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...
Noncommutative Bessel symmetric functions
Novelli, Jean-Christophe; Thibon, Jean-Yves
2006-01-01
The consideration of tensor products of 0-Hecke algebra modules leads to natural analogs of the Bessel J-functions in the algebra of noncommutative symmetric functions. This provides a simple explanation of various combinatorial properties of Bessel functions.
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.
Conformable Fractional Bessel Equation and Bessel Functions
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.
Unified Bessel, Modified Bessel, Spherical Bessel and Bessel-Clifford Functions
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...
Some integrals involving Bessel functions
Glasser, M. Lawrence; Montaldi, Emilio
1993-01-01
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of products of three Bessel functions.
Cohomology and Bessel functions Theory
Mekhfi, Mustapha
2002-01-01
By studying cohomological quantum mechanics on the punctured plane,we were led to identify (reduced) Bessel functions with homotopic loops living on the plane.This identification led us to correspondence rules between exponentials and Bessel functions.The use of these rules makes us retrieve known but also new formulas in Bessel functions theory.
Rogov, V. -B. K.
2000-01-01
The modified q-Bessel functions and the q-Bessel-Macdonald functions of the first and second kind are introduced. Their definition is based on representations as power series. Recurrence relations, the q-Wronskians, asymptotic decompositions and q-integral representations are received. In addition, the q-Bessel-Macdonald function of kind 3 is determined by its q-integral representation.
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.
Generalized Bessel functions of the first kind
Baricz, Árpád
2010-01-01
In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. Our aim is to present interesting geometric properties and functional inequalities for these generalized Bessel functions. Moreover, we extend many known inequalities involving circular and hyperbolic functions to Bessel and modified Bessel functions.
A weak kernel formula for Bessel functions
Chai, Jingsong
2015-01-01
In this paper, we prove a weak kernel formula of Bessel functions attached to irreducible generic representations of p-adic $GL(n)$. As an application, we show that the Bessel function defined by Bessel distribution coincides with the Bessel function defined via uniqueness of Whittaker models on the open Bruhat cell.
Van der Corput inequalities for Bessel functions
Baricz, Árpád; Laforgia, Andrea; Pogány, Tibor K.
2014-01-01
In this note we offer some log-concavity properties of certain functions related to Bessel functions of the first kind and modified Bessel functions of the first and second kind, by solving partially a recent conjecture on the log-convexity/log-concavity properties for modified Bessel functions of the first kind and their derivatives. Moreover, we give an application of the mentioned results by extending two inequalities of van der Corput to Bessel and modified Bessel functions of the first k...
Numerical analysis for the moments of Bessel functions and Bessel-trigonometric functions
Wang, Yinkun; Ying LI; Luo, Jianshu
2016-01-01
The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel functions. To evaluate the moments of Bessel functions numerically, a fast and efficient scheme is also proposed to approximate the integral of Bessel function of the first kind and of zero order. The moments of Bessel-trigonometric functions are proved to be ...
Extension of Oppenheim's Problem to Bessel Functions
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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.
Extension of Oppenheim's Problem to Bessel Functions
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Ling Zhu
2008-01-01
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.
On two-dimensional Bessel functions
Korsch, H. J.; Klumpp, A.; Witthaut, D.
2006-01-01
The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal lines.
Extension of Oppenheim's Problem to Bessel Functions
Ling Zhu; Árpád Baricz
2007-01-01
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.
Numerical Calculation of Bessel Functions
Schwartz, Charles
2012-01-01
A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The Trapezoidal Rule, applied to suitable integral representations, may become the method of choice for evaluation of the many Special Functions of mathematical physics.
Theory of Bessel Functions of High Rank - I: Fundamental Bessel Functions
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.
Tur\\'an determinants of Bessel functions
Baricz, Árpád
2011-01-01
In this paper our aim is to survey the Tur\\'an type inequalities and related problems for the Bessel functions of the first kind. Moreover, we extend the known higher order Tur\\'an type inequalities for Bessel functions of the first kind to real parameters and we deduce new closed integral representation formulae for the second kind Neumann type series of Bessel functions of the first kind occurring in the study of Tur\\'an determinants of Bessel functions of the first kind. At the end of the paper we prove a Tur\\'an type inequality for the Bessel functions of the second kind.
Tur\\'an determinants of Bessel functions
Baricz, Árpád; Pogány, Tibor K.
2011-01-01
In this paper first we survey the Tur\\'an type inequalities and related problems for the Bessel functions of the first kind. Then we extend the known higher order Tur\\'an type inequalities for Bessel functions of the first kind to real parameters and we deduce new closed integral representation formulae for the second kind Neumann type series of Bessel functions of the first kind occurring in the study of Tur\\'an determinants of Bessel functions of the first kind. At the end of the paper we p...
Functional inequalities for modified Bessel functions
Baricz, Árpád; Vuorinen, Matti
2010-01-01
In this paper our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kinds. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact equivalent to the corresponding Tur\\'an type inequalities for these functions. As an application of the results concerning the modified Bessel function of the second kind we prove that the cumulative distribution function of the gamma-gamma distribution is log-concave. At the end of this paper several open problems are posed, which may be of interest for further research.
Redheffer type inequalities for modified Bessel functions
Khaled Mehrez
2016-01-01
In this short note, we give new proofs of Redheffer’s inequality for modified Bessel functions of first kind published by Ling Zhu (2011). In addition, using the Grosswald formula we prove new Redheffer type inequality for the modified Bessel functions of the second kind.
Bessel functions and equations of mathematical physics
Epelde García, Markel
2016-01-01
The aim of this dissertation is to introduce Bessel functions to the reader, as well as studying some of their properties. Moreover, the final goal of this document is to present the most well- known applications of Bessel functions in physics.
K-Bessel functions in two variables
Hacen Dib
2003-01-01
The Bessel-Muirhead hypergeometric system (or 0F1-system) in two variables (and three variables) is solved using symmetric series, with an explicit formula for coefficients, in order to express the K-Bessel function as a linear combination of the J-solutions. Limits of this method and suggestions for generalizations to a higher rank are discussed.
Interlacing of real zeros of Bessel functions
Palmai, Tamas
2010-01-01
We unify the known three distinct inequality sequences [Abramowitz 9.5.2] of real zeros of Bessel functions into a single, generalized one. This result is triggered by a uniqueness proof concerning a particular inverse scattering problem.
Jackson Integral Representations of Modified $q$-Bessel Functions and $q$-Bessel-Macdonald Functions
Olshanetsky, M. A.; Rogov, V-B. K.
1996-01-01
The $q$ analog of Modified Bessel functions and Bessel-Macdonald functions, were defined in our previous work (q-alg/950913) as general solutions of a second order difference equations. Here we present a collection of their representations by the Jackson q-integral.
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....
Generalized Bessel functions in tunnelling ionization
Reiss, H R
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.
Tur\\'an type inequalities for general Bessel functions
Baricz, Árpád; Ponnusamy, Saminathan; Singh, Sanjeev
2015-01-01
In this paper some Tur\\'an type inequalities for the general Bessel function, monotonicity and bounds for its logarithmic derivative are derived. Moreover we find the series representation and the relative extrema of the Tur\\'anian of general Bessel functions. The key tools in the proofs are the recurrence relations together with some asymptotic relations for Bessel functions.
Bessel functions and local converse conjecture of Jacquet
Chai, Jingsong
2014-01-01
In this paper, we prove a kernel formula of Bessel functions attached to irreducible smooth supercuspidal representations of p-adic $GL(n)$. We also show that the Bessel function defined by Bessel distribution coincides with the Bessel function defined via uniqueness of Whittaker models on the open Bruhat cell. As an application we give a proof of the local converse conjecture of Jacquet.
Approximation of Analytic Functions by Bessel's Functions of Fractional Order
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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.
Approximation of Analytic Functions by Bessel's Functions of Fractional Order
Soon-Mo Jung
2011-01-01
We will solve the inhomogeneous Bessel's differential equation x2y″(x)+xy′(x)+(x2-ν2)y(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.
Monotonicity and bounds on Bessel functions
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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.
A linear combination of modified Bessel functions
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.
Some Inequalities for Modified Bessel Functions
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Laforgia Andrea
2010-01-01
Full Text Available We denote by and the Bessel functions of the first and third kinds, respectively. Motivated by the relevance of the function , , in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector (1984, we establish new inequalities for . The results are based on the recurrence relations for and and the Turán-type inequalities for such functions. Similar investigations are developed to establish new inequalities for .
Extension of Frame's type inequalities to Bessel and modified Bessel functions
Mehrez, Khaled
2016-01-01
Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we extend the hyperbolic analogue of these trigonometric inequalities. As an application of these results we present a generalization of Cusa-type inequality to modified Bessel function. Our main motivation to write this paper is a recent publication of Chen and S\\'andor, which we wish to complement.
Exponential generating functions for the associated Bessel functions
International Nuclear Information System (INIS)
Similar to the associated Legendre functions, the differential equation for the associated Bessel functions Bl,m(x) is introduced so that its form remains invariant under the transformation l → -l - 1. A Rodrigues formula for the associated Bessel functions as squared integrable solutions in both regions l l,m(x) may be taken into account as the union of the increasing (decreasing) infinite sequences with respect to l. It is shown that two new different types of exponential generating functions are attributed to the associated Bessel functions corresponding to these rearranged sequences
Three-particle integrals with Bessel functions
Frolov, A. M.; Wardlaw, D. M.
2014-02-01
Analytical formulas for some useful three-particle integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates r 32, r 31, and r 21. The formulas obtained in such an analysis allow us to consider three-particle integrals of more complicated functions of relative/perimetric coordinates. In many actual problems such three-particle integrals can be found in matrix elements of the Hamiltonian and other operators.
Generalized Bessel transform of $(\\beta, \\gamma)$-generalized Bessel Lipschitz functions
DAHER, Radouan; El Hamma, Mohamed
2015-01-01
In this paper, we prove an analog of Younis’s theorem 5.2 in~[4] for the generalized Fourier-Bessel transform on the Half line for functions satisfying the $(\\beta, \\gamma)$-generalized Bessel Lipschitz condition in the space $\\mathrm{L}^{2}_{\\alpha,n}$.
Zeros of Bessel functions: monotonicity, concavity, inequalities
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Andrea Laforgia
2007-12-01
Full Text Available We present a survey of the most important inequalities and monotonicity, concavity (convexity results of the zeros of Bessel functions. The results refer to the deﬁnition Jνκ of the zeros of Cν (x = Jν (x cosα −Yν (x sinα, formulated in [6], where κ is a continuous variable. Sometimes, also the Sturm comparison theorem is an important tool of our results.
Cross-product of Bessel functions: monotonicity patterns and functional inequalities
Baricz, Árpád; Ponnusamy, Saminathan; Singh, Sanjeev
2015-01-01
In this paper we study the Dini functions and the cross-product of Bessel functions. Moreover, we are interested on the monotonicity patterns for the cross-product of Bessel and modified Bessel functions. In addition, we deduce Redheffer-type inequalities, and the interlacing property of the zeros of Dini functions and the cross-product of Bessel and modified Bessel functions. Bounds for logarithmic derivatives of these functions are also derived. The key tools in our proofs are some recently...
Some Unified Integrals Associated with Generalized Bessel-Maitland Function
Abouzaid, M. S.; Abusufian, A. H.; K. S. Nisar
2016-01-01
Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results, we obtained some interesting results of ordinary Bessel function.
Exponential generating functions for the associated Bessel functions
Energy Technology Data Exchange (ETDEWEB)
Fakhri, H [Department of Theoretical Physics and Astrophysics, Physics Faculty, University of Tabriz, PO Box 51666-16471, Tabriz (Iran, Islamic Republic of); Mojaveri, B; Nobary, M A Gomshi [Department of Physics, Faculty of Science, Razi University, Kermanshah (Iran, Islamic Republic of)], E-mail: hfakhri@tabrizu.ac.ir, E-mail: bmojaveri@raziu.ac.ir, E-mail: mnobary@razi.ac.ir
2008-09-26
Similar to the associated Legendre functions, the differential equation for the associated Bessel functions B{sub l,m}(x) is introduced so that its form remains invariant under the transformation l {yields} -l - 1. A Rodrigues formula for the associated Bessel functions as squared integrable solutions in both regions l < 0 and l {>=} 0 is presented. The functions with the same m but with different positive and negative values of l are not independent of each other, while the functions with the same l + m (l - m) but with different values of l and m are independent of each other. So, all the functions B{sub l,m}(x) may be taken into account as the union of the increasing (decreasing) infinite sequences with respect to l. It is shown that two new different types of exponential generating functions are attributed to the associated Bessel functions corresponding to these rearranged sequences.
Exponential generating functions for the associated Bessel functions
Fakhri, H.; Mojaveri, B.; Gomshi Nobary, M. A.
2008-09-01
Similar to the associated Legendre functions, the differential equation for the associated Bessel functions Bl,m(x) is introduced so that its form remains invariant under the transformation l → -l - 1. A Rodrigues formula for the associated Bessel functions as squared integrable solutions in both regions l = 0 is presented. The functions with the same m but with different positive and negative values of l are not independent of each other, while the functions with the same l + m (l - m) but with different values of l and m are independent of each other. So, all the functions Bl,m(x) may be taken into account as the union of the increasing (decreasing) infinite sequences with respect to l. It is shown that two new different types of exponential generating functions are attributed to the associated Bessel functions corresponding to these rearranged sequences.
New addition formula for the little $q$-Bessel functions
Bouzeffour, Fethi
2013-01-01
Starting from the addition formula for little $q$-Jacobi polynomials, we derive a new addition formula for the little $q$-Bessel functions. The result is obtained by the use of a limit transition. We also establish a product formula for little $q$-Bessel functions with a positive and symmetric kernel.
K-Bessel functions associated to 3-rank Jordan algebra
Hacen Dib
2005-01-01
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.
Composition Formulas of Bessel-Struve Kernel Function
K. S. Nisar; Mondal, S.R; P Agarwal
2016-01-01
The object of this paper is to study and develop the generalized fractional calculus operators involving Appell’s function F3(·) due to Marichev-Saigo-Maeda. Here, we establish the generalized fractional calculus formulas involving Bessel-Struve kernel function Sαλz, λ,z∈C to obtain the results in terms of generalized Wright functions. The representations of Bessel-Struve kernel function in terms of exponential function and its relation with Bessel and Struve function are also discussed. The...
Inequalities involving modified Bessel functions of the first kind II
Baricz, Arpad; Neuman, Edward
2007-08-01
The intrinsic properties, including logarithmic convexity (concavity), of the modified Bessel functions of the first kind and some other related functions are obtained. Several inequalities involving functions under discussion are established.
Some unified integrals associated with Bessel-Struve kernel function
K.S. Nisar; P. Agarwal; Jain, S
2016-01-01
In this paper, we discuss the generalized integral formula involving Bessel-Struve kernel function $S_{\\alpha }\\left( \\lambda z\\right) $, which expressed in terms of generalized Wright functions. Many interesting special cases also obtained in this study.
Evaluation of a Family of Bessel Function Integrals
Birrell, Jeremiah
2015-01-01
We investigate a family of integrals involving modified Bessel functions that arise in the context of neutrino scattering. Recursive formulas are derived for evaluating these integrals and their asymptotic expansions are computed. We prove in certain cases that the asymptotic expansion yields the exact result after a finite number of terms. In each of these cases we derive a formula that bounds the order at which the expansion terminates. The method of calculation developed in this paper is applicable to similar families of integrals that involve Bessel or modified Bessel functions.
Bounds for Tur\\'anians of modified Bessel functions
Baricz, Árpád
2012-01-01
Motivated by some applications in applied mathematics, biology, chemistry, physics and engineering sciences, new tight Tur\\'an type inequalities for modified Bessel functions of the first and second kind are deduced. These inequalities provide sharp lower and upper bounds for the Tur\\'anian of modified Bessel functions of the first and second kind, and in most cases the relative errors of the bounds tend to zero as the argument tends to infinity. The chief tools in our proofs are some ideas of Gronwall [19], an integral representation of Ismail [28,29] for the quotient of modified Bessel functions of the second kind, results of Hartman and Watson [24,26,59] and some recent results of Segura [52]. As applications of the main results some sharp Tur\\'an type inequalities are presented for the product of modified Bessel functions of the first and second kind and it is shown that this product is strictly geometrically concave.
The radius of convexity of normalized Bessel functions
Baricz, Árpád; Szász, Róbert
2015-01-01
The radius of convexity of two normalized Bessel functions of the first kind are determined in the case when the order is between $-2$ and $-1.$ Our methods include the minimum principle for harmonic functions, the Hadamard factorization of some Dini functions, properties of the zeros of Dini functions via Lommel polynomials and some inequalities for complex and real numbers.
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.
An integral estimate of Bessel function and its application
Institute of Scientific and Technical Information of China (English)
DING Yong; LI Ran
2008-01-01
In this paper the authors give a new integral estimate of the Bessel function, which parameterized Marcinkiewicz integral μΩρ with variable kernels is of type (2, 2), where the kernel function Ω does not have any smoothness on the unit sphere in Rn.
Inequalities and Asymptotic Formulae Related to Generalizations of the Bessel Functions
Paneva-Konovska, Jordanka
2010-10-01
We consider some families of 3-index generalizations of the Bessel functions of first kind and study the behaviour of such families in domains of the complex plane. We also prove asymptotic formulae for "large" values of indices of these functions. Similar theorems have also been obtained by the author for the Bessel and Bessel-Maitland functions.
The asymptotic behavior of q-exponentials and q-Bessel functions
Rogov, V. -B. K.
2006-01-01
The connections between q-Bessel functions of three types and q-exponential of three types are established. The q-exponentials and the q-Bessel functions are represented as the Laurent series. The asymptotic behaviour of the q-exponentials and the q-Bessel functions is investigated.
CHEBYSHEV APPROXIMATION OF THE SECOND KIND OF MODIFIED BESSEL FUNCTION OF ORDER ZERO
Institute of Scientific and Technical Information of China (English)
张璟; 周哲玮
2004-01-01
The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J. P. Boyd' s rational Chebyshev basis.
Uniform bounds for expressions involving modified Bessel functions
Gaunt, Robert E.
2013-01-01
In this paper, we obtain uniform bounds for a number of expressions that involve derivatives and integrals of modified Bessel functions. These uniform bounds are motivated by the need to bound such expressions in the study of variance-gamma and product normal approximations via Stein's method.
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.
Three-particle integrals with the Bessel functions
Frolov, Alexei M
2012-01-01
Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and trigonometric functions of one interparticle (relative) coordinate $r_{ij}$. Also, we consider the matrix elements of the Uehling potential which describes the lowest order correction to the vacuum polarization between two interacting electric charges.
Monotonic sequences related to zeros of Bessel functions
Lorch, Lee; Muldoon, Martin
2008-12-01
In the course of their work on Salem numbers and uniform distribution modulo 1, A. Akiyama and Y. Tanigawa proved some inequalities concerning the values of the Bessel function J 0 at multiples of π, i.e., at the zeros of J 1/2. This raises the question of inequalities and monotonicity properties for the sequences of values of one cylinder function at the zeros of another such function. Here we derive such results by differential equations methods.
Optimized Kaiser-Bessel Window Functions for Computed Tomography.
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. PMID:26151939
An integral estimate of Bessel function and its application
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper the authors give a new integral estimate of the Bessel function,which is an extension of Calder(?)n-Zygmund’s result.As an application of this result,we prove that the parameterized Marcinkiewicz integralμ_Ω~p with variable kernels is of type (2,2),where the kernel functionΩdoes not have any smoothness on the unit sphere in R~n.
Expansion Formulae for the Kampe De Feriet Function Involving Bessel Function
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A. D. Wadhwa
1971-01-01
Full Text Available In this paper some integrals involving a Kampe de Feriet; function have been evaluated. These have been used to establish some expansion formulae for the Kampe de Feriet function involving Bessel function.
On Tur\\'an type inequalities for modified Bessel functions
Baricz, Árpád
2010-01-01
In this note our aim is to point out that certain inequalities for modified Bessel functions of the first and second kind, deduced recently by Laforgia and Natalini, are in fact equivalent to the corresponding Tur\\'an type inequalities for these functions. Moreover, we present some new Tur\\'an type inequalities for the aforementioned functions and we show that their product is decreasing as a function of the order, which has application in the study of stability of radially symmetric solutions in a generalized FitzHugh-Nagumo equation in two spatial dimensions. At the end of this note a conjecture is posed, which may be of interest for further research.
One some differential subordination involving the Bessel-Struve kernel function
Saiful R. Mondal; Dhuian, Mohamed Al
2016-01-01
In this article we study the inclusion properties of the Bessel-Struve kernel functions in the Janowski class. In particular, we find the conditions for which the Bessel-Struve kernel functions maps the unit disk to right half plane. An open problem in this aspect are also given. The third order differential subordination involving the Bessel-Struve kernel is also considered. The results are derived by defining suitable classes of admissible functions. One of the recurrence relation of the Be...
The Bessel Period Functional on SO(5): The Nontempered Case
Qiu, Yannan
2013-01-01
For automorphic representations in the nontempered cuspidal spectrum of $\\mathrm{SO}_5$, we establish a precise Bessel period formula, in which the square of the global Bessel period is decomposed as an Euler product of regularized local Bessel period integrals of matrix coefficients.
YADOLLAH ORDOKHANI; HANIYE DEHESTANI
2015-01-01
In this paper a collocation method based on the Bessel-hybrid functions is used for approximation of the solution of linear Fredholm-Volterra integro-differential equations (FVIDEs) under mixed conditions. First, we explain the properties of Bessel-hybrid functions, which are combination of block-pulse functions and Bessel functions of first kind. The method is based upon Bessel-hybrid approximations, so that to obtain the operational matrixes and approximation of functions we use the tran...
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.
Ultradiscrete limit of Bessel function type solutions of the Painlev\\'{e} III equation
Isojima, Shin
2014-01-01
An ultradiscrete analog of the Bessel function is constructed by taking the ultradiscrete limit for a $q$-difference analog of the Bessel function. Then, a direct relationship between a class of special solutions for the ultradiscrete Painlev\\'{e} III equation and those of the discrete Painlev\\'{e} III equation which have a determinantal structure is established.
On the subclasses associated with the Bessel-Struve kernel functions
Saiful R. Mondal; Mohammed, Al Dhuain
2016-01-01
The article investigate the necessary and sufficient conditions for the normalized Bessel-struve kernel functions belonging to the classes $\\mathcal{T}_\\lambda(\\alpha)$ , $\\mathcal{L}_\\lambda(\\alpha)$. Some linear operators involving the Bessel-Struve operator are also considered.
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.
Amos-type bounds for modified Bessel function ratios☆
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
Amos-type bounds for modified Bessel function ratios.
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. PMID:24926105
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_\
A Limit Relation for Dunkl-Bessel Functions of Type A and B
Margit Rösler; Michael Voit
2008-01-01
We prove a limit relation for the Dunkl-Bessel function of type $B_N$ with multiplicity parameters $k_1$ on the roots $\\pm e_i$ and $k_2$ on $\\pm e_i\\pm e_j$ 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.
Zeros of combinations of Bessel functions and the mean charge of graphene nanodots
Beneventano, C. G.; Fialkovsky, I. V.; Santangelo, E. M.
2016-04-01
We establish some properties of the zeros of sums and differences of contiguous Bessel functions of the first kind. As a by-product, we also prove that the zeros of the derivatives of Bessel functions of the first kind of different orders are interlaced the same way as the zeros of the Bessel functions themselves. As a physical motivation, we consider gated graphene nanodots subject to Berry-Mondragon boundary conditions. We determine the allowed energy levels and calculate the mean charge at zero temperature. We discuss its dependence on the gate ( chemical) potential in detail and also comment on the effect of temperature.
Indian Academy of Sciences (India)
A K Chattopadhyay; C V S Rao
2003-07-01
Here we describe the superiority of Bessel function as base function for radial expansion 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 saw-tooth oscillation and real experimental x-ray data from W7-AS Stellarator.
q-Sumudu Transforms of q-Analogues of Bessel Functions
Faruk Uçar
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.
Bessel harmonic analysis and approximation of functions on the half-line
Platonov, Sergei S.
2007-10-01
We study problems of approximation of functions on \\lbrack 0, +\\infty) 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.
Bessel harmonic analysis and approximation of functions on the half-line
International Nuclear Information System (INIS)
We study problems of approximation of functions on [0,+∞) in the metric of Lp 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
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.
Diffraction pattern of modulated structures described by Bessel functions
Wolny, Janusz; Buganski, Ireneusz; Strzalka, Radoslaw
2016-05-01
We performed detailed analysis of 1D modulated structure (MS) with harmonic modulation within the statistical approach. By applying two-mode Fourier transform, we were able to derive analytically the structure factor for MS with single harmonic modulation component. We confirmed in a very smooth way that ordinary Bessel functions of the first kind define envelopes tuning the intensities of the diffraction peaks. This applies not only to main reflections of the diffraction pattern but also to all satellites. In the second part, we discussed in details the similarities between harmonically modulated structures with multiple modulations and 1D model quasicrystal. The Fourier expansion of the nodes' positions in the Fibonacci chain gives direct numerical definition of the atomic arrangement in MS. In that sense, we can define 1D quasicrystal as a MS with infinite number of harmonic modulations. We prove that characteristic measures (like v(u) relation typical for statistical approach and diffraction pattern) calculated for MS asymptotically approach their counterparts for 1D quasicrystal as large enough number of modulation terms is taken into account.
Directory of Open Access Journals (Sweden)
YADOLLAH ORDOKHANI
2015-12-01
Full Text Available In this paper a collocation method based on the Bessel-hybrid functions is used for approximation of the solution of linear Fredholm-Volterra integro-differential equations (FVIDEs under mixed conditions. First, we explain the properties of Bessel-hybrid functions, which are combination of block-pulse functions and Bessel functions of first kind. The method is based upon Bessel-hybrid approximations, so that to obtain the operational matrixes and approximation of functions we use the transfer matrix from Bessel-hybrid functions to Taylor polynomials. The matrix equations correspond to a system of linear algebraic equations with the unknown Bessel-hybrid coefficients. Present results and comparisons demonstrate our estimate have good degree of accuracy.
Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions
Betancor, Jorge J; Rodríguez-Mesa, Lourdes
2011-01-01
In this paper we consider the space $BMO_o(\\mathbb{R},X)$ of bounded mean oscillations and odd functions on $\\mathbb{R}$ taking values in a UMD Banach space $X$. The functions in $BMO_o(\\mathbb{R},X)$ are characterized by Carleson type conditions involving Bessel convolutions and $\\gamma$-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain $\\gamma$-radonifying Carleson inequalities for Bessel-Poisson integrals of $BMO_o(\\mathbb{R},X)$ functions hold.
An exactly solvable model of an oscillator with nonlinear coupling and zeros of Bessel functions
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.
Physical Applications of a Simple Approximation of Bessel Functions of Integer Order
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…
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; WANG Yong
2006-01-01
In Phys. Lett. A 313 (2003) 343 we have found that the self-reciprocal Hankel transformation (HT) is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations' transformation in quantum mechanics.
Remarks on the paper: "Bounds for functions involving ratios of modified Bessel functions"
Segura, Javier
2011-01-01
A recent paper by C.G. Kokologiannaki published in J. Math. Anal. Appl. \\cite{Kolo:2012:BFI} gives some properties for ratios of modified Bessel functions and, in particular, some bounds. These bounds are said to improve the range of some inequalities in \\cite{Segura:2011:BRM} or to be sharper. Unfortunately, Kokologiannaki made some mistakes in the comparison and no improvement or extension is made over the results in \\cite{Segura:2011:BRM}. We explain the errors in these comments and show that the bounds given in \\cite{Kolo:2012:BFI} are already contained in \\cite{Segura:2011:BRM}.
Physical applications of a simple approximation of Bessel functions of integer order
International Nuclear Information System (INIS)
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 physical interest. The examples that illustrate our approach are accessible to the undergraduate student
Modeling Delays of Microwave Transistors and Transmission Lines by the 2nd Order Bessel Function
Directory of Open Access Journals (Sweden)
K. Ulovec
2007-04-01
Full Text Available At present, most of simulation programs can characterize gate delays of microwave transistors. However, the delay is mostly approximated by means of first-order differential equations. In the paper, a more accurate way is suggested which is based on an appropriate second-order differential equation. Concerning the transmission line delay, majority of the simulation programs use both Branin (for lossless lines and LCRG (for lossy lines models. However, the first causes extreme simulation times, and the second causes well-known spurious oscillations in the simulation results. In the paper, an unusual way for modeling the transmission line delay is defined, which is also based on the second-order Bessel function. The proposed model does not create the spurious oscillations and the simulation times are comparable with those obtained with the classical models. Properties of the implementation of the second-order Bessel function are demonstrated by analyses of both digital and analog microwave circuits.
A new type of sharp bounds for ratios of modified Bessel functions
Ruiz-Antolin, D.; J. Segura
2016-01-01
The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications. We obtain new bounds which are accurate in a large region of parameters and which are shaper than previous bounds. The new bounds are obtained by a qualitative analysis of the Riccati equation satisfied by these ratios. A procedure is considered in which the bounds obtained from the analysis of the Riccati equation ...
Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions
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
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...... first order modified Bessel function of the first kind I1, including inequalities, monotonicity, unimodality, and convexity....
On infinite series concerning zeros of Bessel functions of the first kind
Giusti, Andrea; Mainardi, Francesco
2016-06-01
A relevant result independently obtained by Rayleigh and Sneddon on an identity on series involving the zeros of Bessel functions of the first kind is derived by an alternative method based on Laplace transforms. Our method leads to a Bernstein function of time, expressed by Dirichlet series, that allows us to recover the Rayleigh-Sneddon sum. We also consider another method arriving at the same result based on a relevant formula by Calogero. Moreover, we also provide an electrical example in which this sum results to be extremely useful in order to recover the analytical expression for the response of the system to a certain external input.
McDonald, Kirk T
2000-01-01
Scalar Bessel beams are derived both via the wave equation and via diffraction theory. While such beams have a group velocity that exceeds the speed of light, this is a manifestation of the "scissors paradox" of special relativty. The signal velocity of a modulated Bessel beam is less than the speed of light. Forms of Bessel beams that satisfy Maxwell's equations are also given.
Product Bessel Distributions of the First and Second Kinds
Saralees Nadarajah
2007-01-01
A new Bessel function distribution is introduced by taking the product of a Bessel function pdf of the first kind and a Bessel function pdf of the second kind. Various particular cases and expressions for moments are derived.
International Nuclear Information System (INIS)
General expressions for the dependence of the polarization of the radiation emitted in an atomic electronic transition upon the angle of emission are derived on the basis of a vector-spherical-harmonic/Bessel-function description of the photon. The concept of a photon of a specific multipolarity, i.e. quadrupole, octupole, etc, and identifiable as such, is found to be unviable. The angular distribution and dependence upon distance from the source of the transverse and parallel components of the electric and magnetic fields arising from E1, E2, M1 and M2 atomic electronic emissions are elucidated. (paper)
Grinter, Roger
2014-04-01
General expressions for the dependence of the polarization of the radiation emitted in an atomic electronic transition upon the angle of emission are derived on the basis of a vector-spherical-harmonic/Bessel-function description of the photon. The concept of a photon of a specific multipolarity, i.e. quadrupole, octupole, etc, and identifiable as such, is found to be unviable. The angular distribution and dependence upon distance from the source of the transverse and parallel components of the electric and magnetic fields arising from E1, E2, M1 and M2 atomic electronic emissions are elucidated.
Transcendentality of zeros of higher dereivatives of functions involving Bessel functions
Directory of Open Access Journals (Sweden)
Martin E. Muldoon
1995-09-01
Full Text Available C.L. Siegel established in 1929 [Ges. Abh., v.1, pp. 209-266] the deep results that (i all zeros of Jv(x and JÃ¢Â€Â²v(x are transcendental when v is rational, xÃ¢Â‰Â 0, and (ii JÃ¢Â€Â²v(x/Jv(x is transcendental when v is rational and x algebraic. As usual, Jv(x is the Bessel function of first kind and order v. Here it is shown that simple arguments permit one to infer from Siegel's results analogous but not identical properties of the zeros of higher derivatives of xÃ¢ÂˆÂ’uJv(x when ÃŽÂ¼ is algebraic and v rational. In particular, JÃ¢Â€Â´1(Ã‚Â±3=0 while all other zeros of JÃ¢Â€Â´1(x and all zeros of JÃ¢Â€Â´v(x, v2Ã¢Â‰Â 1, xÃ¢Â‰Â 0, are transcendental. Further, J0(4(Ã‚Â±3=0 while all other zeros of J0(4(x, xÃ¢Â‰Â 0, and of Jv(4(x, vÃ¢Â‰Â 0, xÃ¢Â‰Â 0, are transcendental. All zeros of Jv(n(x, xÃ¢Â‰Â 0, are transcendental, n=5,Ã¢Â€Â¦,18, when v is rational. For most values of n, the proofs used the symbolic computation package Maple V (Release 1.
Keldysh theory re-examined: Application of the generalized Bessel functions
Bauer, J H
2015-01-01
A derivation of the ionization rate for the hydrogen-like ion in the strong linearly polarized laser field is presented. This derivation utilizes the famous Keldysh probability amplitude in the length gauge (in the dipole approximation) and without Coulomb effects in the final state of the ionized electron. No further approximations are being made, because the amplitude has been expanded in the double Fourier series in a time domain (with the help of the generalized Bessel functions). Thus, our theory has no other limitations characteristic of the original Keldysh theory. We compare our "exact" theory with the original Keldysh one, studying photoionization energy spectra and total ionization rates. We show breakdown of the original Keldysh theory for higher frequencies. In the barrier-suppresion regime the "exact" Keldysh theory gives results closer to well-known numerical or other analytical results.
n阶变型Bessel函数两个定理的证明%Proof of Two Theorem Composed of n Order Modified Bessel Functions
Institute of Scientific and Technical Information of China (English)
蓝新华
2011-01-01
Base on the properties of the modified Bessel function, we proof the orthogonality of functions systems of two n order modified Bessel functions, give the expression of their lengths.%利用n阶变型Bessel函数的相关性质，证明了由n阶变型Bessel函数组成的两个函数系具有正交性，并给出了长度表达式。
Mikusi\\'nski's Operational Calculus with Algebraic Foundations and Applications to Bessel Functions
Bengochea, Gabriel; G, Gabriel López
2013-01-01
We construct an operational calculus supported on the algebraic operational calculus introduced by Bengochea and Verde. With this operational calculus we study the solution of certain Bessel type equations.
On hyperbolic Bessel processes and beyond
Jakubowski, Jacek; Wiśniewolski, Maciej
2013-01-01
We investigate distributions of hyperbolic Bessel processes. We find links between the hyperbolic cosine of hyperbolic Bessel processes and functionals of geometric Brownian motion. We present an explicit formula for the Laplace transform of the hyperbolic cosine of a hyperbolic Bessel process and some other interesting probabilistic representations of this Laplace transform. We express the one-dimensional distribution of a hyperbolic Bessel process in terms of other, known and independent pr...
Creation of matter wave Bessel beams
Ryu, C.; Henderson, K. C.; Boshier, M. G.
2013-01-01
Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because of their property of limited diffraction and their capacity to 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 t...
The generalized Abel-Plana formula. Applications to Bessel functions and Casimir effect
International Nuclear Information System (INIS)
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)
Revisiting the orthogonality of Bessel functions of the first kind on an infinite interval
International Nuclear Information System (INIS)
The rigorous proof of the orthogonality integral ∫0∞ρ Jν(kρ)Jν(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 Jν(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)
Intensity transformation of vector Bessel beams using a multilayer system
Novitsky, Andrey V.
2008-01-01
We theoretically investigate the generation of vector Bessel beams of the order m using a phase shifted superposition of TE and TM electromagnetic Bessel beams. Such Bessel beams are characterized by the intensity profile described by the superposition of squared Bessel functions of the orders m-1 and m+1.
The generalized Abel-Plana formula with applications to Bessel functions and casimir effect
International Nuclear Information System (INIS)
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)
On hyperbolic Bessel processes and beyond
Wisniewolski, Maciej
2011-01-01
We investigate distributions of hyperbolic Bessel processes. We find links between the hyperbolic cosinus of the hyperbolic Bessel processes and the functionals of geometric Brownian motion. We present an explicit formula of Laplace transform of hyperbolic cosinus of hyperbolic Bessel processes and some interesting different probabilistic representations of this Laplace transform. We express the one-dimensional distribution of hyperbolic Bessel process in terms of other, known and independent processes. We present some applications including a new proof of Bougerol's identity and it's generalization. We characterize the distribution of the process being hyperbolic sinus of hyperbolic Bessel processes.
The Bessel Numbers and Bessel Matrices
Institute of Scientific and Technical Information of China (English)
Sheng Liang YANG; Zhan Ke QIAO
2011-01-01
In this paper,using exponential Riordan arrays,we investigate the Bessel numbers and Bessel matrices.By exploring links between the Bessel matrices,the Stirling matrices and the degenerate Stirling matrices,we show that the Bessel numbers are special case of the degenerate Stirling numbers,and derive explicit formulas for the Bessel numbers in terms of the Stirling numbers and binomial coefficients.
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.
International Nuclear Information System (INIS)
Two accurate, yet simple, analytic approximations to the integral of the Bessel function J0 are presented. These first and second-order approximations are obtained by improving on the recently developed method known as two-point quasi-rational approximations. The accuracy of the first-order approximant is better than 0.05. The second-order approximant is practically indistinguishable from the true integral, even for very large values of the argument (overall accuracy is better than 0.002 05). Our approximants are, in addition, analytic and therefore replace with significant advantages both the well known power series and the asymptotic formulae of the integral. Approximants to the transmittance function of a plane wave through a circular aperture are derived, a problem which arises in diffraction theory and particle scattering. The second-order approximant to the transmittance is analytic too, and can be evaluated for small and large values of the argument, just with a hand-calculator. Its accuracy is better than 0.0011. As an extension, two first-order approximations to the integrals of the Bessel functions Jν, of fractional order ν, are derived. (author)
Banica, Teodor; Belinschi, Serban; Capitaine, Mireille; Collins, Benoit
2007-01-01
We introduce and study a remarkable family of real probability measures $\\pi_{st}$, that we call free Bessel laws. These are related to the free Poisson law $\\pi$ via the formulae $\\pi_{s1}=\\pi^{\\boxtimes s}$ and $\\pi_{1t}=\\pi^{\\boxplus t}$. Our study includes: definition and basic properties, analytic aspects (supports, atoms, densities), combinatorial aspects (functional transforms, moments, partitions), and a discussion of the relation with random matrices and quantum groups.
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
Ebaid, Abdelhalim; Al-Blowy, Ahmed B.
2016-05-01
In this article, a simple approach is suggested to calculate the approximate dates of opposition and conjunction of Earth and Mars since their opposition on August 28, 2003 (at perihelion of Mars). The goal of this article has been achieved via using accurate analytical solution to Kepler's equation in terms of Bessel function. The periodicity property of this solution and its particular values at specified times are discussed through some lemmas. The mathematical conditions of opposition and conjunction of the two planets are formulated. Moreover, the intervals of opposition and conjunction have been determined using the graphs of some defined functions. The calculations reveal that there are nine possible oppositions and conjunctions for Earth and Mars during 20 years started on August 28, 2003. The dates of such oppositions and conjunctions were approximately determined and listed in Tables. It is found that our calculations differ few days from the published real dates of Earth-Mars oppositions due to the neglected effects of the gravitational attraction of other planets in the Solar system on the motion of two planets. The period of 20 years can be extended for any number of years by following the suggested analysis. Furthermore, the current approach may be extended to study the opposition and conjunction of the Earth and any outer planet.
Terahertz plasmonic Bessel beamformer
Energy Technology Data Exchange (ETDEWEB)
Monnai, Yasuaki; Shinoda, Hiroyuki [Graduate School of Frontier Sciences, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan); Jahn, David; Koch, Martin [Department of Physics, Philipps University of Marburg, Renthof 5, 35032 Marburg (Germany); Withayachumnankul, Withawat [School of Electrical and Electronics Engineering, The University of Adelaide, Adelaide, SA 5005 (Australia)
2015-01-12
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.
Sasaki, Ryu
2016-01-01
Exact solvability (ES) of one-dimensional quantum potentials $V(x)$ is a vague concept. We propose that beyond its most conventional range the ES status should be attributed also to many less common interaction models for which the wave functions remain piecewise proportional to special functions. The claim is supported by constructive analysis of a toy model $V(x)= -g^2\\exp (-|x|)$. The detailed description of the related bound-state and scattering solutions of Schr\\"{o}dinger equation is provided in terms of Bessel functions which are properly matched in the origin.
Scale space smoothing, image feature extraction and bessel filters
Mahmoodi S.; Gunn S.
2011-01-01
The Green function of Mumford-Shah functional in the absence of discontinuities is known to be a modified Bessel function of the second kind and zero degree. Such a Bessel function is regularized here and used as a filter for feature extraction. It is demonstrated in this paper that a Bessel filter does not follow the scale space smoothing property of bounded linear filters such as Gaussian filters. The features extracted by the Bessel filter are therefore scale invariant. Edges, blobs, and j...
Johannisson, P; Lisak, M; Marklund, M; Johannisson, Pontus; Anderson, Dan; Lisak, Mietek; Marklund, Mattias
2003-01-01
The effect of the Kerr nonlinearity on linear non-diffractive Bessel beams is investigated analytically and numerically using the nonlinear Schr\\"odinger equation. The nonlinearity is shown to primarily affect the central parts of the Bessel beam, giving rise to radial compression or decompression depending on whether the nonlinearity is focusing or defocusing, respectively. The dynamical properties of Gaussian-truncated Bessel beams are also analysed in the presence of a Kerr nonlinearity. It is found that although a condition for width balance in the root-mean-square sense exists, the beam profile becomes strongly deformed during propagation and may exhibit the phenomena of global and partial collapse.
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; 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.
Using Bessel functions to find fixed solutions to wave equations%利用Bessel函数求解波动方程的定解问题
Institute of Scientific and Technical Information of China (English)
金启胜
2014-01-01
分离变量法是求解波动方程定解问题的一种重要方法。分离变量法的重点在于求特征值及其对应的特征函数。Bessel函数是应用很广泛的一种特征函数，运用Bessel函数的有关性质可以很方便地求解波动方程的定解问题。%The method of separation of variables is an important method for finding solutions to heat conduction equations. The method is used to find the characteristic values of characteristic functions. Bessel functions are characteristic functions,which can be widely used to find fixed solutions to wave equations.
Large Degree Asymptotics of Generalized Bessel Polynomials
López, J. L.; Temme, Nico
2011-01-01
Asymptotic 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 origin in the $z-$plane. New forms of expansions in terms of elementary functions valid in sectors not containing the turning points $z=\\pm i/n$ are derived, and a new expansion in terms of modified Bessel fu...
Apertured paraxial Bessel beams.
Umul, Yusuf Z
2010-03-01
The paraxial Bessel beam is obtained by applying an approximation in the wavenumbers. The scattering of the beams by a circular aperture in an absorbing screen is investigated. The scattered fields are expressed in terms of the Fresnel integrals by evaluating the Kirchhoff diffraction integral in the paraxial approximation. The results are examined numerically. PMID:20208927
Eigenvalue asymptotics for Dirac-Bessel operators
Hryniv, Rostyslav O.; Mykytyuk, Yaroslav V.
2016-06-01
In this paper, we establish the eigenvalue asymptotics for non-self-adjoint Dirac-Bessel operators on (0, 1) with arbitrary real angular momenta and square integrable potentials, which gives the first step for solution of the related inverse problem. The approach is based on a careful examination of the corresponding characteristic functions and their zero distribution.
Large degree asymptotics of generalized Bessel polynomials
López, J.L.; Temme, N.M.
2011-01-01
Asymptotic 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 origin in t
Bessel potential spaces in Beurling's distributions
Sohn, Byung Keun
2009-01-01
We introduce the generalized Bessel potential spaces in the Beurling’s distributions. We give the topological characterizations of the generalized Bessel potential spaces and consider multiplication and convolution operations in the generalized Bessel potential spaces.
Directory of Open Access Journals (Sweden)
Hatem Mokhtari
2012-08-01
Full Text Available This paper investigates on the propagation in a coaxial cable with the assumption that the distributed parameters are variable with the longitudinal distance from the source due to a linear temperature variation. This work addresses the problem of propagation in borehole conditions where the temperature varies by approximately 3°C/100m. In addition to the temperature variation along the coax we have considered the high frequency domain where the skin effect is severe and leading to very high losses. Unlike the uniform temperature distribution study this case is very complex and that is the reason why we have provided a model for PSPICE simulator to represent the cascaded cells because the analytic solution is extremely tedious to solve. The idea is thus to replace the coax cable by cascaded elements whose resistance and impedance are calculated via Kelvin-Bessel functions. Because the number of cells is huge we have written a C language program to generate automatically the PSPICE .CIR file. Each cell has its own resistance and inductance according to its temperature. The capacity is assumed to be constant along the coax for each cell. Besides the PSPICE program, and for comparison, we have developed a recursive method for computing the attenuation due to the whole cascaded cells. The comparison between PSPICE and the recursive method has shown results in very good agreement.
Finite extensions of Bessel sequences
Bakić, Damir; Berić, Tomislav
2015-01-01
The paper studies finite extensions of Bessel sequences in infinite-dimensional Hilbert spaces. We provide a characterization of Bessel sequences that can be extended to frames by adding finitely many vectors. We also characterize frames that can be converted to Parseval frames by finite-dimensional perturbations. Finally, some results on excesses of frames and near-Riesz bases are derived.
McLaren, Melanie; Leach, Jonathan; Roux, Filippus S; Padgett, Miles J; Forbes, Andrew
2012-01-01
Orbital angular momentum (OAM) entanglement is investigated in the Bessel-Gauss (BG) basis. Having a readily adjustable radial scale, BG modes provide a more favourable basis for OAM entanglement over Laguerre-Gaussian (LG) modes. The OAM bandwidth in terms of BG modes can be increased by selection of particular radial modes and leads to a flattening of the spectrum. The flattening of the spectrum allows for higher entanglement. We demonstrate increased entanglement in terms of BG modes by performing a Bell-type experiment and violating the appropriate Clauser Horne Shimony Holt (CHSH) inequality. In addition, we reconstruct the quantum state of BG modes entangled in high-dimensions.
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics. PMID:25401574
Single Bessel tractor-beam tweezers
Mitri, F G
2014-01-01
The tractor behavior of a zero-order Bessel acoustic beam acting on a fluid sphere, and emanating from a finite circular aperture (as opposed to waves of infinite extent) is demonstrated theoretically. Conditions for an attractive force acting in opposite direction of the radiating waves, determined by the choice of the beam's half-cone angle, the size of the radiator, and its distance from a fluid sphere, are established and discussed. Numerical predictions for the radiation force function, which is the radiation force per unit energy density and cross-sectional surface, are provided using a partial-wave expansion method stemming from the acoustic scattering. The results suggest a simple and reliable analysis for the design of Bessel beam acoustical tweezers and tractor beam devices.
The probability distributions of the first hitting times of Bessel processes
Hamana, Yuji; Matsumoto, Hiroyuki
2011-01-01
We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions and for the densities by means of the zeros of the Bessel functions. The results extend the classical ones and cover all the cases.
Propagation and self-healing ability of a Bessel-Gaussian beam modulated by Bessel gratings
Qiao, Chunhong; Feng, Xiaoxing; Chu, Xiuxiang
2016-04-01
A new type of Bessel-like beam which can be generated by using Bessel gratings to modulate the amplitude and phase of a Bessel beam is proposed. In analogy to study a Bessel beam in free space, the intensity evolution and self-healing property of the Bessel-like beam have been studied. Meanwhile, based on the Fresnel diffraction integral, the propagation of the Bessel-like beam in free space has also been investigated. Results show that the Bessel-like beam and the Bessel-Gaussian-like beams have some special and interesting properties.
Müller, Angelina; Wallrabe, Ulrike
2016-01-01
We present a ring aperture with independently switchable segments for the three-dimensional control of quasi propagation invariant beams. We demonstrate that our liquid crystal design concept preserves coherence and generates the Bessel beam structure.
Harmonic Analysis Associated with the Generalized q-Bessel Operator
Ahmed Abouelaz; Radouan Daher; El Mehdi Loualid
2016-01-01
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.
Review of nondiffracting Bessel beams
Lapointe, Michael R.
1991-01-01
The theory of nondiffracting beam propagation and experimental evidence for nearly-nondiffractive Bessel beam propagation are reviewed. The experimental results are reinterpreted using simple optics formulas, which show that the observed propagation distances are characteristic of the optical systems used to generate the beams and do not depend upon the initial beam profiles. A set of simple experiments are described which support this interpretation. It is concluded that nondiffracting Bessel beam propagation has not yet been experimentally demonstrated.
Heat kernel analysis for Bessel operators on symmetric cones
DEFF Research Database (Denmark)
Möllers, Jan
2014-01-01
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...... on the complexification $G_{\\mathbb C}/K_{\\mathbb C}$ of $Ω$, the weight being expressed explicitly in terms of a multivariable $K$-Bessel function on $Ω$. Even in the special case of the symmetric cone $Ω=\\mathbb{R}_+$ these results seem to be new....
Studies of Transverse Momentum Dependent Parton Distributions and Bessel Weighting
Aghasyan, M; De Sanctis, E; Gamberg, L; Mirazita, M; Musch, B; Prokudin, A; Rossi, P
2014-01-01
In this paper we present a new technique for analysis of transverse momentum dependent parton distribution functions, based on the Bessel weighting formalism. 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. Using a fully differential cross section for the process, the effect of four momentum conservation is analyzed using various input models for transverse momentum distributions and fragmentation functions. 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/Q2. We find that the Bessel weighting technique provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics du...
Selfhealing of asymmetric Bessel-like modes
DEFF Research Database (Denmark)
Israelsen, Stine Møller; Rishøj, Lars Søgaard; Rottwitt, Karsten
2014-01-01
We numerically investigate asymmetric Bessel-like modes in an aircladding fiber. The selfhealing ability of asymmetric Bessel-like modes is demonstrated and quantified including the angular dependency of this ability.......We numerically investigate asymmetric Bessel-like modes in an aircladding fiber. The selfhealing ability of asymmetric Bessel-like modes is demonstrated and quantified including the angular dependency of this ability....
Expansion of Bessel and g -Bessel sequences to dual frames and dual g -frames
Golsa Kavian; Mohammad Sadegh Asgari
2014-01-01
In this paper we study the duality of Bessel and $g$-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.
Maximal inequalities for bessel processes
Directory of Open Access Journals (Sweden)
Graversen SE
1998-01-01
Full Text Available It is proved that the uniform law of large numbers (over a random parameter set for the -dimensional ( Bessel process started at 0 is valid: for all stopping times for . The rate obtained (on the right-hand side is shown to be the best possible. The following inequality is gained as a consequence: for all stopping times for , where the constant satisfies as . This answers a question raised in [4]. The method of proof relies upon representing the Bessel process as a time changed geometric Brownian motion. The main emphasis of the paper is on the method of proof and on the simplicity of solution.
Ablation of metal thin films using femtosecond laser Bessel vortex beams
Sahin, Ramazan; Ersoy, Tansu; Akturk, Selcuk
2015-01-01
Femtosecond lasers can provide submicron ablation resolution, making them suitable and attractive for various micro/nanofabrication applications. Laser beam shaping lends further advantages and increases the versatility of these sources. In this work, we report on the use of femtosecond laser pulses with first-order Bessel function (Bessel vortex) beam profiles in ablation of metal thin films. The diffraction-free nature of Bessel beams provides significant convenience regarding alignment and repeatability. Ablation profiles with Bessel vortex beams generally consist of single or multiple concentric rings, determined by pulse fluence on target. We investigate single-pulse ablation behavior with two laser wavelengths (1,030 and 515 nm) and three different Bessel beam cone angles. For each case, we measure inner and outer ring diameters and compare our results with theoretical calculations.
Belyi, V. N.; Khilo, P. A.; Kazak, N. S.; Khilo, N. A.
2016-07-01
The generation of wavefront phase dislocations of vortex Bessel light beams under acousto-optic (AO) diffraction in uniaxial crystals has been investigated. For the first time the process of AO interaction is studied with participation of Bessel acoustic beams instead of plane waves. A mathematical description of AO interaction is provided, which supposes the satisfaction of two types of phase-matching condition. The acousto-optic processes of transferring optical singularities onto the wavefront of BLBs are investigated and the generation of high-order optical vortices is considered at the interaction of optical and acoustical Bessel beams. The change of Bessel function order or phase dislocation order is explained as a result of the spin–orbital interaction under acousto-optic diffraction of vortex Bessel beams.
Generalized weighted Besov spaces on the Bessel hypergroup
Directory of Open Access Journals (Sweden)
Miloud Assal
2006-01-01
Full Text Available In this paper we study generalized weighted Besov type spaces on the Bessel-Kingman hypergroup. We give different characterizations of these spaces in terms of generalized convolution with a kind of smooth functions and by means of generalized translation operators. Also a discrete norm is given to obtain more general properties on these spaces.
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.
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].
A relativistic study of Bessel beams
International Nuclear Information System (INIS)
We present a fully relativistic analysis of Bessel beams revealing some noteworthy features that are not explicit in the standard description. It is shown that there is a reference frame in which the field takes a particularly simple form, the wave appearing to rotate in circles. The concepts of polarization and angular momentum for Bessel beams are also reanalysed
A relativistic study of Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Hacyan, S; Jauregui, R [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apdo. Postal 20-364, Mexico DF 01000 (Mexico)
2006-04-14
We present a fully relativistic analysis of Bessel beams revealing some noteworthy features that are not explicit in the standard description. It is shown that there is a reference frame in which the field takes a particularly simple form, the wave appearing to rotate in circles. The concepts of polarization and angular momentum for Bessel beams are also reanalysed.
A relativistic study of Bessel beams
Hacyan, S
2006-01-01
We present a fully relativistic analysis of Bessel beams revealing some noteworthy features that are not explicit in the standard description. It is shown that there is a reference frame in which the field takes a particularly simple form, the wave appearing to rotate in circles. The concepts of polarization and angular momentum for Bessel beams is also reanalyzed.
The Bessel polynomials and their differential operators
International Nuclear Information System (INIS)
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
Superluminal Behaviour of Modified Bessel Waves
Institute of Scientific and Technical Information of China (English)
WANG Zhi-Yong; XIONG Cai-Dong
2006-01-01
@@ Much experimental evidence of superluminal phenomena has been available by electromagnetic wave propagation experiments, with the results showing that the phase time describes the barrier traversal time. Based on the extrapolated phase time approach and numerical methods, we show that, in contrast to the ordinary Bessel waves of real argument, the group velocities of modified Bessel waves are superluminal. We obtain the following results.
Fourier-Bessel heat kernel estimates
Malecki, Jacek; Serafin, Grzegorz; Zorawik, Tomasz
2015-01-01
We provide sharp two-sided estimates of the Fourier-Bessel heat kernel and we give sharp two-sided estimates of the transition probability density for the Bessel process in (0,1) killed at 1 and killed or reflected at 0.
On the Diamond Bessel Heat Kernel
Wanchak Satsanit
2011-01-01
We study the heat equation in n dimensional by Diamond Bessel operator. We find the solution by method of convolution and Fourier transform in distribution theory and also obtain an interesting kernel related to the spectrum and the kernel which is called Bessel heat kernel.
Energy Technology Data Exchange (ETDEWEB)
Yuste, Santos Bravo; Abad, Enrique, E-mail: santos@unex.es [Departamento de Fisica, Universidad de Extremadura, E-06071 Badajoz (Spain)
2011-02-18
We present an iterative method to obtain approximations to Bessel functions of the first kind J{sub p}(x) (p > -1) via the repeated application of an integral operator to an initial seed function f{sub 0}(x). The class of seed functions f{sub 0}(x) leading to sets of increasingly accurate approximations f{sub 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{sub 0}(x) = 1. This set of polynomials is useful not only for the computation of J{sub 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.
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.
Bessel multipliers in Hilbert $C^\\ast$--modules
Khosravi, Amir; Mirzaee Azandaryani, Morteza
2015-01-01
In this paper we introduce Bessel multipliers, g-Bessel multipliers and Bessel fusion multipliers in Hilbert $C^\\ast$--modules and we show that they share many useful properties with their corresponding notions in Hilbert and Banach spaces. We show that various properties of multipliers are closely related to their symbols and Bessel sequences, especially we consider multipliers when their Bessel sequences are modular Riesz bases and we see that in this case multipliers can be ...
Detection of Bessel beams with digital axicons
Trichili, Abderrahmen; Ismail, Yaseera; Roux, Filippus; McLaren, Melanie; Zghal, Mourad; Forbes, Andrew
2014-01-01
We propose a simple method for the detection of Bessel beams with arbitrary radial and azimuthal indices, and then demonstrate it in an all-digital setup with a spatial light modulator. We confirm that the fidelity of the detection method is very high, with modal cross-talk below 5%, even for high orbital angular momentum carrying fields with long propagation ranges. To illustrate the versatility of the approach we use it to observe the modal spectrum changes during the self-reconstruction process of Bessel beams after encountering an obstruction, as well as to characterize modal distortions of Bessel beams propagating through atmospheric turbulence.
Materials processing with superposed Bessel beams
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.
Causal (anticausal Bessel derivative and the ultrahyperbolic Bessel operator
Directory of Open Access Journals (Sweden)
Manuel Aguirre Téllez
1997-11-01
Full Text Available Let B^α_C and B^α_A be ultrahyperbolic Bessel operator causal (anticausal of the order α defined by B^α_C f = G_α ( P + i0, m, n ∗ f , B^α f = G_α ( P −i0, m, n ∗ f and let D^α_C and D^α_A be generalized causal (anticausal Bessel derivative of order α defined by D^α_C f = G_{−α} ( P − i0, m, n ∗ f , D^α_A f =G_{−α} ( P + i0, m, n ∗ f . In this note we give a sense to several relations of type: B^α_C (B^β_ A f + B^α_A (B^β_C f , D^ α_C (D^β_ A f + D^α_A (D^β_C f , . . .
Bessel bridges decomposition with varying dimension. Applications to finance
Faraud, Gabriel
2012-01-01
We consider a class of stochastic processes containing the classical and well-studied class of Squared Bessel processes. Our model, however, allows the dimension be a function of the time. We first give some classical results in a larger context where a time-varying drift term can be added. Then in the non-drifted case we extend many results already proven in the case of classical Bessel processes to our context. Our deepest result is a decomposition of the Bridge process associated to this generalized squared Bessel process, much similar to the much celebrated result of J. Pitman and M. Yor. On a more practical point of view, we give a methodology to compute the Laplace transform of additive functionals of our process and the associated bridge. This permits in particular to get directly access to the joint distribution of the value at t of the process and its integral. We finally give some financial applications to illustrate the panel of applications of our results.
Catenary nanostructures as compact Bessel beam generators
Li, Xiong; Pu, Mingbo; Zhao, Zeyu; Ma, Xiaoliang; Jin, Jinjin; Wang, Yanqin; Gao, Ping; Luo, Xiangang
2016-02-01
Non-diffracting Bessel beams, including zero-order and high-order Bessel Beams which carry orbital angular momentum (OAM), enable a variety of important applications in optical micromanipulation, sub-diffraction imaging, high speed photonics/quantum communication, etc. The commonly used ways to create Bessel beams, including an axicon or a digital hologram written to a spatial light modulator (SLM), have great challenges to operate at the nanoscale. Here we theoretically design and experimentally demonstrate one kind of planar Bessel beam generators based on metasurfaces with analytical structures perforated in ultra-thin metallic screens. Continuous phase modulation between 0 to 2π is realized with a single element. In addition, due to the dispersionless phase shift stemming from spin-orbit interaction, the proposed device can work in a wide wavelength range. The results may find applications in future optical communication, nanofabrication and super-resolution imaging, etc.
Catenary nanostructures as compact Bessel beam generators.
Li, Xiong; Pu, Mingbo; Zhao, Zeyu; Ma, Xiaoliang; Jin, Jinjin; Wang, Yanqin; Gao, Ping; Luo, Xiangang
2016-01-01
Non-diffracting Bessel beams, including zero-order and high-order Bessel Beams which carry orbital angular momentum (OAM), enable a variety of important applications in optical micromanipulation, sub-diffraction imaging, high speed photonics/quantum communication, etc. The commonly used ways to create Bessel beams, including an axicon or a digital hologram written to a spatial light modulator (SLM), have great challenges to operate at the nanoscale. Here we theoretically design and experimentally demonstrate one kind of planar Bessel beam generators based on metasurfaces with analytical structures perforated in ultra-thin metallic screens. Continuous phase modulation between 0 to 2π is realized with a single element. In addition, due to the dispersionless phase shift stemming from spin-orbit interaction, the proposed device can work in a wide wavelength range. The results may find applications in future optical communication, nanofabrication and super-resolution imaging, etc. PMID:26843142
Bessel's Differential Equation and Its Hyers-Ulam Stability
Directory of Open Access Journals (Sweden)
Kim Byungbae
2007-01-01
Full Text Available We solve the inhomogeneous Bessel differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Bessel differential equation.
Bessel's Differential Equation and Its Hyers-Ulam Stability
Directory of Open Access Journals (Sweden)
Soon-Mo Jung
2007-12-01
Full Text Available We solve the inhomogeneous Bessel differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Bessel differential equation.
Propagation of Bessel beam for ground-to-space applications
Ituen, Iniabasi; Birch, Philip; Young, Rupert; Chatwin, Chris
2015-01-01
We model the propagation of Gaussian and Bessel beams from ground through 22km altitude of atmospheric turbulence. We observe the Bessel beam has better performance based on RMS intensity error and the captured beam power
On Relations between Bessel Potential Spaces and Riesz Potential Spaces
Kurokawa, Takahide
2000-01-01
We present a relation between the Bessel potential spaces and the Riesz potential spaces. The ideas of the proof are to characterize each potential spaces and to give a correspondence between individual Bessel potentials and Riesz potentials.
Identities involving Bessel polynomials arising from linear differential equations
Kim, Taekyun; Kim, Dae San
2016-01-01
In this paper, we study linear di?erential equations arising from Bessel polynomials and their applications. From these linear differential equations, we give some new and explicit identities for Bessel polynomials.
Multipliers of pg-Bessel sequences in Banach spaces
Abdollahpour, M. R.; Najati, A.; Gavruta, P.
2015-01-01
In this paper, we introduce (p,q)g-Bessel multipliers in Banach spaces and we show that under some conditions a (p,q)g-Bessel multiplier is invertible. Also, we show the continuous dependency of (p,q)g-Bessel multipliers on their parameters.
A Determinant Expression for the Generalized Bessel Polynomials
Sheng-liang Yang; Sai-nan Zheng
2013-01-01
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.
Bessel beams with spatial oscillating polarization
Fu, Shiyao; Zhang, Shikun; Gao, Chunqing
2016-08-01
Bessel beams are widely used in optical metrology mainly because of their large Rayleigh range (focal length). Radial/azimuthal polarization of such beams is of interest in the fields of material processing, plasma absorption or communication. In this paper an experimental set-up is presented, which generates a Bessel-type vector beam with a spatial polarization, oscillating along the optical axis, when propagating in free space. A first holographic axicon (HA) HA1 produces a normal, linearly polarized Bessel beam, which by a second HA2 is converted into the spatial oscillating polarized beam. The theory is briefly discussed, the set-up and the experimental results are presented in detail.
Bessel beams with spatial oscillating polarization.
Fu, Shiyao; Zhang, Shikun; Gao, Chunqing
2016-01-01
Bessel beams are widely used in optical metrology mainly because of their large Rayleigh range (focal length). Radial/azimuthal polarization of such beams is of interest in the fields of material processing, plasma absorption or communication. In this paper an experimental set-up is presented, which generates a Bessel-type vector beam with a spatial polarization, oscillating along the optical axis, when propagating in free space. A first holographic axicon (HA) HA1 produces a normal, linearly polarized Bessel beam, which by a second HA2 is converted into the spatial oscillating polarized beam. The theory is briefly discussed, the set-up and the experimental results are presented in detail. PMID:27488174
Microwave bessel beams generation using guided modes
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.
Quantum-mechanical properties of Bessel beams
International Nuclear Information System (INIS)
Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. As we show explicitly, the operators that are usually associated with linear momentum, orbital angular momentum, and spin do not satisfy the algebra of the translation and rotation group. Nevertheless, we identify some components of these operators that represent observable quantities in an appropriate basis, thus characterizing the quantum numbers of Bessel photons. Some physical consequences of these results are discussed
The Logvinenko-Sereda Theorem for the Fourier-Bessel transform
Ghobber, Saifallah
2012-01-01
The aim of this paper is to establish an analogue of Logvinenko-Sereda's theorem for the Fourier-Bessel transform (or Hankel transform) $\\ff_\\alpha$ of order $\\alpha>-1/2$. Roughly speaking, if we denote by $PW_\\alpha(b)$ the Paley-Wiener space of $L^2$-functions with Fourier-Bessel transform supported in $[0,b]$, then we show that the restriction map $f\\to f|_\\Omega$ is essentially invertible on $PW_\\alpha(b)$ if and only if $\\Omega$ is sufficiently dense. Moreover, we give an estimate of the norm of the inverse map. As a side result we prove a Bernstein type inequality for the Fourier-Bessel transform.
Burkholder inequalities for submartingales, Bessel processes and conformal martingales
Bañuelos, Rodrigo
2011-01-01
The motivation for this paper comes from the following question on comparison of norms of conformal martingales $X$, $Y$ in $\\R^d$, $d\\geq 2$. Suppose that $Y$ is differentially subordinate to $X$. For $01$ is not an integer, which has further interesting applications to stopped Bessel processes and to the behavior of smooth functions on Euclidean domains. The inequality for conformal martingales, which has its roots on the study of the $L^p$ norms of the Beurling-Ahlfors singular integral operator \\cite{BW}, extends a recent result of Borichev, Janakiraman and Volberg \\cite{BJV2}.
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.
Institute of Scientific and Technical Information of China (English)
王强; 李顺初; 蒲俊
2015-01-01
This paper solved a boundary value problem of Riccati - Bessel equation;and the similar kernel function and similar structure of the solution were obtained. By further analysis and solving this class of boundary value problem,the guiding functions were firstly constructed by using two linearly independent solutions of Riccati- Bessel equation,and then the similar kernel function was assembled by the guiding functions and coefficient of right boundary value condition. The solution to the boundary value problem was assembled by similar kernel func-tion and coefficient of left boundary value condition. Therefore a new idea is put forward for solving this class of boundary value problem of Riccati - Bessel equation:similar structure.%针对 Riccati - Bessel 方程一类边值问题进行求解，获得了解式的相似核函数和相似结构，通过进一步分析，发现求解该类边值问题可先利用 Riccati - Bessel 方程的两个线性无关解构造引解函数，再结合右边值条件的系数组装得到相似核函数；通过相似核函数和左边值条件的系数组装就可以得到 Riccati - Bessel 方程边值问题的解，由此提出了解决该类 Riccati - Bessel 方程边值问题的一种新思路———相似构造。
On the $q$-Bessel Fourier transform
Dhaouadi, Lazhar
2013-01-01
In this work, we are interested by the $q$-Bessel Fourier transform with a new approach. Many important results of this $q$-integral transform are proved with a new constructive demonstrations and we establish in particular the associated $q$-Fourier-Neumen expansion which involves the $q$-little Jacobi polynomials.
Bessel potential space on the Laguerre hypergroup
Directory of Open Access Journals (Sweden)
Ahmed Taieb
2011-01-01
Full Text Available Abstract In this article, we define the fractional differentiation Dδ of order δ, δ > 0, induced by the Laguerre operator L and associated with respect to the Haar measure dmα. We obtain a characterization of the Bessel potential space using Dδ and different equivalent norms.
Point vortex equilibria related to Bessel polynomials
O'Neil, Kevin A.
2016-05-01
The method of polynomials is used to construct two families of stationary point vortex configurations. The vortices are placed at the reciprocals of the zeroes of Bessel polynomials. Configurations that translate uniformly, and configurations that are completely stationary, are obtained in this way.
Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms
Ikhabisimov, D. K.; Debabov, A. S.; Kolosov, B. I.; Usikov, D. A.
1979-01-01
Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.
Bessel filters applied in biomedical image processing
Mesa Lopez, Juan Pablo; Castañeda Saldarriaga, Diego Leon
2014-06-01
A magnetic resonance is an image obtained by means of an imaging test that uses magnets and radio waves to create body images, however, in some images it's difficult to recognize organs or foreign agents present in the body. With these Bessel filters the objective is to significantly increase the resolution of magnetic resonance images taken to make them much clearer in order to detect anomalies and diagnose the illness. As it's known, Bessel filters appear to solve the Schrödinger equation for a particle enclosed in a cylinder and affect the image distorting the colors and contours of it, therein lies the effectiveness of these filters, since the clear outline shows more defined and easy to recognize abnormalities inside the body.
Quantum Mechanical Properties of Bessel Beams
Jauregui, R.; Hacyan, S.
2004-01-01
Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. The algebra of these operators is analyzed in detail; it is shown that the operators that are usually associated to linear momentum, orbital angular momentum and spin do not satisfy the algebra of the translation and rotation group. In particular, what seems to be the spin is more similar to the helicity. Some physi...
Ladder operators and recursion relations for the associated Bessel polynomials
International Nuclear Information System (INIS)
Introducing the associated Bessel polynomials in terms of two non-negative integers, and under an integrability condition we simultaneously factorize their corresponding differential equation into a product of the ladder operators by four different ways as shape invariance symmetry equations. This procedure gives four different pairs of recursion relations on the associated Bessel polynomials. In spite of description of Bessel and Laguerre polynomials in terms of each other, we show that the associated Bessel differential equation is factorized in four different ways whereas for Laguerre one we have three different ways
Ladder operators and recursion relations for the associated Bessel polynomials
Fakhri, H.; Chenaghlou, A.
2006-10-01
Introducing the associated Bessel polynomials in terms of two non-negative integers, and under an integrability condition we simultaneously factorize their corresponding differential equation into a product of the ladder operators by four different ways as shape invariance symmetry equations. This procedure gives four different pairs of recursion relations on the associated Bessel polynomials. In spite of description of Bessel and Laguerre polynomials in terms of each other, we show that the associated Bessel differential equation is factorized in four different ways whereas for Laguerre one we have three different ways.
Ladder operators and recursion relations for the associated Bessel polynomials
Energy Technology Data Exchange (ETDEWEB)
Fakhri, H. [Institute for Studies in Theoretical Physics and Mathematics (IPM), PO Box 19395-5531, Tehran (Iran, Islamic Republic of) and Department of Theoretical Physics and Astrophysics, Physics Faculty, Tabriz University, PO Box 51666-16471, Tabriz (Iran, Islamic Republic of)]. E-mail: hfakhri@ipm.ir; Chenaghlou, A. [Institute for Studies in Theoretical Physics and Mathematics (IPM), PO Box 19395-5531, Tehran (Iran, Islamic Republic of) and Physics Department, Faculty of Science, Sahand University of Technology, PO Box 51335-1996, Tabriz (Iran, Islamic Republic of)]. E-mail: a.chenaghlou@sut.ac.ir
2006-10-30
Introducing the associated Bessel polynomials in terms of two non-negative integers, and under an integrability condition we simultaneously factorize their corresponding differential equation into a product of the ladder operators by four different ways as shape invariance symmetry equations. This procedure gives four different pairs of recursion relations on the associated Bessel polynomials. In spite of description of Bessel and Laguerre polynomials in terms of each other, we show that the associated Bessel differential equation is factorized in four different ways whereas for Laguerre one we have three different ways.
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....
Geometric Bessel models for GSp_4 and multiplicity one
Lysenko, Sergey
2004-01-01
I this paper, which is a sequel to math.AG/0310361, we study Bessel models of representations of GSp_4 over a local non archimedian field in the framework of the geometric Langlands program. The Bessel module over the nonramified Hecke algebra of GSp_4 admits a geometric counterpart, the Bessel category of perverse sheaves on some ind-algebraic stack. We use it to prove a geometric version of the multiplicity one for Bessel models. It implies a geometric Casselman-Shalika type formula for the...
Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid
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.
Optical trapping with Bessel beams generated from semiconductor lasers
International Nuclear Information System (INIS)
In this paper, we study generation of Bessel beams from semiconductor lasers with high beam propagation parameter M2 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
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...
Bessel type inequalities in Hilbert C*-modules
S. S. Dragomir; M. Khosravi; Moslehian, M. S.
2009-01-01
Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombiari and Boas--Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert $C^*$-modules.
Orthogonal fast spherical Bessel transform on uniform grid
Serov, Vladislav V
2015-01-01
We propose an algorithm for the orthogonal fast discrete spherical Bessel transform on an uniform grid. Our approach is based upon the spherical Bessel transform factorization into the two subsequent orthogonal transforms, namely the fast Fourier transform and the orthogonal transform founded on the derivatives of the discrete Legendre orthogonal polynomials.
Efficient Generation of Truncated Bessel Beams using Cylindrical Waveguides
Ilchenko, Vladimir S.; Mohageg, Makan; Savchenkov, Anatoliy A.; Matsko, Andrey B.; Maleki, Lute
2007-01-01
In this paper we address efficient conversion between a Gaussian beam (a truncated plane wave) and a truncated Bessel beam of agiven order, using cylindrical optical waveguides and whispering gallery mode resonators. Utilizing a generator based on waveguides combined with whispering gallery mode resonators, we have realized Bessel beams of the order of 200 with a conversion efficiency exceeding 10 %.
Electromagnetic modified Bessel-Gauss beams and waves.
Seshadri, S R
2008-01-01
The transverse magnetic (TM) modified Bessel-Gauss beams and their full-wave generalizations are treated. Attention is paid to the spreading properties on propagation of the null in the radiation intensity pattern for the azimuthal mode numbers m=0 and 1. The rate of spreading of the null in the propagation direction is significantly less for the TM modified Bessel-Gauss waves than those for the corresponding TM Bessel-Gauss waves. The total power transported by the waves is determined and compared with that of the corresponding paraxial beam to estimate the quality of the paraxial beam approximation of the wave. The dependence of the quality of the paraxial beam approximation on the azimuthal mode number, the beam shape parameter, and the ratio of the beam waist to the wavelength has a regular pattern for the TM Bessel-Gauss wave and not for the TM modified Bessel-Gauss wave. PMID:18157205
Nanolithography using Bessel Beams of Extreme Ultraviolet Wavelength.
Fan, Daniel; Wang, Li; Ekinci, Yasin
2016-01-01
Bessel beams are nondiffracting light beams with large depth-of-focus and self-healing properties, making them suitable as a serial beam writing tool over surfaces with arbitrary topography. This property breaks the inherent resolution vs. depth-of-focus tradeoff of photolithography. One approach for their formation is to use circularly symmetric diffraction gratings. Such a ring grating was designed and fabricated for the extreme ultraviolet (EUV) wavelength of 13.5 nm, a candidate wavelength for future industrial lithography. Exposure of the aerial images showed that a Bessel beam with an approximately 1 mm long z-invariant central core of 223 nm diameter had been achieved, in good agreement with theory. Arbitrary patterns were written using the Bessel spot, demonstrating possible future application of Bessel beams for serial beam writing. Lithographic marks of ~30 nm size were also observed using a high resolution Bessel beam. PMID:27501749
Generation and application of bessel beams in electron microscopy.
Grillo, Vincenzo; Harris, Jérémie; Gazzadi, Gian Carlo; Balboni, Roberto; Mafakheri, Erfan; Dennis, Mark R; Frabboni, Stefano; Boyd, Robert W; Karimi, Ebrahim
2016-07-01
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. PMID:27203186
Optical forces in higher order Bessel beam
Czech Academy of Sciences Publication Activity Database
Šiler, Martin; Jákl, Petr; Chvátal, Lukáš; Zemánek, Pavel
Bellingham : SPIE, 2012, 86970R:1-6. ISBN 978-0-8194-9481-8. [CPS 2012. Czech-Polish-Slovak Optical Conference on Wave and Quantum Aspects of Contemporary Optics /18./. Ostravice (CZ), 03.09.2012-07.09.2012] R&D Projects: GA MŠk LH12018; GA MŠk ED0017/01/01; GA ČR GPP205/12/P868 Institutional support: RVO:68081731 Keywords : Bessel beam * optical vortex * optical forces * generalized Lorenz-Mie theory * size-effect Subject RIV: BH - Optics, Masers, Lasers
Time-reversal and the Bessel equation
Alfinito, Eleonora; Vitiello, Giuseppe
2015-07-01
The system of two damped/amplified oscillator equations is of widespread interest in the study of many physical problems and phenomena, from inflationary models of the Universe to thermal field theories, in condensed matter physics as well in high energy physics, and also in neuroscience. In this report we review the equivalence, in a suitable parametrization, between such a system of equations and the Bessel equations. In this connection, we discuss the breakdown of loop-antiloop symmetry, its relation with time-reversal symmetry and the mechanism of group contraction. Euclidean algebras such as e(2) and e(3) are also discussed in relation with Virasoro-like algebra.
Quantum Mechanical Properties of Bessel Beams
Jauregui, R
2004-01-01
Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. The algebra of these operators is analyzed in detail; it is shown that the operators that are usually associated to linear momentum, orbital angular momentum and spin do not satisfy the algebra of the translation and rotation group. In particular, what seems to be the spin is more similar to the helicity. Some physical consequences of these results are examined.
Microparticle trapping in an ultrasonic Bessel beam
Choe, Youngki; Kim, Jonathan W; Shung, K. Kirk; Kim, Eun Sok
2011-01-01
This paper describes an acoustic trap consisting of a multi-foci Fresnel lens on 127 μm thick lead zirconate titanate sheet. The multi-foci Fresnel lens was designed to have similar working mechanism to an Axicon lens and generates an acoustic Bessel beam, and has negative axial radiation force capable of trapping one or more microparticle(s). The fabricated acoustic tweezers trapped lipid particles ranging in diameter from 50 to 200 μm and microspheres ranging in diameter from 70 to 90 μm at...
Second-harmonic generation with Bessel beams
Shatrovoy, Oleg
We present the results of a numerical simulation tool for modeling the second-harmonic generation (SHG) interaction experienced by a diffracting beam. This code is used to study the simultaneous frequency and spatial profile conversion of a truncated Bessel beam that closely resembles a higher-order mode (HOM) of an optical fiber. SHG with Bessel beams has been investigated in the past and was determined have limited value because it is less efficient than SHG with a Gaussian beam in the undepleted pump regime. This thesis considers, for the first time to the best of our knowledge, whether most of the power from a Bessel-like beam could be converted into a second-harmonic beam (full depletion), as is the case with a Gaussian beam. We study this problem because using HOMs for fiber lasers and amplifiers allows reduced optical intensities, which mitigates nonlinearities, and is one possible way to increase the available output powers of fiber laser systems. The chief disadvantage of using HOM fiber amplifiers is the spatial profile of the output, but this can be transformed as part of the SHG interaction, most notably to a quasi-Gaussian profile when the phase mismatch meets the noncollinear criteria. We predict, based on numerical simulation, that noncollinear SHG (NC-SHG) can simultaneously perform highly efficient (90%) wavelength conversion from 1064 nm to 532 nm, as well as concurrent mode transformation from a truncated Bessel beam to a Gaussian-like beam (94% overlap with a Gaussian) at modest input powers (250 W, peak power or continuous-wave operation). These simulated results reveal two attractive features -- the feasibility of efficiently converting HOMs of fibers into Gaussian-like beams, and the ability to simultaneously perform frequency conversion. Combining the high powers that are possible with HOM fiber amplifiers with access to non-traditional wavelengths may offer significant advantages over the state of the art for many important applications
Institute of Scientific and Technical Information of China (English)
邱振兴; 吴逢铁; 郭东栋
2008-01-01
理论分析Bessel光束和Bessel-Gauss光束的相互联系及区别,数值模拟理想Bessel光束和Bessel-Gauss光束在任意平面的径向光强分布,以及光腰半径和谐振腔腔长对输出Bessel-Gauss光束的影响.模拟结果表明,相对于Bessel光,Bessel-Gauss光衰减较快,实验结果也验证了理论分析.同时,光腰半径越大,光强的径向分布衰减越慢;而腔长越大,其主模式的振幅分布衰减越慢.
Bessel Series in the Space H1(D)%H1(D)空间的Bessel级数
Institute of Scientific and Technical Information of China (English)
木乐华
2001-01-01
An identity concerning the partial sums of Bessel series and power series for H1(D) functions is given.Based on it,many of precise extimates about the deviation of the partial sums of Bessel series can be obtained.%本文给出关于H1(D)空间中函数的Bessel级数的部分和用幂级数的部分和表示的一个恒等式.基于它，可以得到Bessel级数部分和偏差的诸多精确估计.
Multifunctional diffractive optical elements for the generation of higher order Bessel-like-beams
Vijayakumar, A.; Bhattacharya, Shanti
2015-01-01
Higher Order Bessel Beams (HOBBs) have many useful applications in optical trapping experiments. The generation of HOBBs is achieved by illuminating an axicon by a Laguerre-Gaussian beam generated by a spiral phase plate. It can also be generated by a Holographic Optical Element (HOE) containing the functions of the Spiral Phase Plate (SPP) and an axicon. However the HOBB's large focal depth reduces the intensity at each plane. In this paper, we propose a multifunctional Diffractive Optical Element (DOE) containing the functions of a SPP, axicon and a Fresnel Zone Lens (FZL) to generate higher efficiency higher order Bessel-like-beams with a reduced focal depth. The functions of a SPP and a FZL were combined by shifting the location of zones of FZL in a spiral fashion. The resulting element is combined with an axicon by modulo-2π phase addition technique. The final composite element contains the functions of SPP, FZL and axicon. The elements were designed with different topological charges and fabricated using electron beam direct writing. The elements were tested and the generation of a higher order Bessel-like-beams is confirmed. Besides, the elements also generated high quality donut beams at two planes equidistant from the focal plane of the FZL.
Confined nanoparticle measurement using Bessel Beam Microscopy
Chakraborty, Chumki; Snoeyink, Craig
2015-11-01
With the advent of Lab-on-chip technologies, study of near surface phenomenon has gained a lot of importance due to their huge impact on bulk fluid properties. Such studies demand imaging techniques with utmost precision to capture the intricate details of the interface. But, resolution for most of the optical imaging systems is limited due to the light spreading effects of diffraction. This diffraction limited resolution, can be improved by the use of Bessel Beam microscopy. Bessel beam imaging technique when combined with a TIRF (Total Internal Reflection Fluorescence) system can be used for high resolution particle tracking experiments, to reveal detailed information about near surface particle positions and motions with their velocity profile and distribution. With the experimental set up combining these two powerful tools, we plan to present our particle tracking velocimetry results in the interface regime of confined nanoparticles in a binary fluid mixture. Such a study can contribute towards a better understanding of near surface fluid-particle interfaces.
Bessel and Grüss Type Inequalities in Inner Product Modules over Banach -Algebras
Directory of Open Access Journals (Sweden)
Dragomir SS
2011-01-01
Full Text Available We give an analogue of the Bessel inequality and we state a simple formulation of the Grüss type inequality in inner product -modules, which is a refinement of it. We obtain some further generalization of the Grüss type inequalities in inner product modules over proper -algebras and unital Banach -algebras for -seminorms and positive linear functionals.
Behavior of obliquely incident vector Bessel beams at planar interfaces
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.
Generation of spatial Bessel beams using holographic metasurface.
Cai, Ben Geng; Li, Yun Bo; Jiang, Wei Xiang; Cheng, Qiang; Cui, Tie Jun
2015-03-23
We propose to use backward radiations of leaky waves supported by a holographic metasurface to produce spatial Bessel beams in the microwave frequency regime. The holographic metasurface consists of a grounded dielectric slab and a series of metal patches. By changing the size of metal patches, the surface-impedance distribution of the holographic metasurface can be modulated, and hence the radiation properties of the leaky waves can be designed to realize Bessel beams. Both numerical simulations and experiments verify the features of spatial Bessel beams, which may be useful in imaging applications or wireless power transmissions with the dynamic focal-depth controls. PMID:25837097
Jacobi-Bessel analysis of reflector antennas with elliptical apertures
Rahmat-Samii, Yahya
1987-01-01
Although many reflector antennas possess circular projected apertures, there are recent satellite and ground antenna applications for which it is desirable to employ reflectors with elliptical apertures. Here a modification of the Jacobi-Bessel expansion is presented for the diffraction analysis of reflectors with elliptical apertures. A comparative study is also performed between this modified Jacobi-Bessel algorithm and the one which uses the Jacobi-Bessel expansion over a circumscribing circular region. Numerical results are presented for offset reflectors with elliptical and circular apertures and the improved convergence properties of the modified algorithm are highlighted.
Surface multipole solitons on photorefractive media with Bessel optical lattices
Hong, Woo-Pyo
2015-03-01
We find the existence conditions for new surface crescent, dipole, tripole, and quadrupole solitons formed at the interface of a focusing photorefractive medium and a medium imprinted with a Bessel optical lattice. We demonstrate by using numerical simulations that the crescent and the dipole solitons show oscillatory behaviors in their amplitude and shape while the tripole and the quadrupole solitons maintain a remarkable rigidity during propagation. Based on a linear stability analysis, we classify the stability region of the tripole and the quadrupole surface solitons in terms of the Bessel optical lattice strength and the Bessel index.
Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid
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 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 \\beta, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) due to the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigati...
Millijoule femtosecond micro-Bessel beams for ultra-high aspect ratio machining.
Mitra, Sambit; Chanal, Margaux; Clady, Raphaël; Mouskeftaras, Alexandros; Grojo, David
2015-08-20
We report on a functional experimental design for Bessel beam generation capable of handling high-energy ultrashort pulses (up to 1.2 mJ per pulse of 50 fs duration). This allows us to deliver intensities exceeding the breakdown threshold for air or any dielectric along controlled micro-filaments with lengths exceeding 4 mm. It represents an unprecedented upscaling in comparison to recent femtosecond Bessel beam micromachining experiments. We produce void microchannels through glass substrates to demonstrate that aspect ratios exceeding 1200∶1 can be achieved by using single high-intensity pulses. This demonstration must lead to new methodologies for deep-drilling and high-speed cutting applications. PMID:26368773
Gouesbet, Gérard
2016-06-01
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.
Riesz's and Bessel's Operators in Bilateral Grand Lebesgue Spaces
Ostrovsky, E; Sirota, L
2009-01-01
In this paper we obtain the non - asymptotic estimations for Riesz's and Bessel's potential integral operators in the so - called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities.
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...... dual frames. If the given Bessel sequences are Gabor systems in L2(R), the extension can be chosen to have Gabor structure as well. We also show that if the generators of the given Gabor Bessel sequences are compactly supported, we can choose the generators of the added Gabor systems to be compactly...... supported as well. This is a significant improvement compared to the extension of a Bessel sequence to a tight frame, where the added generator only can be compactly supported in some special cases. We also analyze the wavelet case, and find sufficient conditions under which a pair of wavelet systems can be...
Long-distance Bessel beam propagation through Kolmogorov turbulence.
Birch, Philip; Ituen, Iniabasi; Young, Rupert; Chatwin, Chris
2015-11-01
Free-space optical communication has the potential to transmit information with both high speed and security. However, since it is unguided it suffers from losses due to atmospheric turbulence and diffraction. To overcome the diffraction limits the long-distance propagation of Bessel beams is considered and compared against Gaussian beam properties. Bessel beams are shown to have a number of benefits over Gaussian beams when propagating through atmospheric turbulence. PMID:26560921
Second-Harmonic Generation of Bessel Beams in Lossy Media
Institute of Scientific and Technical Information of China (English)
丁德胜; 许坚毅; 王耀俊
2002-01-01
We present a further analysis for the second-harmonic generation of Bessel beams in lossy media. The emphasis is put on the effect of absorption to the radial pattern of the second-harmonic beam. It is shown that within the absorption length of the second harmonic, the Bessel second-harmonic beam approaches limited diffraction in the radial direction and behaves as in the case of lossless media.
GENERALIZED BROWNIAN SHEET IMAGES AND BESSEL-RIESZ CAPACITY
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Let (W) be a two-parameter Rd-valued generalized Brownian sheet. The author obtains an explicit Bessel-Riesz capacity estimate for the images of a two-dimensional set under (W). He also presents the connections between the Lebesgue measure of the image of (W) and Bessel-Riesz capacity. His conclusions also solve a problem proposed by J.P.Kahane.
Light scattering of a non-diffracting zero-order Bessel beam by uniaxial anisotropic bispheres
International Nuclear Information System (INIS)
Based on the generalized multi-particle Mie theory and the Fourier transformation approach, light scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes illuminated by a zero-order Bessel beam (ZOBB) is investigated. The size and configuration of the particles are arbitrary. The expansion expressions of the ZOBB are given in terms of the spherical vector wave functions (SVWFs) and the expansion coefficients are derived. Utilizing the vector addition theorem of the SVWFs, the interactive scattering coefficients are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. The effects of the conical angle, beam centre position, sphere separation distance, and anisotropic parameters on the far-region field distributions are numerically analyzed in detail. Some results are compared with those results for a Gaussian beam incidence. Selected results of bispheres consisting of typical medium such as TiO2, SiO2, Silicon, water are exhibited. This investigation could provide an effective test for further research on the scattering characteristic of an aggregate of anisotropic spheres by a high-order Bessel vortex beam and radiation forces, which are important in optical tweezers and particle manipulation applications. - Highlights: • Scattering of a zero-order Bessel beam by uniaxial anisotropic bispheres is studied. • The parallel primary optical axes of the anisotropic spheres are considered. • The accuracy of the theory and codes is verified. • Scattering performances of uniaxial anisotropic bispheres are numerically discussed. • Different properties of multiple scattering by a zero-order Bessel beam are shown
Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid.
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. PMID:26470043
Combinatorial proofs of inverse relations and log-concavity for Bessel numbers
Han, Hyuk; Seo, Seunghyun
2004-01-01
Let the Bessel number of the second kind B(n,k) be the number of set partitions of [n] into k blocks of size one or two, and let the Bessel number of the first kind b(n,k) be a certain coefficient in n-th Bessel polynomial. In this paper, we show that Bessel numbers satisfy two properties of Stirling numbers: The two kinds of Bessel numbers are related by inverse formulas, and both Bessel numbers of the first kind and the second kind form log-concave sequences. By constructing sign-reversing ...
Non-linear optical measurements using a scanned, Bessel beam
Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.
2015-03-01
Oftentimes cells are removed from the body for disease diagnosis or cellular research. This typically requires fluorescent labeling followed by sorting with a flow cytometer; however, possible disruption of cellular function or even cell death due to the presence of the label can occur. This may be acceptable for ex vivo applications, but as cells are more frequently moving from the lab to the body, label-free methods of cell sorting are needed to eliminate these issues. This is especially true of the growing field of stem cell research where specialized cells are needed for treatments. Because differentiation processes are not completely efficient, cells must be sorted to eliminate any unwanted cells (i.e. un-differentiated or differentiated into an unwanted cell type). In order to perform label-free measurements, non-linear optics (NLO) have been increasingly utilized for single cell analysis because of their ability to not disrupt cellular function. An optical system was developed for the measurement of NLO in a microfluidic channel similar to a flow cytometer. In order to improve the excitation efficiency of NLO, a scanned Bessel beam was utilized to create a light-sheet across the channel. The system was tested by monitoring twophoton fluorescence from polystyrene microbeads of different sizes. Fluorescence intensity obtained from light-sheet measurements were significantly greater than measurements made using a static Gaussian beam. In addition, the increase in intensity from larger sized beads was more evident for the light-sheet system.
Sum-type Kaiser-Bessel windows for apodized antenna arrays
Anukhin, I. P.; Lukin, V. V.; Ponomarenko, N. N.; Zelensky, A. A.; Saramaki, Tapio; Zbaida, K.
1997-01-01
A class of sum-type Kaiser-Bessel windows is introduced. These windows are optimized for improving the performance of apodized array patterns. Compared with the basic Kaiser-Bessel windows, the proposed windows are shown provide several benefits.
Shao, Zhuhong; Shu, Huazhong; Wu, Jiasong; Chen, Beijing; Coatrieux, Jean-Louis
2014-01-01
In this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results show that quaternion Bessel-Fourier moments lead to better performance for color image reconstruction t...
A short note on the propagation of a Bessel beam in conducting media
Mugnai, D.
2009-01-01
Recently, the use of Bessel beams in evaluating the possibility of using them for a new generation of GPR (ground penetrating radar) systems has been considered. Therefore, an analysis of the propagation of Bessel beam in conducting media is worthwhile. We present here an analysis of this type. Specifically, for normal incidence we analyze the propagation of a Bessel beam coming from a perfect dielectric and impinging on a conducting medium, i.e. the propagation of a Bessel beam generated by ...
Propagation of Bessel beams from a dielectric to a conducting medium
Mugnai, D.
2010-01-01
Recently, the use of Bessel beams in evaluating the possibility of using them for a new generation of GPR (ground penetrating radar) systems has been considered. Therefore, an analysis of the propagation of Bessel beam in conducting media is worthwhile. We present here an analysis of this type. Specifically, for normal incidence we analyze the propagation of a Bessel beam coming from a perfect dielectric and impinging on a conducting medium, i.e. the propagation of a Bessel beam generated by ...
RIEMANN-HILBERT CHARACTERIZATION FOR MAIN BESSEL POLYNOMIALS WITH VARYING LARGE NEGATIVE PARAMETERS
Institute of Scientific and Technical Information of China (English)
段萍; 杜金元
2014-01-01
In this article, we establish the Bessel polynomials with varying large negative parameters and discuss their orthogonality based on the generalized Bessel polynomials. By using the Riemann-Hilbert boundary value problem on the positive real axis, we get the Riemann-Hilbert characterization of the main Bessel polynomials with varying large negative parameters.
Change of the size of vector Bessel beam rings under reflection
Novitsky, Andrey V.; Novitsky, Denis V.
2008-01-01
We theoretically predict the change of the size of Bessel beam rings under reflection. Considered electromagnetic Bessel beam is the superposition of phase shifted TE and TM polarized Bessel beams. Reflection from a semi-infinite medium and from a slab are studied. The sets of parameters maximizing the effect are discussed.
High-Order Bessel-Gaussian Beam and its Propagation Properties
Institute of Scientific and Technical Information of China (English)
陆璇辉; 陈许敏; 张蕾; 薛大建
2003-01-01
A high-order Bessel-Gaussian mode is introduced to describe hollow beams. The results for high-order BesselGaussian beams propagating through lens focusing system and free space are derived in terms of Collins integral formula. The diffraction patterns and profile for high-order Bessel-Gaussian beams propagating through the above-mentioned optical systems are illustrated.
Indian Academy of Sciences (India)
Hüseyin Yildirim; M Zeki Sarikaya; Sermin Öztürk
2004-11-01
In this article, the operator $\\Diamond^k_B$ is introduced and named as the Bessel diamond operator iterated times and is defined by $$\\Diamond^k_B=[(B_{x_1}+B_{x_2}+\\cdots +B_{x_p})^2-(B_{x_{p+1}}+\\cdots +B_{x_{p+q}})^2]^k,$$ where $p + q = n, B_{x_i} = \\frac{^2}{ x^2_i}+\\frac{2_i}{x_i}\\frac{}{ x_i}$, where $2_i = 2_i + 1, _i > - \\frac{1}{2} [8], x_i > 0, i = 1, 2,\\ldots ,n, k$ is a non-negative integer and is the dimension of $\\mathbb{R}^+_n$. In this work we study the elementary solution of the Bessel diamond operator and the elementary solution of the operator $\\Diamond^k_B$ is called the Bessel diamond kernel of Riesz. Then, we study the Fourier–Bessel transform of the elementary solution and also the Fourier–Bessel transform of their convolution.
Generation of high-order Bessel-Gauss beams%高阶Bessel-Gauss光束的产生方法
Institute of Scientific and Technical Information of China (English)
靳李丽; 朱艳英; 魏勇; 沈军峰; 窦红星; 李云涛
2012-01-01
Higher-order Bessel - Gauss beams shows "diffraction-free" characteristics under certain conditions. It is a kind of hollow beam that has broad application prospect. In this paper, we summarize and classify the generation methods. They can be divided into two categories-active way and passive way. The present generation methods-Resonator method, Geometrical optics method, Optical holographic method, computer generated hologram, Nonlinear optical method are described and analyzed. Finally we introduce the advantages and disadvantages of each method.%高阶贝塞尔-高斯(Bessel-Gauss)光束在一定条件下呈现“无衍射”特性,是一种具有广阔应用前景的空心光束.本文首先对高阶Bessel-Gauss光束的产生方法进行了分析和归类,将其产生方式分为主动式和被动式两大类.其次对获得高阶Bessel-Gauss光束的谐振腔法、几何光学法、光学全息法、计算全息法、非线性光学法等实验方法进行了阐述.最后总结了各种方法产生高阶Bessel-Gauss光束的优缺点.
Bessel beam fluorescence lifetime tomography of live embryos (Conference Presentation)
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.
Optical orbital angular momentum of evanescent Bessel waves.
Yang, Zhenshan
2015-05-18
We show that the orbital angular momentum (OAM) of evanescent light is drastically different from that of traveling light. Specifically, the paraxial contribution (typically the most significant part in a traveling wave) to the OAM vanishes in an evanescent Bessel wave when averaged over the azimuthal angle. Moreover, the OAM per unit energy for the evanescent Bessel field is reduced by a factor of (1+κ2/k2) from the standard result for the corresponding traveling field, where k and κ are the wave number and the evanescent decay rate, respectively. PMID:26074524
Practical realization of a microwave Bessel beam launcher
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.
Jacobi-Bessel Analysis Of Antennas With Elliptical Apertures.
Rahmat-Samii, Y.
1989-01-01
Coordinate transformation improves convergence pattern analysis of elliptical-aperture antennas. Modified version of Jacobi-Bessel expansion for vector diffraction analysis of reflector antennas uses coordinate transformation to improve convergence with elliptical apertures. Expansion converges rapidly for antennas with circular apertures, but less rapidly for elliptical apertures. Difference in convergence behavior between circular and elliptical Jacobi-Bessel algorithms indicated by highest values of indices m, n, and p required to achieve same accuracy in computed radiation pattern of offset paraboloidal antenna with elliptical aperture.
Gannot, Oran
2015-01-01
This paper considers boundary value problems for a class of singular elliptic operators which appear naturally in the study of anti-de Sitter spacetimes. These problems involve a singular Bessel operator acting in the normal direction. After formulating a Lopatinskii condition, elliptic estimates are established for functions supported near the boundary. A global Fredholm property follows from additional hypotheses in the interior. The results of this paper provide a rigorous framework for the study of quasinormal modes on anti-de Sitter black holes for the full range of boundary conditions considered in the physics literature.
Generation of arbitrary order Bessel beams via 3D printed axicons at the terahertz frequency range.
Wei, Xuli; Liu, Changming; Niu, Liting; Zhang, Zhongqi; Wang, Kejia; Yang, Zhengang; Liu, Jinsong
2015-12-20
We present the generation of arbitrary order Bessel beams at 0.3 THz through the implementation of suitably designed axicons based on 3D printing technology. The helical axicons, which possess thickness gradients in both radial and azimuthal directions, can convert the incident Gaussian beam into a high-order Bessel beam with spiral phase structure. The evolution of the generated Bessel beams are characterized experimentally with a three-dimensional field scanner. Moreover, the topological charges carried by the high-order Bessel beams are determined by the fork-like interferograms. This 3D-printing-based Bessel beam generation technique is useful not only for THz imaging systems with zero-order Bessel beams but also for future orbital-angular-momentum-based THz free-space communication with higher-order Bessel beams. PMID:26837031
Bessel process, Schramm-Loewner evolution, and Dyson model
Katori, Makoto
2011-01-01
Bessel process is defined as the radial part of the Brownian motion (BM) in the $D$-dimensional space, and is considered as a one-parameter family of one-dimensional diffusion processes indexed by $D$, BES$^{(D)}$. It is well-known that $D_{\\rm c}=2$ is the critical dimension. Bessel flow is a notion such that we regard BES$^{(D)}$ with a fixed $D$ as a one-parameter family of initial value. There is another critical dimension $\\bar{D}_{\\rm c}=3/2$ and, in the intermediate values of $D$, $\\bar{D}_{\\rm c} < D < D_{\\rm c}$, behavior of Bessel flow is highly nontrivial. The dimension D=3 is special, since in addition to the aspect that BES$^{(3)}$ is a radial part of the three-dimensional BM, it has another aspect as a conditional BM to stay positive. Two topics in probability theory and statistical mechanics, the Schramm-Loewner evolution (SLE) and the Dyson model (Dyson's BM model with parameter $\\beta=2$), are discussed. The SLE$^{(D)}$ is introduced as a 'complexification' of Bessel flow on the upper-h...
Asymmetric skew Bessel processes and their applications to finance
M. Decamps; M.J. Goovaerts; W. Schoutens
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 Besse
Two-photon flow cytometer with laser scanning Bessel beams
Wang, Yongdong; Ding, Yu; Ray, Supriyo; Paez, Aurelio; Xiao, Chuan; Li, Chunqiang
2016-03-01
Flow cytometry is an important technique in biomedical discovery for cell counting, cell sorting and biomarker detection. In vivo flow cytometers, based on one-photon or two-photon excited fluorescence, have been developed for more than a decade. One drawback of laser beam scanning two-photon flow cytometer is that the two-photon excitation volume is fairly small due to the short Rayleigh range of a focused Gaussian beam. Hence, the sampling volume is much smaller than one-photon flow cytometry, which makes it challenging to count or detect rare circulating cells in vivo. Bessel beams have narrow intensity profiles with an effective spot size (FWHM) as small as several wavelengths, making them comparable to Gaussian beams. More significantly, the theoretical depth of field (propagation distance without diffraction) can be infinite, making it an ideal solution as a light source for scanning beam flow cytometry. The trade-off of using Bessel beams rather than a Gaussian beam is the fact that Bessel beams have small concentric side rings that contribute to background noise. Two-photon excitation can reduce this noise, as the excitation efficiency is proportional to intensity squared. Therefore, we developed a two-photon flow cytometer using scanned Bessel beams to form a light sheet that intersects the micro fluidic channel.
Fractional Solutions of Bessel Equation with N-Method
Erdal Bas; Resat Yilmazer; Etibar Panakhov
2013-01-01
This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N ν method, we derive the fractional solutions of the equation.
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.
Seipt, D; Surzhykov, A; Fritzsche, S
2016-01-01
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 ultra-violet (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, analogue 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 t...
Mitri, F. G.
2011-11-01
Mathematical expressions for the acoustic scattering, instantaneous (linear), and time-averaged (nonlinear) forces resulting from the interaction of a new type of Bessel beam, termed here a first-order non-diffracting Bessel trigonometric beam (FOBTB) with a sphere, are derived. The beam is termed "trigonometric" because of the dependence of its phase on the cosine function. The FOBTB is regarded as a superposition of two equi-amplitude first-order Bessel vortex (helicoidal) beams having a unit positive and negative order (known also as topological charge), respectively. The FOBTB is non-diffracting, possesses an axial null, a geometric phase, and has an azimuthal phase that depends on cos( ϕ± ϕ0), where ϕ0 is an initial arbitrary phase angle. Beam rotation around its wave propagation axis can be achieved by varying ϕ0. The 3D directivity patterns are computed, and the resulting modifications of the scattering are illustrated for a rigid sphere centered on the beam's axis and immersed in water. Moreover, the backward and forward acoustic scattering by a sphere vanish for all frequencies. The present paper will shed light on the novel scattering properties of an acoustical FOBTB by a sphere that may be useful in particle manipulation and entrapment, non-destructive/medical imaging, and may be extended to other potentially useful applications in optics and electromagnetism.
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 TiO2, SiO2, 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.
Light scattering of a non-diffracting zero-order Bessel beam by uniaxial anisotropic bispheres
Li, Z. J.; Wu, Z. S.; Qu, T.; Li, H. Y.; Bai, L.; Gong, L.
2015-09-01
Based on the generalized multi-particle Mie theory and the Fourier transformation approach, light scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes illuminated by a zero-order Bessel beam (ZOBB) is investigated. The size and configuration of the particles are arbitrary. The expansion expressions of the ZOBB are given in terms of the spherical vector wave functions (SVWFs) and the expansion coefficients are derived. Utilizing the vector addition theorem of the SVWFs, the interactive scattering coefficients are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. The effects of the conical angle, beam centre position, sphere separation distance, and anisotropic parameters on the far-region field distributions are numerically analyzed in detail. Some results are compared with those results for a Gaussian beam incidence. Selected results of bispheres consisting of typical medium such as TiO2, SiO2, Silicon, water are exhibited. This investigation could provide an effective test for further research on the scattering characteristic of an aggregate of anisotropic spheres by a high-order Bessel vortex beam and radiation forces, which are important in optical tweezers and particle manipulation applications.
Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes
Katori, Makoto
2016-01-01
The Bessel process with parameter $D>1$ and the Dyson model of interacting Brownian motions with coupling constant $\\beta >0$ are extended to the processes, in which the drift term and the interaction terms are given by the logarithmic derivatives of Jacobi's theta functions. They are called the elliptic Bessel process, eBES$^{(D)}$, and the elliptic Dyson model, eDYS$^{(\\beta)}$, respectively. Both are realized on the circumference of a circle $[0, 2 \\pi r)$ with radius $r >0$ as temporally inhomogeneous processes defined in a finite time interval $[0, t_*), t_* < \\infty$. Transformations of them to Schr\\"odinger-type equations with time-dependent potentials lead us to proving that eBES$^{(D)}$ and eDYS$^{(\\beta)}$ can be constructed as the time-dependent Girsanov transformations of Brownian motions. In the special cases where $D=3$ and $\\beta=2$, observables of the processes are defined and the processes are represented for them using the Brownian paths winding round a circle and pinned at time $t_*$. We...
Helicon waves in uniform plasmas. IV. Bessel beams, Gendrin beams, and helicons
Urrutia, J. M.; Stenzel, R. L.
2016-05-01
Electromagnetic waves in the low frequency whistler mode regime are investigated experimentally and by digital data superposition. The radiation from a novel circular antenna array is shown to produce highly collimated helicon beams in a uniform unbounded plasma. The differences to Bessel beams in free space are remarked upon. Low divergence beams arise from the parallel group velocity of whistlers with phase velocity either along the guide field or at the Gendrin angle. Waves with angular momentum are produced by phasing the array in the circular direction. The differences in the field topologies for positive and negative modes numbers are shown. It is also shown that in uniform plasmas, the radial amplitude profile of the waves depends on the antenna field topology. Thus, there are no helicon "eigenmodes" with radial Bessel function profiles in uniform plasmas. It is pointed out that phase measurements in helicon devices indicate radial wave propagation which is inconsistent with helicon eigenmode theory based on paraxial wave propagation. Trivelpiece-Gould modes also exist in uniform unbounded plasmas.
Spherical space Bessel-Legendre-Fourier localized modes solver for electromagnetic waves.
Alzahrani, Mohammed A; Gauthier, Robert C
2015-10-01
Maxwell's vector wave equations are solved for dielectric configurations that match the symmetry of a spherical computational domain. The electric or magnetic field components and the inverse of the dielectric profile are series expansion defined using basis functions composed of the lowest order spherical Bessel function, polar angle single index dependant Legendre polynomials and azimuthal complex exponential (BLF). The series expressions and non-traditional form of the basis functions result in an eigenvalue matrix formulation of Maxwell's equations that are relatively compact and accurately solvable on a desktop PC. The BLF matrix returns the frequencies and field profiles for steady states modes. The key steps leading to the matrix populating expressions are provided. The validity of the numerical technique is confirmed by comparing the results of computations to those published using complementary techniques. PMID:26480087
Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams
Porras, Miguel A,; Ruiz-Jimenez, Carlos; Losada, Juan Carlos
2015-01-01
In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NL-UBB) whose inward H\\"ankel be...
Controllable light capsules employing modified Bessel-Gauss beams
Gong, Lei; Zhao, Qian; Ren, Yuxuan; Qiu, Xingze; Zhong, Mincheng; Li, Yinmei
2016-01-01
We report, in theory and experiment, on a novel class of controlled light capsules with nearly perfect darkness, directly employing intrinsic properties of modified Bessel-Gauss beams. These beams are able to naturally create three-dimensional bottle-shaped region during propagation as long as the parameters are properly chosen. Remarkably, the optical bottle can be controlled to demonstrate various geometries through tuning the beam parameters, thereby leading to an adjustable light capsule. We provide a detailed insight into the theoretical origin and characteristics of the light capsule derived from modified Bessel-Gauss beams. Moreover, a binary digital micromirror device (DMD) based scheme is first employed to shape the bottle beams by precise amplitude and phase manipulation. Further, we demonstrate their ability for optical trapping of core-shell magnetic microparticles, which play a particular role in biomedical research, with holographic optical tweezers. Therefore, our observations provide a new rou...
Quasi-Bessel beams from asymmetric and astigmatic illumination sources.
Müller, Angelina; Wapler, Matthias C; Schwarz, Ulrich T; Reisacher, Markus; Holc, Katarzyna; Ambacher, Oliver; Wallrabe, Ulrike
2016-07-25
We study the spatial intensity distribution and the self-reconstruction of quasi-Bessel beams produced from refractive axicon lenses with edge emitting laser diodes as asymmetric and astigmatic illumination sources. Comparing these to a symmetric mono-mode fiber source, we find that the asymmetry results in a transition of a quasi-Bessel beam into a bow-tie shaped pattern and eventually to a line shaped profile at a larger distance along the optical axis. Furthermore, we analytically estimate and discuss the effects of astigmatism, substrate modes and non-perfect axicons. We find a good agreement between experiment, simulation and analytic considerations. Results include the derivation of a maximal axicon angle related to astigmatism of the illuminating beam, impact of laser diode beam profile imperfections like substrate modes and a longitudinal oscillation of the core intensity and radius caused by a rounded axicon tip. PMID:27464190
Bessel beam Grueneisen photoacoustic microscopy with extended depth of field
Shi, Junhui; Wang, Lidai; Noordam, Cedric; Wang, Lihong V.
2016-03-01
The short focal depth of a Gaussian beam limits the volumetric imaging speed of optical resolution photoacoustic microscopy (OR-PAM). A Bessel beam, which is diffraction-free, provides a long focal depth, but its side-lobes may deteriorate image quality when the Bessel beam is directly employed to excite photoacoustic signals in ORPAM. Here, we present a nonlinear approach based on the Grueneisen relaxation effect to suppress the side-lobe artifacts in photoacoustic imaging. This method extends the focal depth of OR-PAM and speeds up volumetric imaging. We experimentally demonstrated a 1-mm focal depth with a 7-μm lateral resolution and volumetrically imaged a carbon fiber and red blood cell samples.
Fabrication of microchannels in fused silica using femtosecond Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Yashunin, D. A., E-mail: yashuninda@yandex.ru [Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Str., Nizhny Novgorod 603950 (Russian Federation); Nizhny Novgorod State Technical University, 24 Minin St., Nizhny Novgorod 603950 (Russian Federation); Malkov, Yu. A. [Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Str., Nizhny Novgorod 603950 (Russian Federation); Mochalov, L. A.; Stepanov, A. N. [Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Str., Nizhny Novgorod 603950 (Russian Federation); Nizhny Novgorod State Technical University, 24 Minin St., Nizhny Novgorod 603950 (Russian Federation); Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., Nizhny Novgorod 603950 (Russian Federation)
2015-09-07
Extended birefringent waveguiding microchannels up to 15 mm long were created inside fused silica by single-pulse irradiation with femtosecond Bessel beams. The birefringent refractive index change of 2–4 × 10{sup −4} is attributed to residual mechanical stress. The microchannels were chemically etched in KOH solution to produce 15 mm long microcapillaries with smooth walls and a high aspect ratio of 1:250. Bessel beams provide higher speed of material processing compared to conventional multipulse femtosecond laser micromachining techniques and permit simple control of the optical axis direction of the birefringent waveguides, which is important for practical applications [Corrielli et al., “Rotated waveplates in integrated waveguide optics,” Nat. Commun. 5, 4249 (2014)].
Manipulation of metallic nanoparticle with evanescent vortex Bessel beam.
Rui, Guanghao; Wang, Xiaoyan; Cui, Yiping
2015-10-01
In this work, we propose a novel strategy to optically trap and manipulate metallic nanoparticles using evanescent vortex Bessel beam (EVBB). A versatile method is presented to generate evanescent Bessel beam with tunable optical angular momentum by focusing a radially polarized vortex beam onto a one-dimensional photonics band gap structure. The behavior of a metallic nanoparticle in the EVBB is numerically studied. We show that such particle can be stably trapped near the surface. The orbital angular momentum drives the metallic nanoparticle to orbit around the beam axis, and the direction of the orbital motion is controlled by the handedness of the helical phase front. The technique demonstrated in this work may open up new avenues for optical manipulation, and the non-contact tunable orbiting dynamics of the trapped particle may find important applications in higher resolution imaging techniques. PMID:26480086
Random Brownian scaling identities and splicing of Bessel processes
Pitman, Jim; Yor, Marc
1998-01-01
An identity in distribution due to Knight for Brownian motion is extended in two different ways: first by replacing the supremum of a reflecting Brownian motion by the range of an unreflected Brownian motion and second by replacing the reflecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excursions. The first extension is related to two different constructions of Itô’s law of ...
Active MMW/Terahertz Security System Based on Bessel Beams
Igor Minin; Oleg Minin
2013-01-01
The novel concept of the security system based on THz Bessel beams is offered. The system is based on a novel THz diffractive optics for scanning the person (without the application of THz laser) and on a sensitive scheme for the detection of the reflected and scattered THz radiation. The development of enabling technology, namely, sensitive detector arrays and Millimeter wave/THz diffractive optics, will allow building compact, easy-to-use millimeter wave/THz imaging systems without expensiv...
From amorphous speckle pattern to reconfigurable Bessel beam via wavefront shaping
Di Battista, Diego; Leonetti, Marco; Zacharakis, Giannis
2015-01-01
Bessel beams are non-diffracting light structures, which can be produced with simple tabletop optical elements such as axicon lenses or ring spatial filters and coherent laser beams. One of their main characteristic is that Bessel beams maintain their spatial characteristics after meters of propagation. In this paper we demonstrate a system and method for generating Bessel beams from amorphous speckle patterns, exploiting adaptive optimization by a spatial light modulator. These speckles are generated by light modes transmitted through a scattering curtain and selected by a ring shaped filter. With the proposed strategy it is possible to produce at user defined positions, reconfigurable, non-diffracting Bessel beams through a disordered medium.
Optical force exerted on a Rayleigh particle by a vector arbitrary-order Bessel beam
Yang, Ruiping; Li, Renxian
2016-07-01
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.
Efficient Coupler for a Bessel Beam Dispersive Element
Savchenkov, Anatoliy; Iltchenko, Vladimir; Matsko, Andrey; Le, Thanh; Yu, nan; Maleki, Lute
2008-01-01
A document discusses overcoming efficient optical coupling to high orbital momentum modes by slightly bending the taper dispersive element. This little shape distortion is not enough to scramble the modes, but it allows the use of regular, free-beam prism coupling, fiber coupling, or planar fiber on-chip coupling with, ultimately, 100 percent efficiency. The Bessel-beam waveguide is bent near the contact with the coupler, or a curved coupler is used. In this case, every Bessel-beam mode can be successfully coupled to a collimated Gaussian beam. Recently developed Bessel-beam waveguides allow long optical delay and very high dispersion. Delay values may vary from nanoseconds to microseconds, and dispersion promises to be at 100 s/nm. Optical setup consisted of a red laser, an anamorphic prism pair, two prism couplers, and a bent, single-mode fiber attached to prisms. The coupling rate increased substantially and corresponded to the value determined by the anamorphic prism pair.
Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone
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.
Vijayakumar, Anand; Bhattacharya, Shanti
2015-11-01
Binary composite diffractive optical elements with the functions of a spiral phase plate (SPP), an axicon, and a Fresnel zone lens (FZL) were designed with different topological charges. The element was designed in two steps. In the first step, the function of an SPP was combined with that of an axicon by spiraling the periods of the axicon with respect to the phase of the SPP followed by a modulo-2π phase addition with the phase of an FZL in the second step. The higher-order Bessel beams generated by the binary phase spiral axicon are superposed at the FZL's focal plane. Although location of the focal plane is wavelength dependent, the radius of the flower-like beams generated by the element was found to be independent of wavelength. The element was fabricated using electron-beam direct writing. The evaluation results matched well with the simulation results, generating flower-like beams at the focal plane of the FZL.
Bessel equation as an operator identity's matrix element in quantum mechanics
International Nuclear Information System (INIS)
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
About a theorem of Wiener on the Bessel-Kingman Hypergroup
Innig, Lukas
2016-01-01
A theorem of Wiener on the circle group was strengthened and extended by Fournier in [2] to locally compact abelian groups and extended further to the Bessel-Kingman hypergroup with parameter {\\alpha} = 1 / 2 by Bloom/Fournier/Leinert in [1]. We further extend this theorem to Bessel-Kingman hypergroups with parameter {\\alpha} > 1 / 2 .
Institute of Scientific and Technical Information of China (English)
Mehmet Zeki SARIKAYA; Hüseyin YILDIRIM
2009-01-01
In this paper, we define the generalized Gauss-Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the general-ized Riesz and Bessel potentials, generated by the generalized shift operators and associated with the Laplace Bessel differential operator.
S^{2}-imaging of Bessel-like Beams
DEFF Research Database (Denmark)
Ingerslev, Kasper; Israelsen, Stine Møller; Rottwitt, Karsten
Bessel-like beams generated in a double cladding fiber are characterized for the first time using S2-imaging. The wavelength independence across the beam is examined numerically.......Bessel-like beams generated in a double cladding fiber are characterized for the first time using S2-imaging. The wavelength independence across the beam is examined numerically....
International Nuclear Information System (INIS)
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)
He, Xi; Wu, Fengtie; Chen, Ziyang; Pu, Jixiong; Chavez-Cerda, Sabino
2016-05-01
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.
部分Bessel形电磁波%Partial Bessel electromagnetic wave∗
Institute of Scientific and Technical Information of China (English)
李粮生; 闫华; 侯兆国; 殷红成
2013-01-01
We present the spatially self-bending solutions (the partial Bessel functions) of the Maxwell equations, where the self-bending wave can be produced through launching a group of plane waves that interfere with each other by modulating their initial phases and the emission directions. The self-bending electromagnetic waves accelerating in a circular trajectory preserve the beam shape within a certain propagation distance. Unlike Ariy wave packet, the bending angle of the new self-accelerating wave can be much larger than that of Ariy beam. The Poynting vector of the half Bessel beam shows that the main lobe maintains a propagation-invariant structure and can complete a turn close to 180◦. In addition, one pair of half Bessel electromagnetic waves is forbidden to propagate inside a certain area where the designed beam generates the self-shielding region.% 给出了满足Maxwell方程的自弯曲电磁波解(部分Bessel函数)，其可以通过发射调制初始相位和发射方向的一组平面波干涉合成来实现。自弯曲电磁波在一定传播距离内保持波束形状不变，其传播轨道接近圆形。这类曲线加速的电磁波不同于Ariy波束，其中部分Bessel波束的弯曲角度可以远大于Ariy波。半Bessel波束的Poynting矢量表明主瓣能够保持能量不扩散且偏转接近180◦。此外，同时发射一对半Bessel电磁波能够在一定区域内实现对消，即在该域内实现电磁波自屏蔽。
Non-diffracting chirped Bessel waves in optical antiguides
Chremmos, Ioannis
2015-01-01
Chirped Bessel waves are introduced as stable (non-diffracting) solutions of the paraxial wave equation in optical antiguides with a power-law radial variation in their index of refraction. Through numerical simulations, we investigate the propagation of apodized (finite-energy) versions of such waves, with or without vorticity, in antiguides with practical parameters. The new waves exhibit a remarkable resistance against the defocusing effect of the unstable index potentials, outperforming standard Gaussians with the same full width at half maximum. The chirped profile persists even under conditions of eccentric launching or antiguide bending and is also capable of self-healing like standard diffraction-free beams in free space.
Observation of sine modulated Bessel behavior in microwave biased SQUIDs
International Nuclear Information System (INIS)
The amplitudes of the signal lobes (Bessel Maxima) observed in several types of thin film SQUIDs excited at 9.2 GHz exhibit pronounced periodic intensity modulation. This behavior is consistent with the simplified flux entry model proposed by Mercereau in the limit of tau approximately T, where T is the shortest time between successive flux entry into loop and tau is the flux passage time. From the results, tau was deduced to be approximately 1012 seconds for both proximity effect and narrow constriction devices
Propagation of Gauss-Bessel beams in turbulent atmosphere
Institute of Scientific and Technical Information of China (English)
Chen Bao-Suan; Pu Ji-Xiong
2009-01-01
This paper studies the propagation properties of Gauss鈥擝essel beams in a turbulent atmosphere. Based on the extended Huygens-Fresnel principle, it derives the intensity distribution expression for such beams propagating in a turbulent atmosphere. Then the influence of turbulence and source beam parameters on the beam propagation is studied in great detail. It finds that the intensity distribution of Gauss-Bessel beams will change into Gaussian profile in a turbulent atmosphere, and that stronger turbulence and smaller topological charges will lead to a faster changing.
Partially coherent n onpar axial modified Bessel-Gauss beams
Institute of Scientific and Technical Information of China (English)
Gao Zeng-Hui; Lü Bai-Da
2006-01-01
The concept of partially coherent nonparaxial modified Bessel-Gauss (MBG) beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG beams in free space are derived and analysed, and some special cases are discussed. In particular, under the paraxial approximation our results reduce to the corresponding paraxial ones. Numerical calculation examples are given to illustrate the dependence of intensity and spectral degree of coherence on the beam order m,ξ and f parameters, and to compare the difference between the paraxial and nonparaxial results.
An optical tweezer in asymmetrical vortex Bessel-Gaussian beams
Kotlyar, V. V.; Kovalev, A. A.; Porfirev, A. P.
2016-07-01
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.
Multicolor 4D Fluorescence Microscopy using Ultrathin Bessel Light Sheets.
Zhao, Teng; Lau, Sze Cheung; Wang, Ying; Su, Yumian; Wang, Hao; Cheng, Aifang; Herrup, Karl; Ip, Nancy Y; Du, Shengwang; Loy, M M T
2016-01-01
We demonstrate a simple and efficient method for producing ultrathin Bessel ('non-diffracting') light sheets of any color using a line-shaped beam and an annulus filter. With this robust and cost-effective technology, we obtained two-color, 3D images of biological samples with lateral/axial resolution of 250 nm/400 nm, and high-speed, 4D volume imaging of 20 μm sized live sample at 1 Hz temporal resolution. PMID:27189786
Reformulation of the Fourier-Bessel steady state mode solver
Gauthier, Robert C.
2016-09-01
The Fourier-Bessel resonator state mode solver is reformulated using Maxwell's field coupled curl equations. The matrix generating expressions are greatly simplified as well as a reduction in the number of pre-computed tables making the technique simpler to implement on a desktop computer. The reformulation maintains the theoretical equivalence of the permittivity and permeability and as such structures containing both electric and magnetic properties can be examined. Computation examples are presented for a surface nanoscale axial photonic resonator and hybrid { ε , μ } quasi-crystal resonator.
Application of Bessel beams to 2D microfabrication
International Nuclear Information System (INIS)
Fs laser-based two-photon polymerisation (2PP) has been widely reported as a means of directly writing three-dimensional nanoscale structures. Usually the voxel of a high numerical aperture microscope objective is scanned through the resin to build up the required model. In the case of high aspect ratio two-dimensional structures, such as cell scaffolds, repeated scanning is required to build up the height. The voxel shape can be substantially elongated by the inclusion of an axicon lens in the laser beam line. In this report we describe the use of a Bessel beam produced in the region beyond the focus of an objective lens when the beam has been modified in this way. A Ti:sapphire laser was used to write a range of 2D square cell structures in a Zr-loaded sol-gel system. The process was characterised, in terms of the dimensions of the polymerised Bessel region, for different processing conditions. Examples of the structures are also described
Application of Bessel beams to 2D microfabrication
Li, X.-F.; Winfield, R. J.; O'Brien, S.; Crean, G. M.
2009-03-01
Fs laser-based two-photon polymerisation (2PP) has been widely reported as a means of directly writing three-dimensional nanoscale structures. Usually the voxel of a high numerical aperture microscope objective is scanned through the resin to build up the required model. In the case of high aspect ratio two-dimensional structures, such as cell scaffolds, repeated scanning is required to build up the height. The voxel shape can be substantially elongated by the inclusion of an axicon lens in the laser beam line. In this report we describe the use of a Bessel beam produced in the region beyond the focus of an objective lens when the beam has been modified in this way. A Ti:sapphire laser was used to write a range of 2D square cell structures in a Zr-loaded sol-gel system. The process was characterised, in terms of the dimensions of the polymerised Bessel region, for different processing conditions. Examples of the structures are also described.
Controllable light capsules employing modified Bessel-Gauss beams.
Gong, Lei; Liu, Weiwei; Zhao, Qian; Ren, Yuxuan; Qiu, Xingze; Zhong, Mincheng; Li, Yinmei
2016-01-01
We report, in theory and experiment, on a novel class of controlled light capsules with nearly perfect darkness, directly employing intrinsic properties of modified Bessel-Gauss beams. These beams are able to naturally create three-dimensional bottle-shaped region during propagation as long as the parameters are properly chosen. Remarkably, the optical bottle can be controlled to demonstrate various geometries through tuning the beam parameters, thereby leading to an adjustable light capsule. We provide a detailed insight into the theoretical origin and characteristics of the light capsule derived from modified Bessel-Gauss beams. Moreover, a binary digital micromirror device (DMD) based scheme is first employed to shape the bottle beams by precise amplitude and phase manipulation. Further, we demonstrate their ability for optical trapping of core-shell magnetic microparticles, which play a particular role in biomedical research, with holographic optical tweezers. Therefore, our observations provide a new route for generating and controlling bottle beams and will widen the potentials for micromanipulation of absorbing particles, aerosols or even individual atoms. PMID:27388558
On a Linear Combination Operator of Neumann-Bessel Series%关于Neumann-Bessel级数的线性组合算子
Institute of Scientific and Technical Information of China (English)
王淑云; 何甲兴
2008-01-01
In this paper we construct a new operator H(N,B)n,r(f;z) by means of the partial sums S(N,B)n(f;z) of Neumann-Bessel series.The operator converges uniformly to any fixed continuous function f(z) on the unit circle |z|= 1 and has the best approximation order for f(z) on |z|= 1.
Cotterell, Michael I; Mason, Bernard J; Carruthers, Antonia E; Walker, Jim S; Orr-Ewing, Andrew J; Reid, Jonathan P
2014-02-01
A single horizontally-propagating zeroth order Bessel laser beam with a counter-propagating gas flow was used to confine single fine-mode aerosol particles over extended periods of time, during which process measurements were performed. Particle sizes were measured by the analysis of the angular variation of light scattered at 532 nm by a particle in the Bessel beam, using either a probe beam at 405 nm or 633 nm. The vapour pressures of glycerol and 1,2,6-hexanetriol particles were determined to be 7.5 ± 2.6 mPa and 0.20 ± 0.02 mPa respectively. The lower volatility of hexanetriol allowed better definition of the trapping environment relative humidity profile over the measurement time period, thus higher precision measurements were obtained compared to those for glycerol. The size evolution of a hexanetriol particle, as well as its refractive index at wavelengths 532 nm and 405 nm, were determined by modelling its position along the Bessel beam propagation length while collecting phase functions with the 405 nm probe beam. Measurements of the hygroscopic growth of sodium chloride and ammonium sulfate have been performed on particles as small as 350 nm in radius, with growth curves well described by widely used equilibrium state models. These are the smallest particles for which single-particle hygroscopicity has been measured and represent the first measurements of hygroscopicity on fine mode and near-accumulation mode aerosols, the size regimes bearing the most atmospheric relevance in terms of loading, light extinction and scattering. Finally, the technique is contrasted with other single particle and ensemble methods, and limitations are assessed. PMID:24346588
Fourier-Bessel Field Calculation and Tuning of a CW Annular Array
DEFF Research Database (Denmark)
Fox, Paul D.; Cheng, Jiqi; Lu, Jian-yu
2002-01-01
A 1-D Fourier-Bessel series method for computing and tuning the linear lossless field of flat continuous wave (CW) annular arrays is given and discussed with both numerical simulation and experimental verification. The technique provides a new method for modelling and manipulating the propagated...... field by linking the quantized surface pressure profile to a set of limited diffraction Bessel beams propagating into the medium. In the limit, these become a known set of nondiffracting Bessel beams satisfying the lossless linear wave equation, which allow us to derive a linear matrix formulation for...
Generation of Electron Bessel Beams with Nondiffractive Spreading by a Nanofabricated Annular Slit
Saitoh, Koh; Hirakawa, Kazuma; Nambu, Hiroki; Tanaka, Nobuo; Uchida, Masaya
2016-04-01
The shaping of a wavefront of free electrons has been experimentally realized very recently. We report the generation of an electron Bessel beam using a nanofabricated annular slit. We directly observe that electron Bessel beams propagate while maintaining a narrow beam width over a long propagation distance. In addition, we experimentally verify the self-healing property of these electron beams, which can reconstruct their shape after passing an obstacle. The experimental results are compared with simulation results of the propagation including a hexagonal slit. The present technique of electron Bessel beam generation can be used to develop a novel electron-beam-shaping, an atomic manipulation technique, and a new electron microscopy.
Stankevičius, Evaldas; Garliauskas, Mantas; Gedvilas, Mindaugas; Račiukaitis, Gediminas
2015-11-01
Here, we report the formation of Bessel-like beam array from periodic patterns fabricated by the four-beam interference lithography. Characteristics of the generated Bessel-like beams depend on geometrical parameters of the fabricated microaxicon-like structures, which can be easily controlled via the laser processing parameters. The output beam characteristics disclose the attributes of Bessel beams. The demonstrated method enables an easy fabrication of angular-tolerant wavefront detectors, optical tweezers, optical imaging systems or materials processing tools, having a broad range of applications. PMID:26561125
Laguerre-Gauss beams versus Bessel beams showdown: peer comparison.
Mendoza-Hernández, Job; Arroyo-Carrasco, Maximino Luis; Iturbe-Castillo, Marcelo David; Chávez-Cerda, Sabino
2015-08-15
We present for the first time a comparison under similar circumstances between Laguerre-Gauss beams (LGBs) and Bessel beams (BB), and show that the former can be a better option for many applications in which BBs are currently used. By solving the Laguerre-Gauss differential equation in the asymptotic limit of a large radial index, we find the parameters to perform a peer comparison, showing that LGBs can propagate quasi-nondiffracting beams within the same region of space where the corresponding BBs do. We also demonstrate that LGBs, which have the property of self-healing, are more robust in the sense that they can propagate further than BBs under similar initial conditions. PMID:26274648
Radially Polarized Bessel-Gauss Beams in ABCD Optical Systems and Fiber-Based Generation
Schimpf, Damian; Putnam, William P.; Grogan, Michael D.; Ramachandran, Siddharth; Kaertner, Franz
2013-01-01
We derive solutions for radially polarized Bessel-Gauss beams in ABCD optical systems by superimposing decentered Gaussian beams with linear polarization states. We experimentally confirm the expression by employing a fiber-based mode-converter.
Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams
Porras, Miguel A.; Ruiz-Jiménez, Carlos; Losada, Juan Carlos
2015-12-01
In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NLUBB) whose inward Hänkel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines the NLUBB attractor is given. Steady or unsteady propagation depends on whether the attracting NLUBB has a small, exponentially growing, unstable mode. In the case of unsteady propagation, periodic, quasiperiodic, or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.
Fourier-bessel based image analysis for multi-parameter particle characterization
Vandewiele, Stijn; Drobchak, Oksana; Beunis, Filip; Neyts, Kristiaan; Strubbe, Filip
2014-01-01
We demonstrate a novel particle characterization method based on decomposition of conventional microscopy images in Fourier-Bessel (FB) components. This allows the simultaneous measurement of size, refractive index, 3D position and orientation of single colloidal particles.
Generation of Bessel Surface Plasmon Polaritons in a Finite-Thickness Metal Film
Directory of Open Access Journals (Sweden)
S. N. Kurilkina
2013-01-01
Full Text Available A theory of generation of low- and high-index Bessel surface plasmon polaritons and their superposition in a metal film of a finite thickness is developed. Correct analytical expressions are obtained for the field of two families of Bessel surface plasmon polariton modes formed inside and outside the metal layer. The intensity distribution near the boundary of the layer has been calculated and analyzed. A scheme for the experimental realization of a superposition of Bessel surface plasmon polaritons is suggested. Our study demonstrates that it is feasible to use the superposition of Bessel surface plasmon polaritons as a virtual tip for near-field optical microscopy with a nanoscale resolution.
Generating a Bessel-Gaussian beam for the application in optical engineering.
Chu, Xiuxiang; Sun, Quan; Wang, Jing; Lü, Pin; Xie, Wenke; Xu, Xiaojun
2015-01-01
Bessel beam is the important member of the family of non-diffracting beams and has many novel properties which can be used in many areas. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, based on the coherent combining technology, we have proposed a method which can be used to generate a high-power Bessel beam. Even more, we give an innovative idea to form vortex phase by using discontinuous piston phase. To confirm the validity of this method, the intensity evolution of the combined beam and the Bessel-Gaussian beam at different propagation distance have been studied and compared. Meanwhile, the experimental realization has been discussed from the existing experimental result related to the coherent combining technology. PMID:26690264
Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams
Porras, Miguel A; Losada, Juan Carlos
2015-01-01
In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NL-UBB) whose inward H\\"ankel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines de NL-UBB attractor is given. Steady or unsteady propagation depends on whether the attracting NL-UBB has a small, exponentially growing, unstable mode. In case of unsteady propagation, periodic, quasi-periodic or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.
Extension of filament propagation in water with Bessel-Gaussian beams
KAYA, G.; Kaya, N.; M. Sayrac; Y. Boran; Strohaber, J.; Kolomenskii, A. A.; M. Amani; Schuessler, H. A.
2016-01-01
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 o...
Generation of J0 Bessel Beams with controlled spatial coherence features
Carbajal-Dominguez, Adrian; Bernal, Jorge; Martin-Ruiz, Alberto; Niconoff, Gabriel Martínez
2010-01-01
An alternative method to generate J0 Bessel beams with controlled spatial partial coherence properties is introduced. Far field diffraction from a discrete number of source points on an annular region is calculated. The average for different diffracted fields produced at several rotation angles is numerically calculated and experimentally detected. Theoretical and experimental results show that for this particular case, J0 Bessel beam is a limit when the number of points tends towards infinit...
Institute of Scientific and Technical Information of China (English)
李芬
2014-01-01
A-new-robust-watermarking-scheme-based-on-normalization-and-Bessel-Fourier-moment-is-proposed-to-enhance-the-capability-of-watermark-against-geometric-attacks.-Firstly,-the-original-image-is-normalized,-and-the-Bessel-Fourier-moment-of-this-image-is-Rotation,-Scaling-and-Translation(RST)-invariant.-Then-watermark-is-added-to-the-spatial-domain-intensity-of-image-using-Bessel-Fourier-polynomial,-and-the-embedding-strength-is-controlled-by-an-modifying-and-verifying-program-for-iterative-characteristics,-avoiding-bring-error-into-the-process-of-watermark-embedding-and-detection.-Large-quantities-of-experimental-results-show-that-the-proposed-scheme-is-robust-against-the-geometric-attacks-as-well-as-common-image-processing.%为了增强水印的抗几何攻击能力，提出了一种基于归一化和 Bessel-Fourier 矩的鲁棒水印算法。首先对图像进行归一化，使图像的 Bessel-Fourier 矩具有旋转、缩放和平移(RST)不变性；然后通过使用 Bessel-Fourier 多项式直接将水印添加到图像的空域强度中，嵌入强度由一个迭代特征修改和验证程序控制，可以避免在水印嵌入和检测过程中引入错误。大量的实验结果表明，本文提出的水印算法对几何攻击以及一般的信号处理具有很好的鲁棒性。
Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.
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. PMID:27140133
Yang, Yanlong; Zhou, Xing; Li, Runze; Van Horn, Mark; Peng, Tong; Lei, Ming; Wu, Di; Chen, Xun; Yao, Baoli; Ye, Tong
2015-03-01
Bessel beams have been used in many applications due to their unique optical properties of maintaining their intensity profiles unchanged during propagation. In imaging applications, Bessel beams have been successfully used to provide extended focuses for volumetric imaging and uniformed illumination plane in light-sheet microscopy. Coupled with two-photon excitation, Bessel beams have been successfully used in realizing fluorescence projected volumetric imaging. We demonstrated previously a stereoscopic solution-two-photon fluorescence stereomicroscopy (TPFSM)-for recovering the depth information in volumetric imaging with Bessel beams. In TPFSM, tilted Bessel beams were used to generate stereoscopic images on a laser scanning two-photon fluorescence microscope; upon post image processing we could successfully provide 3D perception of acquired volume images by wearing anaglyph 3D glasses. However, tilted Bessel beams were generated by shifting either an axicon or an objective laterally; the slow imaging speed and severe aberrations made it hard to use in real-time volume imaging. In this article, we report recent improvements of TPFSM with newly designed scanner and imaging software, which allows 3D stereoscopic imaging without moving any of the optical components on the setup. This improvement has dramatically improved focusing qualities and imaging speed so that the TPFSM can be performed potentially in real-time to provide 3D visualization in scattering media without post image processing.
Fractional Vector Calculus and Fractional Special Function
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.
International Nuclear Information System (INIS)
The suggested algorithm is based on a linear version of the variable phase approach. The regular and irregular wave-functions of scattering by the above sum of potentials are represented as an infinite series in which the distance and momentum are separated from each other as well as in the Bessel - Clifford expansions for the Coulomb functions. The construction of the finite uniformly approximating these series under well-defined conditions is reduced to the solution of the simplest differential problems. 12 refs
Scattering of Bessel beam by arbitrarily shaped composite particles with core–shell structure
International Nuclear Information System (INIS)
This study investigates the scattering of Bessel beam by composite particles with core–shell structure. Specifically, the vector expressions of zero-th order Bessel beam that satisfy well Maxwell's equations in combination with the rotation Euler angles are used to represent the arbitrarily incident Bessel beams. An efficient numerical method based on surface integral equations is introduced to formulate the scattering problems involving arbitrarily shaped composite particles with core–shell structure. Solutions are performed iteratively by using the multilevel fast multipole algorithm. The numerical results for differential scattering cross sections of several selected composite particles are presented and analyzed. This investigation is expected to provide useful guidance for techniques of laser detection on particle, diagnosis, and manipulation. - Highlights: • The scattering of Bessel beam by composite particles is numerically investigated. • A detailed description of the arbitrarily incident Bessel beam is presented. • The surface integral equation method is used to solve the studied scattering problem. • The numerical results of several typical composite particles are presented
Shape invariant higher-order Bessel-like beams carrying orbital angular momentum
International Nuclear Information System (INIS)
We present a method for generating higher-order Bessel beams with z-dependent cone angles. Such fields, if engineered correctly, are shape invariant during propagation and thus do not suffer from a transition from a Bessel-shaped intensity profile in the near field to an annular ring in the far field. We demonstrate the production of such fields in the laboratory with an optical system comprising a combination of two axicons and a lens, allowing for control of the cone angle of the resulting field. While the resulting shape invariant fields are not perfectly non-diffracting, they do maintain many of the same properties as Bessel beams, including self-reconstruction. (paper)
Acoustical pulling force on rigid spheroids in single Bessel vortex tractor beams
Mitri, F. G.
2015-11-01
The theoretical formalism for acoustical Bessel vortex (helicoidal) tractor beams and results presented here are the first to demonstrate the emergence of a pulling force of attraction on non-spherical oblate and prolate rigid spheroidal particles centered on the beam's axis of wave propagation. Numerical predictions for the axial acoustic radiation force illustrate the theory with particular emphasis on the aspect ratio of the spheroid, the half-cone angle and order of the beam, as well as the dimensionless size parameter. It is demonstrated here that the Bessel vortex beam parameters may be tailored in such a way that the spheroid is pulled against the forward linear momentum density flux associated with the incoming waves. Those results potentially suggest the use of Bessel vortex beams in the development of emergent technologies for non-contact remote sampling and particle characterization.
Limitations to laser machining of silicon using femtosecond micro-Bessel beams in the infrared
Energy Technology Data Exchange (ETDEWEB)
Grojo, David, E-mail: grojo@lp3.univ-mrs.fr; Mouskeftaras, Alexandros; Delaporte, Philippe [Aix-Marseille University, CNRS, LP3 UMR 7341, F-13288 Marseille (France); Lei, Shuting [Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, Kansas 66506 (United States)
2015-04-21
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{sup 11 }W cm{sup −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.
Formation of high-order acoustic Bessel beams by spiral diffraction gratings
Jiménez, Noé; Sánchez-Morcillo, Víctor; Romero-García, Vicent; García-Raffi, Lluis M; Staliunas, Kestutis
2016-01-01
The formation of high-order Bessel beams by a passive acoustic device consisting of an Archimedes' spiral diffraction grating is theoretically, numerically and experimentally reported in this work. These beams are propagation-invariant solutions of the Helmholtz equation and are characterized by an azimuthal variation of the phase along its annular spectrum producing an acoustic vortex in the near field. In our system, the scattering of plane acoustic waves by the spiral grating leads to the formation of the acoustic vortex with zero pressure on-axis and the angular phase dislocations characterized by the spiral geometry. The order of the generated Bessel beam and, as a consequence, the size of the generated vortex can be fixed by the number of arms in the spiral diffraction grating. The obtained results allow to obtain Bessel beams with controllable vorticity by a passive device, which has potential applications in low-cost acoustic tweezers and acoustic radiation force devices.
Propagation characteristics of Bessel beams generated by continuous, incoherent light sources.
Altıngöz, Ceren; Yalızay, Berna; Akturk, Selcuk
2015-08-01
We investigate the propagation behavior of Bessel beams generated by incoherent, continuous light sources. We perform experiments with narrowband and broadband light emitting diodes, and, for comparison, with a laser diode. We observe that the formation of Bessel beams is affected minimally by temporal coherence, while spatial coherence determines the longitudinal evolution of the beam profile. With spatially incoherent beams, the fringe contrast is comparable to the coherent case at the beginning of the Bessel zone, while it completely fades away by propagation, turning into a cylindrical light pipe. Our results show that beam shaping methods can be extended to cases of limited spatial coherence, paving the way for potential new uses and applications of such sources. PMID:26367302
Bessel beams in tunable acoustic gradient index lenses and optical trap assisted nanolithography
McLeod, Euan
2009-12-01
Bessel beams are laser beams whose shape gives them nondiffracting and self-healing properties. They find use in applications requiring a narrow laser beam with a high depth of field. The first part of this thesis presents the study of a new adaptive optical element capable of generating rapidly tunable Bessel beams: the tunable acoustic gradient index (TAG) lens. This device uses piezoelectrically-generated acoustic waves to modulate a fluid's density and refractive index, leading to electrically controllable lensing behavior. Both modeling and experiment are used to explain the observed multiscale Bessel beams. Because the TAG lens operates at frequencies of hundreds of kilohertz, the effective Bessel beam cone angle continuously varies at timescales on the order of microseconds or smaller-orders of magnitude faster than other existing technologies. In addition, the TAG lens may be driven with a Fourier superposition of multiple frequencies, which could enable the generation of arbitrary patterns. The second part of this thesis presents the application of Bessel beams in a new probe-based direct-write optical nanolithography method called optical trap assisted nanolithography (OTAN). When compared to alternative techniques, OTAN makes probe placement and parallelization easier. The method uses Bessel beam optical tweezers to trap dielectric microspheres in close proximity to a surface. These microspheres are then illuminated with pulses from a second laser beam, whose fluence is enhanced directly below the microsphere by focusing and near-field effects to a level great enough to modify the substrate. This technique is used to produce 100 nm features, which are less than lambda/3, and whose sizes agree well with finite-difference time-domain models of the experiment. A demonstration is given of how the technique can be parallelized by trapping multiple microspheres with multiple beams and exposing all spheres in unison with a single pulsed beam. Finally, modeling
Thermooptical excitation of sound by Bessel light beams in crystalline media with internal stress
International Nuclear Information System (INIS)
The thermooptical excitation of sound by Bessel light beams in crystalline media with internal stress has been studied. The dependence of the thermoelastic coupling coefficient, which is due to the modulated absorption of laser radiation, on the initial strain in a crystalline sample is taken into account. The expression for the photoacoustic signal amplitude is obtained, and it is shown that, in the range of high modulation frequencies of TE modes of Bessel light beams, resonant phenomena occur which can be used to increase the resolution of laser photoacoustic diagnostics of elastically strained crystals.
Orbital angular momentum of a high-order Bessel light beam
Energy Technology Data Exchange (ETDEWEB)
Volke-Sepulveda, K [Instituto Nacional de Astrofisica, Optica y Electronica, Apdo. Postal 51/216, Puebla, Pue., Mexico 72000 (Mexico); Garces-Chavez, V [School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, Scotland (United Kingdom); Chavez-Cerda, S [Instituto Nacional de Astrofisica, Optica y Electronica, Apdo. Postal 51/216, Puebla, Pue., Mexico 72000 (Mexico); Arlt, J [School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, Scotland (United Kingdom); Dholakia, K [School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, Scotland (United Kingdom)
2002-04-01
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.
Free-space orbital angular momentum division multiplexing with Bessel beams
International Nuclear Information System (INIS)
We present an apparatus for multiplexing and demultiplexing free-space beams carrying different values of orbital angular momentum (OAM), at a wavelength of 633 nm. We have considered nondiffracting Bessel beams of order from 0 to 3, produced by means of suitable binary-amplitude computer-generated holograms and carrying an OAM per photon directly proportional to the beam order. The effectiveness of the OAM division multiplexing technique has been experimentally verified by monitoring the output ports of a demultiplexing interferometer with rotated Dove prisms in the arms. This interferometer is capable of discriminating the even-order Bessel beams from the odd-order ones
Spin-to-orbital angular momentum conversion for Bessel light beams in crystals
International Nuclear Information System (INIS)
We have studied the spatial dynamics of spin-to-orbital angular momentum conversion for zero-order and higherorder circularly polarized Bessel light beams, propagating along the optic axes of uniaxial and biaxial crystals. We have established that interaction of the Bessel beam with a uniaxial crystal slab makes possible practically complete conversion of the optical spin [angular] momentum to [orbital] angular [momentum]. In a biaxial crystal slab, during such a conversion the angular momentum is partially transferred to the medium, and as a result the slab undergoes rotation. (author)
Extension of filament propagation in water with Bessel-Gaussian beams
Kaya, G.; Kaya, N.; Sayrac, M.; Boran, Y.; Strohaber, J.; Kolomenskii, A. A.; Amani, M.; Schuessler, H. A.
2016-03-01
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.
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.
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.
The reactance wave diffraction problem by a strip in a scale of Bessel potential spaces
Directory of Open Access Journals (Sweden)
Luís P. Castro
2006-01-01
Full Text Available We consider a boundary-transmission problem for the Helmholtz equation, in a Bessel potential space setting, which arises within the context of wave diffraction theory. The boundary under consideration consists of a strip, and certain reactance conditions are assumed on it. Operator theoretical methods are used to deal with the problem and, as a consequence, several convolution type operators are constructed and associated to the problem. At the end, the well-posedness of the problem is shown for a range of regularity orders of the Bessel potential spaces, and for a set of possible reactance numbers (dependent on the wave number.
Spectral behavior of pulsed Bessel beams focused by a dispersive lens
Pan, Liuzhan; Ding, Chaoliang; Yuan, Xiao; Lü, Baida
2008-08-01
Starting from the Huygens-Fresnel diffraction integral, the analytical expression for the power spectrum of pulsed Bessel beams focused by a dispersive aperture lens is derived and used to study the spectral anomalies of pulsed Bessel beams in the focused field. Numerical calculation results are given to illustrate the dependence of spectral anomalous behavior on the pulse parameters, truncation parameter and material dispersion of the lens. It is shown that near the phase singularities the spectral anomalies may take place. The potential applications of spectral anomalies of ultrashort pulsed beams in information encoding and information transmission are considered.
Dynamics of polarized vortex solitons in nonlocal media with Bessel optical lattices.
Zhang, Bingzhi; Chen, Zhifeng
2015-09-21
We investigate the formation of polarized vortex solitons in nonlocal media with Bessel optical lattices and show the various dynamics of these solitons. Particularly, the stable high-order polarized vortex solitons, which are not found in local media with Bessel optical lattices, are found in nonlocal media. It is found that the nonlocal nonlinearity plays an important role in the stability of these solitons which is similar to that of phase vortex solitons. However, we show that the dynamics of these polarized vortex solitons are quite different from the phase vortex solitons. PMID:26406632
Behavior of asymmetric Bessel beam in focal plane of high numerical aperture objective
Stafeev, Sergey S.; Kotlyar, Victor V.; Porfirev, Alexey P.
2016-04-01
Tight focusing of a linearly-polarized asymmetric Bessel beam, which has a crescent profile, was investigated numerically and experimentally. FDTD calculations show that a binary zone plate of numerical aperture NA = 0.995 forms a crescent in the focal plane, which is rotated clockwise around the optical axis, moving away from the focal plane. Using the Debye formulae it was shown that a direction of polarization of incident light has a significant influence on intensity distribution in focal plane. The crescent in the focal plane was also observed experimentally by focusing of the asymmetric Bessel beam using an immersive objective (NA = 1.25).
Nondiffracting Bessel beams with polarization state that varies with propagation distance.
Moreno, Ignacio; Davis, Jeffrey A; Sánchez-López, María M; Badham, Katherine; Cottrell, Don M
2015-12-01
We generate nondiffracting Bessel beams whose polarization state varies with propagation distance. We use a reflective geometry where a single parallel-aligned spatial light modulator device is used to spatially modulate two orthogonal linear polarizations with two axicon phase profiles. Then, by adding an extra phase retardation radial profile between these linear states, we are able to modulate the state of polarization along the line focus of the axicon. We provide experimental results that demonstrate the polarization axial control with zero-order and higher order Bessel beams. PMID:26625023
Bessel beam transformation in c-cuts of uniaxial crystals by varying the source wavelength
Paranin, V. D.
2016-04-01
Transformation of Bessel beam of a zero order to Bessel beam of the second order in c-cut of CaCO3 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 CaCO3 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.
The Propagation Model of Bessel Beams%Bessel光束的传输模型(英文)
Institute of Scientific and Technical Information of China (English)
杨性愉; 宋继恩
2002-01-01
研究了参量对Bessel光束性质的影响并发现了参量kr与无衍射距离之间的关系,进一步建立了Bessel光束的传输模型并用数值误差计算进行了证明.%The effect of the parameters on the properties of the Bessel beams was studied,and the relationship between the parameter kr and the non-diffracting distance was found.Finally,we establish the propagation model of Bessel beams and prove out it by numerical error calculation.
基于 Bessel 滤波器特性的鲁棒控制器研究%A Study of the Robust Controller Based on Bessel Filter
Institute of Scientific and Technical Information of China (English)
王启志; 王晓霞; 王永初
2001-01-01
根据低频无调节余差的优化控制系统，具有理想的低通滤波器特性，本文采用 Bessel 滤波器特性来校正闭环控制系统，不仅方法简单易行，而且所校正的系统具有很高的鲁棒性。
Gatto, A Eduardo; Urbina, Wilfredo
2011-01-01
In this paper we will study the boundedness of Riesz Potentials, Bessel potentials and Fractional Derivatives on Gaussian Besov-Lipschitz spaces $B_{p,q}^{\\alpha}(\\gamma_d)$. Also these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups.
Electromagnetic waves in uniaxial crystals: General formalism with an application to Bessel beams
Hacyan, S
2008-01-01
We present a mathematical formalism describing the propagation of a completely general electromagnetic wave in a birefringent medium. Analytic formulas for the refraction and reflection from a plane interface are obtained. As a particular example, a Bessel beam impinging at an arbitrary angle is analyzed in detail. Some numerical results showing the formation and destruction of optical vortices are presented.
Faraday effect and Bessel beams in a magneto-optic medium
Energy Technology Data Exchange (ETDEWEB)
Hacyan, S; Jauregui, R [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apdo. Postal 20-364, Mexico DF 01000 (Mexico)
2008-01-14
We present a detailed theoretical study of Bessel beams propagating parallel to a magnetic field in a magneto-optic medium. Exact solutions of the Maxwell equations are presented from which the Faraday effect follows. The mechanical properties of light and some possible effects on the medium are also analysed.
Faraday effect and Bessel beams in a magneto-optic medium
International Nuclear Information System (INIS)
We present a detailed theoretical study of Bessel beams propagating parallel to a magnetic field in a magneto-optic medium. Exact solutions of the Maxwell equations are presented from which the Faraday effect follows. The mechanical properties of light and some possible effects on the medium are also analysed
Schimpf, Damian N; Putnam, William P; Grogan, Michael D W; Ramachandran, Siddharth; Kärtner, Franz X
2013-07-29
We derive solutions for radially polarized Bessel-Gauss beams in free-space by superimposing decentered Gaussian beams with differing polarization states. We numerically show that the analytical result is applicable even for large semi-aperture angles, and we experimentally confirm the analytical expression by employing a fiber-based mode-converter. PMID:23938719
Off-axial acoustic radiation force of repulsor and tractor bessel beams on a sphere.
Silva, Glauber T; Lopes, J Henrique; Mitri, Farid G
2013-06-01
Acoustic Bessel beams are known to produce an axial radiation force on a sphere centered on the beam axis (on-axial configuration) that exhibits both repulsor and tractor behaviors. The repulsor and the tractor forces are oriented along the beam's direction of propagation and opposite to it, respectively. The behavior of the acoustic radiation force generated by Bessel beams when the sphere lies outside the beam's axis (off-axial configuration) is unknown. Using the 3-D radiation force formulas given in terms of the partial wave expansion coefficients for the incident and scattered waves, both axial and transverse components of the force exerted on a silicone- oil sphere are obtained for a zero- and a first-order Bessel vortex beam. As the sphere departs from the beam's axis, the tractor force becomes weaker. Moreover, the behavior of the transverse radiation force field may vary 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 ka values. These results are particularly important for the design of acoustical tractor beam devices operating with Bessel beams. PMID:25004483
Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on Cn
Institute of Scientific and Technical Information of China (English)
CHANG Der-Chen; GRIENER Peter; TIE Jingzhi
2006-01-01
Given a principal value convolution on the Heisenberg group Hn = Cn × R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.
Generation of diffraction-free plasmonic beams with one-dimensional Bessel profiles
DEFF Research Database (Denmark)
García Ortíz, César Eduardo; Coello, Victor; Han, Zhanghua;
2013-01-01
We demonstrate experimentally generation of diffraction-free plasmonic beams with zeroth- and first-order Bessel intensity profiles using axicon-like structures fabricated on gold film surfaces and designed to operate at a wavelength of 700nm. The central beam features a very low divergence (∼8π...
International Nuclear Information System (INIS)
We study the peculiarities of the formation of Bessel beams in semiconductor lasers with a high propagation parameter M2. It is shown that the propagation distance of the Bessel beam is determined by the divergence of the quasi-Gaussian beam with high M2 rather than the geometric parameters of the optical scheme. It is demonstrated that technologically inevitable rounding of the axicon tip leads to a significant increase in the transverse dimension of the central part of the Bessel beam near the axicon. (semiconductor lasers. physics and technology)
Chen, Ye; Liu, Jonathan T.C.
2015-01-01
Bessel beams have recently been investigated as a means of improving deep-tissue microscopy in highly scattering and heterogeneous media. It has been suggested that the long depth-of-field and self-reconstructing property of a Bessel beam enables an increased penetration depth of the focused beam in tissues compared to a conventional Gaussian beam. However, a study is needed to better quantify the magnitude of the beam steering as well as the distortion of focused Gaussian and Bessel beams in...
On the degree five L-function for GSp(4)
File, Daniel
2012-01-01
I give a new integral representation for the degree five (standard) L-function for automorphic representations of GSp(4) that is a refinement of integral representation of Piatetski-Shapiro and Rallis. The new integral representation unfolds to produce the Bessel model for GSp(4) which is unique. The local unramified calculation uses an explicit formula for the Bessel model and differs completely from Piatetski-Shapiro and Rallis.
Zhu, Long; Wang, Jian
2015-12-01
By designing and optimizing complex phase pattern combining with axicon phase distribution, we report data multicasting from a single Gaussian mode to multiple Bessel modes using a single phase-only spatial light modulator. Under the obstructed path conditions, obstruction-free data-carrying N-fold Bessel modes multicasting is demonstrated in the experiment. We also experimentally study N-fold multicasting of a 20 Gbit/s quadrature phase-shift keying signal from a single Gaussian mode to multiple Bessel modes and measure the link performance. All the multicasted Bessel modes show relatively low crosstalk from their neighboring modes and achieve a bit-error rate of less than 1e-3. PMID:26625026
Institute of Scientific and Technical Information of China (English)
Ismail EKINCIOGLU; Ayhan SERBETCI
2005-01-01
In this paper, we establish sufficient conditions on weights which ensure that high-order Riesz-Bessel transformations generated by the generalized shift operator act boundedly from one weighted Lp-space into another.
Some Contour Integrals Involving Generalised Hypergeometric Function
Directory of Open Access Journals (Sweden)
S. D. Bajpai
1970-04-01
Full Text Available Contour integral involving Fox's H-function and modified Bessel function of the first kind has been calculated. Some important properties and particular cases of H-function, which is a generalization of G-function, have been derived and discussed.
Mitri, F G
2016-01-01
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 st...
Milione, Giovanni; Nguyen, Thien An; Chakraborty, Ougni; Karimi, Ebrahim; Forbes, Andrew; Alfano, Robert R
2014-01-01
We experimentally measured the self-healing of the spatially inhomogeneous states of polarization of radial and azimuthal polarized vector Bessel beams. Radial and azimuthal polarized vector Bessel beams were generated via a digital version of Durnin's method, using a spatial light modulator in concert with a liquid crystal $q$-plate. As a proof of principle, their intensities and spatially inhomogeneous states of polarization were measured using Stokes polarimetry as they propagated through two disparate obstructions. It was found, similar to their intensities, the spatially inhomogeneous states of polarization of a radial and azimuthal polarized vector Bessel beams self-heal. Similar to scalar Bessel beams, the self-healing of vector Bessel beams can be understood via geometric optics, i.e., the interference of the unobstructed conical rays in the shadow region of the obstruction. The self-healing of vector Bessel beams may have applications in, for example, optical trapping.
Surface solitons supported by one-dimensional composite Bessel optical lattices
Institute of Scientific and Technical Information of China (English)
Dong Liang-Wei; Yang Xiao-Yu; Chen Hai-Yun
2008-01-01
We address the existence of surface solitons at an interface in a defocnsing cubic medium with an imprinted one-dimensional (1D) composite Bessel optical lattice. This setting is composed of two Bessel lattices with different orders and different modulation depths, separated beside both sides of an interface. Stability analysis and numerical propagation simulations prove that solitons supported by the model are dynamically stable in the entire domain of their existence. The order of lattice determines the shape of soliton, and the amplitude of soliton depends on the lattice modulation depth.The experimental realization of the scheme is also proposed.Our results may provide another effective way of controlling the shapes of surface solitons and thus their evolutions by introducing a new freedom degree.
Generation of J0-Bessel-Gauss Beam by an heterogeneous refractive index map
Alerigi, Damian P San Roman; Benslimane, Ahmed; Zhang, Yaping; Alsunaidi, Mohammad; Ooi, Boon S; 10.1364/JOSAA.29.001252
2012-01-01
In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of such device by solving the inverse electromagnetic problem. The computed conversion e?ficiency is 90%. The theoretical results, obtained from the beam conversion efi?ciency, self-regeneration, and propagation through an opaque obstruction; demonstrate that a 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 ?rst demonstration of such beam transformation by means of a 2D index-mapping which is fully integrable in silicon photonics based planar lightwave circuits (PLC). The concept device is signi?cant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and non-linear beam diode lasers.
Spin and orbital angular momentum correlations in parametric downconversion of Bessel beams
International Nuclear Information System (INIS)
We present a full vectorial analysis of the parametric downconversion process using a pump Bessel beam and a photon description based on Bessel wavefunctions. We find that, under the considered geometry, optical angular momentum is conserved but the crystal induces a coupling between the optical spin angular momentum (SAM) and the optical orbital angular momentum (OAM) ruled by the nonlinear properties of the crystal via the second order susceptibility tensor χijk(2). This leads to nontrivial correlations between the expected values of the SAM and OAM of the resulting two-photon states. Distributions of orbital angular momentum of the downconverted photons are evaluated in detail for a specific set-up
Chaotic dynamics of dilute thermal atom clouds on stationary optical Bessel beams
International Nuclear Information System (INIS)
We characterize the semiclassical dynamics of dilute thermal atom clouds located in three-dimensional optical lattices generated by stationary optical Bessel beams. The dynamics of the cold atoms is explored in the quasi-Hamiltonian regime that arises using laser beams with far-off resonance detuning. Although the transverse structure of Bessel beams exhibits a complex topological structure, it is found that the longitudinal motion along the main propagation axis of the beam is the detonator of a high sensitivity of the atoms' motion to the initial conditions. This effect would not be properly described by bidimensional models. We show that an experimental implementation can be highly simplified by an analysis of the behaviour of the dynamical system under scale transformations. Experimentally feasible signatures of the chaotic dynamics of the atom clouds are also identified. (paper)
Controlling Fano resonance of ring/crescent-ring plasmonic nanostructure with Bessel beam.
Xiao, Fajun; Zhu, Weiren; Premaratne, Malin; Zhao, Jianlin
2014-01-27
We propose a method to dynamically control the Fano resonance of a ring/crescent-ring gold nanostructure by spatially changing the phase distribution of a probe Bessel beam. We demonstrate that a highly tunable Fano interference between the quadrupole and bright dipole modes can be realized in the near-infrared range. Even though a complex interference between a broad resonance and a narrower resonance lead to these observations, we show that a simple coupled oscillator model can accurately describe the behavior, providing valuable insights into the dynamics of the system. A further analysis of this structure uncovers a series of interesting phenomena such as anticrossing, sign changing of coupling and the spectral inversion of quadrupole and bright dipole modes. We further show that near field enhancement at Fano resonance can be actively controlled by modulating the phase distribution of the exciting incident Bessel beam. PMID:24515223
A precise method for analyzing Bessel-like beams generated by broadband waves
Cheng, Zhiming; Wu, Fengtie; Fan, Dandan; Fang, Xiang
2013-11-01
The current study proposes spectrum analysis, which is a novel analytical method proposed for the first time, for analyzing Bessel-like beams generated by broadband wave. The main idea is to decompose the consecutive spectrum into an incoherent superposition of a series of different wavelengths. Integrating spheres play a significant role in spectrum analysis and a series of wavelengths matched with relative intensity can be read according to the spectrum measured by an integral ball. Moreover, the Sellmeier dispersion equation, which indicates that the refractive index can be matched with wavelength, is also employed. Combining with the Fresnel diffraction integral formula, the distribution of fields behind an axicon is obtained. Two broadband sources, including a light-emitting diode (LED) with a narrow band and a halogen lamp with a broad band, are used to generate a Bessel-like beam. The experimental results fit well with the theoretical analysis.
Laser controlled deposition of metal microstructures via nondiffracting Bessel beam illumination
Drampyan, Rafael; Leonov, Nikita; Vartanyan, Tigran
2016-04-01
The technique of the laser controlled deposition of sodium and rubidium deposits on the sapphire substrate is presented. The metals were deposited on the clean sapphire substrate from the vapor phase contained in the evacuated and sealed cell. We use an axicon to produce a non-diffracting Bessel beam out of the beam got from the cw diode laser with 200 mW power at the wavelength of 532 nm. After 30 minutes of the laser-controlled deposition the substrates were examined in the optical microscope. The obtained metal deposits form the sharp-cut circles with the pitch of 10 μm, coincident with the tens of dark rings of the Bessel beam. Reduction of the laser power leads to the build up of the continuous metal film over the whole substrate.
Bessel-beam Grueneisen relaxation photoacoustic microscopy with extended depth of field.
Shi, Junhui; Wang, Lidai; Noordam, Cedric; Wang, Lihong V
2015-11-01
The short focal depth of a Gaussian beam limits the volumetric imaging speed of optical resolution photoacoustic microscopy (OR-PAM). A Bessel beam, which is diffraction free, provides a long focal depth, but its side lobes deteriorate image quality when the Bessel beam is directly employed to excite photoacoustic (PA) signals in OR-PAM. We present a nonlinear approach based on the Grueneisen relaxation effect to suppress the side-lobe artifacts in PA imaging. This method extends the focal depth of OR-PAM and speeds up volumetric imaging. We experimentally demonstrated a 1-mm focal depth with a 7-μm lateral resolution and volumetrically imaged a carbon fiber and red blood cell samples. PMID:26524679
Bessel光束的频率特性%The Frequency Property of the Apertured Bessel Beams
Institute of Scientific and Technical Information of China (English)
宋继恩; 杨广强; 杨性愉
2001-01-01
The propagation properties of Bessel beams are numericallycalculated. A Einstein shift is found under free propagation of the apertured Bessel beams.And we find that with the increase in z the Einstein shift decreases apparently after a certain distance and when z→∞, the Einstein shift decrease to zero.%在利用数值计算研究Bessel光束在自由光场空间传播中，发现Bessel光束在自由光场空间传播中存在着频率红移现象；而且当达到一定的传播距离后，频率红移量开始随着传播距离增大而明显减小，当z→∞时，红移量趋于零.
On hitting times, Bessel bridges and Schrödinger’s equation
Hernandez-del-Valle, Gerardo
2013-01-01
In this paper we establish relationships between four important concepts: (a) hitting time problems of Brownian motion, (b) 3-dimensional Bessel bridges, (c) Schr\\"odinger's equation with linear potential, and (d) heat equation problems with moving boundary. We relate (a) and (b) by means of Girsanov's theorem, which suggests a strategy to extend our ideas to problems in $\\mathbb{R}^n$ and general diffusions. This approach also leads to (c) because we may relate, through a Feynman-Kac represe...
Columnar deformation of human red blood cell by highly localized fiber optic Bessel beam stretcher
Lee, Sungrae; Joo, Boram; Jeon, Pyo Jin; Im, Seongil; Oh, Kyunghwan
2015-01-01
A single human red blood cell was optically stretched along two counter-propagating fiber-optic Bessel-like beams in an integrated lab-on-a-chip structure. The beam enabled highly localized stretching of RBC, and it induced a nonlinear mechanical deformation to finally reach an irreversible columnar shape that has not been reported. We characterized and systematically quantified this optically induced mechanical deformation by the geometrical aspect ratio of stretched RBC and the irreversible...
Electron acceleration by two crossed Bessel-Gaussian beams in vacuum
Institute of Scientific and Technical Information of China (English)
Zhao Zhi-Guo; Lü Bai-Da
2006-01-01
The direct acceleration of electrons by using two linearly polarized crossed Bessel-Gaussian (BG) beams with equal frequency and amplitude in vacuum is proposed and studied. It is shown that two linearly polarized BG beams of the same order (0 or 1) with a π-rad phase difference have a resultant non-zero longitudinal electric field on the z-axis and can be used, in principle, to accelerate electrons.
Off-axial acoustic radiation force of pressor and tractor Bessel beams on a sphere
Silva, Glauber T; Lobo, Tiago P; Mitri, Farid G
2012-01-01
Acoustic Bessel beams are known to produce an axial radiation force on a sphere centered on the beam axis (on-axial configuration) that exhibits both "pressor" and "tractor" behaviors. The pressor and the tractor forces are oriented along the beam's direction of propagation and opposite to it, respectively. The behavior of the acoustic radiation force generated by Bessel beams when the sphere lies outside the beam's axis (off-axial configuration) is unknown. Using the 3D radiation force formulas given in terms of the partial wave expansion coefficients for the incident and scattered waves, both axial and transverse components of the force exerted on a silicone-oil sphere are obtained for a zero- and a first-order Bessel vortex beam. As the sphere departs from the beam's axis, the tractor force becomes weaker. Moreover, the behavior of the transverse radiation force field may vary with the sphere's size factor $ka$ (where $k$ is the wavenumber and $a$ is the sphere radius). Both stable and unstable equilibrium...
Quantifying the influence of Bessel beams on image quality in optical coherence tomography.
Curatolo, Andrea; Munro, Peter R T; Lorenser, Dirk; Sreekumar, Parvathy; Singe, C Christian; Kennedy, Brendan F; Sampson, David D
2016-01-01
Light scattered by turbid tissue is known to degrade optical coherence tomography (OCT) image contrast progressively with depth. Bessel beams have been proposed as an alternative to Gaussian beams to image deeper into turbid tissue. However, studies of turbid tissue comparing the image quality for different beam types are lacking. We present such a study, using numerically simulated beams and experimental OCT images formed by Bessel or Gaussian beams illuminating phantoms with optical properties spanning a range typical of soft tissue. We demonstrate that, for a given scattering parameter, the higher the scattering anisotropy the lower the OCT contrast, regardless of the beam type. When focusing both beams at the same depth in the sample, we show that, at focus and for equal input power and resolution, imaging with the Gaussian beam suffers less reduction of contrast. This suggests that, whilst Bessel beams offer extended depth of field in a single depth scan, for low numerical aperture (NA 0.95), superior contrast (by up to ~40%) may be obtained over an extended depth range by a Gaussian beam combined with dynamic focusing. PMID:27009371
Efficient second-harmonic imaging of collagen in histological slides using Bessel beam excitation.
Vuillemin, Nelly; Mahou, Pierre; Débarre, Delphine; Gacoin, Thierry; Tharaux, Pierre-Louis; Schanne-Klein, Marie-Claire; Supatto, Willy; Beaurepaire, Emmanuel
2016-01-01
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. PMID:27435390
Institute of Scientific and Technical Information of China (English)
吴逢铁; 马亮; 张前安; 郑维涛; 蒲继雄
2012-01-01
Reconstruction of focused high order Bessel-Gauss beam by using thin lens is proposed.Based on the diffraction theory,reconstruction behavior of focused high order Bessel-Gauss beam is analyzed.The three-dimensional optical intensity distribution and the cross-section optical intensity distribution of the high order Bessel-Gauss beam focused by first thin lens,and then reconstructed by the second thin lens are numerical simulated.Result shows that the high order Bessel-Gauss beam passing through the single thin lens can generate Bottle beam,and the bright ring is obtained at focus.To rectify the beam divergence after focus,another thin lens is introduced at suitable position.After that,the beam keeps the Bessel distribution.Experiment is conducted,and experimental results are in agrement with the theoretical analyses.Research result shows its significance in providing a guidance for optical tweezers,particle trapping and controlling.%提出利用薄透镜元件对聚焦后的高阶Bessel-Gauss光束进行重建.基于衍射理论,分析了高阶Bessel-Gauss光束聚焦后的重建行为,数值模拟高阶Bessel-Gauss光束经薄透镜聚焦再通过另一薄透镜重建的三维光场分布和截面光强分布图.结果表明,高阶Bessel-Gauss光束经单个薄透镜后产生中空的局域空心光束,在焦点位置处为圆环,尔后迅速发散;在焦点后合适位置处放入另一薄透镜可矫正焦点后发散的光束,使得其后光场不变,仍满足Bessel分布;实验结果与理论分析相符合.研究结果对光镊、粒子捕获与操控具有一定的指导意义.
Gao, Jie; Zhang, Yixin; Dan, Weiyi; Hu, Zhengda
2015-06-29
The turbulent effects of strong irradiance fluctuations on the probability densities and the normalized powers of the orbital angular momentum (OAM) modes are modeled for fractional Bessel Gauss beams in paraxial turbulence channel. We find that the probability density of signal OAM modes is a function of position deviation from the beam center, and the farther away from the beam center the detection position is, the smaller the probability density is. For fractional OAM quantum numbers, the average probability densities of signal/crosstalk modes oscillate along the beam radius except the half-integer. When the beam waist of source decreases or the irradiance fluctuation increases, the average probability density of the signal OAM mode drops. The peak of the average probability density of crosstalk modes shifts to outward of the beam center as beam waist gets larger. In the nearby region of beam center, the larger the quantum number deviation of OAM, the smaller the beam waist and the turbulence fluctuations are, the lower average probability densities of crosstalk OAM modes are. Especially, the increase of turbulence fluctuations can make the crosstalk stronger and more concentrated. Lower irradiance fluctuation can give rise to higher the normalized powers of the signal OAM modes, which is opposite to the crosstalk normalized powers. PMID:26191711
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.
Chen, Ye; Liu, Jonathan T C
2015-04-01
Bessel beams have recently been investigated as a means of improving deep-tissue microscopy in highly scattering and heterogeneous media. It has been suggested that the long depth-of-field and self-reconstructing property of a Bessel beam enables an increased penetration depth of the focused beam in tissues compared to a conventional Gaussian beam. However, a study is needed to better quantify the magnitude of the beam steering as well as the distortion of focused Gaussian and Bessel beams in tissues with microscopic heterogeneities. Here, we have developed an imaging method and quantitative metrics to evaluate the motion and distortion of low-numerical-aperture (NA) Gaussian and Bessel beams focused in water, heterogeneous phantoms, and fresh mouse esophagus tissues. Our results indicate that low-NA Bessel beams exhibit reduced beam-steering artifacts and distortions compared to Gaussian beams, and are therefore potentially useful for microscopy applications in which pointing accuracy and beam quality are critical, such as dual-axis confocal (DAC) microscopy. PMID:25909015
(p,Y)-算子Bessel列的广义扰动%General perturbation of(p,Y)-operator Bessel sequence
Institute of Scientific and Technical Information of China (English)
刘楠; 魏妙
2012-01-01
运用算子理论,研究了Banach空间中(p,Y)-算子Bessel列的一些广义扰动形式.通过定义新的算子列,证明了已知(p,Y)-算子Bessel列在下三角形式或全矩阵形式的系数矩阵的作用下得到的算子列仍然是(p,Y)-算子Bessel列的充分条件,并得到了通过数列作用在已知(p,Y)-算子Bessel列上构造的一些算子列仍然是(p,Y)-算子Bessel列的充分条件.%By the operator theory,some general perturbations of(p,Y)-operator Bessel sequences in Banach space are mainly studied in this paper.Through defining a new operator sequence,the sufficient conditions are proved for a lower triangular or a full form of coefficient matrix effecting to a given(p,Y)-operator Bessel sequence,such that the resulted sequence will be still a(p,Y)-operator Bessel sequence.The sufficient conditions for a sequence of operators compounded by some scalar sequences effecting to a given(p,Y)-operator Bessel sequence to be a(p,Y)-operator operator Bessel are also obtained.
Superluminal Behaviors in Bessel-beams Propagation%论Bessel波束超光速现象
Institute of Scientific and Technical Information of China (English)
黄志洵
2013-01-01
The Bessel beams have very singular properties. For example,the motion of Bessel beam is a non - diffracting beam, and the experimental measurements showed that Bessel beams have a group velocity greater than the light speed . A simple explanation for the superluminal motion is given by the interference of spherical wave fronts on the symmetry axis. And in 2006 the researchers show that, in contrary to the ordinary Bessel waves of real argument, the group velocities of imaginary argument modified Bessel waves are superluminal.%Bessel波束具有奇异的特性，例如在传播中不发生衍射，而且实验测量证明其群速比光速c要大。对其超光速运动可以用球面波前在对称轴上的干涉作简单解释。2006年有研究人员指出，不仅通常的实宗量Bessel波，虚宗量修正Bessel波也有群速超光速现象。
Institute of Scientific and Technical Information of China (English)
陈宗荣; 李顺初
2011-01-01
In this paper, we solve the general boundary value problem of Bessel equations, and obtain the similar structure and the similar kernel function of solutions. A new idea and method for solving this kind of problems is formed: so called "similar structure construction". This idea and method can be used to analyze inner properties of solutions, to solve some practical problems and to write analytical softwares.%对Bessel方程的一般边值问题进行求解,得到了解式的相似结构和相似核函数及求解Bessel方程边值问题的一个新思想和新方法:相似结构构造法.该方法有利于进一步分析解的内在规律、解决相应的应用问题、方便编制相应的分析软件.
Riaud, Antoine; Baudoin, Michael; Matar, Olivier Bou
2015-01-01
Despite their self-reconstruction properties in heterogeneous media, Bessel beams are known to degenerate when they are refracted from an isotropic to an anisotropic medium. In this paper, we study the converse situation wherein an anisotropic Bessel beam is refracted into an isotropic medium. It is shown that these anisotropic Bessel beams also degenerate, leading to confined vortical waves that may serve as localized particle trap for acoustical tweezers. The linear nature of this degeneration allows the 3D control of this trap position by wavefront correction. Theory is confronted to experiments performed in the field of acoustics. A swirling surface acoustic wave is synthesized at the surface of a piezoelectric crystal by a MEMS integrated system and radiated inside a miniature liquid vessel. The wavefront correction is operated with inverse filter technique. This work opens perspectives for contactless on-chip manipulation devices.
Cang, Ji; Xiu, Peng; Liu, Xu
2013-12-01
Based on the extended Huygens-Fresnel diffraction integral, the expressions for the average intensity and the effective size of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams propagating through a paraxial ABCD optical system are obtained in the turbulent atmosphere. The influences of the source coherence and atmospheric turbulence on the propagation of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams in the turbulent atmosphere are investigated in detail. It is found that the beam profile will eventually evolve into a Gaussian-like distribution through turbulence in contrast to ring-shaped far-field pattern in free space. The effective size of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams with lower source coherence is less affected by turbulence. The parameter β and index n of the sources have some effects on intensity distribution and beam spreading through atmospheric turbulence.
Banach空间中的Xd Bessel列%Sequences of Xd Bessel for a Banach space
Institute of Scientific and Technical Information of China (English)
王亚丽; 曹怀信; 张巧卫
2011-01-01
研究了Banach空间X中的Xd Bessel列、Xd框架、Xd独立框架、Xd紧框架与Xd Riesz基.证明了当Xd为BK-空间时,(BXXd,‖·‖)是数域F上的Banach空间；当Xd是BK-空间且X自反时,通过定义算子Tf,建立了空间BXXd与算子空间B(X*,Xd)之间的等距同构,为利用算子论的方法研究Xd Bessel列提供了必要的理论依据.最后,给出了Banach空间X中Xd Bessel列的等价刻画并证明了独立的Xd框架与Xd Riesz基是一致的.%Xd Bessel sequences, Xd frames, Xd independent frames, Xd tight frames and Xd Riesz basis for a Banach space X ate introduced and discussed. It is proved that (Bxxd || ? || ) is a Banach space when Xd is a BK-space. By de fining an operator Tf, an isometric isomorphism from Bxxd to B(X* ,Xd) is established when Xd is a BK-space and X is reflexive, which provides a necessary theoretical basis for studying Xd Bessel sequences by the operator theory. Finally, the equivalent characterizations of Xd Bessel sequences for a Banach space X are given. Also, it is proved that independ ent Xd frames and Xd Riesz bases for a Banach space X are the same.
All-optical 3D atomic loops generated with Bessel light fields
Volke-Sepulveda, K
2008-01-01
The propagation invariance of Bessel beams as well as their transversal structure are 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 center 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.
All-optical 3D atomic loops generated with Bessel light fields
Energy Technology Data Exchange (ETDEWEB)
Volke-Sepulveda, Karen; Jauregui, RocIo [Departamento de Fisica Teorica, Instituto de Fisica, Universidad Nacional Autonoma de Mexico, A.P. 20-364, Mexico 01000 D.F. (Mexico)], E-mail: karen@fisica.unam.mx, E-mail: rocio@fisica.unam.mx
2009-04-28
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.
All-optical 3D atomic loops generated with Bessel light fields
International Nuclear Information System (INIS)
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.
Avramov-Zamurovic, S.; Nelson, C.; Guth, S.; Korotkova, O.; Malek-Madani, R.
2016-01-01
We report on experimental generation of Electromagnetic Bessel-Gaussian Schell-Model [EBGSM] beams via incoherent superposition of two mutually orthogonal electric field components, both originated from a laser source, whose phases are spatially modified by two nematic liquid crystal Spatial Light Modulators. The EBGSM beam is then passed through a weakly fluctuating turbulent channel and examined for contrast in its fluctuating intensity. It is demonstrated that after passing through turbulence the electromagnetic beam exhibits reduction in the scintillation index on the order of 50%, as compared with that for an equivalent scalar beam, in strong agreement with recent theoretical predictions.
Efficient phase-matching for difference frequency generation with pump of Bessel laser beams.
Liu, Pengxiang; Shi, Wei; Xu, Degang; Zhang, Xinzheng; Zhang, Guizhong; Yao, Jianquan
2016-01-25
A type of phase matching for difference frequency generation with Bessel-type pump beams is proposed. In this geometry, the phase matching is achieved in a cone around the laser path by properly controlling the beam profile. An experimental case that 1.5THz generation with ~2μm lasers pumped bulk GaAs crystal is considered. Calculations of the energy conversion characteristics are performed based on a semi-analytical model. The results indicate that this configuration could relax the phase matching condition in a wide range of nonlinear crystals and pump wavelengths. PMID:26832473
Application of nondiffracting Bessel beams for shaping of surface metal microstructures
Drampyan, Rafael; Leonov, Nikita; Vartanyan, Tigran
2016-08-01
A novel method of laser-controlled shaping of metal microstructures based on the processes of metal atoms adsorption on the surface of crystalline substrate and simultaneous control of photostimulated desorption of atoms by spatially modulated nondiffracting laser beam illumination is presented. The experiments were performed for sodium atoms deposition to the sapphire substrate, which was illuminated by Bessel beam at 532 nm wavelength and 2 W/cm2 intensity. Experiments showed that the optical pattern was well reproduced in the sodium deposits thus creating the annularly microstructured metal film with few tens nanometre thickness.
Columnar deformation of human red blood cell by highly localized fiber optic Bessel beam stretcher.
Lee, Sungrae; Joo, Boram; Jeon, Pyo Jin; Im, Seongil; Oh, Kyunghwan
2015-11-01
A single human red blood cell was optically stretched along two counter-propagating fiber-optic Bessel-like beams in an integrated lab-on-a-chip structure. The beam enabled highly localized stretching of RBC, and it induced a nonlinear mechanical deformation to finally reach an irreversible columnar shape that has not been reported. We characterized and systematically quantified this optically induced mechanical deformation by the geometrical aspect ratio of stretched RBC and the irreversible stretching time. The proposed RBC mechanism can realize a versatile and compact opto-mechanical platform for optical diagnosis of biological substances in the single cell level. PMID:26601005
Collinear Acousto-Optical Transformation of Bessel Light Beams in Biaxial Gyrotropic Crystals
Belyi, V. N.; Kulak, G. V.; Krokh, G. V.; Shakin, O. V.
2016-05-01
The collinear acousto-optical transformation of Bessel light beams in biaxial gyrotropic crystals into two annular, internal conical refraction beams with orthogonal elliptical polarization is studied. It is found that the diffraction efficiency is maximal (~50-60%) for low ultrasound intensities and varies slightly with further increases in acoustic power. At high ultrasound intensities, the intensities of the transmitted and diffracted annular beams differ insignificantly. The possible use of this acousto-optical interaction for creating collinear tuneable narrow-band acousto-optical filters at low ultrasonic frequencies is demonstrated.
Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Huang, Qingqing
2016-08-01
Rytov theory was employed to establish the transmission model for the optical vortices carried by Bessel-Gaussian (BG) beams in weak anisotropic turbulence based on the generalized anisotropic von Karman spectrum. The influences of asymmetry anisotropic turbulence eddies and source parameters on the signal orbital angular momentum (OAM) mode detection probability of partially coherent BG beams in anisotropic turbulence were discussed. Anisotropic characteristics of the turbulence could enhance the OAM mode transmission performance. The spatial partially coherence of the beam source would increase turbulent aberration's effect on the optical vortices. BG beams could dampen the influences of the turbulence because of their nondiffraction and self-healing characteristics. PMID:27505641
Bessel spatial profile of a soft x-ray laser beam
Tissandier, F.; Sebban, S.; Ribière, M.; Gautier, J.; Zeitoun, Ph.; Lambert, G.; Goddet, J.-Ph.; Burgy, F.; Valentin, C.; Rousse, A.; Nejdl, J.; Mocek, T.; Maynard, G.
2010-12-01
We report far-field profile measurements of an optical-field-ionized high-order harmonic-seeded soft x-ray laser. We show that the beam transverse profile can be controlled between a regular Gaussian shape and a Bessel profile exhibiting several rings via the infrared laser pump intensity. These experimental data are supported by a complete numerical modeling including a two-dimensional plasma amplifier simulation and a two-level soft x-ray amplification using a Maxwell-Bloch treatment. This model takes into account the experimental high-order harmonic wavefront and intensity before it is numerically amplified.
Generalized Fourier-grid R-matrix theory: a discrete Fourier-Riccati-Bessel transform approach
International Nuclear Information System (INIS)
We present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. We apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, we have hopes to broaden the formalism to many types of problems. (author)
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...... tuning the propagated field by linking the quantized surface pressure profile to a known set of limited diffraction Bessel beams propagating into the medium. This enables derivation of an analytic expression for the field at any point in space and time in terms of the transducer surface pressure profile...
Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces
International Nuclear Information System (INIS)
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
Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map
San-Román-Alerigi, Damián P.
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.
Purnapatra, Subhajit B.; Bera, Sampa; Mondal, Partha Pratim
2012-09-01
Monitoring and visualizing specimens at a large penetration depth is a challenge. At depths of hundreds of microns, several physical effects (such as, scattering, PSF distortion and noise) deteriorate the image quality and prohibit a detailed study of key biological phenomena. In this study, we use a Bessel-like beam in-conjugation with an orthogonal detection system to achieve depth imaging. A Bessel-like penetrating diffractionless beam is generated by engineering the back-aperture of the excitation objective. The proposed excitation scheme allows continuous scanning by simply translating the detection PSF. This type of imaging system is beneficial for obtaining depth information from any desired specimen layer, including nano-particle tracking in thick tissue. As demonstrated by imaging the fluorescent polymer-tagged-CaCO3 particles and yeast cells in a tissue-like gel-matrix, the system offers a penetration depth that extends up to 650 µm. This achievement will advance the field of fluorescence imaging and deep nano-particle tracking.
Negative optical spin torque wrench of a nondiffracting non-paraxial fractional Bessel vortex beam
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 and the beam's half-cone angle. When the beam order is zero, the axial spin torque component vanishes. However, when the beam order 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 to induce 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, the design of optically-engineered metamateri...
Hilbert空间中的Bessel序列%Bessel Sequences in a Hilbert Space
Institute of Scientific and Technical Information of China (English)
曹怀信
2000-01-01
In this paper,we introduce and study the Bessel sequences in a Hilbert space H.By using operator-theoretic-methods,we give some conditions for a Bessel sequence to be a frame(resp,tight frame,independent frame,Riesz basis,orthonormal basis) in H.We also give a corresponding relationship between these sequences and the related operators from H into l2 and a unified method to construct these sequences.%研究了Hilbert空间H中的Bessel序列,应用算子论方法给出了这种序列成为H中的框架、紧框架、独立框架、Risez基、正规正交基的条件;建立了这些序列与H到l2中的相应算子之间的对应关系与构造这些序列的统一方法.
Khai, D. Q.; Tri, N. M.
2016-01-01
In this paper, we prove some results on the existence and decay properties of high order derivatives in time and space variables for local and global solutions of the Cauchy problem for the Navier-Stokes equations in Bessel-potential spaces.
Mitri, F. G.
2014-03-01
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.
Perturbations of Bessel Sequences of Order p in a Banach Space%Banach空间中P阶Bessel列的扰动
Institute of Scientific and Technical Information of China (English)
王秋芬; 曹怀信; 武海辉
2011-01-01
应用算子论方法研究Banach空间X中p(1＜P＜∞)阶Bessel列的扰动问题,对X中的任一p阶Bessel列f={fi}i∈I,定义了有界线性算子Tf:X*→lp,建立了从全体p阶Bessel列组成的Banach空间BpX(Ⅰ)到算子空间B(X*,lp)上的等距线性同构α:f→Tf,并给出了p阶Bessel列的扰动定理.%With the aid of operator theory, some perturbations of Bessel sequences of order p in a Banach space X were discussed. For a Bessel sequence f = {fi} i∈I of order p in X, we defined a bounded linear operator Tf from X* into lp and established a linear isometry isomorphism a from the space BpX (I) of all the Bessel sequences of order p in a Banach space X into the operator space B(X*,lp) defined by α(f) = Tr. In the light of operator theory, some results on perturbations of Bessel sequences of order p were given, which are helpful to the study of frames of order p for a Banach space.
Special functions for scientists and engineers
Bell, W W
2004-01-01
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
Transform analysis of generalized functions
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
A class of Bessel function integrals with application in particle physics
International Nuclear Information System (INIS)
Many problems in particle physics and field theory require the evaluation of complex integrals. Our investigation arose in connection with a new method of partial wave mass renormalization of the electron self-energy in quantum electrodynamics (QED) where these integrals play a crucial role. Previous studies appear not to have led to expressions which are readily computable. We derive an explicit formula for the general case and a recursive method of construction which allows us to generate all cases of practical interest to high precision. Our algorithms are highly efficient on scalar computers and readily vectorize on suitable machines. (author)
International Nuclear Information System (INIS)
One of the paradigmatic classes of problems that frequently arise in piping stress analysis discipline is the effect of local stresses created by supports and restraints attachments. Over the past 20 years, concerns have been identified by both regulatory agencies in the nuclear power industry and others in the process and chemicals industries concerning the effect of various stiff clamping arrangements on the expected life of the pipe and its various piping components. In many of the commonly utilized geometries and arrangements of pipe clamps, the elasticity problem becomes the axisymmetric stress and deformation determination in a hollow cylinder (pipe) subjected to the appropriate boundary conditions and respective loads per se. One of the geometries that serve as a pipe anchor is comprised of two pipe clamps that are bolted tightly to the pipe and affixed to a modified shoe-type arrangement. The shoe is employed for the purpose of providing an immovable base that can be easily attached either by bolting or welding to a structural steel pipe rack. Over the past 50 years, the computational tools available to the piping analyst have changed dramatically and thereby have caused the implementation of solutions to the basic problems of elasticity to change likewise. The need to obtain closed form elasticity solutions, however, has always been a driving force in engineering. The employment of symbolic calculus that is currently available through numerous software packages makes closed form solutions very economical. This paper briefly traces the solutions over the past 50 years to a variety of axisymmetric stress problems involving hollow circular cylinders employing a Fourier series representation. In the present example, a properly chosen Fourier series represent the mathematical simulation of the imposed axial displacements on the outside diametrical surface. A general solution technique is introduced for the axisymmetric discontinuity stresses resulting from an anchor restraint on a selected of pipe geometry. These solutions can be economically implemented on today's symbolic calculus software packages with no loss in solution accuracy when compared to often more expensive techniques such as the finite element method. Verification of the axisymmetric solution technique is illustrated by the comparison of results for the closed form solutions versus those approximated by the finite element technique. Extensions of the general axisymmetric solution technique to other geometries and applied loads are also discussed while the numerical and graphical results are tendered
Wave-optics description of self-healing mechanism in Bessel beams
Aiello, Andrea
2014-01-01
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.
Large-Angle Bending Transport of Microparticles by Acoustic Half-Bessel Beams
Li, Yixiang; Xu, Shengjun; Ke, Manzhu; Liu, Zhengyou
2014-01-01
Conventional microparticle transports by light or sound are realized along a straight line. Recently, this limit has been overcome in optics as the growing up of the self-accelerating Airy beams, which are featured by many peculiar properties, e.g., bending propagation, diffraction-free and self-healing. However, the bending angles of Airy beams are rather small since they are only paraxial solutions of the two-dimensional (2D) Helmholtz equation. Here we propose a novel micromanipulation by using acoustic Half-Bessel beams, which are strict solutions of the 2D Helmholtz equation. Compared with that achieved by Airy beams, the bending angle of the particle trajectory attained here is much steeper (exceeding 90o). The large-angle bending transport of microparticles, which is robust to complex scattering environment, enables a wide range of applications from the colloidal to biological sciences.
Low-temperature Bessel beam trap for single submicrometer aerosol particle studies
Energy Technology Data Exchange (ETDEWEB)
Lu, Jessica W.; Chasovskikh, Egor; Stapfer, David [Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich (Switzerland); Isenor, Merrill; Signorell, Ruth [Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich (Switzerland); Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, British Columbia V6T 1Z1 (Canada)
2014-09-01
We report on a new instrument for single aerosol particle studies at low temperatures that combines an optical trap consisting of two counter-propagating Bessel beams (CPBBs) and temperature control down to 223 K (−50 °C). The apparatus is capable of capturing and stably trapping individual submicrometer- to micrometer-sized aerosol particles for up to several hours. First results from studies of hexadecane, dodecane, and water aerosols reveal that we can trap and freeze supercooled droplets ranging in size from ∼450 nm to 5500 nm (radius). We have conducted homogeneous and heterogeneous freezing experiments, freezing-melting cycles, and evaporation studies. To our knowledge, this is the first reported observation of the freezing process for levitated single submicrometer-sized droplets in air using optical trapping techniques. These results show that a temperature-controlled CPBB trap is an attractive new method for studying phase transitions of individual submicrometer aerosol particles.
Acoustical radiation torque and force for spheres and Bessel beam extinction efficiency
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.
Knyazev, B. A.; Choporova, Yu. Yu.; Mitkov, M. S.; Pavelyev, V. S.; Volodkin, B. O.
2015-10-01
Bessel vortex beams with topological charges of l =±1 and l =±2 were produced in the terahertz spectral range from a free electron laser Gaussian beam (λ =141 μ m ) transformed using silicon binary diffractive optical elements. The spatial characteristics of the beams were obtained using a microbolometer array. A radius to path length ratio of 1 ∶100 was achieved for nondiffractive beams with the average power of 30 W. Surface plasmon polaritons (SPPs) on gold-zinc-sulphide-air interfaces were generated due to diffraction of vortex beams on a sample edge. A new effect, a dependence of the efficiency of SPP generation on the direction of the azimuthal component of incident-radiation Poynting vector, was revealed.
High aspect ratio nanochannel machining using single shot femtosecond Bessel beams
International Nuclear Information System (INIS)
We report high aspect ratio nanochannel fabrication in glass using single-shot femtosecond Bessel beams of sub-3 μJ pulse energies at 800 nm. We obtain near-parallel nanochannels with diameters in the range 200-800 nm, and aspect ratios that can exceed 100. An array of 230 nm diameter channels with 1.6 μm pitch illustrates the reproducibility of this approach and the potential for writing periodic structures. We also report proof-of-principle machining of a through-channel of 400 nm diameter in a 43 μm thick membrane. These results represent a significant advance of femtosecond laser ablation technology into the nanometric regime.
A New Bessel-Box Energy Analyzer for Sputtered Neutral Mass Spectrometry
Yoshikawa, Hideki; Shimizu, Ryuichi
1990-02-01
A new type energy analyzer with an electron impact ionizer for sputtered neutral mass spectrometry (SNMS), which is compact enough to be mounted in secondary ion mass spectrometry (SIMS) instruments, has been developed. The compact energy analyzer, called a modified Bessel-Box, enables energy distribution of slow charged particles with different energy resolutions to be obtained by changing the ratio of voltages applied to the analyzer. Applying this system for SNMS of Al-Mg alloy under different partial pressures of oxygen, it has been confirmed that SNMS is free from oxygen enhancement, allowing the quantification of matrix elements with considerable accuracy. It has also been revealed that the space-charge effect caused by bombarding electrons becomes fairly marked, resulting in the deformation and shift of energy distributions of the postionized particles.
Super-resolution deep imaging with hollow Bessel beam STED microscopy
Yu, Wentao; Dong, Dashan; Yang, Xusan; Xiao, Yunfeng; Gong, Qihuang; Xi, Peng; Shi, Kebin
2015-01-01
Stimulated emission depletion (STED) microscopy has become a powerful imaging and localized excitation method beating the diffraction barrier for improved lateral spatial resolution in cellular imaging, lithography, etc. Due to specimen-induced aberrations and scattering distortion, it has been a great challenge for STED to maintain consistent lateral resolution deeply inside the specimens. Here we report on a deep imaging STED microscopy by using Gaussian beam for excitation and hollow Bessel beam for depletion (GB-STED). The proposed scheme shows the improved imaging depth up to ~155{\\mu}m in solid agarose sample, ~115{\\mu}m in PDMS and ~100{\\mu}m in phantom of gray matter in brain tissue with consistent super resolution, while the standard STED microscopy shown a significantly reduced lateral resolution at the same imaging depth. The results indicate the excellent imaging penetration capability of GB-STED, making it a promising tool for deep 3D imaging optical nanoscopy and laser fabrication.
Knyazev, B A; Choporova, Yu Yu; Mitkov, M S; Pavelyev, V S; Volodkin, B O
2015-10-16
Bessel vortex beams with topological charges of l=±1 and l=±2 were produced in the terahertz spectral range from a free electron laser Gaussian beam (λ=141 μm) transformed using silicon binary diffractive optical elements. The spatial characteristics of the beams were obtained using a microbolometer array. A radius to path length ratio of 1:100 was achieved for nondiffractive beams with the average power of 30 W. Surface plasmon polaritons (SPPs) on gold-zinc-sulphide-air interfaces were generated due to diffraction of vortex beams on a sample edge. A new effect, a dependence of the efficiency of SPP generation on the direction of the azimuthal component of incident-radiation Poynting vector, was revealed. PMID:26550877
Laser-plasma interactions with a Fourier-Bessel Particle-in-Cell method
Andriyash, Igor A; Lifschitz, Agustin
2016-01-01
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 commonly used 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.
Laser-plasma interactions with a Fourier-Bessel particle-in-cell method
Andriyash, Igor A.; Lehe, Remi; Lifschitz, Agustin
2016-03-01
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.
Low-temperature Bessel beam trap for single submicrometer aerosol particle studies
International Nuclear Information System (INIS)
We report on a new instrument for single aerosol particle studies at low temperatures that combines an optical trap consisting of two counter-propagating Bessel beams (CPBBs) and temperature control down to 223 K (−50 °C). The apparatus is capable of capturing and stably trapping individual submicrometer- to micrometer-sized aerosol particles for up to several hours. First results from studies of hexadecane, dodecane, and water aerosols reveal that we can trap and freeze supercooled droplets ranging in size from ∼450 nm to 5500 nm (radius). We have conducted homogeneous and heterogeneous freezing experiments, freezing-melting cycles, and evaporation studies. To our knowledge, this is the first reported observation of the freezing process for levitated single submicrometer-sized droplets in air using optical trapping techniques. These results show that a temperature-controlled CPBB trap is an attractive new method for studying phase transitions of individual submicrometer aerosol particles
VizieR Online Data Catalog: O-M stars model atmospheres (Bessell+ 1998)
Bessell, M. S.; Castelli, F.; Plez, B.
1998-03-01
Broad band colors and bolometric corrections in the Johnson-Cousins-Glass system (Bessell, 1990PASP..102.1181B; Bessell & Brett, 1988PASP..100.1134B) have been computed from synthetic spectra from new model atmospheres of Kurucz (1995a, priv. comm.), Castelli (1997, priv. comm.), Plez, Brett & Nordlund (1992A&A...256..551P), Plez (1995-97, priv. comm.), and Brett (1995A&A...295..736B, 1995A&AS..109..263B). These atmospheres are representative of larger grids that are currently being completed. We discuss differences between the different grids and compare theoretical color-temperature relations and the fundamental color temperature relations derived from: (a) the infrared-flux method (IRFM) for A-K stars (Blackwell & Lynas-Gray 1994A&A...282..899B; Alonso et al. 1996A&AS..117..227A) and M dwarfs (Tsuji et al. 1996A&A...305L...1T); (b) lunar occultations (Ridgway et al. 1980ApJ...235..126R) and (c) Michelson interferometry (Di Benedetto & Rabbia 1987A&A...188..114D; Dyck et al. 1996AJ....111.1705D; Perrin et al. 1998A&A...331..619P) for K-M giants, and (d) eclipsing binaries for M dwarfs. We also compare color-color relations and color-bolometric correction relations and find good agreement except for a few colors. The more realistic fluxes and spectra of the new model grids should enable accurate population synthesis models to be derived and permit the ready calibration of non-standard photometric passbands. As well, the theoretical bolometric corrections and temperature-color relations will permit reliable transformation from observed color magnitude diagrams to theoretical HR diagrams. (6 data files).
Institute of Scientific and Technical Information of China (English)
程传福; 刘曼; 滕树云; 宋洪胜; 陈建平; 徐至展
2003-01-01
A method for the extracting the correlation functions of random surfaces is proposed by using the image speckle intensity. Theoretically, we analyse the integral expression of average intensity of the image speckles, and compare it with the pair of Fourier-Bessel-transform-and-the-inversion of the exponential function of the height-height correlation function of the random surfaces. Then the algorithm is proposed numerically to complement the lacking Bessel function factor in the expression of the average speckle intensity, which changes the intensity data into the pair of the Fourier-Bessel-transform. Experimentally, we measure the average image speckle intensities versus the radius of the filtering aperture in the 4 f system and extract the height-height correlation function by using the proposed algorithm. The results of the practical measurements for three surface samples and the comparison with those by atomic force microscopy validate the feasibility of this method.
Jakubowski, Jacek
2011-01-01
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of special functional of geometric Brownian motion using the squared Bessel and radial Ornstein-Uhlenbeck processes. Knowing the transition density functions of the above we obtain computable formulas for certain expectations of the concerned functional. As an example we find the moments of processes representing an asset price in the lognormal volatility ans Stein models. We also present links among the geometric Brownian motion, the Markov processes studied by Matsumoto and Yor and the hyperbolic Bessel processes.
Mitri, F G
2016-09-01
Energy and angular momentum flux density characteristics of an optical nondiffracting nonparaxial vector Bessel vortex beam of fractional order are examined based on the dual-field method for the generation of symmetric electric and magnetic fields. Should some conditions determined by the polarization state, the half-cone angle as well as the beam-order (or topological charge) be met, the axial energy and angular momentum flux densities vanish (representing Poynting singularities), before they become negative. These negative counterintuitive properties suggest retrograde (negative) propagation as well as a rotation reversal of the angular momentum with respect to the beam handedness. These characteristics of nondiffracting nonparaxial Bessel fractional vortex beams of progressive waves open new capabilities in optical tractor beam tweezers, optical spanners, invisibility cloaks, optically engineered metamaterials, and other applications. PMID:27607486
Pump-probe imaging of the fs-ps-ns dynamics during femtosecond laser Bessel beam drilling in PMMA.
Yu, Yanwu; Jiang, Lan; Cao, Qiang; Xia, Bo; Wang, Qingsong; Lu, Yongfeng
2015-12-14
A pump-probe shadowgraph imaging technique was used to reveal the femtosecond-picosecond-nanosecond multitimescale fundamentals of high-quality, high-aspect-ratio (up to 287:1) microhole drilling in poly-methyl-meth-acrylate (PMMA) by a single-shot femtosecond laser Bessel beam. The propagation of Bessel beam in PMMA (at 1.98 × 10⁸ m/s) and it induced cylindrical pressure wave expansion (at 3000-3950 m/s in radius) were observed during drilling processes. Also, it was unexpectedly found that the expansion of the cylindrical pressure wave in PMMA showed a linear relation with time and was insensitive to the laser energy fluctuation, quite different from the case in air. It was assumed that the energy insensitivity was due to the anisotropy of wave expansion in PMMA and the ambient air. PMID:26699062
Murukeshan, V. M.; Jesmond, Hong Xun J.; Shinoj, V. K.; Baskaran, M.; Tin, Aung
2015-07-01
Primary angle closure glaucoma is a major form of disease that causes blindness in Asia and worldwide. In glaucoma, irregularities in the ocular aqueous outflow system cause an elevation in intraocular pressure (IOP) with subsequent death of retinal ganglion cells, resulting in loss of vision. High resolution visualization of the iridocorneal angle region has great diagnostic value in understanding the disease condition which enables monitoring of surgical interventions that decrease IOP. None of the current diagnostic techniques such as goniophotography, ultrasound biomicroscopy (UBM), anterior segment optical coherence tomography (AS-OCT) and RetCam™ can image with molecular specificity and required spatial resolution that can delineate the trabecular meshwork structures. This paper in this context proposes new concepts and methodology using Bessel beams based illumination and imaging for such diagnostic ocular imaging applications. The salient features using Bessel beams instead of the conventional Gaussian beam, and the optimization challenges in configuring the probe system will be illustrated with porcine eye samples.
3D micromanipulation at low numerical aperture with a single light beam: the focused-Bessel trap.
Ayala, Yareni A; Arzola, Alejandro V; Volke-Sepúlveda, Karen
2016-02-01
Full-three-dimensional (3D) manipulation of individual glass beads with radii in the range of 2-8 μm is experimentally demonstrated by using a single Bessel light beam focused through a low-numerical-aperture lens (NA=0.40). Although we have a weight-assisted trap with the beam propagating upward, we obtain a stable equilibrium position well away from the walls of the sample cell, and we are able to move the particle across the entire cell in three dimensions. A theoretical analysis for the optical field and trapping forces along the lateral and axial directions is presented for the focused-Bessel trap. This trap offers advantages for 3D manipulation, such as an extended working distance, a large field of view, and reduced aberrations. PMID:26907437
Schulze, Christian; Dudley, Angela; Brüning, Robert; Duparré, Michael; Forbes, Andrew
2014-09-10
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 by correlation filters, from which the optical field can be retrieved in amplitude and phase. The derived OAM densities are compared to those obtained from previously stated azimuthal decomposition yielding consistent results. PMID:25321673
Polysheroidal periodic functions
International Nuclear Information System (INIS)
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
Inequalities for formal power series and entire functions
Grinshpan, Arcadii Z.
2008-02-01
We present several integral and exponential inequalities for formal power series and for both arbitrary entire functions of exponential type and generalized Borel transforms. They are obtained through certain limit procedures which involve the multiparameter binomial inequalities, integral inequalities for continuous functions, and weighted norm inequalities for analytic functions. Some applications to the confluent hypergeometric functions, Bessel functions, Laguerre polynomials, and trigonometric functions are discussed. Also some generalizations are given.
Analysis for the Potential Function of the Digital Microstructure Image of Porous Media
Institute of Scientific and Technical Information of China (English)
XUYou-Sheng; LINJi; LIHua-Mei; WUPeng-Min
2003-01-01
Making use of the full information obtained in our previous discussions, a new analytical solutions for the potential function of the digital microstructure image of porous media is reported in this paper. It is demonstrated that the distribution of potential function depends on the zeroth order Bessel function. All these will be helpful for analyzing the similar subjects in porous media.
Analysis for the Potential Function of the Digital Microstructure Image of Porous Media
Institute of Scientific and Technical Information of China (English)
XU You-Sheng; LIN Ji; LI Hua-Mei; WU Feng-Min
2003-01-01
Making use of the full information obtained in our previous discussions, a new analytical solutions for thepotential function of the digital microstructure image of porous media is reported in this paper. It is demonstrated that the distribution of potential function depends on the zeroth order Bessel function. All these will be helpful for analyzingthe similar subjects in porous media.
Implementation of Bessel's method for solar eclipses prediction in the WRF-ARW model
Montornes, Alex; Codina, Bernat; Zack, John W.; Sola, Yolanda
2016-05-01
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 x 10-3 degrees (i
Radiation forces on a three-level atom in the high-order Bessel beams
Institute of Scientific and Technical Information of China (English)
Wang Zheng-Ling; Yin Jian-Ping
2008-01-01
The general expressions of the average dissipative and dipole forces acting on a A-configuration three-level atom in an arbitrary light field are derived by means of the optical Bloch equations based on the atomic density matrix elements, and the general properties of the average dissipative and dipole forces on a three-level atom in the linearly-polarized high-order Bessel beams (HBBs) are analysed. We find a resonant property (with two resonant peaks) of the dissipative force and a non-resonant property (with two pairs of non-resonant peaks) of the dipole force on the three-level atom, which are completely different from those on the two-level atom. Meanwhile we find a saturation effect of the average dissipative force in the HBB, which comes from the saturation of the upper-level population. Our study shows that the general expressions of the average dissipative and dipole forces on the three-level atom will be simplified to those of the two-level atom under the approximation of large detuning. Finally, we study the axial and azimuthal Doppler cooling of atoms in 1D optical molasses composed of two counter-propagating HBBs and discuss the azimuthal influence of the HBB on the Doppler cooling limit. We also find that the Doppler limit of atoms in the molasses HBB is slightly below the conventional Doppler limit of hг/(2кB) due to the orbital angular momentum lh of the HBB.
Stability of Two-Component Bose-Einstein Condensates in Bessel Optical Lattices
Institute of Scientific and Technical Information of China (English)
FU Hong-Zhi; CHEN Hai-Jun; LI De-Hua; LI Hao-Cai; PENG Feng; XUE Ju-Kui; GAO Tao; CHENG Xin-Lu
2008-01-01
The stability of the ground state of two-component Bose-Einstein condensates (BECs) loaded into the central well of an axially symmetric Bessel lattices (BLs) potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross-Pitaevskii equation (GPE). By using the variational method, we find that stable ground state of two-component BECs can exist in BLs. The BLs's depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BECs in BLs is also studied and a collapse condition for trapped two-component BECs is obtained. It is shown that the two-component BECs exhibit rich collapse dynamics. That is, the two-component BECs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BECs in BLs is discussed in detail The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BECs can be controlled by temporal modulation of the atom interaction.
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.
Correction of amplitude distortions for truncated Bessel beam and SER estimation for 4ASK
Eyyuboğlu, Halil T.
2016-08-01
We apply amplitude corrections to a truncated Bessel beam that has propagated through turbulent atmosphere modelled by random phase screens. These corrections are realized via transmitting an unmodulated beam in parallel to the one carrying the 4 amplitude shift keying (ASK) modulated message signal. On the receiver side, the amplitude corrections are obtained by dividing the intensity of the unmodulated beam by its free space equivalence. The corrections are then used to restore the amplitude distortions of the beam carrying the 4ASK modulated message signal and in the determination of decision boundaries for the received 4ASK symbols. The success of the system is visually inspected by comparing the received intensity profiles before and after the application of corrections. Furthermore, simulation analysis of symbol error rate (SER) is made, where the proposed set-up is found to be quite insensitive to wavelength difference between the unmodulated and modulated beams. On the other hand, the difference in the structure constant values of these two beams seems to have profound effect on system performance.
Ultrahigh resolution optical coherence elastography using a Bessel beam for extended depth of field
Curatolo, Andrea; Villiger, Martin; Lorenser, Dirk; Wijesinghe, Philip; Fritz, Alexander; Kennedy, Brendan F.; Sampson, David D.
2016-03-01
Visualizing stiffness within the local tissue environment at the cellular and sub-cellular level promises to provide insight into the genesis and progression of disease. In this paper, we propose ultrahigh-resolution optical coherence elastography, and demonstrate three-dimensional imaging of local axial strain of tissues undergoing compressive loading. The technique employs a dual-arm extended focus optical coherence microscope to measure tissue displacement under compression. The system uses a broad bandwidth supercontinuum source for ultrahigh axial resolution, Bessel beam illumination and Gaussian beam detection, maintaining sub-2 μm transverse resolution over nearly 100 μm depth of field, and spectral-domain detection allowing high displacement sensitivity. The system produces strain elastograms with a record resolution (x,y,z) of 2×2×15 μm. We benchmark the advances in terms of resolution and strain sensitivity by imaging a suitable inclusion phantom. We also demonstrate this performance on freshly excised mouse aorta and reveal the mechanical heterogeneity of vascular smooth muscle cells and elastin sheets, otherwise unresolved in a typical, lower resolution optical coherence elastography system.
Institute of Scientific and Technical Information of China (English)
赵喜来; 崔群法
2009-01-01
Root of characteristic equation for cylindrical Bessel equation eigenvalue prob-lems on general interval is of great real physical importance at engineering and physical. First, the characteristic equation of cylindrical Bessel equation eigenvalue problem on general interval is given, second, by mean of compared method, we obtaining roots of characteristic equation with Matlab program is discussed.
Riaud, Antoine; Thomas, Jean-Louis; Baudoin, Michael; Bou Matar, Olivier
2015-12-01
Despite their self-reconstruction properties in heterogeneous media, Bessel beams are known to degenerate when they are refracted from an isotropic to an anisotropic medium. In this paper, we study the converse situation wherein an anisotropic Bessel beam is refracted into an isotropic medium. It is shown that these anisotropic Bessel beams also degenerate, leading to confined vortical waves that may serve as localized particle trap for acoustical tweezers. The linear nature of this degeneration allows the three-dimensional control of this trap position by wavefront correction. Theory is confronted to experiments performed in the field of acoustics. A swirling surface acoustic wave is synthesized at the surface of a piezoelectric crystal by a microelectromechanical integrated system and radiated inside a miniature liquid vessel. The wavefront correction is operated with inverse filter technique. This work opens perspectives for contactless on-chip manipulation devices. PMID:26764844
Solid-state Q-switch laser generating pulsed Bessel beam%全固态调Q激光器产生脉冲Bessel光束
Institute of Scientific and Technical Information of China (English)
王涛; 杜团结; 庄凤江; 吴逢铁
2014-01-01
使用连续式输出的砷化镓半导体激光器泵浦的掺钕钒酸钇激光器作为光源，被动式通过轴棱锥产生Bessel光束。在激光谐振腔内加入Cr4+：YAG晶体调Q产生脉冲Bessel光束。理论模拟了1064 nm波长光束经过轴棱锥之后的三维传播图和截面光强分布。通过实验得到了1064 nm波长脉冲Bessel光束的脉冲宽度和脉冲重复率，并计算得到了单脉冲Bessel光束的能量和峰值功率。利用光束分析仪记录了1064 nm波长Bessel光束的截面光强分布，并测量了中心光斑的直径，得到的数据与理论计算基本吻合。%The laser diode pumped Nd:YVO4 laser was used as light source, Bessel beam was generated by passively passing through axicon. The pulsed Bessel beam was generated by putting the Cr4+:YAG in the laser resonator. The propagation and cross- section distribution of 1 064 nm Bessel beam were simulated. In experiment, the pulse width and pulse repetition rate of 1 064 nm pulse Bessel beam were obtained, the energy and the peak power of pulsed Bessel beam were calculated. The cross- section intensity distribution of Bessel beam was recorded by the laser beam analysis and the diameter of centre spot was measured. The experimental results agrees well with the simulation.
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.
Hong, ZhenYu; Zhang, Jie; Drinkwater, Bruce W
2015-05-29
We observe distinct regimes of orbital angular momentum (OAM) transfer from two-dimensional Bessel-shaped acoustic vortices to matter. In a homogeneous diphasic mixture of microparticles and water, slow swirling about the vortex axis is seen. This effect is driven by the absorption of OAM across the mixture, the motion following the OAM density distribution. Larger particles are formed into clusters by the acoustic radiation force, making the mixture nonhomogeneous. Here, the OAM transfer to the microparticle clusters dominates and they spin at high speeds entraining the surrounding fluid. PMID:26066437
Wang, Zhe; Zhang, Qingbin; Wang, Shaoyi; Lu, Peixiang
2011-01-01
The generation of isolated attosecond pulses with high efficiency and high beam quality is essential for attosec- ond spectroscopy. We numerically investigate the supercontinuum generation in a neutral rare-gas medium driven by a two-color Bessel-Gauss beam. The results show that an efficient smooth supercontinuum in the plateau is obtained after propagation, and the spatial profile of the generated attosecond pulse is Gaussian-like with the divergence angle of 0.1 degree in the far field. This bright source with high beam quality is beneficial for detecting and controlling the microscopic processes on attosecond time scale.
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. PMID:26618522
He, Fei; Yu, Junjie; Chu, Wei; Wang, Zhaohui; Tan, Yuanxin; Cheng, Ya; Sugioka, Koji
2016-03-01
For higher-density integration and acceleration of operating speed in Si ICs, 3D integration of wafers and/or dies is essential. Fabrication of current 3D ICs relies on 3D assembly which electrically connects stacked chips to form a single circuit. A key technology for the 3D assembly is TSVs which are vertical electrical connections passing completely through silicon chips to electrically connect vertically assembled Si ICs. Typical TSVs have wide features, with diameters of a range from several microns to 50 μm and depths up to 500 μm with aspect ratios up to 15 depending on the application and integration scheme. In this work, we present high-throughput, taper-free TSVs fabrication using femtosecond Bessel beams operated at different wavelengths from 400 nm to 2.4 μm. Furthermore, special phase filters are designed to suppress the damages induced by the side-lobes of Bessel beams for high-quality TSVs fabrication. Our technique can be potentially used for 3D assembly in manufacture of 3D silicon integrated circuits.
On bounds of certain classes of special functions
Directory of Open Access Journals (Sweden)
C. M. Joshi
2001-03-01
Full Text Available Inequalities of the ratios of Whittaker function, which include in its fold inequalities of a large class of special functions, are obtained. In the sequel inequalities of the ratios of Bessel functions of 2nd kind and inequalities of the ratios $ J_v(x / Y_v(x $ are also derived. Finally, we point out some correction which appear in the paper of Joshi and Bissu (J. Aust. Math. Soc., Ser. A. 50(1991, 333-342.
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
A complete description of vector Bessel (vortex) beams in the context of the generalized Lorenz–Mie theory (GLMT) for the electromagnetic (EM) resonance scattering by a dielectric sphere is presented, using the method of separation of variables and the subtraction of a non-resonant background (corresponding to a perfectly conducting sphere of the same size) from the standard Mie scattering coefficients. Unlike the conventional results of standard optical radiation, the resonance scattering of a dielectric sphere in air in the field of EM Bessel beams is examined and demonstrated with particular emphasis on the EM field’s polarization and beam order (or topological charge). Linear, circular, radial, azimuthal polarizations as well as unpolarized Bessel vortex beams are considered. The conditions required for the resonance scattering are analyzed, stemming from the vectorial description of the EM field using the angular spectrum decomposition, the derivation of the beam-shape coefficients (BSCs) using the integral localized approximation (ILA) and Neumann–Graf’s addition theorem, and the determination of the scattering coefficients of the sphere using Debye series. In contrast with the standard scattering theory, the resonance method presented here allows the quantitative description of the scattering using Debye series by separating diffraction effects from the external and internal reflections from the sphere. Furthermore, the analysis is extended to include rainbow formation in Bessel beams and the derivation of a generalized formula for the deviation angle of high-order rainbows. Potential applications for this analysis include Bessel beam-based laser imaging spectroscopy, atom cooling and quantum optics, electromagnetic instrumentation and profilometry, optical tweezers and tractor beams, to name a few emerging areas of research
Energy Technology Data Exchange (ETDEWEB)
Mitri, F.G., E-mail: F.G.Mitri@ieee.org [Chevron, Area 52 Technology–ETC, 5 Bisbee Ct., Santa Fe, NM 87508 (United States); Li, R.X., E-mail: rxli@mail.xidian.edu.cn [School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071 (China); Collaborative Innovation Center of Information Sensing and Understanding, Xidian University, Xi’an 710071 (China); Guo, L.X. [School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071 (China); Collaborative Innovation Center of Information Sensing and Understanding, Xidian University, Xi’an 710071 (China); Ding, C.Y. [School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071 (China)
2015-10-15
A complete description of vector Bessel (vortex) beams in the context of the generalized Lorenz–Mie theory (GLMT) for the electromagnetic (EM) resonance scattering by a dielectric sphere is presented, using the method of separation of variables and the subtraction of a non-resonant background (corresponding to a perfectly conducting sphere of the same size) from the standard Mie scattering coefficients. Unlike the conventional results of standard optical radiation, the resonance scattering of a dielectric sphere in air in the field of EM Bessel beams is examined and demonstrated with particular emphasis on the EM field’s polarization and beam order (or topological charge). Linear, circular, radial, azimuthal polarizations as well as unpolarized Bessel vortex beams are considered. The conditions required for the resonance scattering are analyzed, stemming from the vectorial description of the EM field using the angular spectrum decomposition, the derivation of the beam-shape coefficients (BSCs) using the integral localized approximation (ILA) and Neumann–Graf’s addition theorem, and the determination of the scattering coefficients of the sphere using Debye series. In contrast with the standard scattering theory, the resonance method presented here allows the quantitative description of the scattering using Debye series by separating diffraction effects from the external and internal reflections from the sphere. Furthermore, the analysis is extended to include rainbow formation in Bessel beams and the derivation of a generalized formula for the deviation angle of high-order rainbows. Potential applications for this analysis include Bessel beam-based laser imaging spectroscopy, atom cooling and quantum optics, electromagnetic instrumentation and profilometry, optical tweezers and tractor beams, to name a few emerging areas of research.
The functions of mathematical physics
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
Li, Yixiang; Qiu, Chunyin; Xu, Shengjun; Ke, Manzhu; Liu, Zhengyou
2015-01-01
Conventional microparticle transports by light or sound are realized along a straight line. Recently, this limit has been overcome in optics as the growing up of the self-accelerating Airy beams, which are featured by many peculiar properties, e.g., bending propagation, diffraction-free and self-healing. However, the bending angles of Airy beams are rather small since they are only paraxial solutions of the two-dimensional (2D) Helmholtz equation. Here we propose a novel micromanipulation by using acoustic Half-Bessel beams, which are strict solutions of the 2D Helmholtz equation. Compared with that achieved by Airy beams, the bending angle of the particle trajectory attained here is much steeper (exceeding 90(o)). The large-angle bending transport of microparticles, which is robust to complex scattering environment, enables a wide range of applications from the colloidal to biological sciences. PMID:26279478
Li, Ye; Zhang, Yixin; Wang, Donglin; Shan, Lei; Xia, Mingchao; Zhao, Yuanhang
2016-05-01
The effects of strong turbulence on the orbital angular momentum (OAM) states of infrared and non-diffraction beam propagation in a terrestrial atmosphere are investigated. A new probability density model for OAM states of Bessel-Gaussian-Schell beam in the paraxial and strong turbulent channel is modeled based on the modified Rytov approximation. We find that the normalization energy weight of signal OAM modes at each OAM level is approximate equivalence in strong turbulence regime, one can constitute multiple mode channels by choosing OAM modes with large energy level difference between modes to reduce mode interference, and one can utilize BGS beam with OAM modes increasing the channel capacity of optical communications.
Passive cavity laser and tilted wave laser for Bessel-like beam coherently coupled bars and stacks
Ledentsov, N. N.; Shchukin, V. A.; Maximov, M. V.; Gordeev, N. Y.; Kaluzhniy, N. A.; Mintairov, S. A.; Payusov, A. S.; Shernyakov, Yu. M.; Vashanova, K. A.; Kulagina, M. M.; Schmidt, N. Y.
2015-03-01
Ultralarge output apertures of semiconductor gain chips facilitate novel applications that require efficient feedback of the reflected laser light. Thick (10-30 μm) and ultrabroad (>1000 μm) waveguides are suitable for coherent coupling through both near-field of the neighboring stripes in a laser bar and by applying external cavities. As a result direct laser diodes may become suitable as high-power high-brightness coherent light sources. Passive cavity laser is based on the idea of placing the active media outside of the main waveguide, for example in the cladding layers attached to the waveguide, or, as in the case of the Tilted Wave Laser (TWL) in a thin waveguide coupled to the neighboring thick waveguide wherein most of the field intensity is localized in the broad waveguide. Multimode or a single vertical mode lasing is possible depending on the coupling efficiency. We demonstrate that 1060 nm GaAs/GaAlAs-based Tilted Wave Lasers (TWL) show wall-plug efficiency up to ~55% with the power concentrated in the two symmetric vertical beams having a full width at half maximum (FWHM) of 2 degrees each. Bars with pitch sizes in the range of 25-400 μm are studied and coherent operation of the bars is manifested with the lateral far field lobes as narrow as 0.1° FWHM. As the near field of such lasers in the vertical direction represents a strongly modulated highly periodic pattern of intensity maxima such lasers or laser arrays generate Bessel-type beams. These beams are focusable similar to the case of Gaussian beams. However, opposite to the Gaussian beams, such beams are self-healing and quasi non-divergent. Previously Bessel beams were generated using Gaussian beams in combination with an axicon lens or a Fresnel biprism. A new approach does not involve such complexity and a novel generation of laser diodes evolves.
Generalised partition functions: inferences on phase space distributions
Treumann, Rudolf A.; Baumjohann, Wolfgang
2016-06-01
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 corresponding nonextensive statistical mechanics.
Arakelyan, Ilya
In this dissertation we report the results of two experimental projects with laser-cooled rubidium atoms: I. Application of Bessel beams for atom optics, and II. Spectroscopic measurements of Rydberg blockade effect. The first part of the thesis is devoted to the development of new elements of atom optics based on blue-detuned high-order Bessel beams. Properties of a 4thorder Bessel beam as an atomic guide were investigated for various parameters of the hollow beam, such as the detuning from an atomic resonance, size and the order of the Bessel beam. We extended its application to create more complicated interferometer-type structures by demonstrating a tunnel lock, a novel device that can split an atomic cloud, transport it, delay, and switch its propagation direction between two guides. We reported a first-time demonstration of an atomic beam switch based on the combination of two crossed Bessel beams. We achieved the 30% efficiency of the switch limited by the geometrical overlap between the cloud and the intersection volume of the two tunnels, and investigate the heating processes induced by the switch. We also showed other applications of crossed Bessel beams, such as a 3-D optical trap for atoms confined in the intersection volume of two hollow beams and a splitter of the atomic density. The second part of this dissertation is devoted to the spectroscopic measurements of the Rydberg blockade effect, a conditional suppression of Rydberg excitations depending on the state of a control atom. We assembled a narrow-linewidth, tunable, frequency stabilized laser system at 480 nm to excite laser-cooled rubidium atoms to Rydberg states with a high principal quantum number n ˜ 50 through a two-photon transition. We applied the laser system to observe the Autler-Townes splitting of the intermediate 5p3/2 state and used the broadening of the resonance features to investigate the enhancement of Rydberg-Rydberg interactions in the presence of an external electric field.
International Nuclear Information System (INIS)
A study is made of the dynamics of the spin-to-orbital angular momentum conversion for zero-order and high order circularly polarized Bessel beams propagating along the optical axes of homogeneous uniaxial and biaxial crystals. Implementation of Bessel beams and a slab of homogeneous uniaxial crystal allow one to realize a highly efficient (about 100%) optical process in which the direct conversion of the optical angular momentum from the spin form to the orbital form takes place. It is shown that only in a biaxial crystal is there freedom from compensation of spin and orbital angular momentum exchanges with matter and, as a result, the optical torque emerges, which influences the plate. (paper)
Mitri, F. G.
2016-01-01
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...
Accurate calculation of Green functions on the d-dimensional hypercubic lattice
International Nuclear Information System (INIS)
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.
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.
绿光LED产生无衍射Bessel光束%Non-diffraction bessel-like beam generated by green LED source
Institute of Scientific and Technical Information of China (English)
程治明; 吴逢铁; 范丹丹; 方翔
2012-01-01
Ideal Bessel-like beam was generated by monochromatic LED source for the first time. In this paper, the possibility of using monochromatic LED source to generate quite ideal Bessel-like beam was discussed from the angle of spatial and temporal coherence, then we knew it's possible if a diaphragm was involved to increase spatial coherence. Optical system was designed: light wave emitted from LED passed axicon after the optical system, and then Bessel-like beam was obtained, the size of center bright spots and non-diffraction distance was accord well with the results which obtained from theoretical calculations, it demonstrated LED source could used to generate quite ideal Bessel-like beam. At last we discussed how the diaphragm's diameter affected the quality of Bessel beam, and found that the light intensity increased but contrast ratio of section intensity declined as the diaphragm's diameter enlarged.%采用单色LED光源得到较理想的近似无衍射Bessel光束.文中从LED光源的时空相干性出发分析用单色LED灯珠产生Bessel光束的可能性,利用光阑提高光场的空间相干性得于实现.设计实验光学系统,让LED光源发出的光经过一套光学系统后透过轴棱锥,得到了近似Bessel光束,光束中心亮斑大小及最大无衍射距离均与理论计算所得相符,证明用LED光源也能够产生较理想的近似Bessel光束.最后讨论了光阑孔径对所产生Bessel光束质量的影响,发现光阑孔径增大时所得Bessel光束强度变大但截面光强明暗对比度下降.
Institute of Scientific and Technical Information of China (English)
柯熙政; 郭新龙
2015-01-01
大气湍流引起大气折射率随机变化, 导致空间不均匀性.高阶贝塞尔光束在大气湍流中传输时, 空间不均匀性会使光子波函数改变,形成不同的光子态引起轨道角动量的弥散.在Rytov近似下,计算了高阶贝塞尔光束在大气斜程传输中各分量所占光束总能量的权重. 讨论并对比折射率结构常数,光束波长,天顶角,轨道角动量数,接收孔径和光斑大小等参数对螺旋谱的影响,并给予相应的物理解释. 结果表明:随着折射率结构常数,天顶角和传输距离的增加以及光束波长的减小,螺旋谐波主分量对应的谱减小,轨道角动量弥散越大,而且望远镜接收孔径和光斑大小对轨道角动量弥散的影响非常小.%Atmospheric turbulence can cause random variations of the refractive index, resulting in a spatial inhomogeneity. When a high order Bessel Gaussian beam is propagating through the atmospheric turbulence, spatial inhomogeneity can bring about the change of photon wave function that causes the disperse of the orbital angular momentum to form different photon states. Under the Rytov approximation, when the high order Bessel beam was propagating in a slant-path atmospheric turbulence, the weight of the spiral harmonic component of the beam energy was calculated. And then, the impact on the spiral spectrum of the beam propagating in the slant ways, caused by refractive index structure constant, the wavelength of the beam, the zenith, orbital angular momentum, the receiver aperture, spot size were discussed and compared and a series of concrete explanations were given. The research results show that with increasing refractive index structure constant and the zenith and with decreasing wavelength of the beam, the spectrum of the spiral harmonic main component reduces and the orbital angular momentum disperses more serious. The receiver aperture and spot size have little effect on the orbital angular momentum disperse .
On a method for generating inequalities for the zeros of certain functions
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.
Energy Technology Data Exchange (ETDEWEB)
Bakewell, D J, E-mail: d.bakewell@liv.ac.uk [Department of Electrical Engineering and Electronics, University of Liverpool, Brownlow Hill, Liverpool, L69 3GJ (United Kingdom)
2011-03-02
A Fourier-Bessel (FB) series solution is derived that describes the dielectrophoretic-driven transport of nanoparticles in a microdevice. The solution assumes that the nanoparticles do not interact and is based on a linear Fokker-Planck equation that includes the effects of thermal diffusion. The solution is applicable for a dielectrophoretic force that varies exponentially in the microdevice, such as in the far field of planar interdigitated arrays. Important applications of the FB solution are demonstrated that include simulation and system classification of nanoparticle movement under the action of weak and strong dielectrophoretic forces. Methods are demonstrated for the inverse process of estimating model parameters, such as the dielectrophoretic force, based on nanoparticle concentration data obtained experimentally. Data decomposition into separate spatial and temporal modes is demonstrated and Fourier transformation of the series solution yields a representation in the frequency domain. The frequency response predicted by transforming the time-dependent FB solution indicates the presence of a dielectrophoresis modulation bandwidth that concurs with observations of preliminary experiments.
Ding, C.; Pan, L.; Lü, B.
2010-04-01
By using the generalized Huygens-Fresnel diffraction integral, the analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse of apertured stochastic electromagnetic modified Bessel-Gauss beams (MBGBs) through a paraxial optical ABCD system are derived, and used to study the changes in the state of polarization of apertured stochastic electromagnetic MBGBs propagating in free space. The invariance of the on-axis state of polarization of unapertured stochastic electromagnetic MBGBs propagating through paraxial optical ABCD systems is illustrated analytically and numerically. For apertured stochastic electromagnetic MBGBs, the on-axis spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse increase with increasing propagation distance, and approach asymptotic values when the propagation distance is large enough. There is a uniform distribution region of the state of polarization around the center of the beams whose range decreases with increasing truncation parameter. In addition, the state of polarization of apertured stochastic electromagnetic MBGBs upon propagation can be modulated by controlling the truncation parameter.
Fast calculation of the line-spread-function by transversal directions decoupling
Parravicini, Jacopo; Tartara, Luca; Hasani, Elton; Tomaselli, Alessandra
2016-07-01
We propose a simplified method to calculate the optical spread function of a paradigmatic system constituted by a pupil-lens with a line-shaped illumination (‘line-spread-function’). Our approach is based on decoupling the two transversal directions of the beam and treating the propagation by means of the Fourier optics formalism. This requires simpler calculations with respect to the more usual Bessel-function-based method. The model is discussed and compared with standard calculation methods by carrying out computer simulations. The proposed approach is found to be much faster than the Bessel-function-based one (CPU time ≲ 5% of the standard method), while the results of the two methods present a very good mutual agreement.
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
Second-harmonic generation of the Bessel sound beam of several lobes%小瓣数贝塞尔声束的二次谐波
Institute of Scientific and Technical Information of China (English)
戴玉蓉; 丁德胜
2011-01-01
采用高斯展开法,研究了具有三个瓣的小瓣数贝塞尔声束的基波和二次谐波的传播性质.根据准线性近似下Khokhlov-Zabolotskaya-Kuznetsov方程的积分形式解,分析了媒质的声吸收（声衰减）对波束形状的影响.结果表明：吸收参量对二次谐波径向分布有很大的影响.当瓣数较少时,实际的有限孔径贝塞尔声束二次谐波仍然具有理想无限大孔径贝塞尔声束的主要特征,在近场无衍射区,径向几乎无衍射.%By the Gaussian expansion approach we investigate fundamental-and second-harmonic generation in practical Bessel beams of several lobes.The analysis is based on the integral solutions of the Khokhlov-Zabolotskaya-Kuznetsov equation under the quasilinear approximation.The influence of the medium attenuation on beam profile is considered.Numerical results show that the absorption parameter has a significant effect on the beam profile of the second harmonic.Under certain circumstances,the second harmonic of a practical Bessel beam with several lobes still has the main properties of an ideal Bessel beam of infinite aperture when it propagates within its depth of field.
Self-healing of Gaussian and Bessel beams: a critical comparison
Aiello, Andrea
2015-01-01
Contrarily to a common belief, any beam of light possesses to a some extent the ability to "reconstruct itself" after hitting an obstacle. The celebrated Arago spot phenomenon is nothing but a manifestation of this property. In this work we analyze the self-healing mechanism from both a mathematical and a physical point of view, eventually finding a new expression for the minimum reconstruction distance, which is valid for \\emph{any} kind of beam, including Gaussian ones. Finally, a witness function that quantify the self-reconstruction capability of a beam is proposed and tested. The results presented here help clarifying the physics underlying self-healing mechanism in optical beams.
基于小波分析的Bessel声场预处理%Bessel field pre-treatment based on wavelet analysis
Institute of Scientific and Technical Information of China (English)
李琴; 谭冠政
2012-01-01
The simulated sound field of an annular ultrasound transducer is given based on Fourier-Bessel series method. After analyzing the axial acoustic pressure, especially the near-field disturbance, wavelet multi-resolution analysis of the noise reduction is carried out for removing the near-field complex frequency components and increasing the sound pressure amplitude. The results show that the wavelet analysis technique can be used for improving the fundamental ultrasound imaging quality of Bessel field.%采用Fourier-Bessel方法对环型换能器的声场进行数值计算,并对仿真声场进行了深入讨论.通过对换能器轴向声压分布的分析,针对声近场明显的扰动,提出一种新的方法对声场进行预处理,即利用小波多分辨率分析降噪,去除近场杂频率成分,提高声压幅度.研究结果表明,小波分析技术能提高Bessel声场的基波成像质量,对于小波变换在Bessel超声成像中的应用提供了很好的依据.
Mitri, F G
2016-12-01
The goal of this work is to demonstrate the emergence of a spin torque singularity (i.e. zero spin torque) and a spin rotation reversal of a small Rayleigh lipid/fat viscous fluid sphere located arbitrarily in space in the field of an acoustical Bessel vortex beam. This counter-intuitive property of negative spin torque generation suggests a direction of spin rotation in opposite handedness of the angular momentum carried by the incident beam. Such effects may open new capabilities in methods of quantitative characterization to determine physical properties such as viscosity, viscoelasticity, compressibility, stiffness, etc., and other techniques for the rotation and positioning using acoustical tractor beams and tweezers, invisibility cloaks, and acoustically-engineered composite metamaterials to name a few examples. Based on the descriptions for the velocity potential of the incident beam and the scattering coefficients of the sphere in the long-wavelength approximation limit, simplified expressions for the spin and orbital radiation torque components are derived. For beams with (positive or negative) unit topological charge (m=±1), the axial spin torque component for a Rayleigh absorptive sphere is maximal at the center of the beam, while it vanishes for |m|>1 therein. Moreover, the longitudinal orbital torque component, causing the sphere to rotate around the center of the beam is evaluated based on the mathematical decomposition using the gradient, scattering and absorption transverse radiation force vector components. It is shown that there is no contribution of the gradient transverse force to the orbital torque, which is only caused by the scattering and absorption transverse force components. Though the incident acoustical vortex beam carrying angular momentum causes the sphere to rotate in the same orbital direction of the beam handedness, it induces a spin torque singularity (i.e. zero spin torque) and subsequent sign reversal. This phenomenon of
Mitri, F. G.
2016-02-01
Moreover, the corrected plots that should replace the dashed (blue) curves, corresponding to the results for a first-order Bessel vortex beam in Figs. 2 and 3 of [1], are provided. Note that the plots shown in the (black) solid and (red) dot-dashed lines are accurate, and are plotted here for convenience.
Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P. J.; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J.; Ashrafi, Solyman; Molisch, Andreas F.; Tur, Moshe; Willner, Alan E.
2016-03-01
We experimentally investigate the potential of using ‘self-healing’ Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively.
Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P J; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J; Ashrafi, Solyman; Molisch, Andreas F; Tur, Moshe; Willner, Alan E
2016-01-01
We experimentally investigate the potential of using 'self-healing' Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively. PMID:26926068
Dual integral equations with Fox's H-function kernel
Directory of Open Access Journals (Sweden)
R. N. Kalia
1984-01-01
Full Text Available The dual integral equations involving Bessel function kernels were first considered by Weber in 1873. The problem comprised of finding potential of an electrified disc which belongs to a general category of mixed boundary value problems. Titchmarsh gave the formal solution using Wiener-Hopf procedure. We use this direct method as improvised by Busbridge to solve a class of dual integral equations which can be reduced to other known kernels by particularizing the parameters in the Fox's H-function.
Analytic integration of a common set of microwave beam intensity functions
Energy Technology Data Exchange (ETDEWEB)
Potter, S.D. [New York Univ., New York, NY (United States)
1994-12-31
When designing a wireless power transmission system, a virtually limitless number of aperture illumination functions are available. However, a commonly-used set of beam tapers results in received intensities that involve Bessel functions. This family of intensities is convenient to study and compare systematically. A cosntraint on the calculation of reception efficiency is the need to write numerical routines to integrate such functions. It is shown that these functions can be integrated analytically, resulting in a concise formula for reception efficiency as a function of rectifying antenna (rectenna) diameter.
Balogh, Ferenc
2015-01-01
Gessel's famous Bessel determinant formula gives the generating function to enumerate permutations without increasing subsequences of a given length. Ekhad and Zeilberger recently proposed the challenge to find a suitable generalization to count words of length rn in an alphabet consisting of n letters in which each letter appears exactly r times and which have no increasing subsequences of length d. In this paper we present a generating function for arbitrary values of r expressible as multi...
Gauthier, Robert C.
2013-10-01
The whispering-gallery mode space of a cylindrically symmetric silicon micro-optic bottle resonator with an axial Gaussian dielectric profile is theoretically examined. Maxwell's wave equation for the magnetic field, expressed in cylindrical coordinates, is converted into an eigenvalue problem using a Fourier-Bessel basis space to expand the inverse dielectric and field components. The order of the eigen-matrix is reduced using symmetry arguments and azimuthal order segmentation such that the matrix can be solved on a desktop PC. The eigen-space reveals that several states can be confined in the bottle region, whereas another set of states extends the axial length of the structure similar to ridge waveguide modes. The hollow core bottle is also presented as a design modification. The micro-optic bottle resonator structure size makes it directly compatible with silicon-based photonics increasing its potential as a key component in sensing, communication, and other applications.
一种Bessel矩和相位不变性的目标跟踪算法%A way of objective tracking using Bessel moment and phase congruent
Institute of Scientific and Technical Information of China (English)
马金林
2012-01-01
为了提高目标跟踪的准确率,提出一种基于Bessel矩、相位不变性和梯度信息的多特征目标跟踪方法.该方法利用Bessel矩形状特征、相位不变性特征和梯度特征,充分发挥Bessel矩高效的形状描述能力,避免相位不变性对图像对比度的影响.与RGB颜色直方图算法和PC_RGB算法相比,本算法可以准确提取目标区域的形状信息和细微的明度变化信息,对目标跟踪具有更强的鲁棒性.实验结果验证了该方法的可行性和有效性.%In order to improve the effectiveness of objective tracking,a new algorithm is proposed based on Bessel moment, phase congruent and gradient magnitude for objective tracking. This method utilizes effective shape describing ability of Bessel moment. The method also can fill up an efficiency of the contrast invariant of phase congruent. Compared with the RGB color histogram and PC combined with RBG color histogram, the proposed algorithm can extracts effectively the shape feature and subtle variance of luminance in the target region, which characterizes better and represents more robustly the target. The experiments show feasibility and effect of the proposed method.
Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies
Bzowski, Adam; Skenderis, Kostas
2015-01-01
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...
Hexadecapole interacting boson approximation structure functions in neodymium isotopes
Energy Technology Data Exchange (ETDEWEB)
Perrino, R.; Blasi, N.; Bordewijk, J.A.; De Leo, R.; Harakeh, M.N.; de Jager, C.W.; Micheletti, S.; Pignanelli, M.; Sandor, R.K.J.; de Vries, H.; van der Werf, S.Y.; Wesseling, J. (Universita di Lecce and Sezione Istituto Nazionale di Fisica Nucleare di Lecce, I-73100 Lecce (Italy) Dipartimento di Fisica dell' Universita di Milano, Milano (Italy) Sezione Istituto Nazionale di Fisica Nucleare di Milano I-20133 Milano (Italy) Kernfysisch Versneller Instituut, 9747 AA Groningen (Netherlands) Dipartimento di Fisica dell' Universita di Bari, I-70100 Bari (Italy) Sezione Istituto Naionale di Fisica Nucleare di Lecce, I-73100 Lecce (Italy) Faculteit Natuurkunde en Sterrenkunde, Vrije Universiteit, de Boelelaan 1081, 1081 HV Amsterdam (Netherlands) Nationaal Instituut voor Kernfysica en Hoge-Energie-Fysica, Sectie K, P.O. Box 41882, 1009 DB Amsterdam (Netherlands))
1993-04-01
Low-lying hexadecapole states in stable even-even neodymium isotopes have been investigated by means of inelastic electron scattering. Transition charge densities were extracted in a Fourier-Bessel analysis of the form factors. The analysis of the experimental results within the interacting [ital sdg]-boson model with only one [ital g] boson allowed the extraction of the radial shapes of the hexadecapole structure functions of three of the different boson-pair configurations (i.e., [ital dd], [ital sg], and [ital dg]) involved in the hexadecapole excitations.
吉田, 年雄||ヨシダ, トシオ||Yoshida, Toshio
2013-01-01
In this paper, we describe numerical methods for special functions, especially Bessel function Jn(x) and modified Bessel function In(x) with real argument x, Bessel function Jn(z) and modified Bessel function In(z) with complex argument z, Bessel function Yν(x) and modified Bessel function Kν(x) with real order ν, incomplete gamma function Γ(ν, x), and so on.
Coulomb Green's function and image potential near a cylindrical diffuse interface
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.
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.
Acoustics of a flanged cylindrical pipe using singular basis functions
Amir; Matzner; Shtrikman
2000-02-01
The problem of acoustic radiation from a cylindrical pipe with an infinite flange has been discussed in a number of papers. The most common approach is to decompose the field inside the pipe over a basis of Bessel functions. A very large number of basis functions is usually required, with a large degree of ripple appearing as an artifact in the solution. In this paper it is shown that a close analysis of the velocity field near the corner yields a new family of functions, which are called "edge functions." Using this set of functions as test functions and applying the moment method on the boundary between the waveguide and free space, a solution is obtained with greatly improved convergence properties and no ripple. PMID:10687680
Institute of Scientific and Technical Information of China (English)
宋启根; 徐梁; 宋丹
2001-01-01
本文提出一个计算Bessel函数Jp(x)及Np(x)的近似方法并在-∞＜p＜∞和x＞0的范围内验证了方法的适用性,进而提出了截面按幂函数变化的变截面梁柱的刚度方程并研究了其临界力.
AMDLIBAE, IBM 360 Subroutine Library, Special Function, Polynomials, Differential Equation
International Nuclear Information System (INIS)
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: XY; B458S A ARGFDXPD: DP XY; 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-Cotes; D
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}.
Institute of Scientific and Technical Information of China (English)
邵先喜; 尹传存
2001-01-01
对暂留Bessel过程X，令I(t)=infs>tX(s)及ξ(t)＝inf{u≥t：X(u)＝I(t)}， 本文求出了I(t)，ξ(t)及Xt的联合分布.%For a transient Bessel process X let I(t) ＝ inf>tX(s) and ε(t) ＝ inf{u >t: X(u) ＝ I(t)}. In this note we compute the joint distribution of I(t),ε(t) and Xt.
International Nuclear Information System (INIS)
An expression for the structure function F2 in the form of Bessel functions at small values of the Bjorken variable x is used. This expression was derived for a flat initial condition in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. The argument of the strong coupling constant was chosen in such a way as to annihilate the singular part of the anomalous dimensions in the next-to-leading-order of perturbation theory. This choice, together with the frozen and analytic versions of the strong coupling constant, is used to analyze combined data of the H1 and ZEUS Collaborations obtained recently for the structure function F2
Kotikov, A. V.; Shaikhatdenov, B. G.
2015-06-01
An expression for the structure function F 2 in the form of Bessel functions at small values of the Bjorken variable x is used. This expression was derived for a flat initial condition in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. The argument of the strong coupling constant was chosen in such a way as to annihilate the singular part of the anomalous dimensions in the next-to-leading-order of perturbation theory. This choice, together with the frozen and analytic versions of the strong coupling constant, is used to analyze combined data of the H1 and ZEUS Collaborations obtained recently for the structure function F 2.
International Nuclear Information System (INIS)
We demonstrate the possibility of realizing, all-optical switching in gold nanosol. Two overlapping laser beams are used for this purpose, due to which a low-power beam passing collinear to a high-power beam will undergo cross phase modulation and thereby distort the spatial profile. This is taken to advantage for performing logic operations. We have also measured the threshold pump power to obtain a NOT gate and the minimum response time of the device. Contrary to the general notion that the response time of thermal effects used in this application is of the order of milliseconds, we prove that short pump pulses can result in fast switching. Different combinations of beam splitters and combiners will lead to the formation of other logic functions too.
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
A novel energy analyzer with a simple-structured Bessel-box has been successfully developed and incorporated into ionization gauges and quadrupole mass spectrometers (QMS) to improve their measurement of the total and partial pressures,respectively.We found that the energy analyzer may not only effectively separate the gas phase ions and electron stimulated desorption (ESD) ions produced in the ionizer,but also screen the ion collector from irradiation of the soft X-rays and VUVphotons generated in the ionizer.The screening effects considerably better the trace impurity detection limit of the QMS down to a few tens ppb in the pressure range of 10-3 Pa.The modified ionization gauge is capable of measuring pressure ranging from 10-11 to 10-6 Pa in the pulse counting mode and its upper limit may extends to 10-3 Pa in DC ion current mode with typical sensitivities factor of(6.7±0.2)×10-3 Pa-1 for N2 and (2.3±0.2)×10-3 Pa-1 for H2,respectively.No ESD ions was observed in the simple-looking spectrum obtained with the modified QMS.We also found that the energy spectra of fragment ions depend strongly on species of parent ions.
Inequalities for a unified family of Voigt functions in several variables
Srivastava, H. M.; Pogány, T. K.
2007-06-01
The classical Voigt functions occur frequently in a wide variety of problems in astrophysical spectroscopy, emission, absorption and transfer of radiation in heated atmosphere, and plasma dispersion, and indeed also in the theory of neutron reactions. Here, in the present paper, by applying several known upper bounds for the first-kind Bessel function J ν ( x) given recently by (for example) Landau, Olenko and Krasikov, sharp bounding inequalities are obtained for the unified multivariable Voigt function V μ, ν (x; y) in terms of the confluent Fox-Wright function 1ψ0 and its incomplete variant 1ψ0. Connections of the unified multivariable Voigt function V μ, ν (x; y) with other unifications and generalizations of the classical Voigt function are also briefly pointed out.
A generalization of Bessel's integral for the Bessel coefficients
DEFF Research Database (Denmark)
Karlsson, Per W.
2007-01-01
We derive an integral over the m-dimensional unit hypercube that generalizes Bessel’s integral for Jn(x). The integrand is G(xψ(t)) exp(−2π i n · t), where G is analytic, and ψ(t) =e2πit1+. . .+e2πitm+e−2πi(t1+...+tm), while n is a set of non-negative integers. In particular, we consider the case...
Plante, Ianik
2016-01-01
The exact Green's function of the diffusion equation (GFDE) is often considered to be the gold standard for the simulation of partially diffusion-controlled reactions. As the GFDE with angular dependency is quite complex, the radial GFDE is more often used. Indeed, the exact GFDE is expressed as a Legendre expansion, the coefficients of which are given in terms of an integral comprising Bessel functions. This integral does not seem to have been evaluated analytically in existing literature. While the integral can be evaluated numerically, the Bessel functions make the integral oscillate and convergence is difficult to obtain. Therefore it would be of great interest to evaluate the integral analytically. The first term was evaluated previously, and was found to be equal to the radial GFDE. In this work, the second term of this expansion was evaluated. As this work has shown that the first two terms of the Legendre polynomial expansion can be calculated analytically, it raises the question of the possibility that an analytical solution exists for the other terms.
Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.
Moreira, Wendel Lopes; Neves, Antonio Alvaro Ranha; Garbos, Martin K; Euser, Tijmen G; Cesar, Carlos Lenz
2016-02-01
Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system. PMID:26906812
Nonlinear Dependence of the Phase Screen Structure Function on the Atmospheric Layer Thickness
Mathar, Richard J
2011-01-01
The phase structure function accumulated by two parallel rays after transmission through a layer of turbulent air is best known by a proportionality to the 5/3rd power of the lateral distance in the aperture, derived from an isotropic Kolmogorov spectrum of the refractive index. For a von-Karman spectrum of the refractive index, a dependence involving a modified Bessel function of the ratio of the distance over the outer scale is also known. A further standard proposition is a proportionality to the path length through the atmospheric layer. The manuscript modifies this factor through a refined calculation of an integral representation of the structure function. The correction establishes a sub-linearity as the lateral distance grows in proportion to the layer thickness; it is more important for large than for small outer scales.
Bounds for Hecke eigenforms and their allied L-functions
Zhang, Qing
We consider Hecke eigenforms and their allied L-functions from three aspects in this thesis. First we generalize the Iwaniec's spectral large sieve estimates of Maass cusp form to the local version for all congruence groups of level q. Our approach is based on an inequality for a general bilinear form involving Kloosterman sums and Bessel functions. The exceptional eigenvalues emerge in the course of the proof. In the second part, we extend Luo's result to prove a general optimal bound for L4-norms of the dihedral Maass forms associated to Hecke's grossencharacters of a fixed real quadratic field. Given a fixed quadratic field with discriminant D, we remove the condition that the narrow class number of K is 1. The key ingredients are Watson and Ichino's formula and the local spectral large sieve inequality established in the first part. Finally we obtain a long equation intended to establish an upper bound for the second moment of symmetric square L-functions. Petersson trace formula plays an important role and we study thoroughly an analogue of Estermann series using Hurwitz zeta function and establish its meromorphic extension and functional equation. This work provides a useful approach to the further study for the central value of the symmetric square L-functions.
International Nuclear Information System (INIS)
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 In2O3 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
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.
Indefinite integrals of products of some exponential and trigonometric functions
Rostafinski, W. A.
1972-01-01
Two integrals have been developed which are needed to solve certain problems of mathematical physics related to the Bessel and Euler equations. Integrals of this type have known application in problems using cylindrical coordinates.
Force Density Function Relationships in 2-D Granular Media
Youngquist, Robert C.; Metzger, Philip T.; Kilts, Kelly N.
2004-01-01
An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms
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.
High resolution multiplexed functional imaging in live embyros (Conference Presentation)
Xu, Dongli; Peng, Leilei
2016-03-01
Optical projection tomography (OPT) creates isotropic 3D imaging of tissue. Two approaches exist today: Wide-field OPT illuminates the entire sample and acquires projection images with a camera; Scanning-laser optical tomography (SLOT) generates the projection with a moving laser beam and point detector. SLOT has superior light collecting efficiency than wide-field optical tomography, making it ideal for tissue fluorescence imaging. Regardless the approach, traditional OPT has to compromise between the resolution and the depth of view. In traditional SLOT, the focused Gaussian beam diverges quickly from the focused plane, making it impossible to achieve high resolution imaging through a large volume specimen. We report using Bessel beam instead of Gaussian beam to perform SLOT. By illuminating samples with a narrow Bessel beam throughout an extended depth, high-resolution projection images can be measured in large volume. Under Bessel illumination, the projection image contains signal from annular-rings of the Bessel beam. Traditional inverse Radon transform of these projections will result in ringing artifacts in reconstructed imaging. Thus a modified 3D filtered back projection algorithm is developed to perform tomography reconstructing of Bessel-illuminated projection images. The resulting 3D imaging is free of artifact and achieved cellular resolution in extended sample volume. The system is applied to in-vivo imaging of transgenic Zebrafish embryos. Results prove Bessel SLOT a promising imaging method in development biology research.
Institute of Scientific and Technical Information of China (English)
孙阳; 高华; 徐海亭
2003-01-01
@@ 1、引言 在声学、弹性力学、电磁学等物理问题的数值计算中常常用到球Bessel函数,一般进行数值运算所用的Matlab软件对球Bessel函数的计算没有建立库函数,要通过球Bessel函数与柱Bessel函数之间的变换公式计算.对于实变量,由变换公式计算的结果是准确的,但是对于参数为复宗量的情况,如计算吸声材料、阻尼材料及其它一些粘弹性材料的球形物体声散射,这种变换公式计算出的结果是不准确的.因此,需要研究复宗量球Bessel函数的计算.
Institute of Scientific and Technical Information of China (English)
木乐华
2001-01-01
先给出Neumann-Bessel级数的核函数的精确的渐近表示,然后讨论该级数的部分和的收敛速度及其Fejer和的类逼近问题.从中说明了对于非三角级数也能得到相应三角级数中类逼近的精密结果.
Institute of Scientific and Technical Information of China (English)
程炜
2015-01-01
讨论一个球形区域上的球对称热传导方程的定解问题,目标是建立用球Bessel函数为特征函数的级数解.采用分离变量法借助于球Bessel函数及其性质求出所研究问题级数解的表达式.
Hypergeometric type functions and their symmetries
Dereziński, Jan
2013-01-01
We give a systematic and unified discussion of various classes of hypergeometric type equations: the hypergeometric equation, the confluent equation, the F_1 equation (equivalent to the Bessel equation), the Gegenbauer equation and the Hermite equation. In particular, we discuss recurrence relations of their solutions, their integral representations and discrete symmetries.
Functional swept source optical coherence tomography
International Nuclear Information System (INIS)
Optical coherence tomography (OCT) is a non-invasive imaging modality capable of providing information about a sample structure along the three spatial dimensions with micrometer scale resolution. A new chapter opened with the development of functional OCT that provides additional information to the standard structural imaging. Among those extensions is Doppler OCT (D-OCT) that yields knowledge about the motion of the sample and/or its substructure. Its main application in biomedical imaging is the assessment of blood flow. D-OCT is therefore often associated with blood velocity measurement and recently with the visualization of the vascular network. Blood flow and vasculature are important markers of tissue health. Their assessment provides crucial information for diagnostics, treatment planning and monitoring. OCT is in a good position, as a non-invasive technique, to become an alternative to current fluorescence based techniques, allowing thereby also more frequent examination and broader screenings and, as a high resolution modality, to give insight into potential changes at the capillary level. An important challenge of in vivo imaging is patient motion that decreases the quality of acquisitions. One solution to that issue is high-speed imaging. Recently swept source OCT (SSOCT) revealed to be an efficient technology to achieve high-speed. This thesis investigates the use of swept sources for qualitative and quantitative vasculature imaging. It is presented via five journal papers that form its backbone. Prior to that, main concepts of FDOCT, D-OCT and SS systems are presented. The first paper reports a SSOCT system for skin imaging. In standard OCT systems, improving the lateral resolution comes at a cost of reduced depth of focus. This should be avoided in order to be able to assess different vascular beds in depth while keeping the speed advantage of FDOCT. Employing a Bessel beam for illumination of the sample allows circumventing this issue. The image
Energy Technology Data Exchange (ETDEWEB)
Kotikov, A. V., E-mail: kotikov@theor.jinr.ru; Shaikhatdenov, B. G. [Joint Institute for Nuclear Research (Russian Federation)
2015-06-15
An expression for the structure function F{sub 2} in the form of Bessel functions at small values of the Bjorken variable x is used. This expression was derived for a flat initial condition in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. The argument of the strong coupling constant was chosen in such a way as to annihilate the singular part of the anomalous dimensions in the next-to-leading-order of perturbation theory. This choice, together with the frozen and analytic versions of the strong coupling constant, is used to analyze combined data of the H1 and ZEUS Collaborations obtained recently for the structure function F{sub 2}.
On computation and use of Fourier coefficients for associated Legendre functions
Gruber, Christian; Abrykosov, Oleh
2016-02-01
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.
Dispersive and dissipative medium response to an ultrashort pulse: A Green's function approach
Wilhelmsson, Hans; Trombert, Jean-Hughes; Eloy, Jean-François
1995-07-01
The propagation of an ultrashort pulse in a dispersive and dissipative medium may conveniently be described by using a Green's function analysis. The advantage would be that all details of the initial pulse, however short, could be probed by an "infinitely" sharp δ-pulse and subsequently deciphered in a modified form, after the influence of the medium, at a later time and at a new observation point. The Green's function for a dispersive and dissipative, plasma or dielectric (molecular) medium, is constructed for an infinitely extended three-dimensional case by using symbolic algebra for time-differential operators. The solution consists of two parts: a displaced δ-function part and a Bessel-function part, describing a wake field which for dominating dispersion is of oscillatory nature. For a certain ratio between the dispersive and dissipative parameters (plasma frequency and damping) a critical limit is found where the wake oscillations disappear completely. In the particular limits of vanishing dispersion or vanishing dissipation one recovers from the generalized solution the well-known results for a pure conductor (metal) and a pure dispersive medium (cold collisionless plasma) described by the Klein-Gordon equation. The response of the medium to an initially localized ulrashort electromagnetic pulse, of an arbitrary shape, can be expressed by an integral in time and space, of the product of the Green's function and the initial pulse.
On computation and use of Fourier coefficients for associated Legendre functions
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.
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.
EGAD, Ground Level Gamma Doses Function of Gamma Energy for Radioactive Releases
International Nuclear Information System (INIS)
1 - Description of problem or function: EGAD calculates gamma dose integrals to a ground level receptor, for incremental values of the vertical dispersion parameter sigma-z, as a function of gamma energy and spatial distribution of the radioactive material. The dose integrals are representative of sector averages since the distribution of material is assumed to be Gaussian in the vertical, homogeneous in the horizontal, and bounded between ground level and an inversion lid. Calculated dose integrals are independent of radioactive decay, transport velocity, downwind distance, and sector width. Space attenuation and buildup are taken into account. 2 - Method of solution: The plume of radioactive material is assumed to remain constant in shape and size during passage over a receptor point. The space distribution of material is then represented as parallel line sources. The line contributions are integrated analytically by transforming to Bessel and related functions, reducing the spatial distribution to a vertical plane at the receptor point. Plane integrations are then performed by Gaussian quadratures. 3 - Unusual features of the program: EGAD provides an efficient means of compiling tabular data of dose integrals as a function of incremental values of energy and the vertical dispersion parameter. These data may then be interpolated for specific values of the variables resulting in large computational savings if large amounts of meteorology data are to be processed
Sofotasios, Paschalis C
2011-01-01
This article provides novel analytical results for the Rice function, the incomplete Toronto function and the incomplete Lipschitz-Hankel Integrals. Firstly, upper and lower bounds are derived for the Rice function, $Ie(k,x)$. Secondly, explicit expressions are derived for the incomplete Toronto function, $T_{B}(m,n,r)$, and the incomplete Lipschitz-Hankel Integrals of the modified Bessel function of the first kind, $Ie_{\\mu,n}(a,z)$, for the case that $n$ is an odd multiple of 0.5 and $m \\geq n$. By exploiting these expressions, tight upper and lower bounds are subsequently proposed for both $T_{B}(m,n,r)$ function and $Ie_{\\mu,n}(a,z)$ integrals. Importantly, all new representations are expressed in closed-form whilst the proposed bounds are shown to be rather tight. Based on these features, it is evident that the offered results can be utilized effectively in analytical studies related to wireless communications. Indicative applications include, among others, the performance evaluation of digital communica...
A spectral scheme for Kohn–Sham density functional theory of clusters
International Nuclear Information System (INIS)
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
A spectral scheme for Kohn–Sham density functional theory of clusters
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Amartya S., E-mail: baner041@umn.edu; Elliott, Ryan S., E-mail: relliott@umn.edu; James, Richard D., E-mail: james@umn.edu
2015-04-15
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.
Sun, Ying
2011-01-01
This article proposes an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outward ordering induced by band depth for functional data, the descriptive statistics of a functional boxplot are: the envelope of the 50% central region, the median curve, and the maximum non-outlying envelope. In addition, outliers can be detected in a functional boxplot by the 1.5 times the 50% central region empirical rule, analogous to the rule for classical boxplots. The construction of a functional boxplot is illustrated on a series of sea surface temperatures related to the El Niño phenomenon and its outlier detection performance is explored by simulations. As applications, the functional boxplot and enhanced functional boxplot are demonstrated on children growth data and spatio-temporal U.S. precipitation data for nine climatic regions, respectively. This article has supplementary material online. © 2011 American Statistical Association.