operator. The solutions of the n-dimensional Bessel diamond operator and the Fourier–Bessel transform of their convolution. 375. Elliptic regularity. Limits of functions and elliptic operators.

  3. Effects of periodic modulation on the nonlinear Landau–Zener tunneling

    International Nuclear Information System (INIS)

    Li-Hua, Wu; Wen-Shan, Duan

    2009-01-01

    We study the Landau–Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger. (general)

  4. Second-order moments of Schell-model beams with various correlation functions in atmospheric turbulence.

    Science.gov (United States)

    Zheng, Guo; Wang, Jue; Wang, Lin; Zhou, Muchun; Xin, Yu; Song, Minmin

    2017-11-15

    The general formulae for second-order moments of Schell-model beams with various correlation functions in atmospheric turbulence are derived and validated by the Bessel-Gaussian Schell-model beams and cosine-Gaussian-correlated Schell-model beams. Our finding shows that the second-order moments of partially coherent Schell-model beams are related to the second-order partial derivatives of source spectral degree of coherence at the origin. The formulae we provide are much more convenient to analyze and research propagation problems in turbulence.

  5. Pramana – Journal of Physics | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    In this work, conventional semiclassical JWKB solution (named after Jeffreys, Wentzel, Kramers and Brillouin) of the LP is being obtained by first transforming the related Bessel's equation into the normal form 'via the suggested change of independent variable'. JWKB approximation of the first-order Bessel functions ( ν = 1 ) ...

  6. Vortex-like and string-like solutions for the 2+1 dimensional SU(2) Yang-Mills theory with the Chern-Simons term

    International Nuclear Information System (INIS)

    Teh, R.

    1989-07-01

    Vortex-like and string-like solutions of 2+1 Dim. SU(2) YM theory with the Chern-Simons term are discussed. Two ansatze are constructed which yield respectively analytic Bessel function solutions and elliptic function solutions. The Bessel function solutions are vortex-like and tend to the same vacuum state as the Ginzburg-Landau vortex solution at large ρ. The Jacobi elliptic function solutions are string-like, have finite energy and magnetic flux concentrated along a line in the x 1 - x 2 plane. (author). 18 refs

  7. Calculation of Rayleigh type sums for zeros of the equation arising in spectral problem

    Science.gov (United States)

    Kostin, A. B.; Sherstyukov, V. B.

    2017-12-01

    For zeros of the equation (arising in the oblique derivative problem) μ J n ‧ ( μ ) cos α + i n J n ( μ ) sin α = 0 , μ ∈ ℂ , with parameters n ∈ ℤ, α ∈ [-π/2, π/2] and the Bessel function Jn (μ) special summation relationships are proved. The obtained results are consistent with the theory of well-known Rayleigh sums calculating by zeros of the Bessel function.

  8. Bessel Fourier orientation reconstruction: an analytical EAP reconstruction using multiple shell acquisitions in diffusion MRI.

    Science.gov (United States)

    Hosseinbor, Ameer Pasha; Chung, Moo K; Wu, Yu-Chien; Alexander, Andrew L

    2011-01-01

    The estimation of the ensemble average propagator (EAP) directly from q-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed. One, in particular, is Diffusion Propagator Imaging (DPI) which is based on the Laplace's equation estimation of diffusion signal for each shell acquisition. Viewed intuitively in terms of the heat equation, the DPI solution is obtained when the heat distribution between temperatuere measurements at each shell is at steady state. We propose a generalized extension of DPI, Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition. That is, the heat distribution between shell measurements is no longer at steady state. In addition to being analytical, the BFOR solution also includes an intrinsic exponential smootheing term. We illustrate the effectiveness of the proposed method by showing results on both synthetic and real MR datasets.

  9. Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies

    Science.gov (United States)

    Bzowski, Adam; McFadden, Paul; Skenderis, Kostas

    2016-03-01

    We present a comprehensive discussion of renormalisation of 3-point functions of scalar operators in conformal field theories in general dimension. We have previously shown that conformal symmetry uniquely determines the momentum-space 3-point functions in terms of certain integrals involving a product of three Bessel functions (triple- K integrals). The triple- K integrals diverge when the dimensions of operators satisfy certain relations and we discuss how to obtain renormalised 3-point functions in all cases. There are three different types of divergences: ultralocal, semilocal and nonlocal, and a given divergent triple- K integral may have any combination of them. Ultralocal divergences may be removed using local counterterms and this results in new conformal anomalies. Semilocal divergences may be removed by renormalising the sources, and this results in CFT correlators that satisfy Callan-Symanzik equations with beta functions. In the case of non-local divergences, it is the triple- K representation that is singular, not the 3-point function. Here, the CFT correlator is the coefficient of the leading nonlocal singularity, which satisfies all the expected conformal Ward identities. Such correlators exhibit enhanced symmetry: they are also invariant under dual conformal transformations where the momenta play the role of coordinates. When both anomalies and beta functions are present the correlators exhibit novel analytic structure containing products of logarithms of momenta. We illustrate our discussion with numerous examples, including free field realisations and AdS/CFT computations.

  10. Characteristic impedance of a microchannel with two immiscible microfluids

    Science.gov (United States)

    Jaramillo Raquejo, Daniela

    2014-05-01

    Consider the case of a microcapillary of radius R with two microfluidic immiscible. The micro-capillary region 0 expressed in terms of Bessel functions. Similarly, the characteristic impedance of the microcapillary is expressed by a complex formula Bessel functions. Obtain the analytical results are important for designing engineering microdevices with applications in pharmaceutical, food engineering, nanotechnology and biotechnology in general in particular. For future research it is interesting to consider the case of boundary conditions with memory effects.

  11. Complete Monotonicity of a Difference Between the Exponential and Trigamma Functions and Properties Related to a Modified Bessel Function

    DEFF Research Database (Denmark)

    Qi, Feng; Berg, Christian

    2013-01-01

    In the paper, the authors find necessary and sufficient conditions for a difference between the exponential function αeβ/t, α, β > 0, and the trigamma function ψ (t) to be completely monotonic on (0,∞). While proving the complete onotonicity, the authors discover some properties related to the fi...

  12. Computation of the brightness of the variably-polarizing undulator

    International Nuclear Information System (INIS)

    Dattoli, G.; Torre, A.; Schettini, G.; Carpanese, M.

    1999-02-01

    Undulators, producing variably polarized radiation, generate magnetic fields which induce different types of electron motion (vertically, horizontally sinusoidal and helical). The properties of the emitted radiation reflect the complexity of the motion and cannot be described with the method based on the conventional Bessel functions expansion. It's shown that the problem can be overcome by exploiting a method which employs generalized forms of Bessel functions. The proposed technique provides an effective tool to analyze the properties of the emitted radiation [it

  13. Exact solution for the reflection and diffraction of atomic de Broglie waves by a travelling evanescent laser wave

    International Nuclear Information System (INIS)

    Witte, N.S.

    1997-01-01

    The exact solution to the problem of reflection and diffraction of atomic de Broglie waves by a travelling evanescent wave is found starting with a bare-state formulation. The solution for the wavefunctions, the tunnelling losses and the non-adiabatic losses are given exactly in terms of hyper-Bessel functions, and are valid for all detuning and Rabi frequencies, thus generalizing previous approximate methods. Furthermore we give the limiting cases of all amplitudes in the uniform semiclassical limit, which is valid in all regions including near the classical turning points, and in the large and weak coupling cases. Exact results for the zero detuning case are obtained in terms of Bessel functions. We find our uniform semiclassical limit to be closer to the exact result over the full range of parameter values than the previously reported calculations. The current knowledge of hyper-Bessel function properties is reviewed in order to apply this to the physical problems imposed

  14. More on zeta-function regularization of high-temperature expansions

    International Nuclear Information System (INIS)

    Actor, A.

    1987-01-01

    A recent paper using the Riemann ζ-function to regularize the (divergent) coefficients occurring in the high-temperature expansions of one-loop thermodynamic potentials is extended. This method proves to be a powerful tool for converting Dirichlet-type series Σ m a m (x i )/m s into power series in the dimensionless parameters x i . The coefficients occurring in the power series are (proportional to) ζ-functions evaluated away from their poles - this is where the regularization occurs. High-temperature expansions are just one example of this highly-nontrivial rearrangement of Dirichlet series into power series form. We discuss in considerable detail series in which a m (x i ) is a product of trigonometric, algebraic and Bessel function factors. The ζ-function method is carefully explained, and a large number of new formulae are provided. The means to generalize these formulae are also provided. Previous results on thermodynamic potentials are generalized to include a nonzero constant term in the gauge potential (time component) which can be used to probe the electric sector of temperature gauge theories. (author)

  15. The zeros of az2J″ν(z+bzJ′ν(z+cJν(z as functions of order

    Directory of Open Access Journals (Sweden)

    A. McD. Mercer

    1992-01-01

    Full Text Available If j″νk denotes the kth positive zero of the Bessel function J″ν(x, it has been shown recently by Lorch and Szego [2] that j″ν1 increases with ν in ν>0 and that (with k fixed in 2,3,… j″νk increases in 00. The present paper, by using a different kind of analysis, re-obtains these conclusions as a special case of a more general result concerning the positive zeros of the function az2J″ν(z+bzJ′ν(z+cJν(z. Here, the constants a, b and c are subject to certain mild restrictions.

  16. Cut contribution to momentum autocorrelation function of an impurity in a classical diatomic chain

    Science.gov (United States)

    Yu, Ming B.

    2018-02-01

    A classic diatomic chain with a mass impurity is studied using the recurrence relations method. The momentum autocorrelation function of the impurity is a sum of contributions from two pairs of resonant poles and three branch cuts. The former results in cosine function and the latter in acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical branches are derived as even-order Bessel function expansions. The expansion coefficients are integrals of elliptic functions in the real axis for the acoustic branch and along a contour parallel to the imaginary axis for the optical branch, respectively. An integral is carried out for the calculation of optical branch: ∫0 ϕ dθ/√((1 - r 1 2 sin2 θ)(1 - r 2 2 sin2 θ)) = igsn -1 (sin ϕ) ( r 2 2 > r 1 2 > 1, g is a constant).

  17. Stable source reconstruction from a finite number of measurements in the multi-frequency inverse source problem

    DEFF Research Database (Denmark)

    Karamehmedovic, Mirza; Kirkeby, Adrian; Knudsen, Kim

    2018-01-01

    setting: From measurements made at a finite set of frequencies we uniquely determine and reconstruct sources in a subspace spanned by finitely many Fourier-Bessel functions. Further, we obtain a constructive criterion for identifying a minimal set of measurement frequencies sufficient for reconstruction......, and under an additional, mild assumption, the reconstruction method is shown to be stable." Our analysis is based on a singular value decomposition of the source-to-measurement forward operators and the distribution of positive zeros of the Bessel functions of the first kind. The reconstruction method...

  18. Spatially resolved electron density and electron energy distribution function in Ar magnetron plasmas used for sputter-deposition of ZnO-based thin films

    Energy Technology Data Exchange (ETDEWEB)

    Maaloul, L.; Gangwar, R. K.; Morel, S.; Stafford, L., E-mail: luc.stafford@umontreal.ca [Département de Physique, Université de Montréal, Montréal, Québec H3C 3J7 (Canada)

    2015-11-15

    Langmuir probe and trace rare gases optical emission spectroscopy were used to analyze the spatial structure of the electron density and electron energy distribution function (EEDF) in a cylindrical Ar magnetron plasma reactor used for sputter-deposition of ZnO-based thin films. While a typical Bessel (zero order) diffusion profile was observed along the radial direction for the number density of charged particles at 21 cm from the ZnO target, a significant rise of these populations with respect to the Bessel function was seen in the center of the reactor at 4 cm from the magnetron surface. As for the EEDF, it was found to transform from a more or less Maxwellian far from the target to a two-temperature Maxwellian with a depletion of high-energy electrons where magnetic field confinement effects become important. No significant change in the behavior of the electron density and EEDF across a wide range of pressures (5–100 mTorr) and self-bias voltages (115–300 V) was observed during magnetron sputtering of Zn, ZnO, and In{sub 2}O{sub 3} targets. This indicates that sputtering of Zn, In, and O atoms do not play a very significant role on the electron particle balance and electron heating dynamics, at least over the range of experimental conditions investigated.

  19. HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS

    Directory of Open Access Journals (Sweden)

    Jiameng Wu

    2018-01-01

    Full Text Available The infinite depth free surface Green function (GF and its high order derivatives for diffraction and radiation of water waves are considered. Especially second order derivatives are essential requirements in high-order panel method. In this paper, concerning the classical representation, composed of a semi-infinite integral involving a Bessel function and a Cauchy singularity, not only the GF and its first order derivatives but also second order derivatives are derived from four kinds of analytical series expansion and refined division of whole calculation domain. The approximations of special functions, particularly the hypergeometric function and the algorithmic applicability with different subdomains are implemented. As a result, the computation accuracy can reach 10-9 in whole domain compared with conventional methods based on direct numerical integration. Furthermore, numerical efficiency is almost equivalent to that with the classical method.

  20. Definite Integrals using Orthogonality and Integral Transforms

    Directory of Open Access Journals (Sweden)

    Howard S. Cohl

    2012-10-01

    Full Text Available We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.

  1. Coupling coefficients for tensor product representations of quantum SU(2)

    International Nuclear Information System (INIS)

    Groenevelt, Wolter

    2014-01-01

    We study tensor products of infinite dimensional irreducible * -representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions

  2. Coupling coefficients for tensor product representations of quantum SU(2)

    Science.gov (United States)

    Groenevelt, Wolter

    2014-10-01

    We study tensor products of infinite dimensional irreducible *-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions.

  3. Fast and accurate three-dimensional point spread function computation for fluorescence microscopy.

    Science.gov (United States)

    Li, Jizhou; Xue, Feng; Blu, Thierry

    2017-06-01

    The point spread function (PSF) plays a fundamental role in fluorescence microscopy. A realistic and accurately calculated PSF model can significantly improve the performance in 3D deconvolution microscopy and also the localization accuracy in single-molecule microscopy. In this work, we propose a fast and accurate approximation of the Gibson-Lanni model, which has been shown to represent the PSF suitably under a variety of imaging conditions. We express the Kirchhoff's integral in this model as a linear combination of rescaled Bessel functions, thus providing an integral-free way for the calculation. The explicit approximation error in terms of parameters is given numerically. Experiments demonstrate that the proposed approach results in a significantly smaller computational time compared with current state-of-the-art techniques to achieve the same accuracy. This approach can also be extended to other microscopy PSF models.

  4. Cut-off frequencies of circumferential horizontal shear waves in various functionally graded cylinder shells.

    Science.gov (United States)

    Shen, Xiaoqin; Ren, Dawei; Cao, Xiaoshan; Wang, Ji

    2018-03-01

    In this study, cut-off frequencies of the circumferential SH waves in functionally graded piezoelectric-piezomagnetic material (FGPPM) cylinder shells with traction free, electrical and magnetic open boundary conditions are investigated analytically. The Wentzel-Kramers-Brillouin (WKB) method is employed for solving differential equations with variable coefficients for general cases. For comparison, Bessel functions and Kummer functions are used for solving cut-off frequency problems in homogenous and ideal FGPPM cylinder shells. It is shown that the WKB solution for the cut-off frequencies has good precise. The set of cut-off frequencies is a series of approximate arithmetic progressions, for which the difference is a function of the density and the effective elastic parameter. The relationship between the difference and the gradient coefficient is described. These results provide theoretical guidance for the non-destructive evaluation of curved shells based on the cut-off frequencies. Copyright © 2017 Elsevier B.V. All rights reserved.

  5. Small-x behavior of the structure function F2 and its slope ∂lnF2/∂ln(1/x) for ''frozen'' and analytic strong-coupling constants

    International Nuclear Information System (INIS)

    Cvetic, G.; Kniehl, B.A.; Kotikov, A.V.

    2009-06-01

    Using the leading-twist approximation of the Wilson operator product expansion with ''frozen'' and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F 2 and its slope ∂lnF 2 /∂ln(1/x) at small values of x, obtained for a at initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA. (orig.)

  6. Whimsicality of multi-mode Hasegawa space-charge waves in a complex plasma containing collision-dominated electrons and streaming ions

    Science.gov (United States)

    Lee, Myoung-Jae; Jung, Young-Dae

    2017-09-01

    The influence of collision-dominated electrons on multi-mode Hasegawa space-charge waves are investigated in a complex plasma containing streaming ions. The dispersion relation for the multi-mode Hasegawa space-charge wave propagating in a cylindrical waveguide filled with dusty plasma containing collision-dominated electrons and streaming ions is derived by using the fluid equations and Poisson’s equation which lead to a Bessel equation. By the boundary condition, the roots of the Bessel function would characterize the property of space-charge wave propagation. It is found that two solutions exist for wave frequency, which are affected by the radius of waveguide and the roots of the Bessel function. The damping and growing modes are found to be enhanced by an increase of the radius. However, an increase of electron collision frequency would suppress the damping and the growing modes of the propagating space-charge wave in a cylindrical waveguide plasma.

  7. Eigenfunction expansion for fractional Brownian motions

    International Nuclear Information System (INIS)

    Maccone, C.

    1981-01-01

    The fractional Brownian motions, a class of nonstationary stochastic processes defined as the Riemann-Liouville fractional integral/derivative of the Brownian motion, are studied. It is shown that these processes can be regarded as the output of a suitable linear system of which the input is the white noise. Their autocorrelation is then derived with a study of their standard-deviation curves. Their power spectra are found by resorting to the nonstationary spectral theory. And finally their eigenfunction expansion (Karhunen-Loeve expansion) is obtained: the eigenfunctions are proved to be suitable Bessel functions and the eigenvalues zeros of the Bessel functions. (author)

  8. Determinación de la carga topológica de un haz bessel-gauss mediante el patrón de difracción a través de una abertura triangular equilátera

    Directory of Open Access Journals (Sweden)

    Cristian Hernando Acevedo

    2015-01-01

    Full Text Available La carga topológica de una onda electromagnética CT, está relacionada con su distribucion espacial en el frente de onda. Ondas electromagnéticas con un factor acimutal exp(il en su fase, tienen CT entera (l=m o no entera (l=M. Estas ondas electromagnéticas con un valor definido de carga topológica pueden ser producidas en el régimen visible utilizando máscaras tenedor holográficas generadas por computador. En este artículo se estudia mediante simulaciones numéricas la red triangular formada en el régimen de intensidad de Fraunhofer de haces Bessel-Gauss con CT entera y no entera que han difractado sobre una rendija en forma triangular para determinar su signo y su magnitud. También se presentan los resultados experimentales de la intensidad en campo lejano obtenidos al difractar una onda luminosa Bessel-Gauss con CT entera y no entera a través de una rendija triangular equilátera. Argumentos cualitativos parciales han sido expuestos para explicar el fenómeno de difracción de estos haces con carga topológica. Aquí se presentan argumentos cualitativos y cuantitativos que permiten explicar todos los resultados de la difracción por una abertura triangular de haces con carga topológica obtenidos ya sea por simulación numérica o mediante su realización experimental.

  9. Solution of the scattering T matrix equation in discrete complex momentum space

    International Nuclear Information System (INIS)

    Rawitscher, G.H.; Delic, G.

    1984-01-01

    The scattering solution to the Lippmann-Schwinger equation is expanded into a set of spherical Bessel functions of complex wave numbers, K/sub j/, with j = 1,2 , . . . , M. The value of each K/sub j/ is determined from the condition that the spherical Bessel function smoothly matches onto an asymptotically outgoing spherical Hankel (or Coulomb) function of the correct physical wave number at a matching point R. The spherical Bessel functions thus determined are Sturmian functions, and they form a complete set in the interval 0 to R. The coefficients of the expansion of the scattering function are determined by matrix inversion of a linear set of algebraic equations, which are equivalent to the solution of the T-matrix equation in complex momentum space. In view of the presence of a matching radius, no singularities are encountered for the Green's functions, and the inclusion of Coulomb potentials offers no computational difficulties. Three numerical examples are performed in order to illustrate the convergence of the elastic scattering matrix S with M. One of these consists of a set of coupled equations which describe the breakup of a deuteron as it scatters from the nucleus on 58 Ni. A value of M of 15 or less is found sufficient to reproduce the exact S matrix element to an accuracy of four figures after the decimal point

  10. Recovering functions from the spherical mean transform with data on an ellipse using eigenfunction expansion in elliptical coordinates

    Science.gov (United States)

    Salman, Yehonatan

    2017-09-01

    The aim of this paper is to introduce a new inversion procedure for recovering functions, defined on R2 , from the spherical mean transform, which integrates functions on a prescribed family Λ of circles, where Λ consists of circles whose centers belong to a given ellipse E on the plane. The method presented here follows the same procedure which was used by Norton (J Acoust Soc Am 67:1266-1273, 1980) for recovering functions in case where Λ consists of circles with centers on a circle. However, at some point we will have to modify the method in [24] by using expansion in elliptical coordinates, rather than spherical coordinates, in order to solve the more generalized elliptical case. We will rely on a recent result obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the eigenfunction expansion of the Bessel function in elliptical coordinates.

  11. Transmission characteristics of Bessel-Gaussian vortex beams propagating along both longitudinal and transverse directions in a subway tunnel

    Science.gov (United States)

    Wang, Xiaohui; Song, Yingxiong

    2018-02-01

    By exploiting the non-Kolmogorov model and Rytov approximation theory, a propagation model of Bessel-Gaussian vortex beams (BGVB) propagating in a subway tunnel is derived. Based on the propagation model, a model of orbital angular momentum (OAM) mode probability distribution is established to evaluate the propagation performance when the beam propagates along both longitudinal and transverse directions in the subway tunnel. By numerical simulations and experimental verifications, the influences of the various parameters of BGVB and turbulence on the OAM mode probability distribution are evaluated, and the results of simulations are consistent with the experimental statistics. The results verify that the middle area of turbulence is more beneficial for the vortex beam propagation than the edge; when the BGVB propagates along the longitudinal direction in the subway tunnel, the effects of turbulence on the OAM mode probability distribution can be decreased by selecting a larger anisotropy parameter, smaller coherence length, larger non-Kolmogorov power spectrum coefficient, smaller topological charge number, deeper subway tunnel, lower train speed, and longer wavelength. When the BGVB propagates along the transverse direction, the influences can be also mitigated by adopting a larger topological charge number, less non-Kolmogorov power spectrum coefficient, smaller refractive structure index, shorter wavelength, and shorter propagation distance.

  12. Ultrahigh-sensitive multimode interference-based fiber optic liquid-level sensor realized using illuminating zero-order Bessel-Gauss beam

    Science.gov (United States)

    Saha, Ardhendu; Datta, Arijit; Kaman, Surjit

    2018-03-01

    A proposal toward the enhancement in the sensitivity of a multimode interference-based fiber optic liquid-level sensor is explored analytically using a zero-order Bessel-Gauss (BG) beam as the input source. The sensor head consists of a suitable length of no-core fiber (NCF) sandwiched between two specialty high-order mode fibers. The coupling efficiency of various order modes inside the sensor structure is assessed using guided-mode propagation analysis and the performance of the proposed sensor has been benchmarked against the conventional sensor using a Gaussian beam. Furthermore, the study has been corroborated using a finite-difference beam propagation method in Lumerical's Mode Solutions software to investigate the propagation of the zero-order BG beam inside the sensor structure. Based on the simulation outcomes, the proposed scheme yields a maximum absolute sensitivity of up to 3.551 dB / mm and a sensing resolution of 2.816 × 10 - 3 mm through the choice of an appropriate length of NCF at an operating wavelength of 1.55 μm. Owing to this superior sensing performance, the reported sensing technology expedites an avenue to devise a high-performance fiber optic-level sensor that finds profound implication in different physical, biological, and chemical sensing purposes.

  13. Multiple zeta functions and double wrapping in planar N=4 SYM

    Science.gov (United States)

    Leurent, Sébastien; Volin, Dmytro

    2013-10-01

    Using the FiNLIE solution of the AdS/CFT Y-system, we compute the anomalous dimension of the Konishi operator in planar N=4 SYM up to eight loops, i.e. up to the leading double wrapping order. At this order a non-reducible Euler-Zagier sum, ζ1,2,8, appears for the first time. We find that at all orders in perturbation, every spectral-dependent quantity of the Y-system is expressed through multiple Hurwitz zeta functions, hence we provide a Mathematica package to manipulate these functions, including the particular case of Euler-Zagier sums. Furthermore, we conjecture that only Euler-Zagier sums can appear in the answer for the anomalous dimension at any order in perturbation theory. We also resum the leading transcendentality terms of the anomalous dimension at all orders, obtaining a simple result in terms of Bessel functions. Finally, we demonstrate that exact Bethe equations should be related to an absence of poles condition that becomes especially non-trivial at double wrapping.

  14. Analytic properties for the honeycomb lattice Green function at the origin

    Science.gov (United States)

    Joyce, G. S.

    2018-05-01

    The analytic properties of the honeycomb lattice Green function are investigated, where is a complex variable which lies in a plane. This double integral defines a single-valued analytic function provided that a cut is made along the real axis from w  =  ‑3 to . In order to analyse the behaviour of along the edges of the cut it is convenient to define the limit function where . It is shown that and can be evaluated exactly for all in terms of various hypergeometric functions, where the argument function is always real-valued and rational. The second-order linear Fuchsian differential equation satisfied by is also used to derive series expansions for and which are valid in the neighbourhood of the regular singular points and . Integral representations are established for and , where with . In particular, it is proved that where J 0(z) and Y 0(z) denote Bessel functions of the first and second kind, respectively. The results derived in the paper are utilized to evaluate the associated logarithmic integral where w lies in the cut plane. A new set of orthogonal polynomials which are connected with the honeycomb lattice Green function are also briefly discussed. Finally, a link between and the theory of Pearson random walks in a plane is established.

  15. Correlation functions of the Ising model and the eight-vertex model

    International Nuclear Information System (INIS)

    Ko, L.F.

    1986-01-01

    Calculations for the two-point correlation functions in the scaling limit for two statistical models are presented. In Part I, the Ising model with a linear defect is studied for T T/sub c/. The transfer matrix method of Onsager and Kaufman is used. The energy-density correlation is given by functions related to the modified Bessel functions. The dispersion expansion for the spin-spin correlation functions are derived. The dominant behavior for large separations at T not equal to T/sub c/ is extracted. It is shown that these expansions lead to systems of Fredholm integral equations. In Part II, the electric correlation function of the eight-vertex model for T < T/sub c/ is studied. The eight vertex model decouples to two independent Ising models when the four spin coupling vanishes. To first order in the four-spin coupling, the electric correlation function is related to a three-point function of the Ising model. This relation is systematically investigated and the full dispersion expansion (to first order in four-spin coupling) is obtained. The results is a new kind of structure which, unlike those of many solvable models, is apparently not expressible in terms of linear integral equations

  16. Independent trapping and manipulation of microparticles using dexterous acoustic tweezers

    International Nuclear Information System (INIS)

    Courtney, Charles R. P.; Demore, Christine E. M.; Wu, Hongxiao; Cochran, Sandy; Grinenko, Alon; Wilcox, Paul D.; Drinkwater, Bruce W.

    2014-01-01

    An electronically controlled acoustic tweezer was used to demonstrate two acoustic manipulation phenomena: superposition of Bessel functions to allow independent manipulation of multiple particles and the use of higher-order Bessel functions to trap particles in larger regions than is possible with first-order traps. The acoustic tweezers consist of a circular 64-element ultrasonic array operating at 2.35 MHz which generates ultrasonic pressure fields in a millimeter-scale fluid-filled chamber. The manipulation capabilities were demonstrated experimentally with 45 and 90-μm-diameter polystyrene spheres. These capabilities bring the dexterity of acoustic tweezers substantially closer to that of optical tweezers

  17. Mathematics in physics and engineering

    CERN Document Server

    Irving, J; Massey, H S W; Brueckner, Keith A

    1959-01-01

    Mathematics in Physics and Engineering describes the analytical and numerical (desk-machine) methods that arise in pure and applied science, including wave equations, Bessel and Legendre functions, and matrices. The manuscript first discusses partial differential equations, as well as the method of separation of variables, three-dimensional wave equation, diffusion or heat flow equation, and wave equation in plane and cylindrical polar coordinates. The text also ponders on Frobenius' and other methods of solution. Discussions focus on hypergeometric equation, Bessel's equation, confluent hyper

  18. Calculation of the dielectric tensor for a generalized Lorentzian (kappa) distribution function

    International Nuclear Information System (INIS)

    Summers, D.; Xue, S.; Thorne, R.M.

    1994-01-01

    Expressions are derived for the elements of the dielectric tensor for linear waves propagating at an arbitrary angle to a uniform magnetic field in a fully hot plasma whose constituent particle species σ are modeled by generalized Lorentzian distribution functions. The expressions involve readily computable single integrals whose integrands involve only elementary functions, Bessel functions, and modified plasma dispersion functions, the latter being available in the form of finite algebraic series. Analytical forms for the integrals are derived in the limits λ→0 and λ→∞, where λ=(k perpendicular ρ Lσ ) 2 /2, with k perpendicular the component of wave vector perpendicular to the ambient magnetic field, and ρ Lσ the Larmor radius for the particle species σ. Consideration is given to the important limits of wave propagation parallel and perpendicular to the ambient magnetic field, and also to the cold plasma limit. Since most space plasmas are well modeled by generalized Lorentzian particle distribution functions, the results obtained in this paper provide a powerful tool for analyzing kinetic (micro-) instabilities in space plasmas in a very general context, limited only by the assumptions of linear plasma theory

  19. Simulated Galactic methanol maser distribution to constrain Milky Way parameters

    Science.gov (United States)

    Quiroga-Nuñez, L. H.; van Langevelde, H. J.; Reid, M. J.; Green, J. A.

    2017-08-01

    Context. Using trigonometric parallaxes and proper motions of masers associated with massive young stars, the Bar and Spiral Structure Legacy (BeSSeL) survey has reported the most accurate values of the Galactic parameters so far. The determination of these parameters with high accuracy has a widespread impact on Galactic and extragalactic measurements. Aims: This research is aimed at establishing the confidence with which such parameters can be determined. This is relevant for the data published in the context of the BeSSeL survey collaboration, but also for future observations, in particular from the southern hemisphere. In addition, some astrophysical properties of the masers can be constrained, notably the luminosity function. Methods: We have simulated the population of maser-bearing young stars associated with Galactic spiral structure, generating several samples and comparing them with the observed samples used in the BeSSeL survey. Consequently, we checked the determination of Galactic parameters for observational biases introduced by the sample selection. Results: Galactic parameters obtained by the BeSSeL survey do not seem to be biased by the sample selection used. In fact, the published error estimates appear to be conservative for most of the parameters. We show that future BeSSeL data and future observations with southern arrays will improve the Galactic parameters estimates and smoothly reduce their mutual correlation. Moreover, by modeling future parallax data with larger distance values and, thus, greater relative uncertainties for a larger numbers of sources, we found that parallax-distance biasing is an important issue. Hence, using fractional parallax uncertainty in the weighting of the motion data is imperative. Finally, the luminosity function for 6.7 GHz methanol masers was determined, allowing us to estimate the number of Galactic methanol masers.

  20. Linear Analytical Solutions of Mechanical Sensitivity in Large Deflection of Unsymmetrically Layered Piezoelectric Plate under Pretension

    Directory of Open Access Journals (Sweden)

    Chun-Fu Chen

    2014-03-01

    Full Text Available Linear analytical study on the mechanical sensitivity in large deflection of unsymmetrically layered and laterally loaded piezoelectric plate under pretension is conducted. von Karman plate theory for large deflection is utilized but extended to the case of an unsymmetrically layered plate embedded with a piezoelectric layer. The governing equations thus obtained are simplified by omitting the arising nonlinear terms, yielding a Bessel or modified Bessel equation for the lateral slope. Depending on the relative magnitude of the piezoelectric effect, for both cases, analytical solutions of various geometrical responses are developed and formulated via Bessel and modified Bessel functions. The associated ultimate radial stresses are further derived following lamina constitutive law to evaluate the mechanical sensitivity of the considered plate. For a nearly monolithic plate under a very low applied voltage, the results are in good agreement with those for a single-layered case due to pure mechanical load available in literature, and thus the present approach is checked. For a two-layered unsymmetric plate made of typical silicon-based materials, a sound piezoelectric effect is illustrated particularly in a low pretension condition.

  1. Negative values of quasidistributions and quantum wave and number statistics

    Science.gov (United States)

    Peřina, J.; Křepelka, J.

    2018-04-01

    We consider nonclassical wave and number quantum statistics, and perform a decomposition of quasidistributions for nonlinear optical down-conversion processes using Bessel functions. We show that negative values of the quasidistribution do not directly represent probabilities; however, they directly influence measurable number statistics. Negative terms in the decomposition related to the nonclassical behavior with negative amplitudes of probability can be interpreted as positive amplitudes of probability in the negative orthogonal Bessel basis, whereas positive amplitudes of probability in the positive basis describe classical cases. However, probabilities are positive in all cases, including negative values of quasidistributions. Negative and positive contributions of decompositions to quasidistributions are estimated. The approach can be adapted to quantum coherence functions.

  2. Application of the exact solution for scattering by an infinite cylinder to the estimation of scattering by a finite cylinder.

    Science.gov (United States)

    Wang, R T; van de Hulst, H C

    1995-05-20

    A new algorithm for cylindrical Bessel functions that is similar to the one for spherical Bessel functions allows us to compute scattering functions for infinitely long cylinders covering sizes ka = 2πa/λ up to 8000 through the use of only an eight-digit single-precision machine computation. The scattering function and complex extinction coefficient of a finite cylinder that is seen near perpendicular incidence are derived from those of an infinitely long cylinder by the use of Huygens's principle. The result, which contains no arbitrary normalization factor, agrees quite well with analog microwave measurements of both extinction and scattering for such cylinders, even for an aspect ratio p = l/(2a) as low as 2. Rainbows produced by cylinders are similar to those for spherical drops but are brighter and have a lower contrast.

  3. New Explicit Solutions of (1 + 1)-Dimensional Variable-Coefficient Broer-Kaup System

    International Nuclear Information System (INIS)

    Yan Zhilian; Zhou Jianping

    2010-01-01

    By using the compatibility method, many explicit solutions of the (1 + 1)-dimensional variable-coefficient Broer-Kaup system are constructed, which include new solutions expressed by error function, Bessel function, exponential function, and Airy function. Some figures of the solutions are given by the symbolic computation system Maple. (general)

  4. Efficient evaluation of angular power spectra and bispectra

    Science.gov (United States)

    Assassi, Valentin; Simonović, Marko; Zaldarriaga, Matias

    2017-11-01

    Angular statistics of cosmological observables are hard to compute. The main difficulty is due to the presence of highly-oscillatory Bessel functions which need to be integrated over. In this paper, we provide a simple and fast method to compute the angular power spectrum and bispectrum of any observable. The method is based on using an FFTlog algorithm to decompose the momentum-space statistics onto a basis of power-law functions. For each power law, the integrals over Bessel functions have a simple analytical solution. This allows us to efficiently evaluate these integrals, independently of the value of the multipole l. In particular, this method significantly speeds up the evaluation of the angular bispectrum compared to existing methods. To illustrate our algorithm, we compute the galaxy, lensing and CMB temperature angular power spectrum and bispectrum.

  5. Proceedings – Mathematical Sciences | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    Positive Integer Solutions of Certain Diophantine Equations ... Codismantlability and projective dimension of the Stanley-Reisner ring of special .... Cross-product of bessel functions: monotonicity patterns and functional inequalities∗ ..... Root and Critical Point Behaviors of Certain Sums of Polynomials ..... Current Issue : Vol.

  6. Download this PDF file

    African Journals Online (AJOL)

    user

    In the paper it will be shown that generating functions of hyper Bessel functions due to Humbert and Delerue can be extended to a new class of generating relations for generalized Mittag-Leffler's functions. A number of new and known double and multiple generating functions involving the product of classical polynomials ...

  7. Inducing magneto-electric response in topological insulator

    International Nuclear Information System (INIS)

    Zeng, Lunwu; Song, Runxia; Zeng, Jing

    2013-01-01

    Utilizing electric potential and magnetic scalar potential formulas, which contain zero-order Bessel functions of the first kind and the constitutive relations of topological insulators, we obtained the induced magnetic scalar potentials and induced magnetic monopole charges which are induced by a point charge in topological insulators. The results show that infinite image magnetic monopole charges are generated by a point electric charge. The magnitude of the induced magnetic monopole charges are determined not only by the point electric charge, but also by the material parameters. - Highlights: ► Electric potential and magnetic scalar potential which contain zero-order Bessel function of the first kind were derived. ► Boundary conditions of topological insulator were built. ► Induced monopole charges were worked out.

  8. Special relativity and the Karhunen-Loeve expansion of Brownian motion

    International Nuclear Information System (INIS)

    Maccone, C.

    1987-01-01

    The connection between special relativity and the theory of the time-rescaled Gaussian stochastic processes is brought to light. It is given the general expression of the Karhunen-Loewe expansion for the Brownian motion whose variable is the proper time. The relevant eigenfunctions are proved to be Bessel functions, and their stability is discussed. The eigenvalues are shown to be the zeros of certain linear combinations of the Bessel functions and their partials. The energy distribution of such a class of processes is investigated, and it is given explicit formulae for both its mean value and variance. Finally it is studied in detail the Karhumen-Loeve expansion for a case of relativistic decelerated motion whose analysis is feasible in closed form

  9. bessel functions for axisymmetric elasticity problems of the elastic

    African Journals Online (AJOL)

    HOD

    2, 3DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF NIGERIA, NSUKKA. ENUGU STATE. ... theory of elasticity and in the case of vertical applied loads, was first ... partial differential equations in bodies having cylindrical symmetry.

  10. App. 1. Fourier series and Fourier transform

    International Nuclear Information System (INIS)

    Anon.

    1977-01-01

    Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr

  11. On computation and use of Fourier coefficients for associated Legendre functions

    Science.gov (United States)

    Gruber, Christian; Abrykosov, Oleh

    2016-06-01

    The computation of spherical harmonic series in very high resolution is known to be delicate in terms of performance and numerical stability. A major problem is to keep results inside a numerical range of the used data type during calculations as under-/overflow arises. Extended data types are currently not desirable since the arithmetic complexity will grow exponentially with higher resolution levels. If the associated Legendre functions are computed in the spectral domain, then regular grid transformations can be applied to be highly efficient and convenient for derived quantities as well. In this article, we compare three recursive computations of the associated Legendre functions as trigonometric series, thereby ensuring a defined numerical range for each constituent wave number, separately. The results to a high degree and order show the numerical strength of the proposed method. First, the evaluation of Fourier coefficients of the associated Legendre functions has been done with respect to the floating-point precision requirements. Secondly, the numerical accuracy in the cases of standard double and long double precision arithmetic is demonstrated. Following Bessel's inequality the obtained accuracy estimates of the Fourier coefficients are directly transferable to the associated Legendre functions themselves and to derived functionals as well. Therefore, they can provide an essential insight to modern geodetic applications that depend on efficient spherical harmonic analysis and synthesis beyond [5~× ~5] arcmin resolution.

  12. A summation formula over the zeros of a combination of the associated Legendre functions with a physical application

    International Nuclear Information System (INIS)

    Saharian, A A

    2009-01-01

    By using the generalized Abel-Plana formula, we derive a summation formula for the series over the zeros of a combination of the associated Legendre functions with respect to the degree. The summation formula for the series over the zeros of the combination of the Bessel functions, previously discussed in the literature, is obtained as a limiting case. As an application we evaluate the Wightman function for a scalar field with a general curvature coupling parameter in the region between concentric spherical shells on a background of constant negative curvature space. For the Dirichlet boundary conditions the corresponding mode-sum contains the series over the zeros of the combination of the associated Legendre functions. The application of the summation formula allows us to present the Wightman function in the form of the sum of two integrals. The first one corresponds to the Wightman function for the geometry of a single spherical shell and the second one is induced by the presence of the second shell. The boundary-induced part in the vacuum expectation value of the field squared is investigated. For points away from the boundaries the corresponding renormalization procedure is reduced to that for the boundary-free part.

  13. Pole magnetyczne we wsadzie rurowym nagrzewanym indukcyjnie od wewnatrz

    Czech Academy of Sciences Publication Activity Database

    Piatek, Z.; Doležel, Ivo; Baron, B.

    2005-01-01

    Roč. 81, č. 6 (2005), s. 48-51 ISSN 0033-2097 Institutional research plan: CEZ:AV0Z20570509 Keywords : induction heating * electromagnetic field * Bessel functions Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering

  14. Electromagnetic wave propagation in relativistic magnetized plasmas

    International Nuclear Information System (INIS)

    Weiss, I.

    1985-01-01

    An improved mathematical technique and a new code for deriving the conductivity tensor for collisionless plasmas have been developed. The method is applicable to a very general case, including both hot (relativistic) and cold magnetized plasmas, with only isotropic equilibrium distributions being considered here. The usual derivation starts from the relativistic Vlasov equation and leads to an integration over an infinite sum of Bessel functions which has to be done numerically. In the new solution the integration is carried out over a product of two Bessel functions only. This reduces the computing time very significantly. An added advantage over existing codes is our capability to perform the computations for waves propagating obliquely to the magnetic field. Both improvements greatly facilitate investigations of properties of the plasma under conditions hitherto unexplored

  15. Analytical solutions to the electromagnetic field in a cylindrical shell excited by external axial current

    International Nuclear Information System (INIS)

    Jing, Wu; Chun-Yan, Xiao

    2010-01-01

    The solutions to the electromagnetic field excited by a long axial current outside a conductive and magnetic cylindrical shell of finite length are studied in this paper. The more accurate analytical solutions are obtained by solving the proper boundary value problems by the separation variable method. Then the solutions are simplified according to asymptotic formulas of Bessel functions. Compared with the accurate solutions, the simplified solutions do not contain the Bessel functions and the inverse operation of the singular matrix, and can be calculated out fast by computers. The simplified solutions are more suitable for the cylindrical shell of high permeability and conductivity excited by a high frequency source. Both of the numerical results and the physical experimental results validate the simplified solutions obtained. (classical areas of phenomenology)

  16. Inducing magneto-electric response in topological insulator

    Energy Technology Data Exchange (ETDEWEB)

    Zeng, Lunwu, E-mail: 163.sin@163.com [Jiangsu Key Laboratory for Intelligent Agricultural Equipment, College of Engineering, Nanjing Agricultural University, Nanjing 210031 (China); Song, Runxia [Jiangsu Key Laboratory for Intelligent Agricultural Equipment, College of Engineering, Nanjing Agricultural University, Nanjing 210031 (China); Zeng, Jing [Faculty of Business and Economics, Macquarie University, NSW 2122 (Australia)

    2013-02-15

    Utilizing electric potential and magnetic scalar potential formulas, which contain zero-order Bessel functions of the first kind and the constitutive relations of topological insulators, we obtained the induced magnetic scalar potentials and induced magnetic monopole charges which are induced by a point charge in topological insulators. The results show that infinite image magnetic monopole charges are generated by a point electric charge. The magnitude of the induced magnetic monopole charges are determined not only by the point electric charge, but also by the material parameters. - Highlights: Black-Right-Pointing-Pointer Electric potential and magnetic scalar potential which contain zero-order Bessel function of the first kind were derived. Black-Right-Pointing-Pointer Boundary conditions of topological insulator were built. Black-Right-Pointing-Pointer Induced monopole charges were worked out.

  17. 3D galaxy clustering with future wide-field surveys: Advantages of a spherical Fourier-Bessel analysis

    Science.gov (United States)

    Lanusse, F.; Rassat, A.; Starck, J.-L.

    2015-06-01

    Context. Upcoming spectroscopic galaxy surveys are extremely promising to help in addressing the major challenges of cosmology, in particular in understanding the nature of the dark universe. The strength of these surveys, naturally described in spherical geometry, comes from their unprecedented depth and width, but an optimal extraction of their three-dimensional information is of utmost importance to best constrain the properties of the dark universe. Aims: Although there is theoretical motivation and novel tools to explore these surveys using the 3D spherical Fourier-Bessel (SFB) power spectrum of galaxy number counts Cℓ(k,k'), most survey optimisations and forecasts are based on the tomographic spherical harmonics power spectrum C(ij)_ℓ. The goal of this paper is to perform a new investigation of the information that can be extracted from these two analyses in the context of planned stage IV wide-field galaxy surveys. Methods: We compared tomographic and 3D SFB techniques by comparing the forecast cosmological parameter constraints obtained from a Fisher analysis. The comparison was made possible by careful and coherent treatment of non-linear scales in the two analyses, which makes this study the first to compare 3D SFB and tomographic constraints on an equal footing. Nuisance parameters related to a scale- and redshift-dependent galaxy bias were also included in the computation of the 3D SFB and tomographic power spectra for the first time. Results: Tomographic and 3D SFB methods can recover similar constraints in the absence of systematics. This requires choosing an optimal number of redshift bins for the tomographic analysis, which we computed to be N = 26 for zmed ≃ 0.4, N = 30 for zmed ≃ 1.0, and N = 42 for zmed ≃ 1.7. When marginalising over nuisance parameters related to the galaxy bias, the forecast 3D SFB constraints are less affected by this source of systematics than the tomographic constraints. In addition, the rate of increase of the

  18. Dynamic behaviour of non-uniform Bernoulli-Euler beams subjected ...

    African Journals Online (AJOL)

    This paper investigates the dynamics behaviour of non-uniform Bernoulli-Euler beams subjected to concentrated loads ravelling at variable velocities. The solution technique is based on the Generalized Galerkin Method and the use of the generating function of the Bessel function type. The results show that, for all the ...

  19. Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers

    Science.gov (United States)

    Moon, H.; Donderici, B.; Teixeira, F. L.

    2016-11-01

    We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and conductivity) with uniaxial anisotropy. Analytical expressions are obtained based on the spectral representation of the tensor Green's function based on cylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxial media. Due to the poor scaling of these eigenfunctions for extreme arguments and/or orders, direct numerical evaluation of such expressions can produce numerical instability, i.e., underflow, overflow, and/or round-off errors under finite precision arithmetic. To circumvent these problems, we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain, to yield a robust algorithm for all parameter ranges. Numerical results are presented to illustrate the robustness of the formulation including cases of practical interest.

  20. Hereditary effects in eccentric compact binary inspirals to third post-Newtonian order

    Science.gov (United States)

    Loutrel, Nicholas; Yunes, Nicolás

    2017-02-01

    While there has been much success in understanding the orbital dynamics and gravitational wave emission of eccentric compact binaries in the post-Newtonian formalism, some problems still remain. The largest of these concerns hereditary effects: non-linear phenomena related to the scattering off of the background curved spacetime (tails) and to the generation of gravitational waves by gravitational waves (memory). Currently, these hereditary effects are only known numerically for arbitrary eccentricity through infinite sums of Bessel functions, with closed-form, analytic results only available in the small eccentricity limit. We here calculate, for the first time, closed-form, analytic expressions for all hereditary effects to third post-Newtonian order in binaries with arbitrary eccentricity. For the tails, we first asymptotically expand all Bessel functions in high eccentricity and find a superasymptotic series for each enhancement factor, accurate to better than 10-3 relative to post-Newtonian numerical calculations at all eccentricities. We further improve the small-eccentricity behavior of the superasymptotic series by generating hyperasymptotic expressions for each enhancement factor, typically accurate to better than 10-8 at all eccentricities. For the memory, we discuss its computation within the context of an osculating approximation of the binary’s orbit and the difficulties that arise. Our closed-form analytic expressions for the hereditary fluxes allow us to numerically compute orbital phases that are identical to those found using an infinite sum of Bessel functions to double numerical precision.

  1. Hereditary effects in eccentric compact binary inspirals to third post-Newtonian order

    International Nuclear Information System (INIS)

    Loutrel, Nicholas; Yunes, Nicolás

    2017-01-01

    While there has been much success in understanding the orbital dynamics and gravitational wave emission of eccentric compact binaries in the post-Newtonian formalism, some problems still remain. The largest of these concerns hereditary effects: non-linear phenomena related to the scattering off of the background curved spacetime (tails) and to the generation of gravitational waves by gravitational waves (memory). Currently, these hereditary effects are only known numerically for arbitrary eccentricity through infinite sums of Bessel functions, with closed-form, analytic results only available in the small eccentricity limit. We here calculate, for the first time, closed-form, analytic expressions for all hereditary effects to third post-Newtonian order in binaries with arbitrary eccentricity. For the tails, we first asymptotically expand all Bessel functions in high eccentricity and find a superasymptotic series for each enhancement factor, accurate to better than 10 −3 relative to post-Newtonian numerical calculations at all eccentricities. We further improve the small-eccentricity behavior of the superasymptotic series by generating hyperasymptotic expressions for each enhancement factor, typically accurate to better than 10 −8 at all eccentricities. For the memory, we discuss its computation within the context of an osculating approximation of the binary’s orbit and the difficulties that arise. Our closed-form analytic expressions for the hereditary fluxes allow us to numerically compute orbital phases that are identical to those found using an infinite sum of Bessel functions to double numerical precision. (paper)

  2. Reconfigurable Optical Elements Based on Single and Coupled Microdisk Resonators with Quantum Dot Active Media

    Science.gov (United States)

    2009-08-31

    nO * nd * R * BesselY [m - 2 , ReK * nO * R] - 2 * (m * nO + nd 2 * m * nd) * BesselY [m - 1, ReK* nO * R] ) + (4 * mA2 * (nO - nd) + ReKA2 *nO...m*nO + k* mA2 *nd + ReKA3 * nO * ndA2 * RA2) * BesselJ[m, ReK* nd * R]) * BesselY[m, k * nO * R]) ; A- 7 startRe= ReK; startlm = ImK / glmK , If

  3. On the JWKB solution of the uniformly lengthening pendulum via ...

    Indian Academy of Sciences (India)

    2016-12-24

    Dec 24, 2016 ... a quantization rule regarding the experimental LP parameters is being determined. .... Here, the smallness of ϵ controls the required ...... The graphs of the exact and JWKB-approximated Bessel functions of the first order of ...

  4. Theoretical analysis of nuclear reactors (Phase II), I-V, Part V, Determining the fine neutron flux distribution by Pn method

    International Nuclear Information System (INIS)

    Pop-Jordanov, J.

    1962-10-01

    Expression for spherical harmonic moments were applied. They were obtained by spherical harmonics expansion of monoenergetic transport equation. This report presents the procedure for calculating the neutron flux distribution in the nine-zone reactor cell of the RA reactor in Vinca. The procedure was modelled for digital computer ZUSE Z-23 by expansion of the diagram of the automated P 3 code, which is adequate for P n code with minor changes. The needed subroutines were developed. The most important ones were those for modified first and second order Bessel functions of n-th order. Computer Z-23 was operating only 15 hours during three months, and thus only the subroutines for modified Bessel functions could be tested and the obtained results were excellent. For the mentioned reason the neutron flux distribution will be calculated in the forthcoming period [sr

  5. Extended Nijboer-Zernike approach for the computation of optical point-spread functions.

    Science.gov (United States)

    Janssen, Augustus J E M

    2002-05-01

    New Bessel-series representations for the calculation of the diffraction integral are presented yielding the point-spread function of the optical system, as occurs in the Nijboer-Zernike theory of aberrations. In this analysis one can allow an arbitrary aberration and a defocus part. The representations are presented in full detail for the cases of coma and astigmatism. The analysis leads to stably converging results in the case of large aberration or defocus values, while the applicability of the original Nijboer-Zernike theory is limited mainly to wave-front deviations well below the value of one wavelength. Because of its intrinsic speed, the analysis is well suited to supplement or to replace numerical calculations that are currently used in the fields of (scanning) microscopy, lithography, and astronomy. In a companion paper [J. Opt. Soc. Am. A 19, 860 (2002)], physical interpretations and applications in a lithographic context are presented, a convergence analysis is given, and a comparison is made with results obtained by using a numerical package.

  6. The algorithms for calculating synthetic seismograms from a dipole source using the derivatives of Green's function

    Science.gov (United States)

    Pavlov, V. M.

    2017-07-01

    The problem of calculating complete synthetic seismograms from a point dipole with an arbitrary seismic moment tensor in a plane parallel medium composed of homogeneous elastic isotropic layers is considered. It is established that the solutions of the system of ordinary differential equations for the motion-stress vector have a reciprocity property, which allows obtaining a compact formula for the derivative of the motion vector with respect to the source depth. The reciprocity theorem for Green's functions with respect to the interchange of the source and receiver is obtained for a medium with cylindrical boundary. The differentiation of Green's functions with respect to the coordinates of the source leads to the same calculation formulas as the algorithm developed in the previous work (Pavlov, 2013). A new algorithm appears when the derivatives with respect to the horizontal coordinates of the source is replaced by the derivatives with respect to the horizontal coordinates of the receiver (with the minus sign). This algorithm is more transparent, compact, and economic than the previous one. It requires calculating the wavenumbers associated with Bessel function's roots of order 0 and order 1, whereas the previous algorithm additionally requires the second order roots.

  7. Measurement of the presampled two-dimensional modulation transfer function of digital imaging systems

    International Nuclear Information System (INIS)

    Fetterly, Kenneth A.; Hangiandreou, Nicholas J.; Schueler, Beth A.; Ritenour, E. Russell

    2002-01-01

    The purpose of this work was to develop methods to measure the presampled two-dimensional modulation transfer function (2D MTF) of digital imaging systems. A custom x-ray 'point source' phantom was created by machining 256 holes with diameter 0.107 mm through a 0.5-mm-thick copper plate. The phantom was imaged several times, resulting in many images of individual x-ray 'spots'. The center of each spot (with respect to the pixel matrix) was determined to subpixel accuracy by fitting each spot to a 2D Gaussian function. The subpixel spot center locations were used to create a 5x oversampled system point spread function (PSF), which characterizes the optical and electrical properties of the system and is independent of the pixel sampling of the original image. The modulus of the Fourier transform of the PSF was calculated. Next, the Fourier function was normalized to the zero frequency value. Finally, the Fourier transform function was divided by the first-order Bessel function that defined the frequency content of the holes, resulting in the presampled 2D MTF. The presampled 2D MTF of a 0.1 mm pixel pitch computed radiography system and 0.2 mm pixel pitch flat panel digital imaging system that utilized a cesium iodide scintillator was measured. Comparison of the axial components of the 2D MTF to one-dimensional MTF measurements acquired using an edge device method demonstrated that the two methods produced consistent results

  8. Least Square NUFFT Methods Applied to 2D and 3D Radially Encoded MR Image Reconstruction

    Science.gov (United States)

    Song, Jiayu; Liu, Qing H.; Gewalt, Sally L.; Cofer, Gary; Johnson, G. Allan

    2009-01-01

    Radially encoded MR imaging (MRI) has gained increasing attention in applications such as hyperpolarized gas imaging, contrast-enhanced MR angiography, and dynamic imaging, due to its motion insensitivity and improved artifact properties. However, since the technique collects k-space samples nonuniformly, multidimensional (especially 3D) radially sampled MRI image reconstruction is challenging. The balance between reconstruction accuracy and speed becomes critical when a large data set is processed. Kaiser-Bessel gridding reconstruction has been widely used for non-Cartesian reconstruction. The objective of this work is to provide an alternative reconstruction option in high dimensions with on-the-fly kernels calculation. The work develops general multi-dimensional least square nonuniform fast Fourier transform (LS-NUFFT) algorithms and incorporates them into a k-space simulation and image reconstruction framework. The method is then applied to reconstruct the radially encoded k-space, although the method addresses general nonuniformity and is applicable to any non-Cartesian patterns. Performance assessments are made by comparing the LS-NUFFT based method with the conventional Kaiser-Bessel gridding method for 2D and 3D radially encoded computer simulated phantoms and physically scanned phantoms. The results show that the LS-NUFFT reconstruction method has better accuracy-speed efficiency than the Kaiser-Bessel gridding method when the kernel weights are calculated on the fly. The accuracy of the LS-NUFFT method depends on the choice of scaling factor, and it is found that for a particular conventional kernel function, using its corresponding deapodization function as scaling factor and utilizing it into the LS-NUFFT framework has the potential to improve accuracy. When a cosine scaling factor is used, in particular, the LS-NUFFT method is faster than Kaiser-Bessel gridding method because of a quasi closed-form solution. The method is successfully applied to 2D and

  9. Nobelova cena na dosah - zapomenutý osud fyzika Vladimíra Vanda

    Czech Academy of Sciences Publication Activity Database

    Šolcová, A.; Křížek, Michal

    2008-01-01

    Roč. 53, č. 1 (2008), s. 7-21 ISSN 0032-2423 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : DNA * Fourier transform * Bessel functions Subject RIV: BA - General Mathematics

  10. Approximation theorems for modified Szasz-Mirakjan operators in polynomial weight spaces

    Directory of Open Access Journals (Sweden)

    Monika Herzog

    1999-05-01

    Full Text Available In this paper we will study properties of Szasz-Mirakjan type operators A_n^ν , B_n^ ν defined by modified Bessel function I_ν . We shall present theorems giving a degree of approximation for these operators.

  11. Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem

    Science.gov (United States)

    Ahn, Chi Young; Jeon, Kiwan; Park, Won-Kwang

    2015-06-01

    This study analyzes the well-known MUltiple SIgnal Classification (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so-called multi-static response matrix in limited-view inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic-TM polarization) and so on. Hence, we perform further research to analyze the MUSIC-type imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an infinite series of Bessel functions of integer order of the first kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identified structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition of range of incident and observation directions to apply MUSIC in the limited-view problem.

  12. Sound radiation quantities arising from a resilient circular radiator.

    Science.gov (United States)

    Aarts, Ronald M; Janssen, Augustus J E M

    2009-10-01

    Power series expansions in ka are derived for the pressure at the edge of a radiator, the reaction force on the radiator, and the total radiated power arising from a harmonically excited, resilient, flat, circular radiator of radius a in an infinite baffle. The velocity profiles on the radiator are either Stenzel functions (1-(sigma/a)2)n, with sigma the radial coordinate on the radiator, or linear combinations of Zernike functions Pn(2(sigma/a)2-1), with Pn the Legendre polynomial of degree n. Both sets of functions give rise, via King's integral for the pressure, to integrals for the quantities of interest involving the product of two Bessel functions. These integrals have a power series expansion and allow an expression in terms of Bessel functions of the first kind and Struve functions. Consequently, many of the results in [M. Greenspan, J. Acoust. Soc. Am. 65, 608-621 (1979)] are generalized and treated in a unified manner. A foreseen application is for loudspeakers. The relation between the radiated power in the near-field on one hand and in the far field on the other is highlighted.

  13. Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers

    Energy Technology Data Exchange (ETDEWEB)

    Moon, H., E-mail: haksu.moon@gmail.com [ElectroScience Laboratory, The Ohio State University, Columbus, OH 43212 (United States); Donderici, B., E-mail: burkay.donderici@halliburton.com [Sensor Physics & Technology, Halliburton Energy Services, Houston, TX 77032 (United States); Teixeira, F.L., E-mail: teixeira@ece.osu.edu [ElectroScience Laboratory, The Ohio State University, Columbus, OH 43212 (United States)

    2016-11-15

    We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and conductivity) with uniaxial anisotropy. Analytical expressions are obtained based on the spectral representation of the tensor Green's function based on cylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxial media. Due to the poor scaling of these eigenfunctions for extreme arguments and/or orders, direct numerical evaluation of such expressions can produce numerical instability, i.e., underflow, overflow, and/or round-off errors under finite precision arithmetic. To circumvent these problems, we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain, to yield a robust algorithm for all parameter ranges. Numerical results are presented to illustrate the robustness of the formulation including cases of practical interest.

  14. Untitled

    Indian Academy of Sciences (India)

    where c (t) is the characteristic function corresponding to the distribution law of x and k, the sth semi-invariant of x. These simple properties enable us to discover readily whether any distribution law satisfies M when a study of its moments and semi-invariants are made. Let us consider the Bessel function populations defined ...

  15. K correlations and facet models in diffuse scattering

    NARCIS (Netherlands)

    Hoenders, B.J.; Jakeman, E.; Baltes, H.P.; Steinle, B.

    1979-01-01

    The angular intensity distribution of radiation scattered by a wide range of random media can be accounted for by assuming effective source amplitude correlations involving modified Bessel functions Kv. We investigate how such correlations can be derived from physical models of stochastic scattering

  16. On an integral transform

    Directory of Open Access Journals (Sweden)

    D. Naylor

    1986-01-01

    Full Text Available This paper establishes properties of a convolution type integral transform whose kernel is a Macdonald type Bessel function of zero order. An inversion formula is developed and the transform is applied to obtain the solution of some related integral equations.

  17. Inverse transient thermoelastic deformations in thin circular plates

    Indian Academy of Sciences (India)

    Bessel's functions with the help of the integral transform technique. Thermoelastic deformations are discussed with the help of temperature and are illustrated numer- ically. Keywords. Inverse transient; thermoelastic deformation. 1. Introduction. The inverse thermoelastic problem consists of determination of the temperature, ...

  18. Acoustic Tweezing and Patterning of Concentration Fields in Microfluidics

    DEFF Research Database (Denmark)

    Karlsen, Jonas Tobias; Bruus, Henrik

    2017-01-01

    that weakly perturb the fluid density and speed of sound is presented and applied to study manipulation of concentration fields in rectangular-channel acoustic eigenmodes and in Bessel-function acoustic vortices. In the first example, methods to obtain horizontal and vertical multilayer stratification...

  19. Rapid expansion method (REM) for time‐stepping in reverse time migration (RTM)

    KAUST Repository

    Pestana, Reynam C.; Stoffa, Paul L.

    2009-01-01

    an analytical approximation for the Bessel function where we assume that the time step is sufficiently small. From this derivation we find that if we consider only the first two Chebyshev polynomials terms in the rapid expansion method we can obtain the second

  20. Extended Riemann-Liouville type fractional derivative operator with applications

    Directory of Open Access Journals (Sweden)

    Agarwal P.

    2017-12-01

    Full Text Available The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.

  1. Towards automated human gait disease classification using phase space representation of intrinsic mode functions

    Science.gov (United States)

    Pratiher, Sawon; Patra, Sayantani; Pratiher, Souvik

    2017-06-01

    A novel analytical methodology for segregating healthy and neurological disorders from gait patterns is proposed by employing a set of oscillating components called intrinsic mode functions (IMF's). These IMF's are generated by the Empirical Mode Decomposition of the gait time series and the Hilbert transformed analytic signal representation forms the complex plane trace of the elliptical shaped analytic IMFs. The area measure and the relative change in the centroid position of the polygon formed by the Convex Hull of these analytic IMF's are taken as the discriminative features. Classification accuracy of 79.31% with Ensemble learning based Adaboost classifier validates the adequacy of the proposed methodology for a computer aided diagnostic (CAD) system for gait pattern identification. Also, the efficacy of several potential biomarkers like Bandwidth of Amplitude Modulation and Frequency Modulation IMF's and it's Mean Frequency from the Fourier-Bessel expansion from each of these analytic IMF's has been discussed for its potency in diagnosis of gait pattern identification and classification.

  2. High-dimensional structured light coding/decoding for free-space optical communications free of obstructions.

    Science.gov (United States)

    Du, Jing; Wang, Jian

    2015-11-01

    Bessel beams carrying orbital angular momentum (OAM) with helical phase fronts exp(ilφ)(l=0;±1;±2;…), where φ is the azimuthal angle and l corresponds to the topological number, are orthogonal with each other. This feature of Bessel beams provides a new dimension to code/decode data information on the OAM state of light, and the theoretical infinity of topological number enables possible high-dimensional structured light coding/decoding for free-space optical communications. Moreover, Bessel beams are nondiffracting beams having the ability to recover by themselves in the face of obstructions, which is important for free-space optical communications relying on line-of-sight operation. By utilizing the OAM and nondiffracting characteristics of Bessel beams, we experimentally demonstrate 12 m distance obstruction-free optical m-ary coding/decoding using visible Bessel beams in a free-space optical communication system. We also study the bit error rate (BER) performance of hexadecimal and 32-ary coding/decoding based on Bessel beams with different topological numbers. After receiving 500 symbols at the receiver side, a zero BER of hexadecimal coding/decoding is observed when the obstruction is placed along the propagation path of light.

  3. A Robust Alternative to the Normal Distribution.

    Science.gov (United States)

    1982-07-07

    for any Purpose of the United States Governuent DEPARTMENT OF STATISTICS t -, STANFORD UIVERSITY I STANFORD, CALIFORNIA A Robust Alternative to the...Stanford University Technical Report No. 3. [5] Bhattacharya, S. K. (1966). A Modified Bessel Function lodel in Life Testing. Metrika 10, 133-144

  4. Hidden symmetry of the quantum Calogero-Moser system

    DEFF Research Database (Denmark)

    Kuzentsov, Vadim b

    1996-01-01

    The hidden symmetry of the quantum Calogero-Moser system with an inverse-square potential is algebraically demonstrated making use of Dunkl's operators. We find the underlying algebra explaining the super-integrability phenomenon for this system. Applications to related multi-variable Bessel...... functions are also discussed....

  5. Q 2-evolution of parton densities at small x values. Charm contribution in the combined H1 and ZEUS F 2 data

    Science.gov (United States)

    Kotikov, A. V.; Shaikhatdenov, B. G.

    2017-09-01

    The Bessel-inspired behavior of parton densities at small x, obtained in the case of the flat initial conditions for DGLAP evolution equations, is used in the fixed flavor scheme to analyze precise H1 and ZEUS combined data on the structure function F 2.

  6. A Fast Iterative Bayesian Inference Algorithm for Sparse Channel Estimation

    DEFF Research Database (Denmark)

    Pedersen, Niels Lovmand; Manchón, Carles Navarro; Fleury, Bernard Henri

    2013-01-01

    representation of the Bessel K probability density function; a highly efficient, fast iterative Bayesian inference method is then applied to the proposed model. The resulting estimator outperforms other state-of-the-art Bayesian and non-Bayesian estimators, either by yielding lower mean squared estimation error...

  7. Surface wave propagation in a double liquid layer over a liquid ...

    Indian Academy of Sciences (India)

    The frequency equation is derived for surface waves in a liquidsaturated porous half-space supporting a double layer, that of inhomogeneous and homogeneous liquids. Asymptotic approximations of Bessel functions are used for long and short wavelength cases. Certain other problems are discussed as special cases.

  8. Further comments on the geometrical efficiency of a parallel-disk source and detector system

    International Nuclear Information System (INIS)

    Ruby, L.

    1994-01-01

    A derivation is presented for a previously published formula, which determines the geometrical efficiency of a parallel-disk source and detector system. The formula involves an integral over a product of two Bessel functions. An algebraic approximation to the integral is also discussed. (orig.)

  9. On the Solution of Point-Source Problems Using Fourier Transform and FFT Routines

    Czech Academy of Sciences Publication Activity Database

    Šolín, Pavel

    2003-01-01

    Roč. 48, č. 3 (2003), s. 227-238 ISSN 0001-7043 R&D Projects: GA ČR GP102/01/D114 Institutional research plan: CEZ:AV0Z2057903 Keywords : Maxwells equations * Bessel equation * Hankel functions Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering

  10. Pochhammer symbol with negative indices. A new rule for the method of brackets

    Directory of Open Access Journals (Sweden)

    Gonzalez Ivan

    2016-01-01

    Full Text Available The method of brackets is a method of integration based upon a small number of heuristic rules. Some of these have been made rigorous. An example of an integral involving the Bessel function is used to motivate a new evaluation rule.

  11. Quantum systems with position-dependent mass and spin-orbit interaction via Rashba and Dresselhaus terms

    International Nuclear Information System (INIS)

    Schmidt, Alexandre G. M.; Portugal, L.; Jesus, Anderson L. de

    2015-01-01

    We consider a particle with spin 1/2 with position-dependent mass moving in a plane. Considering separately Rashba and Dresselhaus spin-orbit interactions, we write down the Hamiltonian for this problem and solve it for Dirichlet boundary conditions. Our radial wavefunctions have two contributions: homogeneous ones which are written as Bessel functions of non-integer orders—that depend on angular momentum m—and particular solutions which are obtained after decoupling the non-homogeneous system. In this process, we find non-homogeneous Bessel equation, Laguerre, as well as biconfluent Heun equation. We also present the probability densities for m = 0, 1, 2 in an annular quantum well. Our results indicate that the background as well as the spin-orbit interaction naturally splits the spinor components

  12. Quantum systems with position-dependent mass and spin-orbit interaction via Rashba and Dresselhaus terms

    Energy Technology Data Exchange (ETDEWEB)

    Schmidt, Alexandre G. M., E-mail: agmschmidt@gmail.com; Portugal, L., E-mail: liciniolportugal@gmail.com; Jesus, Anderson L. de [Departamento de Física do polo universitário de Volta Redonda, Instituto de Ciências Exatas—Universidade Federal Fluminense, R. Des. Ellis Hermydio Figueira, 783, Volta Redonda, RJ CEP 27215-350 (Brazil)

    2015-01-15

    We consider a particle with spin 1/2 with position-dependent mass moving in a plane. Considering separately Rashba and Dresselhaus spin-orbit interactions, we write down the Hamiltonian for this problem and solve it for Dirichlet boundary conditions. Our radial wavefunctions have two contributions: homogeneous ones which are written as Bessel functions of non-integer orders—that depend on angular momentum m—and particular solutions which are obtained after decoupling the non-homogeneous system. In this process, we find non-homogeneous Bessel equation, Laguerre, as well as biconfluent Heun equation. We also present the probability densities for m = 0, 1, 2 in an annular quantum well. Our results indicate that the background as well as the spin-orbit interaction naturally splits the spinor components.

  13. Untitled

    Indian Academy of Sciences (India)

    We have checked that the long range (u, wು) and short Tangರಿ (M, W) parts of the wavefunction match exactly at r = b. The functions I,(x) (n = 1/2, 3/25/2) appearing in the above expressions, are the. MOdified Spherical Bessel functions of Second kind, whereas K's are expressible as. linCar Combinations of Second and ...

  14. Surface wave propagation in a double liquid layer over a liquid ...

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Abstract. The frequency equation is derived for surface waves in a liquid- saturated porous half-space supporting a double layer, that of inhomogeneous and homogeneous liquids. Asymptotic approximations of Bessel functions are used for long and short wavelength cases. Certain other problems are discussed as spe-.

  15. The Shock and Vibration Digest. Volume 18, Number 6

    Science.gov (United States)

    1986-06-01

    linear, quadratic, or cubic. Bessel function Reed [124] reported a method for computing solutions were obtained for a truncated pyramid amplitudes of a...86-1198 A. Ragab, Chung C. Fu Seismic Analysis of a Large LMFBR with Flu- Cairo Univ., Giza , Egypt . . *. id-Structure Imteractions Computers Struc

  16. Nonperiodic inspections to guarantee a prescribed level of reliability

    NARCIS (Netherlands)

    Newby, M.J.; Barker, C.T.; Vonta, F.; Nikulin, M; Limnios, N.; Huber-Carol, C.

    2008-01-01

    A cost-optimal nonperiodic inspection policy is derived for complex multicomponent systems. The model takes into consideration the degradation of all the components in the system with the use of a Bessel process with drift. The inspection times are determined by a deterministic function and depend

  17. Simulation of 2D Waves in Circular Membrane Using Excel Spreadsheet with Visual Basic for Teaching Activity

    Science.gov (United States)

    Eso, R.; Safiuddin, L. O.; Agusu, L.; Arfa, L. M. R. F.

    2018-04-01

    We propose a teaching instrument demonstrating the circular membrane waves using the excel interactive spreadsheets with the Visual Basic for Application (VBA) programming. It is based on the analytic solution of circular membrane waves involving Bessel function. The vibration modes and frequencies are determined by using Bessel approximation and initial conditions. The 3D perspective based on the spreadsheets functions and facilities has been explored to show the 3D moving objects in transitional or rotational processes. This instrument is very useful both in teaching activity and learning process of wave physics. Visualizing of the vibration of waves in the circular membrane which is showing a very clear manner of m and n vibration modes of the wave in a certain frequency has been compared and matched to the experimental result using resonance method. The peak of deflection varies in time if the initial condition was working and have the same pattern with matlab simulation in zero initial velocity

  18. A Recursive Formula for the Evaluation of Earth Return Impedance on Buried Cables

    Directory of Open Access Journals (Sweden)

    Reynaldo Iracheta

    2015-09-01

    Full Text Available This paper presents an alternative solution based on infinite series for the accurate and efficient evaluation of cable earth return impedances. This method uses Wedepohl and Wilcox’s transformation to decompose Pollaczek’s integral in a set of Bessel functions and a definite integral. The main feature of Bessel functions is that they are easy to compute in modern mathematical software tools such as Matlab. The main contributions of this paper are the approximation of the definite integral by an infinite series, since it does not have analytical solution; and its numerical solution by means of a recursive formula. The accuracy and efficiency of this recursive formula is compared against the numerical integration method for a broad range of frequencies and cable  configurations. Finally, the proposed method is used as a subroutine for cable parameter calculation in the inverse Numerical Laplace Transform (NLT to obtain accurate transient responses in the time domain.

  19. Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire

    Science.gov (United States)

    Horing, Norman J. M.

    2017-06-01

    This work is concerned with the derivation of the Green's function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green's function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green's function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function). The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ (x ) -potential profile. This retarded Green's function for propagation directly along the wire is determined exactly in terms of the corresponding Green's function for the system without the δ (x ) -potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green's function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.

  20. Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire

    Directory of Open Access Journals (Sweden)

    Norman J. M. Horing

    2017-06-01

    Full Text Available This work is concerned with the derivation of the Green’s function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green’s function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green’s function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function. The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ(x-potential profile. This retarded Green’s function for propagation directly along the wire is determined exactly in terms of the corresponding Green’s function for the system without the δ(x-potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green’s function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.

  1. Classical Analysis of the Shear Vibration Characteristics of an ...

    African Journals Online (AJOL)

    For harmonic displacement response, it was found that the governing partial differential equation reduces to an ordinary differential equation of the Bessel type. This was then solved, subject to the boundary conditions, to obtain the modal shape functions and natural frequencies of vibration. The shear stress distribution ...

  2. Solving pure yang-mills theory in dimensions.

    Science.gov (United States)

    Leigh, Robert G; Minic, Djordje; Yelnikov, Alexandr

    2006-06-09

    We analytically compute the spectrum of the spin zero glueballs in the planar limit of pure Yang-Mills theory in 2 + 1 dimensions. The new ingredient is provided by our computation of a new nontrivial form of the ground state wave functional. The mass spectrum of the theory is determined by the zeroes of Bessel functions, and the agreement with large lattice data is excellent.

  3. Posn(R) and Eisenstein series

    CERN Document Server

    Jorgenson, Jay

    2005-01-01

    Posn(R) and Eisenstein Series provides an introduction, requiring minimal prerequisites, to the analysis on symmetric spaces of positive definite real matrices as well as quotients of this space by the unimodular group of integral matrices. The approach is presented in very classical terms and includes material on special functions, notably gamma and Bessel functions, and focuses on certain mathematical aspects of Eisenstein series.

  4. Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations

    International Nuclear Information System (INIS)

    Clarkson, Peter A

    2013-01-01

    We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations. It is shown that the coefficients in these recurrence relations can be expressed in terms of Wronskians of modified Bessel functions and confluent hypergeometric functions, respectively for the generalized Charlier and generalized Meixner polynomials. These Wronskians arise in the description of special function solutions of the third and fifth Painlevé equations. (paper)

  5. A spectral scheme for Kohn-Sham density functional theory of clusters

    Science.gov (United States)

    Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D.

    2015-04-01

    Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems - the plane-wave method - is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn-Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.

  6. Sadhana | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    ... 0 ≤ r ≤ a , − b / 2 ≤ z ≤ b / 2 . The expressions of unknown heating temperatures and temperature distributions are obtained in series form, involving Bessel's functions with the help of the integral transform technique. Thermoelastic deformations are discussed with the help of temperature and are illustrated numerically.

  7. Zeros of certain cross products of Bessel functions of fractional order

    Science.gov (United States)

    Rostafinski, W. A.

    1974-01-01

    Interpolation between values given in table of zeros is permitted provided curve is traced between at least three values from table. Zeros have been obtained on digital computer and results were rounded off to the fourth decimal point.

  8. Self-reconstruction of diffraction-free and accelerating laser beams in scattering media

    International Nuclear Information System (INIS)

    Ersoy, T.; Yalizay, B.; Akturk, S.

    2012-01-01

    We experimentally investigate propagation of laser beams with different intensity profiles in highly scattering media. We generate transverse laser amplitude profiles with Gaussian, Bessel and Airy function envelopes. We then propagate these beams through optical phantoms formed with variable density intralipid solutions. At the sample exit, we compare change in maximum intensities, as well as beam profile reconstruction. We show that self-reconstruction properties of Bessel and Airy beams bring about slower decrease in maximum intensity with increasing scatterer density. On the other hand, the beam profiles deteriorate faster, as compared to reference Gaussian beams. Slower decrease in the intensity can be attributed to the wavevector spectra providing a continuous flow of energy to the beam center, while beam deterioration is linked to total beam volume in the scattering medium. These results show that beam shaping methods can significantly enhance delivery of intense light deeper into turbid media, but this enhancement is compromised by stronger speckling of beam profiles. -- Highlights: ► We experimentally investigate propagation of shaped laser beams in turbid media. ► Peak intensity of Bessel and Airy beams decrease slower with increasing scatterer. ► Shaped beam profiles deteriorate faster, as compared to reference Gaussian beams. ► Shaped beam profiles can enhance applications of lasers inscattering media.

  9. A relationship between Gel'fand-Levitan and Marchenko kernels

    International Nuclear Information System (INIS)

    Kirst, T.; Von Geramb, H.V.; Amos, K.A.

    1989-01-01

    An integral equation which relates the output kernels of the Gel'fand-Levitan and Marchenko inverse scattering equations is specified. Structural details of this integral equation are studied when the S-matrix is a rational function, and the output kernels are separable in terms of Bessel, Hankel and Jost solutions. 4 refs

  10. Vacuum expectation value of twist fields

    Science.gov (United States)

    Belitsky, A. V.

    2017-09-01

    Twist fields emerge in a number of physical applications ranging from entanglement entropy to scattering amplitudes in four-dimensional gauge theories. In this work, their vacuum expectation values are studied in the path integral framework. By performing a gauge transformation, their correlation functions are reduced to field theory of matter fields in external Aharonov-Bohm vortices. The resulting functional determinants are then analyzed within the zeta-function regularization for the spectrum of Bessel zeros, and concise formulas are derived.

  11. Scattering of light and other electromagnetic radiation

    CERN Document Server

    Kerker, Milton

    1969-01-01

    The Scattering of Light and Other Electromagnetic Radiation discusses the theory of electromagnetic scattering and describes some practical applications. The book reviews electromagnetic waves, optics, the interrelationships of main physical quantities and the physical concepts of optics, including Maxwell's equations, polarization, geometrical optics, interference, and diffraction. The text explains the Rayleigh2 theory of scattering by small dielectric spheres, the Bessel functions, and the Legendre functions. The author also explains how the scattering functions for a homogenous sphere chan

  12. Torsional Vibrations of a Conic Shaft with Opposite Tapers Carrying Arbitrary Concentrated Elements

    Directory of Open Access Journals (Sweden)

    Jia-Jang Wu

    2013-01-01

    Full Text Available The purpose of this paper is to present the exact solution for free torsional vibrations of a linearly tapered circular shaft carrying a number of concentrated elements. First of all, the equation of motion for free torsional vibration of a conic shaft is transformed into a Bessel equation, and, based on which, the exact displacement function in terms of Bessel functions is obtained. Next, the equations for compatibility of deformations and equilibrium of torsional moments at each attaching point (including the shaft ends between the concentrated elements and the conic shaft with positive and negative tapers are derived. From the last equations, a characteristic equation of the form is obtained. Then, the natural frequencies of the torsional shaft are determined from the determinant equation , and, corresponding to each natural frequency, the column vector for the integration constants, , is obtained from the equation . Substitution of the last integration constants into the associated displacement functions gives the corresponding mode shape of the entire conic shaft. To confirm the reliability of the presented theory, all numerical results obtained from the exact method are compared with those obtained from the conventional finite element method (FEM and good agreement is achieved.

  13. Analytical model of contamination during the drying of cylinders of jamonable muscle

    Science.gov (United States)

    Montoya Arroyave, Isabel

    2014-05-01

    For a cylinder of jamonable muscle of radius R and length much greater than R; considering that the internal resistance to the transfer of water is much greater than the external and that the internal resistance is one certain function of the distance to the axis; the distribution of the punctual moisture in the jamonable cylinder is analytically computed in terms of the Bessel's functions. During the process of drying and salted the jamonable cylinder is sensitive to contaminate with bacterium and protozoa that come from the environment. An analytical model of contamination is presents using the diffusion equation with sources and sinks, which is solve by the method of the Laplace transform, the Bromwich integral, the residue theorem and some special functions like Bessel and Heun. The critical times intervals of drying and salted are computed in order to obtain the minimum possible contamination. It is assumed that both external moisture and contaminants decrease exponentially with time. Contaminants profiles are plotted and discussed some possible techniques of contaminants detection. All computations are executed using Computer Algebra, specifically Maple. It is said that the results are important for the food industry and it is suggested some future research lines.

  14. New analytical treatment for a kind of two dimensional integrals in ion-atom collisions

    International Nuclear Information System (INIS)

    Yang Qifeng; Kuang Yurang

    1994-01-01

    A kind of two-dimensional integrals, separated from two-center matrix elements in ion-atom collisions, is analytically integrated by introducing the Laplace transform into the integrals and expressed by the modified Bessel functions. The traditional Feynman transform is very complicated for this kind of more general integrals related to the excited state capture

  15. Introduction to partial differential equations from Fourier series to boundary-value problems

    CERN Document Server

    Broman, Arne

    2010-01-01

    This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.

  16. Computation of potentials from current electrodes in cylindrically stratified media: A stable, rescaled semi-analytical formulation

    Science.gov (United States)

    Moon, Haksu; Teixeira, Fernando L.; Donderici, Burkay

    2015-01-01

    We present an efficient and robust semi-analytical formulation to compute the electric potential due to arbitrary-located point electrodes in three-dimensional cylindrically stratified media, where the radial thickness and the medium resistivity of each cylindrical layer can vary by many orders of magnitude. A basic roadblock for robust potential computations in such scenarios is the poor scaling of modified-Bessel functions used for computation of the semi-analytical solution, for extreme arguments and/or orders. To accommodate this, we construct a set of rescaled versions of modified-Bessel functions, which avoids underflows and overflows in finite precision arithmetic, and minimizes round-off errors. In addition, several extrapolation methods are applied and compared to expedite the numerical evaluation of the (otherwise slowly convergent) associated Sommerfeld-type integrals. The proposed algorithm is verified in a number of scenarios relevant to geophysical exploration, but the general formulation presented is also applicable to other problems governed by Poisson equation such as Newtonian gravity, heat flow, and potential flow in fluid mechanics, involving cylindrically stratified environments.

  17. The magnetic particle in a box: Analytic and micromagnetic analysis of probe-localized spin wave modes

    Science.gov (United States)

    Adur, Rohan; Du, Chunhui; Manuilov, Sergei A.; Wang, Hailong; Yang, Fengyuan; Pelekhov, Denis V.; Hammel, P. Chris

    2015-05-01

    The dipole field from a probe magnet can be used to localize a discrete spectrum of standing spin wave modes in a continuous ferromagnetic thin film without lithographic modification to the film. Obtaining the resonance field for a localized mode is not trivial due to the effect of the confined and inhomogeneous magnetization precession. We compare the results of micromagnetic and analytic methods to find the resonance field of localized modes in a ferromagnetic thin film, and investigate the accuracy of these methods by comparing with a numerical minimization technique that assumes Bessel function modes with pinned boundary conditions. We find that the micromagnetic technique, while computationally more intensive, reveals that the true magnetization profiles of localized modes are similar to Bessel functions with gradually decaying dynamic magnetization at the mode edges. We also find that an analytic solution, which is simple to implement and computationally much faster than other methods, accurately describes the resonance field of localized modes when exchange fields are negligible, and demonstrating the accessibility of localized mode analysis.

  18. Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Degroote, M. [Rice Univ., Houston, TX (United States); Henderson, T. M. [Rice Univ., Houston, TX (United States); Zhao, J. [Rice Univ., Houston, TX (United States); Dukelsky, J. [Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Inst. de Estructura de la Materia; Scuseria, G. E. [Rice Univ., Houston, TX (United States)

    2018-01-03

    We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.

  19. Enhancement of single mode operation in coaxial optical waveguide using DB boundary conditions

    Science.gov (United States)

    Lohia, Pooja; Prajapati, Y.; Saini, J. P.; Rai, B. S.

    2014-11-01

    In this study, a competent numerical strategy to compute the dispersion of optical waveguides is presented and propagation of electromagnetic waves in a coaxial optical waveguide with DB boundary conditions is instigated. For this intend, cylindrical coordinates are here being used to derive the DB boundary conditions and to obtain field components for the modes. The propagation constant for the waveguide to be studied is determined by solving the Bessel and the modified Bessel functions. The cutoff frequencies for various lower order modes have been calculated and their dispersion characteristics are plotted correspondingly. The behavior of the coaxial optical waveguide under DB boundary conditions is shown to be significantly different from that of coaxial optical waveguide and conventional optical waveguide under traditional or tangential boundary conditions. Finally, the effect of waveguide dimensions on the mode cutoff frequencies and fabrication issues are also addressed.

  20. Fourier-like frames on locally compact abelian groups

    DEFF Research Database (Denmark)

    Christensen, Ole; Goh, Say Song

    2015-01-01

    We consider a class of functions, defined on a locally compact abelian group by letting a class of modulation operators act on a countable collection of functions. We derive sufficient conditions for such a class of functions to form a Bessel sequence or a frame and for two such systems to be dual...... frames. Explicit constructions are obtained via various generalizations of the classical B-splines to the setting of locally compact abelian groups. (C) 2014 Elsevier Inc. All rights reserved....