Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map
San Roman Alerigi, Damian; Alsunaidi, Mohammad; Ben Slimane, Ahmed; Ng, Tien Khee; Ooi, Boon S.; Zhang, Yaping
2012-01-01
In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si1-yOy/Si1-x-yGexCy platform or by photo-refractive media. The proposed device is 200 ?m in length and 25 ?m in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers. © 2012 Optical Society of America.
Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map
San Roman Alerigi, Damian
2012-07-01
In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si1-yOy/Si1-x-yGexCy platform or by photo-refractive media. The proposed device is 200 ?m in length and 25 ?m in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers. © 2012 Optical Society of America.
Yao, Hainan; Wang, Fei; Cai, Yangjian
2018-01-01
Two-index Bessel beams (TIBBs) was introduced by Ornigotti and Aiello (2014) theoretically. In this paper, we propose a simple experimental scheme for generation of two-index Bessel-Gauss beams (TIBGBs), as an extension of the TIBBs. The scheme is based on manipulating the amplitude and phase in the Fourier plane with the use of a spatial light modulator and a spiral phase plate. Furthermore, we experimentally report the generation of the several examples of the TIBGBs based on the proposed optical system. The focusing properties of the TIBGB with indices p = 1 and l = 2 passing through a single lens are investigated both theoretically and experimentally. The experimental results agree well with theoretical predictions.
Propagation of obstructed Bessel and Bessel–Gauss beams
CSIR Research Space (South Africa)
Litvin, IA
2008-08-01
Full Text Available and phase of the beam after encountering an obstruction. Although this self reconstruction property has been previously modelled by numerous groups, the techniques involve rigorous, time-consuming computations. In this work we present an efficient method...
Nonparaxial Bessel and Bessel-Gauss pincers light-sheets
Mitri, F. G.
2017-01-01
Nonparaxial optical Bessel and Bessel-Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.
Bessel-like beams modulated by arbitrary radial functions
Herman; Wiggins
2000-06-01
An approximate method for determining the radial and axial intensity of a Bessel-like beam is presented for the general case in which a radial Bessel distribution of any order is modulated by an arbitrary function. For Bessel-Gauss, generalized Bessel-Gauss, and Bessel-super-Gauss beams, this simple approximation yields results that are very close to the exact values, while they are exact for Bessel beams. A practical beam that can be generated with a combination of simple lenses is also analyzed and illustrated.
Nonparaxial Bessel and Bessel–Gauss pincers light-sheets
Energy Technology Data Exchange (ETDEWEB)
Mitri, F.G., E-mail: F.G.Mitri@ieee.org
2017-01-23
Highlights: • Bessel and Bessel–Gauss autofocusing light sheets (i.e. beams in 2D) are developed. • The light-sheets are synthesized based on the angular spectrum decomposition method. • Computations of the scattering, radiation force and torque benefit from the solutions. - Abstract: Nonparaxial optical Bessel and Bessel–Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.
Nonparaxial Bessel and Bessel–Gauss pincers light-sheets
International Nuclear Information System (INIS)
Mitri, F.G.
2017-01-01
Highlights: • Bessel and Bessel–Gauss autofocusing light sheets (i.e. beams in 2D) are developed. • The light-sheets are synthesized based on the angular spectrum decomposition method. • Computations of the scattering, radiation force and torque benefit from the solutions. - Abstract: Nonparaxial optical Bessel and Bessel–Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.
Saha, Ardhendu; Datta, Arijit; Kaman, Surjit
2018-03-01
A proposal toward the enhancement in the sensitivity of a multimode interference-based fiber optic liquid-level sensor is explored analytically using a zero-order Bessel-Gauss (BG) beam as the input source. The sensor head consists of a suitable length of no-core fiber (NCF) sandwiched between two specialty high-order mode fibers. The coupling efficiency of various order modes inside the sensor structure is assessed using guided-mode propagation analysis and the performance of the proposed sensor has been benchmarked against the conventional sensor using a Gaussian beam. Furthermore, the study has been corroborated using a finite-difference beam propagation method in Lumerical's Mode Solutions software to investigate the propagation of the zero-order BG beam inside the sensor structure. Based on the simulation outcomes, the proposed scheme yields a maximum absolute sensitivity of up to 3.551 dB / mm and a sensing resolution of 2.816 × 10 - 3 mm through the choice of an appropriate length of NCF at an operating wavelength of 1.55 μm. Owing to this superior sensing performance, the reported sensing technology expedites an avenue to devise a high-performance fiber optic-level sensor that finds profound implication in different physical, biological, and chemical sensing purposes.
Cylindrically polarized Bessel–Gauss beams
International Nuclear Information System (INIS)
Madhi, Daena; Aiello, Andrea; Ornigotti, Marco
2015-01-01
We present a study of radially and azimuthally polarized Bessel–Gauss (BG) beams in both the paraxial and nonparaxial regime. We discuss the validity of the paraxial approximation and the form of the nonparaxial corrections for BG beams. We show that independently on the ratio between the Bessel aperture cone angle ϑ 0 and the Gaussian beam divergence θ 0 , the nonparaxial corrections are alway very small and therefore negligible. The explicit expressions for the nonparaxial vector electric field components are also reported. (paper)
Spatial-temporal dynamics of broadband terahertz Bessel beam propagation
International Nuclear Information System (INIS)
Semenova, V A; Kulya, M S; Bespalov, V G
2016-01-01
The unique properties of narrowband and broadband terahertz Bessel beams have led to a number of their applications in different fields, for example, for the depth of focusing and resolution enhancement in terahertz imaging. However, broadband terahertz Bessel beams can probably be also used for the diffraction minimization in the short-range broadband terahertz communications. For this purpose, the study of spatial-temporal dynamics of the broadband terahertz Bessel beams is needed. Here we present a simulation-based study of the propagating in non-dispersive medium broadband Bessel beams generated by a conical axicon lens. The algorithm based on scalar diffraction theory was used to obtain the spatial amplitude and phase distributions of the Bessel beam in the frequency range from 0.1 to 3 THz at the distances 10-200 mm from the axicon. Bessel beam field is studied for the different spectral components of the initial pulse. The simulation results show that for the given parameters of the axicon lens one can obtain the Gauss-Bessel beam generation in the spectral range from 0.1 to 3 THz. The length of non-diffraction propagation for a different spectral components was measured, and it was shown that for all spectral components of the initial pulse this length is about 130 mm. (paper)
Techniques to sort Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2013-09-01
Full Text Available -polar coordinate transformation, translating helically phased beams into a transverse phase gradient. By introducing two cylindrical lenses we can focus each of the azimuthal modes associated with each Bessel beam to a different lateral position in the Fourier...
Optical tractor Bessel polarized beams
Mitri, F. G.; Li, R. X.; Guo, L. X.; Ding, C. Y.
2017-01-01
Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications.
Optical tractor Bessel polarized beams
International Nuclear Information System (INIS)
Mitri, F.G.; Li, R.X.; Guo, L.X.; Ding, C.Y.
2017-01-01
Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α_0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications. - Highlights: • Optical tractor Bessel polarized beams are
Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis.
Gutiérrez-Vega, Julio C; Rodríguez-Masegosa, Rodolfo; Chávez-Cerda, Sabino
2003-11-01
A detailed study of the axicon-based Bessel-Gauss resonator with concave output coupler is presented. We employ a technique to convert the Huygens-Fresnel integral self-consistency equation into a matrix equation and then find the eigenvalues and the eigenfields of the resonator at one time. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectories after one or two round trips. The fast-Fourier-transform-based Fox and Li algorithm is applied to describe the three-dimensional intracavity field distribution. Special attention was directed to the dependence of the output transverse profiles, the losses, and the modal-frequency changes on the curvature of the output coupler and the cavity length. The propagation of the output beam is discussed.
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.
Laser-driven acceleration with Bessel beam
International Nuclear Information System (INIS)
Imasaki, Kazuo; Li, Dazhi
2005-01-01
A new approach of laser-driven acceleration with Bessel beam is described. Bessel beam, in contrast to the Gaussian beam, shows diffraction-free'' characteristics in its propagation, which implies potential in laser-driven acceleration. But a normal laser, even if the Bessel beam, laser can not accelerate charged particle efficiently because the difference of velocity between the particle and photon makes cyclic acceleration and deceleration phase. We proposed a Bessel beam truncated by a set of annular slits those makes several special regions in its travelling path, where the laser field becomes very weak and the accelerated particles are possible to receive no deceleration as they undergo decelerating phase. Thus, multistage acceleration is realizable with high gradient. In a numerical computation, we have shown the potential of multistage acceleration based on a three-stage model. (author)
Materials processing with superposed Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Yu, Xiaoming [Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66506 (United States); Trallero-Herrero, Carlos A. [J. R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506 (United States); Lei, Shuting, E-mail: lei@ksu.edu [Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66506 (United States)
2016-01-01
Graphical abstract: - Highlights: • Superpositions of Bessel beams can be generated with >50% efficiency using an SLM and an axicon. • These beams have orders-of-magnitude increase in depth-of-focus compared to Gaussian beams. • Multiple craters can be fabricated on glass with single-shot exposure. • The 1+(−1) superposition can reduce collateral damage caused by the rings in the zero-order Bessel beams. - Abstract: We report experimental results of femtosecond laser processing on the surface of glass and metal thin film using superposed Bessel beams. These beams are generated by a combination of a spatial light modulator (SLM) and an axicon with >50% efficiency, and they possess the long depth-of-focus (propagation-invariant) property as found in ordinary Bessel beams. Through micromachining experiments using femtosecond laser pulses, we show that multiple craters can be fabricated on glass with single-shot exposure, and the 1+(−1) superposed beam can reduce collateral damage caused by the rings in zero-order Bessel beams in the scribing of metal thin film.
Generation of Nondiffracting Electron Bessel Beams
Directory of Open Access Journals (Sweden)
Vincenzo Grillo
2014-01-01
Full Text Available Almost 30 years ago, Durnin discovered that an optical beam with a transverse intensity profile in the form of a Bessel function of the first order is immune to the effects of diffraction. Unlike most laser beams, which spread upon propagation, the transverse distribution of these Bessel beams remains constant. Electrons also obey a wave equation (the Schrödinger equation, and therefore Bessel beams also exist for electron waves. We generate an electron Bessel beam by diffracting electrons from a nanoscale phase hologram. The hologram imposes a conical phase structure on the electron wave-packet spectrum, thus transforming it into a conical superposition of infinite plane waves, that is, a Bessel beam. We verify experimentally that these beams can propagate for 0.6 m without measurable spreading and can also reconstruct their intensity distributions after being partially obstructed by an obstacle. Finally, we show by numerical calculations that the performance of an electron microscope can be increased dramatically through use of these beams.
Microwave bessel beams generation using guided modes
Salem, Mohamed; Kamel, Aladin Hassan; Niver, Edip
2011-01-01
A novel method is devised for Bessel beams generation in the microwave regime. The beam is decomposed in terms of a number of guided transverse electric modes of a metallic waveguide. Modal expansion coefficients are computed from the modal power orthogonality relation. Excitation is achieved by means of a number of inserted coaxial loop antennas, whose currents are calculated from the excitation coefficients of the guided modes. The efficiency of the method is evaluated and its feasibility is discussed. Obtained results can be utilized to practically realize microwave Bessel beam launchers. © 2006 IEEE.
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.
General description of transverse mode Bessel beams and construction of basis Bessel fields
Wang, Jia Jie; Wriedt, Thomas; Lock, James A.; Jiao, Yong Chang
2017-07-01
Based on an analysis of polarized Bessel beams using the Hertz vector potentials and the angular spectrum representation (ASR), a general description of transverse mode Bessel beams is proposed. As opposed to the cases of linearly and circularly polarized Bessel beams, the magnetic and electric fields of a Bessel beam in a transverse mode are orthogonal to each other. Both sets of fields together form a complete set of basis Bessel fields, in terms of which an arbitrary Bessel beam can be regarded as a linear combination. The completeness of the basis Bessel fields is analyzed from the perspectives of waveguide theory and vector wave functions. Decompositions of linearly polarized, circularly polarized, and circularly symmetric n-order Bessel beams in terms of basis Bessel fields are given. The results presented in this paper provide a fresh perspective on the description of Bessel beams, which are useful in casting insights into the experimental generation of Bessel beams and the interpretation of light scattering-related problems in practice.
Controlled acceleration of superimposed Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2013-06-01
Full Text Available spatial light modulator (SLM) to create superimposed, non-canonical, higher-order Bessel beams and a CCD camera to investigate the propagation of the resulting field. It is already known that the intensity profile of the resulting field experiences...
Acoustic manipulation: Bessel beams and active carriers
Rajabi, Majid; Mojahed, Alireza
2017-10-01
In this paper, we address the interaction of zero-order acoustic Bessel beams as an acoustic manipulation tool, with an active spherical shell, as a carrier in drug, agent, or material delivery systems, in order to investigate the controllability of exerted acoustic radiation force as the driver. The active body is comprised of a spherical elastic shell stimulated in its monopole mode of vibrations with the same frequency as the incident wave field via an internally bonded and spatially uniformly excited piezoelectric actuator. The main aim of this work is to examine the performance of a nondiffracting and self-reconstructing zero-order Bessel beam to obtain the full manipulability condition of active carriers in comparison with the case of a plane wave field. The results unveil some unique potentials of the Bessel beams in the company of active carriers, with emphasis on the consumed power of the actuation system. This paper will widen the path toward the single-beam robust acoustic manipulation techniques and may lead to the prospect of combined tweezers and fields, with applications in delivery systems, microswimmers, and trapper designs.
International Nuclear Information System (INIS)
Gouesbet, Gérard
2016-01-01
Localized approximation procedures are efficient ways to evaluate beam shape coefficients of a laser beam. They are particularly useful when other methods are ineffective or inefficient. Several papers in the literature have reported the use of such procedures to evaluate the beam shape coefficients of Bessel beams. Relying on the concept of N-beams, it is demonstrated that care must be taken when constructing a localized approximation for a Bessel beam, namely a localized Bessel beam is satisfactorily close enough to the intended beam only when the axicon angle is small enough. - Highlights: • Localized approximation has been used to evaluate BSCs of Bessel beams. • N-beam procedure fails to provide a localized approximation for Bessel beams. • Localized approximation should be used only for small axicon angles.
Optical trapping with Bessel beams generated from semiconductor lasers
International Nuclear Information System (INIS)
Sokolovskii, G S; Dudelev, V V; Losev, S N; Soboleva, K K; Deryagin, A G; Kuchinskii, V I; Sibbett, W; Rafailov, E U
2014-01-01
In this paper, we study generation of Bessel beams from semiconductor lasers with high beam propagation parameter M 2 and their utilization for optical trapping and manipulation of microscopic particles including living cells. The demonstrated optical tweezing with diodegenerated Bessel beams paves the way to replace their vibronic-generated counterparts for a range of applications towards novel lab-on-a-chip configurations
Efficient sorting of Bessel beams [Conference paper
CSIR Research Space (South Africa)
Mhlanga, T
2013-02-01
Full Text Available measured in entanglement and shown an increased spiral bandwidth17. Exploiting these properties of Bessel beams will make them very useful in the field of long-range, broad bandwidth communication systems. However, in order for these fields to be a... success in the area of optical communication, efficient techniques for extracting the information they carry (i.e. their azimuthal mode indices) need to exist. The ‘fork’ diffraction grating can be used to couple light of a particular OAM state into a...
Generating and measuring non-diffracting vector Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2014-03-01
Full Text Available We demonstrate how to create non-diffracting vector Bessel beams by implementing a spatial light modulator (SLM) to generate scalar Bessel beams which are then converted into vector fields by the use of an azimuthally-varying birefringent plate...
Azimuthally matched interactions and azimuthal correlation of Bessel light beams
International Nuclear Information System (INIS)
Khilo, N A
2000-01-01
A theoretical investigation is reported of the regime of azimuthally matched interactions in the process of conversion of the frequency of Bessel light beams. It is shown that this nonlinear interaction regime is accompanied by the establishment of correlations of the mutual azimuthal orientations of plane-wave components of Bessel beams and by an increase in the overlap integral. (nonlinear optical phenomena)
Higher-order harmonics of limited diffraction Bessel beams
Ding; Lu
2000-03-01
We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.
Second-harmonic generation of practical Bessel beams
Huang, Jin H.; Ding, Desheng; Hsu, Yin-Sung
2009-11-01
A fast Gaussian expansion approach is used to investigate fundamental and second-harmonic generation in practical Bessel beams of finite aperture. The analysis is based on the integral solutions of the KZK equation under the quasilinear approximation. The influence of the medium's attenuation on the beam profile is considered. Analysis results show that the absorption parameter has a significant effect on the far-field beam profile of the second harmonic. Under certain circumstances, the second harmonic of a practical Bessel beam still has the main properties of an ideal Bessel beam of infinite aperture when it propagates within its depth of field.
Spin polarisation with electron Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Schattschneider, P., E-mail: schattschneider@ifp.tuwien.ac.at [Institut für Festkörperphysik, Technische Universität Wien, A-1040 Wien (Austria); USTEM, Technische Universität Wien, A-1040 Wien (Austria); Grillo, V. [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); CNR-IMEM, Parco delle Scienze 37a, I-43100 Parma (Italy); Aubry, D. [Centrale Supelec, MSSMast CNRS 8579, F-92295 Châtenay-Malabry (France)
2017-05-15
The theoretical possibility to use an electron microscope as a spin polarizer is studied. It turns out that a Bessel beam passing a standard magnetic objective lens is intrinsically spin polarized when post-selected on-axis. In the limit of infinitely small detectors, the spin polarisation tends to 100 %. Increasing the detector size, the polarisation decreases rapidly, dropping below 10{sup −4} for standard settings of medium voltage microscopes. For extremely low voltages, the Figure of Merit increases by two orders of magnitude, approaching that of existing Mott detectors. Our findings may lead to new desings of spin filters, an attractive option in view of its inherent combination with the electron microscope, especially at low voltage. - Highlights: • TEM round magnetic lenses can act as spin polarizers when a Bessel beam is sent through. • This is found on theoretical grounds and demonstrated numerically for a few cases. • The effect is small, but can reach a Figure of Merit similar to existing Mott detectors. • This opens the possibility to construct nanometer-sized spin filters or detectors.
Bessel beam CARS of axially structured samples
Heuke, Sandro; Zheng, Juanjuan; Akimov, Denis; Heintzmann, Rainer; Schmitt, Michael; Popp, Jürgen
2015-06-01
We report about a Bessel beam CARS approach for axial profiling of multi-layer structures. This study presents an experimental implementation for the generation of CARS by Bessel beam excitation using only passive optical elements. Furthermore, an analytical expression is provided describing the generated anti-Stokes field by a homogeneous sample. Based on the concept of coherent transfer functions, the underling resolving power of axially structured geometries is investigated. It is found that through the non-linearity of the CARS process in combination with the folded illumination geometry continuous phase-matching is achieved starting from homogeneous samples up to spatial sample frequencies at twice of the pumping electric field wave. The experimental and analytical findings are modeled by the implementation of the Debye Integral and scalar Green function approach. Finally, the goal of reconstructing an axially layered sample is demonstrated on the basis of the numerically simulated modulus and phase of the anti-Stokes far-field radiation pattern.
Generation and application of Bessel beam in alignment works
International Nuclear Information System (INIS)
Gale, D. M.
2009-01-01
The divergence of a Gaussian laser beam is a limiting factor for optical alignment tasks at large distances. Bessel beams have almost zero divergence but are still not widely used. We discuss the construction of an alignment telescope based on Bessel beam generation using a commercial laser diode module. The Bessel beam is generated with conical or plano-convex lenses, and projected using a commercial CCD camera lens to extend the useful range of the beam. Our Bessel beams have diameters of between 0.5 - 1mm over beam lengths of 15m, representing a six-fold improvement compared to Gaussian beams, while the transverse beam structure (Bessel pattern) provides an excellent alignment aid for use with beam target. Another advantage of Bessel beams is their self-regeneration property, which allows the use of multiple beam targets with minimum beam degradation. We are using our crosshair targets with crosshair targets to align optical components in a large astronomical telescope, and can achieve precisions of tens of microns over distances of 20m using purely visual methods. (Author)
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.
Behavior of obliquely incident vector Bessel beams at planar interfaces
Salem, Mohamed; Bagci, Hakan
2013-01-01
We investigate the behavior of full-vector electromagnetic Bessel beams obliquely incident at an interface between two electrically different media. We employ a Fourier transform domain representation of Bessel beams to determine their behavior upon reflection and transmission. This transform, which is geometric in nature, consists of elliptical support curves with complex weighting associated with them. The behavior of the scattered field at an interface is highly complex, owing to its full-vector nature; nevertheless, this behavior has a straightforward representation in the transform domain geometry. The analysis shows that the reflected field forms a different vector Bessel beam, but in general, the transmitted field cannot be represented as a Bessel beam. Nevertheless, using this approach, we demonstrate a method to propagate a Bessel beam in the refractive medium by launching a non- Bessel beam at the interface. Several interesting phenomena related to the behavior of Bessel beams are illustrated, such as polarized reflection at Brewster's angle incidence, and the Goos-Hänchen and Imbert-Federov shifts in the case of total reflection. © 2013 Optical Society of America.
Higher-order harmonics of general limited diffraction Bessel beams
International Nuclear Information System (INIS)
Ding De-Sheng; Huang Jin-Huang
2016-01-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m -th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. (special topic)
Higher-order harmonics of general limited diffraction Bessel beams
Ding, De-Sheng; Huang, Jin-Huang
2016-12-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).
Generation and application of bessel beams in electron microscopy
Energy Technology Data Exchange (ETDEWEB)
Grillo, Vincenzo, E-mail: vincenzo.grillo@cnr.it [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); CNR-IMEM, Parco Area delle Scienze 37/A, I-43124 Parma (Italy); Harris, Jérémie [Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5 (Canada); Gazzadi, Gian Carlo [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); Balboni, Roberto [CNR-IMM Bologna, Via P. Gobetti 101, 40129 Bologna (Italy); Mafakheri, Erfan [Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena (Italy); Dennis, Mark R. [H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL (United Kingdom); Frabboni, Stefano [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena (Italy); Boyd, Robert W.; Karimi, Ebrahim [Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5 (Canada)
2016-07-15
We report a systematic treatment of the holographic generation of electron Bessel beams, with a view to applications in electron microscopy. We describe in detail the theory underlying hologram patterning, as well as the actual electron-optical configuration used experimentally. We show that by optimizing our nanofabrication recipe, electron Bessel beams can be generated with relative efficiencies reaching 37±3%. We also demonstrate by tuning various hologram parameters that electron Bessel beams can be produced with many visible rings, making them ideal for interferometric applications, or in more highly localized forms with fewer rings, more suitable for imaging. We describe the settings required to tune beam localization in this way, and explore beam and hologram configurations that allow the convergences and topological charges of electron Bessel beams to be controlled. We also characterize the phase structure of the Bessel beams generated with our technique, using a simulation procedure that accounts for imperfections in the hologram manufacturing process. - Highlights: • Bessel beams with different convergence, topological charge, visible fringes are demonstrated. • The relation between the Fresnel hologram and the probe shape is explained by detailed calculations and experiments. • Among the holograms here presented the highest relative efficiency is 37%, the best result ever reached for blazed holograms.
Generation and application of bessel beams in electron microscopy
International Nuclear Information System (INIS)
Grillo, Vincenzo; Harris, Jérémie; Gazzadi, Gian Carlo; Balboni, Roberto; Mafakheri, Erfan; Dennis, Mark R.; Frabboni, Stefano; Boyd, Robert W.; Karimi, Ebrahim
2016-01-01
We report a systematic treatment of the holographic generation of electron Bessel beams, with a view to applications in electron microscopy. We describe in detail the theory underlying hologram patterning, as well as the actual electron-optical configuration used experimentally. We show that by optimizing our nanofabrication recipe, electron Bessel beams can be generated with relative efficiencies reaching 37±3%. We also demonstrate by tuning various hologram parameters that electron Bessel beams can be produced with many visible rings, making them ideal for interferometric applications, or in more highly localized forms with fewer rings, more suitable for imaging. We describe the settings required to tune beam localization in this way, and explore beam and hologram configurations that allow the convergences and topological charges of electron Bessel beams to be controlled. We also characterize the phase structure of the Bessel beams generated with our technique, using a simulation procedure that accounts for imperfections in the hologram manufacturing process. - Highlights: • Bessel beams with different convergence, topological charge, visible fringes are demonstrated. • The relation between the Fresnel hologram and the probe shape is explained by detailed calculations and experiments. • Among the holograms here presented the highest relative efficiency is 37%, the best result ever reached for blazed holograms.
Generating superpositions of higher order bessel beams [Conference paper
CSIR Research Space (South Africa)
Vasilyeu, R
2009-10-01
Full Text Available An experimental setup to generate a superposition of higher-order Bessel beams by means of a spatial light modulator and ring aperture is presented. The experimentally produced fields are in good agreement with those calculated theoretically....
Talbot self-imaging phenomenon under Bessel beam illumination
Chakraborty, Rijuparna; Chowdhury, Subhajit Dutta; Chakraborty, Ajoy Kumar
2018-06-01
In this paper, we report the results of our theoretical studies on the phenomenon of self-imaging of periodic object under the illumination of zero-order Bessel beam. Our theoretical analysis indicates that the self-images are visible only after the walk-off distance of the Bessel beam used. It is also observed that the self-images bend around the optical axis of the setup. Besides, the present study justifies the importance of the conditions stipulated by Montgomery.
Vectorial diffraction properties of THz vortex Bessel beams.
Wu, Zhen; Wang, Xinke; Sun, Wenfeng; Feng, Shengfei; Han, Peng; Ye, Jiasheng; Yu, Yue; Zhang, Yan
2018-01-22
A vortex Bessel beam combines the merits of an optical vortex and a Bessel beam, including a spiral wave front and a non-diffractive feature, which has immense application potentials in optical trapping, optical fabrication, optical communications, and so on. Here, linearly and circularly polarized vortex Bessel beams in the terahertz (THz) frequency range are generated by utilizing a THz quarter wave plate, a spiral phase plate, and Teflon axicons with different opening angles. Taking advantage of a THz focal-plane imaging system, vectorial diffraction properties of the THz vortex Bessel beams are comprehensively characterized and discussed, including the transverse (Ex, Ey) and longitudinal (Ez) polarization components. The experimental phenomena are accurately simulated by adopting the vectorial Rayleigh diffraction integral. By varying the opening angle of the axicon, the characteristic parameters of these THz vortex Bessel beams are exhibited and compared, including the light spot size, the diffraction-free range, and the phase evolution process. This work provides the precise experimental and theoretical bases for the comprehension and application of a THz vortex Bessel beam.
Laser-driven acceleration with Bessel and Gaussian beams
International Nuclear Information System (INIS)
Hafizi, B.; Esarey, E.; Sprangle, P.
1997-01-01
The possibility of enhancing the energy gain in laser-driven accelerators by using Bessel laser beams is examined. Scaling laws are derived for the propagation length, acceleration gradient, and energy gain in various accelerators for both Gaussian and Bessel beam drivers. For equal beam powers, the energy gain can be increased by a factor of N 1/2 by utilizing a Bessel beam with N lobes, provided that the acceleration gradient is linearly proportional to the laser field. This is the case in the inverse free electron laser and the inverse Cherenkov accelerators. If the acceleration gradient is proportional to the square of the laser field (e.g., the laser wakefield, plasma beat wave, and vacuum beat wave accelerators), the energy gain is comparable with either beam profile. copyright 1997 American Institute of Physics
Scattering of linearly polarized Bessel beams by dielectric spheres
Shoorian, Hamed
2017-09-01
The scattering of a Linearly Polarized Bessel Beam (LPBB) by an isotropic and homogenous dielectric sphere is investigated. Using analytical relation between the cylindrical and the spherical vector wave functions, all the closed- form analytical expressions, in terms of spherical wave-functions expansions, are derived for the scattered field. It is shown that in the case of conical angle of incident Bessel beam is equal to zero, the Linearly Polarized Bessel Beam becomes a plane wave and its scattering coefficients become the same as the expansion coefficients of plane wave in Mie theory. The transverse Cartesian and spherical components of the electric field, scattered by a sphere are shown in the z-plane for different cases, moreover the intensity of the incident Bessel beam and the effects of its conical angle on the scattered field and the field inside the sphere are investigated. To quantitatively study the scattering phenomenon and the variations of the fields inside and outside of the sphere, the scattering and absorption efficiencies are obtained for the scattering of the linearly-polarized Bessel beam, and are compared with those of the plane wave scattering.
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.
CSIR Research Space (South Africa)
Belyi, VN
2011-05-01
Full Text Available The authors investigate the generation and transformation of Bessel beams through linear and nonlinear optical crystals. They outline the generation of high-order vortices due to propagation of Bessel beams along the optical axis of uniaxial...
Effective and efficient method of calculating Bessel beam fields
CSIR Research Space (South Africa)
Litvin, IA
2005-01-01
Full Text Available Bessel beams have gathered much interest of late due to their properties of near diffraction free propagation and self reconstruction after obstacles. Such laser beams have already found applications in fields such as optical tweezers and as pump...
THz computed tomography system with zero-order Bessel beam
Niu, Liting; Wu, Qiao; Wang, Kejia; Liu, Jinsong; Yang, Zhengang
2018-01-01
Terahertz (THz) waves can penetrate many optically opaque dielectric materials such as plastics, ceramics and colorants. It is effective to reveal the internal structures of these materials. We have built a THz Computed Tomography (CT) system with 0.3 THz zero-order Bessel beam to improve the depth of focus of this imaging system for the non-diffraction property of Bessel beam. The THz CT system has been used to detect a paper cup with a metal rod inside. Finally, the acquired projection data have been processed by the filtered back-projection algorithm and the reconstructed image of the sample has been obtained.
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.
Scattering of a high-order Bessel beam by a spheroidal particle
Han, Lu
2018-05-01
Within the framework of generalized Lorenz-Mie theory (GLMT), scattering from a homogeneous spheroidal particle illuminated by a high-order Bessel beam is formulated analytically. The high-order Bessel beam is expanded in terms of spheroidal vector wave functions, where the spheroidal beam shape coefficients (BSCs) are computed conveniently using an intrinsic method. Numerical results concerning scattered field in the far zone are displayed for various parameters of the incident Bessel beam and of the scatter. These results are expected to provide useful insights into the scattering of a Bessel beam by nonspherical particles and particle manipulation applications using Bessel beams.
Generating superpositions of higher–order Bessel beams [Journal article
CSIR Research Space (South Africa)
Vasilyeu, R
2009-12-01
Full Text Available The authors report the first experimental generation of the superposition of higher-order Bessel beams, by means of a spatial light modulator (SLM) and a ring slit aperture. They present illuminating a ring slit aperture with light which has...
Resonant Self-Trapping and Absorption of Intense Bessel Beams
International Nuclear Information System (INIS)
Fan, J.; Parra, E.; Milchberg, H. M.
2000-01-01
We report the observation of resonant self-trapping and enhanced laser-plasma heating resulting from propagation of high intensity Bessel beams in neutral gas. The enhancement in absorption and plasma heating is directly correlated to the spatial trapping of laser radiation. (c) 2000 The American Physical Society
Special features of local spatial spectrum of Bessel light beams
CSIR Research Space (South Africa)
Belyi, VN
2011-11-01
Full Text Available In this paper the authors consider the angular spectrum of an apertured Bessel beam when the aperture is circular and shifted laterally with respect to the optical axis. Since the perturbation of the resulting angular spectrum is due to a spatially...
An optical tweezer in asymmetrical vortex Bessel-Gaussian beams
Energy Technology Data Exchange (ETDEWEB)
Kotlyar, V. V.; Kovalev, A. A., E-mail: alexeysmr@mail.ru; Porfirev, A. P. [Image Processing Systems Institute, 151 Molodogvardeiskaya St., 443001 Samara (Russian Federation); Department of Technical cybernetics, Samara State Aerospace University, Samara 443086 (Russian Federation)
2016-07-14
We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.
Creating aperiodic photonic structures by synthesized Mathieu-Gauss beams
Vasiljević, Jadranka M.; Zannotti, Alessandro; Timotijević, Dejan V.; Denz, Cornelia; Savić, Dragana M. Jović
2017-08-01
We demonstrate a kind of aperiodic photonic structure realized using the interference of multiple Mathieu-Gauss beams. Depending on the beam configurations, their mutual distances, angles of rotation, or phase relations we are able to observe different classes of such aperiodic optically induced refractive index structures. Our experimental approach is based on the optical induction in a single parallel writing process.
Polarization properties of linearly polarized parabolic scaling Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Guo, Mengwen; Zhao, Daomu, E-mail: zhaodaomu@yahoo.com
2016-10-07
The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge. - Highlights: • We investigated the polarization properties of modified parabolic scaling Bessel beams with linear polarization. • We studied the evolution of transverse intensity profiles for the three components of these beams. • The intensity patterns of the cross polarization and longitudinal components can reflect the sign of the topological charge.
Optical breakdown of helium in Bessel laser radiation beams
International Nuclear Information System (INIS)
Andreev, N E; Pleshanov, I V; Margolin, L Ya; Pyatnitskii, Lev N
1998-01-01
Numerical simulation is used to investigate the dynamics of formation of a helium plasma in Bessel beams, shaped by an axicon and a phase converter from a laser radiation pulse with Gaussian temporal and radial intensity profiles. The beam intensities at the breakdown threshold are determined as a function of the pulse duration for various radial field distributions in a beam characterised by Bessel functions of order m (m = 0 - 5). It is shown that in the investigated range of parameters the threshold intensity is independent of m. The temporal and spatial evolution of the resultant plasma, and the dependence of the plasma characteristics on the pulse parameters are considered. Conditions are found for the formation of tubular plasma channels in beams of orders m≥1. The adopted model of the optical breakdown of helium is shown to be satisfactory because of a good agreement between the results of calculations of the moment of breakdown in a zeroth-order Bessel beam and experimental results. (interaction of laser radiation with matter. laser plasma)
Mean intensity of the fundamental Bessel-Gaussian beam in turbulent atmosphere
Lukin, Igor P.
2017-11-01
In the given article mean intensity of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is studied. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian beam of optical radiation. Distributions of mean intensity of a fundamental Bessel- Gaussian beam optical beam in longitudinal and transverse to a direction of propagation of optical radiation are investigated in detail. Influence of atmospheric turbulence on change of radius of the central part of a Bessel optical beam is estimated. Values of parameters at which it is possible to generate in turbulent atmosphere a nondiffracting pseudo-Bessel optical beam by means of a fundamental Bessel-Gaussian optical beam are established.
Particle confinement by a radially polarized laser Bessel beam
Laredo, Gilad; Kimura, Wayne D.; Schächter, Levi
2017-03-01
The stable trajectory of a charged particle in an external guiding field is an essential condition for its acceleration or for forcing it to generate radiation. Examples of possible guiding devices include a solenoidal magnetic field or permanent periodic magnet in klystrons, a wiggler in free-electron lasers, the lattice of any accelerator, and finally the crystal lattice for the case of channeling radiation. We demonstrate that the trajectory of a point-charge in a radially polarized laser Bessel beam may be stable similarly to the case of a positron that bounces back and forth in the potential well generated by two adjacent atomic planes. While in the case of channeling radiation, the transverse motion is controlled by a harmonic oscillator equation, for a Bessel beam the transverse motion is controlled by the Mathieu equation. Some characteristics of the motion are presented.
Higher-order Bessel like beams with z-dependent cone angles
CSIR Research Space (South Africa)
Ismail, Y
2010-08-01
Full Text Available .64.81.22. Terms of Use: http://spiedl.org/terms Fig.5: Optical design to generate z-dependent Bessel-like beams 4. CONSIDERING A MATHEMATICAL APPROACH TO EXPLAINING Z-DEPENDENT BLB?S The stationary phase method is implemented in order to confirm... on higher-order z-dependent BLB?s [6]. 5. EXPERIMENTALLY GENERATED Z-DEPENDENT BESSEL-LIKE BEAMS From the above in can be deduced that these beams are Bessel-like hence they are so named z-dependent Bessel-like beams. These beams are produced however...
Self-healing of Bessel-like beams with longitudinally dependent cone angles
International Nuclear Information System (INIS)
Litvin, I; Burger, L; Forbes, A
2015-01-01
Bessel beams have been extensively studied, but to date have been created over a finite region inside the laboratory. Recently Bessel-like beams with longitudinally dependent cone angles have been introduced allowing for a potentially infinite quasi non-diffracting propagation region. Here we show that such beams can self-heal. Moreover, in contrast to Bessel beams where the self-healing distance is constant, here the self-healing distance is dependent on where the obstruction is placed in the field, with the distance increasing as the Bessel-like beam propagates farther. We outline the theoretical concept for this self-healing and confirm it experimentally. (paper)
On the validity of localized approximation for an on-axis zeroth-order Bessel beam
International Nuclear Information System (INIS)
Gouesbet, Gérard; Lock, J.A.; Ambrosio, L.A.; Wang, J.J.
2017-01-01
Localized approximation procedures are efficient ways to evaluate beam shape coefficients of laser beams, and are particularly useful when other methods are ineffective or inefficient. Several papers in the literature have reported the use of such procedures to evaluate the beam shape coefficients of Bessel beams. Examining the specific case of an on-axis zeroth-order Bessel beam, we demonstrate that localized approximation procedures are valid only for small axicon angles. - Highlights: • The localized approximation has been widely used to evaluate the Beam Shape Coefficients (BSCs) of Bessel beams. • The validity of this approximation is examined in the case of an on-axis zeroth-order Bessel beam. • It is demonstrated, in this specific example, that the localized approximation is efficient only for small enough axicon angles. • It is easily argued that this result must remain true for any kind of Bessel beams.
Optical force exerted on a Rayleigh particle by a vector arbitrary-order Bessel beam
International Nuclear Information System (INIS)
Yang, Ruiping; Li, Renxian
2016-01-01
An analytical description of optical force on a Rayleigh particle by a vector Bessel beam is investigated. Linearly, radially, azimuthally, and circularly polarized Bessel beams are considered. The radial, azimuthal, and axial forces by a vector Bessel beam are numerically simulated. The effect of polarization, order of beams, and half-cone angle to the optical force are mainly discussed. For Bessel beams of larger half-cone angle, the non-paraxiality of beams plays an important role in optical forces. Numerical calculations show that optical forces, especially azimuthal forces, are very sensitive to the polarization of beams. - Highlights: • Optical force exerted on a Rayleigh particle by a vector Bessel beam is analytically derived. • Radial, azimuthal, and axial forces are numerically analyzed. • The effect of polarization, order of beam, and non-paraxiality is analyzed.
Kiselev, A
2003-01-01
Two new families of exact solutions of the wave equation u sub x sub x + u sub y sub y + u sub z sub z - c sup - sup 2 u sub t sub t = 0 generalizing Bessel-Gauss pulses and Bateman-Hillion relatively undistorted progressive waves, respectively are presented. In each of these families new simple solutions describing localized wave propagation are found. The approach is based on a kind of separation of variables. (letter to the editor)
International Nuclear Information System (INIS)
Peet, V
2014-01-01
The effect of internal conical refraction (CR) in a biaxial crystal was studied using Laguerre–Gauss light beams LG 0 ℓ with ℓ=1 and 2, while the lowest-order LG 0 0 beam was used as a reference. The transition from ordinary double refraction to CR was examined. It has been shown that double refraction of an LG 0 ℓ beam forms two focal spots containing ℓ dark stripes. These stripes evolve into ℓ+1 dark rings over an annular focal image when CR is established, and it results in a fine-structure of ℓ+2 bright focal rings with different intensities. In a sharp contrast to the lowest-order reference, the multiring focal structure has a distinct asymmetry with respect to the focal image plane. It has been shown that bright off-axis ‘hot spot’ can be formed on the far-field profiles of outgoing light beams when the biaxial crystal is slightly tilted, and a small angle between the propagation axis of the beam and the optic axis of the crystal arises. These off-axis light structures emerge as either a charge-one optical vortex or a zero-charge spot with annihilated vorticity. Polarization selection reveals J 1 or J 0 Bessel-like profiles of the corresponding ‘hot spots’, and a complex pattern of forked fringes in the dark region near the beam core. (paper)
Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere
Lukin, Igor P.
2017-11-01
In this paper the theoretical research of coherent properties of the vortex Bessel-Gaussian optical beams propagating in turbulent atmosphere are developed. The approach to the analysis of this problem is based on the analytical solution of the equation for the transverse second-order mutual coherence function of a field of optical radiation. The behavior of integral scale of coherence degree of vortex Bessel-Gaussian optical beams depending on parameters of an optical beam and characteristics of turbulent atmosphere is particularly considered. It is shown that the integral scale of coherence degree of a vortex Bessel-Gaussian optical beam essentially depends on value of a topological charge of a vortex optical beam. With increase in a topological charge of a vortex Bessel-Gaussian optical beam the value of integral scale of coherence degree of a vortex Bessel-Gaussian optical beam are decreased.
Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere
Lukin, Igor P.
2017-11-01
In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.
Transverse particle dynamics in a Bessel beam
Czech Academy of Sciences Publication Activity Database
Milne, G.; Dholakia, K.; McGloin, D.; Volke-Sepulveda, K.; Zemánek, Pavel
2007-01-01
Roč. 15, č. 21 (2007), s. 13972-13987 ISSN 1094-4087 R&D Projects: GA MŠk(CZ) LC06007; GA MPO(CZ) FT-TA2/059 EU Projects: European Commission(XE) 508952 - ATOM3D Institutional research plan: CEZ:AV0Z20650511 Keywords : optical tweezers or optical manipulation * laser trapping * laser beam shaping Subject RIV: BH - Optics, Masers, Lasers Impact factor: 3.709, year: 2007
International Nuclear Information System (INIS)
He, Xi; Wu, Fengtie; Chen, Ziyang; Pu, Jixiong; Chavez-Cerda, Sabino
2016-01-01
The transverse focusing properties at the ‘pseudo-focal’ plane of coherent Bessel beams with angular momentum are analyzed in detail. The transverse magnification of the central dark region of Bessel beams at this pseudo-focal plane is derived for the first time by calculating the ratio of the magnitude of the transverse components of the corresponding wave vectors before and after the focusing lens. We test our results experimentally with coherent laser Bessel beams and excellent agreement is observed. Then, an LED light source is used to generate Bessel beams. By modifying the coherence of the LED light source, we observe that by reducing coherence a smaller and shallower central dark region of Bessel beams with angular momentum is produced at the pseudo-focal plane. This technique can be used as a method to characterize the degree of coherence of vortex beams. (paper)
Investigation of local spatial spectra of Bessel light beams
CSIR Research Space (South Africa)
Belyi, VN
2009-08-01
Full Text Available plane of lens and illuminated by plane wave. The superposition of plane waves in such scheme is proposed to be generated by point sources distributed within the circular diaphragm. In a case when diaphragm is placed outside of lens focus [2], Bessel... beam can be described as an image in lens of spherical waves superposition formed by some effective circular source in object plane of lens. In the scheme of BLB obtaining based on axicons, the appearance of superposition of plane waves can be studied...
Multipole expansion of acoustical Bessel beams with arbitrary order and location.
Gong, Zhixiong; Marston, Philip L; Li, Wei; Chai, Yingbin
2017-06-01
An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.
Ultrafast Bessel beams: advanced tools for laser materials processing
Stoian, Razvan; Bhuyan, Manoj K.; Zhang, Guodong; Cheng, Guanghua; Meyer, Remy; Courvoisier, Francois
2018-05-01
Ultrafast Bessel beams demonstrate a significant capacity of structuring transparent materials with a high degree of accuracy and exceptional aspect ratio. The ability to localize energy on the nanometer scale (bypassing the 100-nm milestone) makes them ideal tools for advanced laser nanoscale processing on surfaces and in the bulk. This allows to generate and combine micron and nano-sized features into hybrid structures that show novel functionalities. Their high aspect ratio and the accurate location can equally drive an efficient material modification and processing strategy on large dimensions. We review, here, the main concepts of generating and using Bessel non-diffractive beams and their remarkable features, discuss general characteristics of their interaction with matter in ablation and material modification regimes, and advocate their use for obtaining hybrid micro and nanoscale structures in two and three dimensions (2D and 3D) performing complex functions. High-throughput applications are indicated. The example list ranges from surface nanostructuring and laser cutting to ultrafast laser welding and the fabrication of 3D photonic systems embedded in the volume.
Low-frequency acousto-optic backscattering of Bessel light beams
Khilo, Nikolai A.; Belyi, Vladimir N.; Khilo, Petr A.; Kazak, Nikolai S.
2018-05-01
The use of Bessel light beams, as well as Bessel acoustic beams, substantially enhances the capabilities of acousto-optic methods for control of optical field. We present a theoretical study of the process of optical Bessel beams conversion by means of backward acousto-optic scattering on a Bessel acoustic field in a transversely isotropic crystal. It is shown that, with an appropriate choice of Bessel beams parameters, the backscattering in visible spectral range can be realized at relatively low acoustic frequencies less than one gigahertz. Under conditions of phase matching and transverse spatial synchronism, the efficiency of backscattering is sufficiently high, which is interesting, for example, for construction of acousto-optic spectral analyzers.
Engineering the on-axis intensity of Bessel beam by a feedback tuning loop
Li, Runze; Yu, Xianghua; Yang, Yanlong; Peng, Tong; Yao, Baoli; Zhang, Chunmin; Ye, Tong
2018-02-01
The Bessel beam belongs to a typical class of non-diffractive optical fields that are characterized by their invariant focal profiles along the propagation direction. However, ideal Bessel beams only rigorously exist in theory; Bessel beams generated in the lab are quasi-Bessel beams with finite focal extensions and varying intensity profiles along the propagation axis. The ability to engineer the on-axis intensity profile to the desired shape is essential for many applications. Here we demonstrate an iterative optimization-based approach to engineering the on-axis intensity of Bessel beams. The genetic algorithm is used to demonstrate this approach. Starting with a traditional axicon phase mask, in the design process, the computed on-axis beam profile is fed into a feedback tuning loop of an iterative optimization process, which searches for an optimal radial phase distribution that can generate a generalized Bessel beam with the desired onaxis intensity profile. The experimental implementation involves a fine-tuning process that adjusts the originally targeted profile so that the optimization process can optimize the phase mask to yield an improved on-axis profile. Our proposed method has been demonstrated in engineering several zeroth-order Bessel beams with customized on-axis profiles. High accuracy and high energy throughput merit its use in many applications.
Generation of the second harmonics of Bessel light beams in a KTP crystal
International Nuclear Information System (INIS)
Belyi, V N; Kazak, N S; Kondratyuk, N V; Khilo, N A; Shagov, A A
1998-01-01
Theoretical and experimental investigations were made of the characteristic features of doubling the frequency of Bessel light beams by the oe - e interaction in a KTP crystal. All possible and scalar interactions of plane-wave components of Bessel beams were observed experimentally. The spatial structure of the second harmonic in the far zone consisted of a central spot and a concentric ring. The diffraction divergence of the central beam was weak ( ∼ 1.7 mrad). The energy conversion efficiency was ∼ 21% for a Bessel beam, which was three times higher than the efficiency of conversion of the initial laser beam. A theoretical model was based on representation of the field of the second harmonic as a superposition of Bessel beams, which provided a correct description of the observed spatial and energy characteristics of the second harmonic. (nonlinear optical phenomena and devices)
CSIR Research Space (South Africa)
Milione, G
2015-02-01
Full Text Available be simply understood via geometric optics [3]. When a portion of a Bessel beam is obstructed in one plane, the unobstructed conical rays interfere in its shadow region in another plane, as shown in Fig. 1(e). Due to this property, Bessel beams have been... extensively studied and have been used for a number of applications; for comprehensive reviews see [4–7]. For example, when using a Bessel beam for optical trapping, it is possible to simultaneously trap multiple particles in well separated planes [8...
Photoacoustic transformation of Bessel light beams in magnetoactive superlattices
Energy Technology Data Exchange (ETDEWEB)
Mityurich, G. S., E-mail: George-mityurich@mail.ru [Belarusian Trade and Economics University of Consumer Cooperatives (Belarus); Chernenok, E. V.; Sviridova, V. V.; Serdyukov, A. N. [Gomel State University (Belarus)
2015-03-15
Photoacoustic transformation of the TE mode of a Bessel light beam (BLB) has been studied for piezoelectric detection in short-period superlattices formed by magnetoactive crystals of bismuth germanate (Bi{sub 12}GeO{sub 20}) and bismuth silicate (Bi{sub 12}SiO{sub 20}) types. It is shown that the resulting signal amplitude can be controlled using optical schemes of BLB formation with a tunable cone angle. A resonant increase in the signal amplitude has been found in the megahertz range of modulation frequencies and its dependences on the BLB modulation frequency, geometric sizes of the two-layer structure and piezoelectric transducer, radial coordinate of the polarization BLB mode, and dissipative superlattice parameters are analyzed.
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.
Tsai, Ko-Fan; Chu, Shu-Chun
2018-03-01
This study proposes a complete and unified method for selective excitation of any specified nearly nondiffracting Helmholtz-Gauss (HzG) beam in end-pumped solid-state digital lasers. Four types of the HzG beams: cosine-Gauss beams, Bessel-Gauss beams, Mathieu-Gauss beams, and, in particular, parabolic-Gauss beams are successfully demonstrated to be generated with the proposed methods. To the best of the authors’ knowledge, parabolic-Gauss beams have not yet been directly generated from any kind of laser system. The numerical results of this study show that one can successfully achieve any lasing HzG beams directly from the solid-state digital lasers with only added control of the laser gain transverse position provided by off-axis end pumping. This study also presents a practical digital laser set-up for easily manipulating off-axis pumping in order to achieve the control of the laser gain transverse gain position in digital lasers. The reported results in this study provide advancement of digital lasers in dynamically generating nondiffracting beams. The control of the digital laser cavity gain position creates the possibility of achieving real-time selection of more laser modes in digital lasers, and it is worth further investigation in the future.
Theory of third-harmonic generation using Bessel beams, and self-phase-matching
International Nuclear Information System (INIS)
Tewari, S.P.; Huang, H.; Boyd, R.W.
1996-01-01
Taking Bessel beams (J 0 beam) as a representation of a conical beam, and a slowly varying envelope approximation (SVEA) we obtain the results for the theory of third-harmonic generation from an atomic medium. We demonstrate how the phenomenon of self-phase-matching is contained in the transverse-phase-matching integral of the theory. A method to calculate the transverse-phase-matching integral containing four Bessel functions is described which avoids the computer calculations of the Bessel functions. In order to consolidate the SVEA result an alternate method is used to obtain the exact result for the third-harmonic generation. The conditions are identified in which the exact result goes over to the result of the SVEA. The theory for multiple Bessel beams is also discussed which has been shown to be the source of the wide width of the efficiency curve of the third-harmonic generation observed in experiments. copyright 1996 The American Physical Society
Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio
Gong, Zhixiong; Li, Wei; Mitri, Farid G.; Chai, Yingbin; Zhao, Yao
2016-11-01
In this paper, the T-matrix (null-field) method is applied to investigate the acoustic scattering by a large-aspect-ratio rigid spheroid immersed in a non-viscous fluid under the illumination of an unbounded zeroth-order Bessel beam with arbitrary orientation. Based on the proposed method, a MATLAB software package is constructed accordingly, and then verified and validated to compute the acoustic scattering by a rigid oblate or prolate spheroid in the Bessel beam. Several numerical examples are carried out to investigate the novel phenomenon of acoustic scattering by spheroids in Bessel beams with arbitrary incidence, with particular emphasis on the aspect ratio (i.e. the ratio of the polar radius over the equatorial radius of the spheroid), the half-cone angle of Bessel beam, the dimensionless frequency, as well as the angle of incidence. The quasi-periodic oscillations are observed in the plots of the far-field backscattering form function modulus versus the dimensionless frequency, owing to the interference between the specular reflection and the Franz wave circumnavigating the spheroid in the surrounding fluid. Furthermore, the 3D far-field scattering directivity patterns at end-on incidence and 2D polar plots at arbitrary angles of incidence are exhibited, which could provide new insights into the physical mechanisms of Bessel beam scattering by flat or elongated spheroid. This research work may provide an impetus for the application of acoustic Bessel beam in engineering practices.
Luo, Zhi; Yin, Kai; Dong, Xinran; Duan, Ji’an
2018-05-01
A numerical algorithm, modelling the transformation from a Gaussian beam to a Bessel beam, is presented for the purpose to study the optimal condition for employing an axicon-generated Bessel beam to fabricate cylindrical microlens arrays (CMLAs). By applying the numerical algorithm to simulate the spatial intensity distribution behind the axicon under different defects of a rotund-apex and different diameter ratios of an incident beam to the axicon, we find that the diffraction effects formed by the axicon edge can be almost eliminated when the diameter ratio is less than 1:2, but the spatial intensity distribution is disturbed dramatically even a few tens of microns deviation of the apex, especially for the front part of the axicon-generated Bessel beam. Fortunately, the lateral intensity profile in the rear part still maintains a desirable Bessel curve. Therefore, the rear part of the Bessel area and the less than 1:2 diameter ratio are the optimal choice for employing an axicon-generated Bessel beam to implement surface microstructures fabrication. Furthermore, by applying the optimal conditions to direct writing microstructures on fused silica with a femtosecond (fs) laser, a large area close-packed CMLA is fabricated. The CMLA presents high quality and uniformity and its optical performance is also demonstrated.
Electromagnetic scattering by a uniaxial anisotropic sphere located in an off-axis Bessel beam.
Qu, Tan; Wu, Zhen-Sen; Shang, Qing-Chao; Li, Zheng-Jun; Bai, Lu
2013-08-01
Electromagnetic scattering of a zero-order Bessel beam by an anisotropic spherical particle in the off-axis configuration is investigated. Based on the spherical vector wave functions, the expansion expression of the zero-order Bessel beam is derived, and its convergence is numerically discussed in detail. Utilizing the tangential continuity of the electromagnetic fields, the expressions of scattering coefficients are given. The effects of the conical angle of the wave vector components of the zero-order Bessel beam, the ratio of the radius of the sphere to the central spot radius of the zero-order Bessel beam, the shift of the beam waist center position along both the x and y axes, the permittivity and permeability tensor elements, and the loss of the sphere on the radar cross section (RCS) are numerically analyzed. It is revealed that the maximum RCS appears in the conical direction or neighboring direction when the sphere is illuminated by a zero-order Bessel beam. Furthermore, the RCS will decrease and the symmetry is broken with the shift of the beam waist center.
Extension of filament propagation in water with Bessel-Gaussian beams
Energy Technology Data Exchange (ETDEWEB)
Kaya, G.; Sayrac, M.; Boran, Y.; Kolomenskii, A. A. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Kaya, N.; Schuessler, H. A. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Science and Petroleum, Texas A& M University at Qatar, Doha 23874 (Qatar); Strohaber, J. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Department of Physics, Florida A& M University, Tallahassee, Florida 32307 (United States); Amani, M. [Science and Petroleum, Texas A& M University at Qatar, Doha 23874 (Qatar)
2016-03-15
We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.
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.
Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model
Wang, Jia Jie; Han, Yi Ping; Chang, Jiao Yong; Chen, Zhu Yang
2018-02-01
Within the framework of generalized Lorenz-Mie theory (GLMT), an eccentrically stratified dielectric sphere model illuminated by an arbitrarily incident Bessel beam is applied to investigate the scattering characteristics of a single nucleated biological cell. The Bessel beam propagating in an arbitrary direction is expanded in terms of vector spherical wave functions (VSWFs), where the beam shape coefficients (BSCs) are calculated rigorously in a closed analytical form. The effects of the half-cone angle of Bessel beam, the location of the particle in the beam, the size ratio of nucleus to cell, and the location of the nucleus inside the cell on the scattering properties of a nucleated cell are analyzed. The results provide useful references for optical diagnostic and imaging of particle having nucleated structure.
Photorefractive Axicon: Study of Light-induced Effect by Bessel Beam in Photorefractive Crystal
International Nuclear Information System (INIS)
Vieira, T A; Gesualdi, M R R; Zamboni-Rached, M; Muramatsu, M
2011-01-01
In this work, we present the theoretical and computational study of the original analysis of the light-induced effects by Bessel beams in photorefractive crystals. Modern applications of these beams as: metrological, alignment of optical systems, optical tweezers, non linear optics, optical communication, and others, becoming a very interesting substitute for a Gaussian beam when this is subject to diffraction and dispersion effects to large distance propagation. On the other hand, the photorefractive crystals are very important materials for applications in non-linear optics, holographic storage, interferometry and optical information processing. We perform an analysis of the index refraction modulation generated by Bessel beam in photorefractive medium discussing the possibility this optical material to control and generation of Bessel beam properties.
Analytical study on the self-healing property of Bessel beam
Chu, X.
2012-10-01
With the help of Babinet principle, an analytical expression for the self-healing of Bessel beam is derived by using the Gaussian absorption function to describe the obstacle. Based on the analytical expression, the self-healing properties of Bessel beam are studied. It shows that Bessel beam has the ability to reconstruct its beam shape disturbed by an obstacle. However, during the self-healing process, not only the intensity of the beam behind the obstacle but also the other part will be affected by the obstruction. Meanwhile, the highlight spot, which intensity is larger than that without the obstacle will appear, and the size and strength of the highlight spot is determined by the size of the obstacle. From the change of Poynting vector and Babinet principle, the physical interpretations for the self-healing ability, the effects of the obstruction on the other part and the appearance of highlight spot are given.
Optical pulling force on a magneto-dielectric Rayleigh sphere in Bessel tractor polarized beams
International Nuclear Information System (INIS)
Mitri, F.G.; Li, R.X.; Yang, R.P.; Guo, L.X.; Ding, C.Y.
2016-01-01
The optical radiation force induced by Bessel (vortex) beams on a magneto-dielectric subwavelength sphere is investigated with particular emphasis on the beam polarization and order l (or topological charge). The analysis is focused on identifying the regions and some of the conditions to achieve retrograde motion of the sphere centered on the axis of wave propagation of the incident beam, or shifted off-axially. Exact non-paraxial analytical solutions are established, and computations for linear, circular, radial, azimuthal and mixed polarizations of the individual plane wave components forming the Bessel (vortex) beams by means of the angular spectrum decomposition method (ASDM) illustrate the theory with particular emphasis on the tractor (i.e. reversal) behavior of the force. This effect results in the pulling of the magneto-dielectric sphere against the forward linear momentum density flux associated with the incoming waves. Should some conditions related to the choice of the beam parameters as well as the permittivity and permeability of the sphere be met, the optical force vanishes and reverses sign. Moreover, the beam polarization is shown to affect differently the axial negative pulling force for either the zeroth- or the first-order Bessel beam. When the sphere is centered on the beam′s axis, the axial force component is always negative for the zeroth-order Bessel beam except for the radial and azimuthal polarization configurations. Nonetheless, for the first-order Bessel beam, the axial force is negative for the radial polarization case only. Additional tractor beam effects arise when the sphere departs from the center of the beam. It is also demonstrated that the tractor beam effect arises from the force component originating from the cross-interaction between the electric and magnetic dipoles. Potential applications are in particle manipulation, optical levitation, tractor beam tweezers, and other emergent technologies using polarized Bessel beams on
Orbital angular momentum of a high-order Bessel light beam
International Nuclear Information System (INIS)
Volke-Sepulveda, K; Garces-Chavez, V; Chavez-Cerda, S; Arlt, J; Dholakia, K
2002-01-01
The orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment. This allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams. Furthermore, we demonstrate experimentally the mechanical transfer of orbital angular momentum to trapped particles in optical tweezers using a high-order Bessel beam. We set transparent particles of known dimensions into rotation, where the sense of rotation can be reversed by changing the sign of the singularity. Quantitative results are obtained for rotation rates. This paper's animations are available from the Multimedia Enhancements page
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.
Nonparaxial propagation of Lorentz-Gauss beams in uniaxial crystal orthogonal to the optical axis.
Wang, Xun; Liu, Zhirong; Zhao, Daomu
2014-04-01
Analytical expressions for the three components of nonparaxial propagation of a polarized Lorentz-Gauss beam in uniaxial crystal orthogonal to the optical axis are derived and used to investigate its propagation properties in uniaxial crystal. The influences of the initial beam parameters and the parameters of the uniaxial crystal on the evolution of the beam-intensity distribution in the uniaxial crystal are examined in detail. Results show that the statistical properties of a nonparaxial Lorentz-Gauss beam in a uniaxial crystal orthogonal to the optical axis are closely determined by the initial beam's parameters and the parameters of the crystal: the beam waist sizes-w(0), w(0x), and w(0y)-not only affect the size and shape of the beam profile in uniaxial crystal but also determine the nonparaxial effect of a Lorentz-Gauss beam; the beam profile of a Lorentz-Gauss beam in uniaxial crystal is elongated in the x or y direction, which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index; with increasing deviation of the ratio from unity, the extension of the beam profile augments. The results indicate that uniaxial crystal provides an effective and convenient method for modulating the Lorentz-Gauss beams. Our results may be valuable in some fields, such as optical trapping and nonlinear optics, where a light beam with a special profile and polarization is required.
Propagation of partially coherent Lorentz-Gauss vortex beam through oceanic turbulence.
Liu, Dajun; Yin, Hongming; Wang, Guiqiu; Wang, Yaochuan
2017-11-01
The partially coherent Lorentz-Gauss vortex beam generated by a Schell-model source has been introduced. Based on the extended Huygens-Fresnel principle, the cross-spectral density function of a partially coherent Lorentz-Gauss vortex beam propagating in oceanic turbulence is derived. The influences of coherence length, topological charge M, and oceanic turbulence on the spreading properties and position of the coherence vortex for a partially coherent Lorentz-Gauss vortex beam are analyzed in detail. The results show that a partially coherent Lorentz-Gauss vortex beam propagating in stronger oceanic turbulence will evolve into a Gaussian-like beam more rapidly as the propagation distance increases, and the number of coherent vortices will change.
Self-healing of Bessel-like beams with longitudinally dependent cone angles
CSIR Research Space (South Africa)
Litvin, I
2015-09-01
Full Text Available non-diffracting propagation region. Here we show that such beams can self-heal. Moreover, in contrast to Bessel beams where the self-healing distance is constant, here the self-healing distance is dependent on where the obstruction is placed...
International Nuclear Information System (INIS)
Bouferguene, Ahmed; Safouhi, Hassan
2006-01-01
In a previous work (Bouferguene 2005 J. Phys. A: Math. Gen. 38 3923), we have shown that in the framework of the Gaussian integral transform, multi-centre integrals over Slater type functions can be evaluated to an acceptable accuracy using a tailored Gauss quadrature in which the weight function has the form W(σ, τ; z) = z ν exp(-σz - τ/z). To be considered a solution worth implementing within a software for routine use in ab initio molecular simulations, the method must also prove to be at least as efficient as those methods previously published in the literature. Two major results are provided in this paper. Firstly, an improvement of the procedure used to generate the roots and weights of the Gauss-Bessel quadrature is proposed. Secondly, a computational cost analysis of the present method and the SD-bar (Safouhi 2001 J. Phys. A: Math. Gen. 34 2801) based approach are compared, hence proving the equivalence of the two from a complexity point of view
Study of graphitic microstructure formation in diamond bulk by pulsed Bessel beam laser writing
Kumar, S.; Sotillo, B.; Chiappini, A.; Ramponi, R.; Di Trapani, P.; Eaton, S. M.; Jedrkiewicz, O.
2017-11-01
The advantages of using Bessel beams for the generation of graphitic structures in diamond bulk are presented. We show that by irradiating the sample with a pulsed Bessel beam whose non-diffracting zone is of the same order of the sample thickness, it is possible to produce without any sample translation straight graphitic through-microstructures, whose size depends on the input pulse energy. The microstructure growth is investigated as a function of the number of irradiating pulses, and the femtosecond and picosecond regimes are contrasted.
Limitations to laser machining of silicon using femtosecond micro-Bessel beams in the infrared
International Nuclear Information System (INIS)
Grojo, David; Mouskeftaras, Alexandros; Delaporte, Philippe; Lei, Shuting
2015-01-01
We produce and characterize high-angle femtosecond Bessel beams at 1300-nm wavelength leading to nonlinearly ionized plasma micro-channels in both glass and silicon. With microjoule pulse energy, we demonstrate controlled through-modifications in 150-μm glass substrates. In silicon, strong two-photon absorption leads to larger damages at the front surface but also a clamping of the intensity inside the bulk at a level of ≈4 × 10 11 W cm −2 which is below the threshold for volume and rear surface modification. We show that the intensity clamping is associated with a strong degradation of the Bessel-like profile. The observations highlight that the inherent limitation to ultrafast energy deposition inside semiconductors with Gaussian focusing [Mouskeftaras et al., Appl. Phys. Lett. 105, 191103 (2014)] applies also for high-angle Bessel beams
Spatial characterization of Bessel-like beams for strong-field physics.
Summers, Adam M; Yu, Xiaoming; Wang, Xinya; Raoul, Maxime; Nelson, Josh; Todd, Daniel; Zigo, Stefan; Lei, Shuting; Trallero-Herrero, Carlos A
2017-02-06
We present a compact, simple design for the generation and tuning of both the spot size and effective focal length of Bessel-like beams. In particular, this setup provides an important tool for the use of Bessel-like beams with high-power, femtosecond laser systems. Using a shallow angle axicon in conjunction with a spherical lens, we show that it is possible to focus Bessel-like modes to comparable focal spot sizes to sharp axicons while maintaining a long effective focal length. The resulting focal profiles are characterized in detail using an accurate high dynamic range imaging technique. Quantitatively, we introduce a metric (R0.8) which defines the spot-size containing 80% of the total energy. Our setup overcomes the typical compromise between long working distances and small spot sizes. This is particularly relevant for strong-field physics where most experiments must operate in vacuum.
Enhancement of photorefractive two wave mixing gain with a Bessel pump beam
International Nuclear Information System (INIS)
Biswas, Dhruba J.; Padma Nilaya, J.; Danailov, Miltcho, B.
2001-07-01
The performance of a photo-refractive amplifier has been shown to greatly improve when a diffraction free beam is employed as the pump source. It has been established experimentally that this behaviour owes primarily to the ability of this beam to propagate in the photo-refractive crystal will less fanning. A qualitative explanation for the reduction of fanning with Bessel beam is offered. (author)
High-power Bessel beams with orbital angular momentum in the terahertz range
Choporova, Yu. Yu.; Knyazev, B. A.; Kulipanov, G. N.; Pavelyev, V. S.; Scheglov, M. A.; Vinokurov, N. A.; Volodkin, B. O.; Zhabin, V. N.
2017-08-01
In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of ±1 and ±2 formed by silicon binary phase axicons (BPAs) with spiral zone structures. The axicons were illuminated with the Novosibirsk free electron laser radiation (a continuous stream of 100-ps pulses at f =5.6 MHz). The cw power of the beams produced reached 30 W and can by doubled via antireflection coating of the axicons. The intensity distribution in the beam cross sections was in good agreement with the Bessel functions and was kept constant within a distance of about L /r ≈190 and 100, where the first ring radii of the beams r were 0.9 and 1.5 mm for the Bessel beams of the first and second orders, respectively. Although the characteristics of the beams (Bessel cross section, "diffraction-free" propagation, self-recovery after passing obstacles, and randomly inhomogeneous media) corresponded to the properties of ideal Bessel beams, their spatial Fourier spectrum (the image in the focal plane of the lens) was, instead of an ideal ring, intertwined segments of arcs with phases shifted by π , the number of which was equal to the double value of the topological charge. This feature can be used, for example, in a demultiplexing unit of a free vortex-wave communication system or for identification of beam topological charge. We also revisited Young's double-slit diffraction and rotation of beams obstructed by a half-plane, previously applied to Laguerre-Gaussian beam characterization, in the case of the Bessel beams. The Young diffraction pattern demonstrated in this case a complicated intensity-phase distribution. It was shown that the Bessel beams formed by BPAs have two important advantages, which can be used in applications, in comparison with other methods of generation, e.g., a combination of an axicon lens with a spiral phase plate. Although the phase jumps of the axicons are designed for a determined wavelength (141 μ m in our case
Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone
Salem, Mohamed; Bagci, Hakan
2013-01-01
The electromagnetic field scattering of a vector Bessel beam in the presence of an infinite circular cone with an impedance boundary on its surface is considered. The impinging field is normal to the tip of the cone and is expanded in terms
Superpositions of higher-order bessel beams and nondiffracting speckle fields
CSIR Research Space (South Africa)
Dudley, Angela L
2009-08-01
Full Text Available speckle fields. The paper reports on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light...
Shape invariant higher-order Bessel-like beams carrying orbital angular momentum
CSIR Research Space (South Africa)
Ismail, Y
2012-09-01
Full Text Available -1 Journal of Optics September 2012/ Vol. 14 Shape invariant higher-order Bessel-like beams carrying orbital angular momentum Y Ismail1,2, N Khilo3, V Belyi3 and A Forbes1,2 1 School of Physics, University of KwaZulu-Natal, Private Bag X54001...
Superpositions of higher-order bessel beams and nondiffracting speckle fields - (SAIP 2009)
CSIR Research Space (South Africa)
Dudley, Angela L
2009-07-01
Full Text Available speckle fields. The paper reports on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light...
Experimental generation and application of the superposition of higher-order Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2009-07-01
Full Text Available Academy of Sciences of Belarus 4 School of Physics, University of Stellenbosch Presented at the 2009 South African Institute of Physics Annual Conference University of KwaZulu-Natal Durban, South Africa 6-10 July 2009 Page 2 © CSIR 2008... www.csir.co.za Generation of Bessel Fields: • METHOD 1: Ring Slit Aperture • METHOD 2: Axicon Adaptation of method 1 to produce superpositions of higher-order Bessel beams: J. Durnin, J.J. Miceli and J.H. Eberly, Phys. Rev. Lett. 58 1499...
Turquet, Léo; Kakko, Joona-Pekko; Karvonen, Lasse; Jiang, Hua; Kauppinen, Esko; Lipsanen, Harri; Kauranen, Martti; Bautista, Godofredo
2017-08-01
Non-diffractive Bessel beams are receiving significant interest in optical microscopy due to their remarkably large depth of field. For example, studies have shown the superiority of Bessel beams over Gaussian beams for volumetric imaging of three-dimensionally thick or extended samples. However, the vectorial aspects of the focal fields of Bessel beams are generally obscured when traditional methods are used to characterize their three-dimensional point-spread function in space, which contains contributions from all optical field components. Here, we show experimentally the three-dimensional spatial distribution and enhanced depth of field of the longitudinal electric field components of a focused linearly-polarized Bessel beam. This is done through second-harmonic generation from well-defined vertically-aligned gallium-arsenide nanowires, whose second-order response is primarily driven by the longitudinal fields at the beam focus.
International Nuclear Information System (INIS)
Li, Renxian; Ren, Kuan Fang; Han, Xiang'e; Wu, Zhensen; Guo, Lixin; Gong, Shuxi
2013-01-01
Debye series expansion (DSE) is employed to the analysis of radiation pressure force (RPF) exerted on biological cells induced by high-order Bessel beams (BB). The beam shape coefficients (BSCs) for high-order Bessel beams are calculated using analytical expressions obtained by the integral localized approximation (ILA). Different types of cells, including a real Chinese Hamster Ovary (CHO) cell and a lymphocyte which are respectively modeled by a coated and five-layered sphere, are considered. The RPF induced by high-order Bessel beams is compared with that by Gaussian beams and zeroth-order Bessel beams, and the effect of different scattering processes on RPF is studied. Numerical calculations show that high-order Bessel beams with zero central intensity can also transversely trap particle in the beam center, and some scattering processes can provide longitudinal pulling force. -- Highlights: ► BSCs for high-order Bessel beam (HOBB) is derived using ILA. ► DSE is employed to study the RPF induced by HOBB exerted on multilayered cells. ► RPF is decided by radius relative to the interval of peaks in intensity profile. ► HOBB can also transversely trap high-index particle in the vicinity of beam axis. ► RPF for some scattering processes can longitudinally pull particles back
Bessel beam transformation in c-cuts of uniaxial crystals by varying the source wavelength
Energy Technology Data Exchange (ETDEWEB)
Paranin, V. D. [Samara State Aerospace University, 34, Moskovskoe shosse, Samara, 443086 (Russian Federation)
2016-04-13
Transformation of Bessel beam of a zero order to Bessel beam of the second order in c-cut of CaCO{sub 3} crystal is experimentally investigated. Possibility of output beam control at changing of wavelength and using of a diffraction axicon is shown. Full transformation of beams at changing of wavelength Δλ=1.5 nanometers is received at initial wavelength λ=637.5 nanometers for a crystal of CaCO{sub 3} with 15 mm long and a diffraction axicon with period of 2 microns. The theoretical value of necessary wavelength changing is Δλ=1.7 nanometers that is according with experimental results.
Radiophotoluminescence of alkali-halide crystals stimulated by Bessel laser beam
Lyakh, V V; Kochubey, D I; Gyunsburg, K E; Zvezdova, N P; Kochubey, D I; Sedova, Y G; Koronkevich, V P; Poleschuk, A G; Sedukhin, A G
2000-01-01
A new approach to realization of optimal high-resolution reading of deep X-ray images in X-ray-sensitive materials on the base of alkali-halide crystals modified with admixtures has been suggested and investigated experimentally. A possibility to use diffraction axicons with ring aperture for forming micron bright light beams (spatially truncated Bessel beams) which can efficiently de-excite radiophotoluminescence centers lying at large depth in crystals is also presented.
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.
Liu, Dajun; Wang, Guiqiu; Wang, Yaochuan
2018-01-01
Based on the Huygens-Fresnel integral and the relationship of Lorentz distribution and Hermite-Gauss function, the average intensity and coherence properties of a partially coherent Lorentz-Gauss beam propagating through oceanic turbulence have been investigated by using numerical examples. The influences of beam parameters and oceanic turbulence on the propagation properties are also discussed in details. It is shown that the partially coherent Lorentz-Gauss beam with smaller coherence length will spread faster in oceanic turbulence, and the stronger oceanic turbulence will accelerate the spreading of partially coherent Lorentz-Gauss beam in oceanic turbulence.
Expansion of a zero-order Bessel beam in spheroidal coordinates by generalized Lorenz–Mie theory
International Nuclear Information System (INIS)
Han, L.; Han, Y.P.; Cui, Z.W.; Wang, J.J.
2014-01-01
An analytic solution to the scattering of the zero-order Bessel beam by a spheroidal particle is constructed on the basis of the generalized Lorenz–Mie theory (GLMT). The spheroidal beam shape coefficients (BSCs) of the zero-order Bessel beam are directly expressed in spheroidal coordinates and computed conveniently using an intrinsic method. Utilizing the tangential continuity of the electromagnetic fields, the expression coefficients of scattered and internal fields are determined. Numerical results concerning scattered field in the far zone are displayed for various parameters of the incident electromagnetic beam and of the scatter. These results are expected to provide useful insights into the scattering of a Bessel beam by spheroidal particles and particle manipulation applications using Bessel beams. - Highlights: • The scattering of zero-order Bessel beam by dielectric spheroid is investigated. • The analytic solution is constructed within the framework of the GLMT. • The spheroidal beam shape coefficients of the zero-order Bessel beam are computed by use an intrinsic method. • Numerical results concerning scattered field are displayed for various parameters
Quasi-ideal dynamics of vortex solitons embedded in flattop nonlinear Bessel beams.
Porras, Miguel A; Ramos, Francisco
2017-09-01
The applications of vortex solitons are severely limited by the diffraction and self-defocusing spreading of the background beam where they are nested. Nonlinear Bessel beams in self-defocusing media are nondiffracting, flattop beams where the nested vortex solitons can survive for propagation distances that are one order of magnitude larger than in the Gaussian or super-Gaussian beams. The dynamics of the vortex solitons is studied numerically and found to approach that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.
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
2016-07-01
Second-harmonic generation (SHG) is the most specific label-free indicator of collagen accumulation in widespread pathologies such as fibrosis, and SHG-based measurements hold important potential for biomedical analyses. However, efficient collagen SHG scoring in histological slides is hampered by the limited depth-of-field of usual nonlinear microscopes relying on focused Gaussian beam excitation. In this work we analyze theoretically and experimentally the use of Bessel beam excitation to address this issue. Focused Bessel beams can provide an axially extended excitation volume for nonlinear microscopy while preserving lateral resolution. We show that shaping the focal volume has consequences on signal level and scattering directionality in the case of coherent signals (such as SHG) which significantly differ from the case of incoherent signals (two-photon excited fluorescence, 2PEF). We demonstrate extended-depth SHG-2PEF imaging of fibrotic mouse kidney histological slides. Finally, we show that Bessel beam excitation combined with spatial filtering of the harmonic light in wave vector space can be used to probe collagen accumulation more efficiently than the usual Gaussian excitation scheme. These results open the way to SHG-based histological diagnoses.
International Nuclear Information System (INIS)
Ryu, C; Henderson, K C; Boshier, M G
2014-01-01
Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because they propagate ‘diffraction-free’ and because they can carry orbital angular momentum. Here we report the creation of a Bessel beam of de Broglie matter waves. The Bessel beam is produced by the free evolution of a thin toroidal atomic Bose–Einstein condensate (BEC) which has been set into rotational motion. By attempting to stir it at different rotation rates, we show that the toroidal BEC can only be made to rotate at discrete, equally spaced frequencies, demonstrating that circulation is quantized in atomic BECs. The method used here can be viewed as a form of wavefunction engineering which might be developed to implement cold atom matter wave holography. (paper)
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 an...
Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel
International Nuclear Information System (INIS)
Tiwari, S K; Ram, S P; Jayabalan, J; Mishra, S R
2010-01-01
By scanning a charge-coupled device (CCD) camera transverse to the beam axis and observing the variation in counts on a marked pixel, we demonstrate that we can measure a laser beam spot size smaller than the size of the CCD-pixel. We find this method particularly attractive for measuring the size of central spot of a Bessel beam, for which the established scanning knife-edge method does not work appropriately because of the large contribution of the rings surrounding the central spot to the signal
Acoustics of finite asymmetric exotic beams: Examples of Airy and fractional Bessel beams
Mitri, F. G.
2017-12-01
The purpose of this investigation is to examine the properties of finite asymmetric exotic scalar (acoustic) beams with unusual properties using the angular spectrum decomposition in plane waves. Such beams possess intrinsic uncommon characteristics that make them attractive from the standpoint of particle manipulation, handling and rotation, and possibly other applications in particle clearing and separation. Assuming a specific apodization function at the acoustic source, the angular spectrum function is calculated and used to synthesize the radiated pressure field (i.e., excluding evanescent waves that decay away from the source) in the forward direction of wave motion (i.e., away from the source). Moreover, a generalized hybrid method combining the angular spectrum approach with the multipole expansion formalism in spherical coordinates is developed, which is applicable to any finite beam of arbitrary wavefront. The improved approach allows adequate computation of the resonance scattering, radiation force, and spin torque components on an object of arbitrary shape, located on or off the axis of the incident beam in space. Considering the illustrative example of a viscous fluid sphere submerged in a non-viscous liquid and illuminated by finite asymmetric beams such as the Airy and the Bessel vortex beam with fractional order, numerical computations for the scattering, radiation force, and torque components are performed with an emphasis on the distance from the source, the arbitrary location of the particle ,and the asymmetric nature of the incident field. Moreover, beamforming calculations are presented with supplementary animations for the pressure field distribution in space, with an emphasis on the intrinsic properties of the selected beams. The numerical predictions illustrate the scattering, radiation force, and spin torque properties depending on the beam parameters and the distance separating the sphere from the source. This study provides a generalized
Bessel-like beams with z-dependent cone angles
CSIR Research Space (South Africa)
Belyi, VN
2009-08-01
Full Text Available beams (keeping the transverse profile at any distances). This new type of beams can be obtained in optical system composed of lens axicon doublet and conical lens. An experimental set-up for producing such beams is realized. It is shown that depending...
International Nuclear Information System (INIS)
Paranin, V D; Karpeev, S V; Khonina, S N; Tukmakov, K N
2016-01-01
Transformation of zero-order Bessel beams into a second-order vortex beam in the process of propagation in a c-cut of lithium niobate LiNbO 3 crystal has been investigated experimentally. The possibility of controlling beam transformation by means of changing the curve radius of the illuminating beam is shown. The possibility of Bessel beam transforming by compact devices on the basis of thin c-cuts of uniaxial crystals with a diffraction mask formed on their surface is proved. (paper)
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.
Rapid volumetric imaging with Bessel-Beam three-photon microscopy
Chen, Bingying; Huang, Xiaoshuai; Gou, Dongzhou; Zeng, Jianzhi; Chen, Guoqing; Pang, Meijun; Hu, Yanhui; Zhao, Zhe; Zhang, Yunfeng; Zhou, Zhuan; Wu, Haitao; Cheng, Heping; Zhang, Zhigang; Xu, Chris; Li, Yulong; Chen, Liangyi; Wang, Aimin
2018-01-01
Owing to its tissue-penetration ability, multi-photon fluorescence microscopy allows for the high-resolution, non-invasive imaging of deep tissue in vivo; the recently developed three-photon microscopy (3PM) has extended the depth of high-resolution, non-invasive functional imaging of mouse brains to beyond 1.0 mm. However, the low repetition rate of femtosecond lasers that are normally used in 3PM limits the temporal resolution of point-scanning three-photon microscopy. To increase the volumetric imaging speed of 3PM, we propose a combination of an axially elongated needle-like Bessel-beam with three-photon excitation (3PE) to image biological samples with an extended depth of focus. We demonstrate the higher signal-to-background ratio (SBR) of the Bessel-beam 3PM compared to the two-photon version both theoretically and experimentally. Finally, we perform simultaneous calcium imaging of brain regions at different axial locations in live fruit flies and rapid volumetric imaging of neuronal structures in live mouse brains. These results highlight the unique advantage of conducting rapid volumetric imaging with a high SBR in the deep brain in vivo using scanning Bessel-3PM.
International Nuclear Information System (INIS)
Mitri, F.G.
2014-01-01
The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to an equilibrium position depending on the chosen size parameter ka (where k is the wave-number and a the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study. -- Highlights: •The axial and transverse forces on a fluid sphere in acoustical Bessel beams tweezers are evaluated. •The attraction or repulsion to an equilibrium position in the standing wave field is examined. •Potential applications are in particle manipulation using standing waves
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.
Conical refraction and formation of multiring focal image with Laguerre-Gauss light beams.
Peet, Viktor
2011-08-01
For a light beam focused through a biaxial crystal along one of its optical axes, the effect of internal conical refraction in the crystal leads to the formation in the focal image plane of two bright rings separated by a dark ring. It is shown that, with circularly polarized Laguerre-Gauss LG(0)(ℓ) beams entering the crystal, this classical double-ring pattern is transformed into a multiring one consisting of ℓ+2 bright rings. © 2011 Optical Society of America
Transmission of a Bessel beam through a circular aperture in an impedance screen
International Nuclear Information System (INIS)
Umul, Yusuf Ziya
2014-01-01
The scattering effect of a circular aperture, located in an impedance plane, on a Bessel beam is investigated by decomposing the scattered wave into two subcomponents, namely the geometrical optics and diffracted fields. The diffracted waves are investigated with the aid of the geometrical theory of diffraction. The detour parameter is evaluated and the existence zones of the geometrical optics fields are determined. The various aspects of the reflected and transmitted scattered waves, including the self healing of the beam, are studied numerically. (letter)
Fahrbach, Florian O; Rohrbach, Alexander
2012-01-17
Laser beams that can self-reconstruct their initial beam profile even in the presence of massive phase perturbations are able to propagate deeper into inhomogeneous media. This ability has crucial advantages for light sheet-based microscopy in thick media, such as cell clusters, embryos, skin or brain tissue or plants, as well as scattering synthetic materials. A ring system around the central intensity maximum of a Bessel beam enables its self-reconstruction, but at the same time illuminates out-of-focus regions and deteriorates image contrast. Here we present a detection method that minimizes the negative effect of the ring system. The beam's propagation stability along one straight line enables the use of a confocal line principle, resulting in a significant increase in image contrast. The axial resolution could be improved by nearly 100% relative to the standard light-sheet techniques using scanned Gaussian beams, while demonstrating self-reconstruction also for high propagation depths.
Generation of an elliptic hollow beam using Mathieu and Bessel functions.
Chakraborty, Rijuparna; Ghosh, Ajay
2006-09-01
A new (to our knowledge) technique for the generation of a propagation-invariant elliptic hollow beam is reported. It avoids the use of the radial Mathieu function and hence is mathematically simpler. Bessel functions with their arguments having elliptic locus are used to generate the mask, which is then recorded using holographic technique. To generate such an elliptic beam, both the angular Mathieu function, i.e., elliptic vortex term, and the expression for the circular vortex are used separately. The resultant mask is illuminated with a plane beam, and the proper filtering of its Fourier transform generates the expected elliptic beam. Results with both vortex terms are satisfactory. It has been observed that even for higher ellipticity the vortices do not separate.
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.
Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers
International Nuclear Information System (INIS)
Mitri, F.G.
2008-01-01
Starting from the exact acoustic scattering from a sphere immersed in an ideal fluid and centered along the propagation axis of a standing or quasi-standing zero-order Bessel beam, explicit partial-wave representations for the radiation force are derived. A standing or a quasi-standing acoustic field is the result of propagating two equal or unequal amplitude zero-order Bessel beams, respectively, along the same axis but in opposite sense. The Bessel beam is characterized by the half-cone angle β of its plane wave components, such that β = 0 represents a plane wave. It is assumed here that the half-cone angle β for each of the counter-propagating acoustic Bessel beams is equal. Fluid, elastic and viscoelastic spheres immersed in water are treated as examples. Results indicate the capability of manipulating spherical targets based on their mechanical and acoustical properties. This condition provides an impetus for further designing acoustic tweezers operating with standing or quasi-standing Bessel acoustic waves. Potential applications include particle manipulation in micro-fluidic lab-on-chips as well as in reduced gravity environments
Shen, Yizhu; Yang, Jiawei; Meng, Hongfu; Dou, Wenbin; Hu, Sanming
2018-04-01
Metasurfaces, orbital angular momenta (OAM), and non-diffractive Bessel beams have been attracting worldwide research. Combining the benefits of these three promising techniques, this paper proposes a metasurface-based reflective-type approach to generate a first-order Bessel beam carrying OAM. To validate this approach, a millimeter-wave metasurface is analyzed, designed, fabricated, and measured. Experimental results agree well with simulation. Moreover, this reflective-type metasurface, generating a Bessel beam with OAM, is inherently integrated with a planar feeding source in the same single-layer printed circuit board. Therefore, the proposed design features low profile, low cost, easy integration with front-end active circuits, and no alignment error between the feeding source and the metasurface.
Terahertz plasmonic Bessel beamformer
International Nuclear Information System (INIS)
Monnai, Yasuaki; Shinoda, Hiroyuki; Jahn, David; Koch, Martin; Withayachumnankul, Withawat
2015-01-01
We experimentally demonstrate terahertz Bessel beamforming based on the concept of plasmonics. The proposed planar structure is made of concentric metallic grooves with a subwavelength spacing that couple to a point source to create tightly confined surface waves or spoof surface plasmon polaritons. Concentric scatterers periodically incorporated at a wavelength scale allow for launching the surface waves into free space to define a Bessel beam. The Bessel beam defined at 0.29 THz has been characterized through terahertz time-domain spectroscopy. This approach is capable of generating Bessel beams with planar structures as opposed to bulky axicon lenses and can be readily integrated with solid-state terahertz sources
Tang, Bin; Jiang, Chun; Zhu, Haibin
2012-08-01
Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.
Two-color above-threshold ionization of atoms and ions in XUV Bessel beams and intense laser light
Seipt, D.; Müller, R. A.; Surzhykov, A.; Fritzsche, S.
2016-11-01
The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultraviolet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target atoms with regard to the beam axis. In addition, analog to the circular dichroism in typical two-color ATI experiments with circularly polarized light, we define and discuss seven different dichroism signals for such vortex Bessel beams that arise from the various combinations of the orbital and spin angular momenta of the two light fields. For localized targets, it is found that these dichroism signals strongly depend on the size and position of the atoms relative to the beam. For macroscopically extended targets, in contrast, three of these dichroism signals tend to zero, while the other four just coincide with the standard circular dichroism, similar as for Bessel beams with a small opening angle. Detailed computations of the dichroism are performed and discussed for the 4 s valence-shell photoionization of Ca+ ions.
Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces
International Nuclear Information System (INIS)
David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth
2015-01-01
We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape
Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces
Energy Technology Data Exchange (ETDEWEB)
David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth, E-mail: rsignorell@ethz.ch [Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich (Switzerland)
2015-04-21
We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.
David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth
2015-04-21
We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.
Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces
David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth
2015-04-01
We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.
Stored polarized beams: MILES, LIMES, SMILE, sine-Bessels and SODOM2 too
International Nuclear Information System (INIS)
Mane, S.R.
2008-01-01
The fundamental theory underlying several computational algorithms for the spin dynamics of stored polarized beams is analyzed. Particular attention is paid to the consequences of the use of finite-dimensional matrices and/or Fourier series. The single resonance model with a pair of diametrically opposed nonorthogonal pointlike Siberian Snakes is analyzed in detail to clarify several points pertaining to the above algorithms, and more generally to the spin dynamics of stored polarized beams in rings with Snakes. New analytical results are also presented, e.g. for the spin tune shift in the nonorthogonal Snakes model, and the sine-Bessel functions for the orthogonal Snakes model. Many results are derived using multiple algorithms, which serves as a check on their mutual consistency
Wave-optics description of self-healing mechanism in Bessel beams.
Aiello, Andrea; Agarwal, Girish S
2014-12-15
Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work, we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.
CSIR Research Space (South Africa)
Schulze, C
2014-09-01
Full Text Available We present the measurement of the orbital angular momentum (OAM) density of Bessel beams and superpositions thereof by projection into a Laguerre–Gaussian basis. This projection is performed by an all-optical inner product measurement performed...
International Nuclear Information System (INIS)
Li, Z.J.; Wu, Z.S.; Qu, T.; Shang, Q.C.; Bai, L.
2016-01-01
Based on the generalized multiparticle Mie theory, multiple scattering of an aggregate of uniaxial anisotropic spheres illuminated by a zero-order Bessel beam (ZOBB) with arbitrary propagation direction is investigated. The particle size and configuration are arbitrary. The arbitrary incident Bessel beam is expanded in terms of spherical vector wave functions (SVWFs). Utilizing the vector addition theorem of SVWFs, interactive and total scattering coefficients are derived through the continuous boundary conditions on which the interaction of the particles is considered. The accuracy of the theory and codes are verified by comparing results with those obtained for arbitrary plane wave incidence by CST simulation, and for ZOBB incidence by a numerical method. The effects of angle of incidence, pseudo-polarization angle, half-conical angle, beam center position, and permittivity tensor elements on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres, such as a linear chain, a 4×4×4 cube-shaped array, and other periodical structures consisting of massive spheres, are numerically analyzed. Selected results on the properties of typical particles such as TiO 2 , SiO 2 , or other particle lattices are calculated. This investigation could provide an effective test for further research on the scattering characteristics of an aggregate of anisotropic spheres by a high-order Bessel vortex beam. The results have important application in optical tweezers and particle manipulation. - Highlights: • Scattering of Bessel beam by an aggregate of uniaxial anisotropic spheres is studied. • The zero-order Bessel beam propagates and polarizes along arbitrary direction. • The accuracy of expansion coefficients, the scattering theory and codes is verified. • Effects of various parameters on scattering properties are numerically discussed. • Scattering properties of several type of periodical array are numerically analyzed.
Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam
International Nuclear Information System (INIS)
Mitri, F.G.
2016-01-01
An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas. - Highlights: • Optical nondiffracting nonparaxial fractional Bessel vortex beam is considered. • Negative spin torque on an absorptive dielectric Rayleigh sphere is predicted numerically. • Negative spin torque occurs as the sphere departs from the center of the beam.
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.
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.
Kou, Na; Yu, Shixing; Li, Long
2017-01-01
A high-order Bessel vortex beam carrying orbital angular momentum (OAM) is generated by using multilayer amplitude-phase-modulated surfaces (APMSs) at 10 GHz. The APMS transmitarray is composed of four-layer conformal square-loop (FCSL) surfaces with both amplitude and phase modulation. The APMS can transform a quasi-spherical wave emitted from the feeding source into a pseudo non-diffractive high-order Bessel vortex beam with OAM. The APMS for a second-order Bessel beam carrying OAM in the n = 2 mode is designed, fabricated, and measured. Full-wave simulation and measurement results confirm that Bessel vortex beams with OAM can be effectively generated using the proposed APMS transmitarray.
International Nuclear Information System (INIS)
Niv, A.; Biener, G.; Kleiner, V.; Hasman, E.
2004-01-01
Full Text:Propagation-invariant scalar fields have been extensively studied both theoretically and experimentally, since they were proposed by Durnin et al. These fields were employed in applications such as optical tweezers and for transport and guiding of microspheres. Although there has recently been considerable theoretical interest in propagation-invariant vectorial beams, experimental studies of such beams have remained somewhat limited. One of the most interesting types of propagation-invariant vectorial beam is the linearly polarized axially symmetric beam (LPASB) [l]. Recently, we introduced and experimentally demonstrated propagation-invariant vectorial Bessel beams with linearly polarized axial symmetry based on quantized Pancharatnam-Berry phase optical elements (QPBOEs) [21 and an axicon. QP-BOEs utilize the geometric phase that accompanies space-variant polarization manipulations to achieve a desired phase modification [31. To test our approach we formed QPBOEs with different polarization orders as computer-generated space-variant sub wavelength gratings upon GaAs wafers for use with 10.6 micron laser radiation. The resultant beams were also transmitted through a polarizer that produced a unique propagation-invariant scalar beam. This beam has a propeller-shaped intensity pattern that can be rotated by simple rotation of the polarizer. We therefore have demonstrated the formation of a vectorial Bessel beam by using simple, lightweight thin elements and exploited that beam to perform a controlled rotation of a propeller-shaped intensity pattern that can be suitable for optical tweezers
Mitri, F G
2010-03-01
Acoustic scattering properties of ultrasound contrast agents are useful in extending existing or developing new techniques for biomedical imaging applications. A useful first step in this direction is to investigate the acoustic scattering of a new class of acoustic beams, known as helicoidal high-order Bessel beams, to improve the understanding of their scattering characteristics by an ultrasound contrast agent, which at present is very limited. The transverse acoustic scattering of a commercially available albuminoidal ultrasound contrast agent shell filled with air or a denser gas such as perfluoropropane and placed in a helicoidal Bessel beam of any order is examined numerically. The shell is assumed to possess an outer radius a=3.5 microns and a thickness of approximately 105 nm. Moduli of the total and resonance transverse acoustic scattering form functions are numerically evaluated in the bandwidth 0scattering of a helicoidal Bessel beam of order m1 so that the dynamics of contrast agents would be significantly altered. The main finding of the present theory is the suppression or enhancement for a particular resonance that may be used to advantage in imaging with ultrasound contrast agents for clinical applications. 2009 Elsevier B.V. All rights reserved.
Vectorial structures of linear-polarized Butterfly-Gauss vortex beams in the far zone
Cheng, Ke; Zhou, Yan; Lu, Gang; Yao, Na; Zhong, Xianqiong
2018-05-01
By introducing the Butterfly catastrophe to optics, the far-zone vectorial structures of Butterfly-Gauss beam with vortex and non-vortex are studied using the angular spectrum representation and stationary phase method. The influence of topological charge, linear-polarized angle, off-axis distance and scaling length on the far-zone vectorial structures, especially in the Poynting vector and angular momentum density of the corresponding beam is emphasized. The results show that the embedded optical vortex at source plane lead to special dark zones in the far zone, where the number of dark zone equals the absolute value of topological charge of optical vortex. Furthermore, the symmetry and direction of the special dark zones can be controlled by off-axis distance and scaling length, respectively. The linear-polarized angle adjusts only the Poynting vectors of TE and TM terms, but it does not affect those of whole beam. Finally, the vectorial expressions also indicate that the total angular momentum density is certainly zero owing to the far-zone stable structures rather than rotation behaviors.
Boshier, Malcolm; Ryu, Changhyun; Blackburn, Paul; Blinova, Alina; Henderson, Kevin
2014-05-01
The painted potential is a time-averaged optical dipole potential which is able to create arbitrary and dynamic two dimensional potentials for Bose Einstein condensates (BECs). This poster reports three recent experiments using this technique. First, we have realized the dc atom SQUID geometry of a BEC in a toroidal trap with two Josephson junctions. We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. Second, we have used free expansion of a rotating toroidal BEC to create matter wave Bessel beams, which are of interest because perfect Bessel beams (plane waves with amplitude profiles described by Bessel functions) propagate without diffraction. Third, we have realized the basic circuit elements necessary to create complex matter wave circuits. We launch BECs at arbitrary velocity along straight waveguides, propagate them around curved waveguides and stadium-shaped waveguide traps, and split them coherently at y-junctions that can also act as switches. Supported by LANL/LDRD.
Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam
Mitri, F. G.
2016-10-01
An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas.
Ambrosio, Leonardo A; Hernández-Figueroa, Hugo E
2010-11-08
Gradient forces on double negative (DNG) spherical dielectric particles are theoretically evaluated for v-th Bessel beams supposing geometrical optics approximations based on momentum transfer. For the first time in the literature, comparisons between these forces for double positive (DPS) and DNG particles are reported. We conclude that, contrary to the conventional case of positive refractive index, the gradient forces acting on a DNG particle may not reverse sign when the relative refractive index n goes from |n|>1 to |n|<1, thus revealing new and interesting trapping properties.
Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan
2012-02-15
Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.
Mitri, F G
2017-02-01
The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto
Mitri, F G; Fellah, Z E A
2011-08-01
The present investigation examines the instantaneous force resulting from the interaction of an acoustical high-order Bessel vortex beam (HOBVB) with a rigid sphere. The rigid sphere case is important in fluid dynamics applications because it perfectly simulates the interaction of instantaneous sound waves in a reduced gravity environment with a levitated spherical liquid soft drop in air. Here, a closed-form solution for the instantaneous force involving the total pressure field as well as the Bessel beam parameters is obtained for the case of progressive, stationary and quasi-stationary waves. Instantaneous force examples for progressive waves are computed for both a fixed and a movable rigid sphere. The results show how the instantaneous force per unit cross-sectional surface and unit pressure varies versus the dimensionless frequency ka (k is the wave number in the fluid medium and a is the sphere's radius), the half-cone angle β and the order m of the HOBVB. It is demonstrated here that the instantaneous force is determined only for (m,n) = (0,1) (where n is the partial-wave number), and vanishes for m>0 because of symmetry. In addition, the instantaneous force and normalized amplitude velocity results are computed and compared with those of a rigid immovable (fixed) sphere. It is shown that they differ significantly for ka values below 5. The proposed analysis may be of interest in the analysis of instantaneous forces on spherical particles for particle manipulation, filtering, trapping and drug delivery. The presented solutions may also serve as a method for comparison to other solutions obtained by strictly numerical or asymptotic approaches. Copyright © 2011 Elsevier B.V. All rights reserved.
Wang, Xiaohui; Song, Yingxiong
2018-02-01
By exploiting the non-Kolmogorov model and Rytov approximation theory, a propagation model of Bessel-Gaussian vortex beams (BGVB) propagating in a subway tunnel is derived. Based on the propagation model, a model of orbital angular momentum (OAM) mode probability distribution is established to evaluate the propagation performance when the beam propagates along both longitudinal and transverse directions in the subway tunnel. By numerical simulations and experimental verifications, the influences of the various parameters of BGVB and turbulence on the OAM mode probability distribution are evaluated, and the results of simulations are consistent with the experimental statistics. The results verify that the middle area of turbulence is more beneficial for the vortex beam propagation than the edge; when the BGVB propagates along the longitudinal direction in the subway tunnel, the effects of turbulence on the OAM mode probability distribution can be decreased by selecting a larger anisotropy parameter, smaller coherence length, larger non-Kolmogorov power spectrum coefficient, smaller topological charge number, deeper subway tunnel, lower train speed, and longer wavelength. When the BGVB propagates along the transverse direction, the influences can be also mitigated by adopting a larger topological charge number, less non-Kolmogorov power spectrum coefficient, smaller refractive structure index, shorter wavelength, and shorter propagation distance.
International Nuclear Information System (INIS)
Qin, Shitong; Li, Renxian; Yang, Ruiping; Ding, Chunying
2017-01-01
The interaction of an axicon-generated vector Bessel beam (AGVBB) with a homogeneous sphere is investigated in the framework of generalized Lorenz-Mie theory (GLMT). An analytical expression of beam shape coefficients (BSCs) is derived using angular spectrum decomposition method (ASDM), and the scattering coefficients are expanded using Debye series (DSE) in order to isolate the contribution of single scattering process. The internal and near-surface electric fields are numerically analyzed, and the effect of beam location, polarization, order of beam, half-cone angle, and scattering process (namely Debye mode p) are mainly discussed. Numerical results show that a curve formed by extreme peaks can be observed, and the electric fields can be locally enhanced after the interaction of AGVBBs with the particle. Internal and near-surface fields, especially its local enhancement, are very sensitive to the beam parameters, including polarization, order, half-cone angle, etc. The internal fields can also be enhanced by various scattering process (or Debye mode p). Such results have important applications in various fields, including particle sizing, optical tweezers, etc. - Highlights: • Debye series is employed to the analysis of internal and near-surface fields for a sphere illuminated by a vector Bessel beam. • Analytical expressions of BSCs for vector Bessel beams with selected polarizations are derived using ASDM. • The local enhancement of internal and near-surface fields is investigated. • The polarization, order, half-cone angle of the beam affect the local enhancement. • The local enhancement of internal fields is sensitive to the scattering process.
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...
Thériault, Gabrielle; Cottet, Martin; Castonguay, Annie; McCarthy, Nathalie; De Koninck, Yves
2014-01-01
Two-photon microscopy has revolutionized functional cellular imaging in tissue, but although the highly confined depth of field (DOF) of standard set-ups yields great optical sectioning, it also limits imaging speed in volume samples and ease of use. For this reason, we recently presented a simple and retrofittable modification to the two-photon laser-scanning microscope which extends the DOF through the use of an axicon (conical lens). Here we demonstrate three significant benefits of this technique using biological samples commonly employed in the field of neuroscience. First, we use a sample of neurons grown in culture and move it along the z-axis, showing that a more stable focus is achieved without compromise on transverse resolution. Second, we monitor 3D population dynamics in an acute slice of live mouse cortex, demonstrating that faster volumetric scans can be conducted. Third, we acquire a stereoscopic image of neurons and their dendrites in a fixed sample of mouse cortex, using only two scans instead of the complete stack and calculations required by standard systems. Taken together, these advantages, combined with the ease of integration into pre-existing systems, make the extended depth-of-field imaging based on Bessel beams a strong asset for the field of microscopy and life sciences in general.
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.
Yang, Yang; Li, Jiafang; Li, Zhi-Yuan; Chen, Yue-Gang
2015-07-01
In this paper, through a vector-spherical harmonics approach, we investigate the optical spectra of plasmonic Au nanoparticles excited by two special accelerating beams: a non-paraxial Airy beam and a Bessel beam. We systematically analyze the impacts of the beam profile, phase, and helical wave front of the electromagnetic fields on the optical spectrum and the excitation of the surface plasmon resonance (SPR). We find that the high-order phase in the Airy beam would result in strong plasmonic oscillations in the optical spectra, while the cone angle and orbital angular momentum carried by the Bessel beam could be employed to engineer the plasmon modes excited in Au nanoparticles. Furthermore, the optical spectrum excited by a combined Airy-Bessel-Gauss beam is discussed. The study could help to deeply explore new ways to manipulate SPR in metal nanoparticles via the wave front engineering of optical beams for enhancing light-matter interaction and optical sensing performance.
Poynting vector and orbital angular momentum density of superpositions of Bessel beams
CSIR Research Space (South Africa)
Litvin, IA
2011-08-01
Full Text Available ?bal, and M. L. Calvo, ?Microparticle movements in optical funnels and pods,? Opt. Express 19(6), 5232?5243 (2011). 36. S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, ?Residue orbital angular momentum in interferenced double vortex beams with unequal... ???? ?? ??? ? ??? ? ???? ? ??? ? + +??? ? ??? ? + ? ??? ? ??? ? +??? ? ??? ? + ? +?? ? ? ? ?? ? ? ? + = ? (13) where we assume both fields are modulated by the same Gaussian beam of width w0, resulting in a Gaussian Rayleigh range of zr, and for brevity we have collapsed the phase terms related to the piston and Gouy phase shifts into the function ?(z...
Simple method for the characterization of intense Laguerre-Gauss vector vortex beams
Allahyari, E.; JJ Nivas, J.; Cardano, F.; Bruzzese, R.; Fittipaldi, R.; Marrucci, L.; Paparo, D.; Rubano, A.; Vecchione, A.; Amoruso, S.
2018-05-01
We report on a method for the characterization of intense, structured optical fields through the analysis of the size and surface structures formed inside the annular ablation crater created on the target surface. In particular, we apply the technique to laser ablation of crystalline silicon induced by femtosecond vector vortex beams. We show that a rapid direct estimate of the beam waist parameter is obtained through a measure of the crater radii. The variation of the internal and external radii of the annular crater as a function of the laser pulse energy, at fixed number of pulses, provides another way to evaluate the beam spot size through numerical fitting of the obtained experimental data points. A reliable estimate of the spot size is of paramount importance to investigate pulsed laser-induced effects on the target material. Our experimental findings offer a facile way to characterize focused, high intensity complex optical vector beams which are more and more applied in laser-matter interaction experiments.
Laguerre-Gauss beam generation in IR and UV by subwavelength surface-relief gratings
DEFF Research Database (Denmark)
Vertchenko, Larissa; Shkondin, Evgeniy; Malureanu, Radu
2017-01-01
layerdepositions and dry etch techniques. We exploit the phenomenon of formbirefringence to give rise to the spin-to-orbital angular momentum conversion.We demonstrate that these plates can generate beams with high quality for theUV and IR range, allowing them to interact with high power laser sources orinside...... laser cavities....
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.
Mitri, F G
2009-04-01
The partial wave series for the scattering of a high-order Bessel beam (HOBB) of acoustic quasi-standing waves by an air bubble and fluid spheres immersed in water and centered on the axis of the beam is applied to the calculation of the acoustic radiation force. A HOBB refers to a type of beam having an axial amplitude null and an azimuthal phase gradient. Radiation force examples obtained through numerical evaluation of the radiation force function are computed for an air bubble, a hexane, a red blood and mercury fluid spheres in water. The examples were selected to illustrate conditions having progressive, standing and quasi-standing waves with appropriate selection of the waves' amplitude ratio. An especially noteworthy result is the lack of a specific vibrational mode contribution to the radiation force determined by appropriate selection of the HOBB parameters.
Yang, Minglin; Wu, Yueqian; Sheng, Xinqing; Ren, Kuan Fang
2017-12-01
Computation of scattering of shaped beams by large nonspherical particles is a challenge in both optics and electromagnetics domains since it concerns many research fields. In this paper, we report our new progress in the numerical computation of the scattering diagrams. Our algorithm permits to calculate the scattering of a particle of size as large as 110 wavelengths or 700 in size parameter. The particle can be transparent or absorbing of arbitrary shape, smooth or with a sharp surface, such as the Chebyshev particles or ice crystals. To illustrate the capacity of the algorithm, a zero order Bessel beam is taken as the incident beam, and the scattering of ellipsoidal particles and Chebyshev particles are taken as examples. Some special phenomena have been revealed and examined. The scattering problem is formulated with the combined tangential formulation and solved iteratively with the aid of the multilevel fast multipole algorithm, which is well parallelized with the message passing interface on the distributed memory computer platform using the hybrid partitioning strategy. The numerical predictions are compared with the results of the rigorous method for a spherical particle to validate the accuracy of the approach. The scattering diagrams of large ellipsoidal particles with various parameters are examined. The effect of aspect ratios, as well as half-cone angle of the incident zero-order Bessel beam and the off-axis distance on scattered intensity, is studied. Scattering by asymmetry Chebyshev particle with size parameter larger than 700 is also given to show the capability of the method for computing scattering by arbitrary shaped particles.
Unravelling Bessel beams: Presentation
CSIR Research Space (South Africa)
Mhlanga, T
2013-07-01
Full Text Available Mhlanga1,3, Angela Dudley1, Martin Lavery2, Miles Padgett2 and Andrew Forbes1,3 1CSIR National Laser Centre, PO Box 395, Pretoria, 0001, South Africa 2Department of Physics & Astronomy, University of Glasgow, Glasgow, UK 3College of Agriculture...,* Thandeka Mhlanga,1Martin Lavery,2 Andre McDonald,1 Filippus S. Roux,1 Miles Padgett,2 and Andrew Forbes1 1CSIR National Laser Centre, PO Box 395, Pretoria 0001, South Africa 2 Department of Physics & Astronomy, University of Glasgow, Glasgow, UK *adudley...
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.
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...
Characteristics of Far Transported Laser Beam
Energy Technology Data Exchange (ETDEWEB)
Park, Dae Yoon; Kim, Ki Sik; Lee, Seung Gol [Inha University, Inchon (Korea, Republic of)
1997-07-01
A beam propagating in free space or in a medium generally experiences diffraction, and hence it suffers an energy loss and an wavefront distortion. It Is essential for a stable and precise communication to eliminate or to minimize the diffraction effect accompanying on propagation. The diffraction-free beam is introduced for that purpose. A typical diffraction-free beam is the Bessel beam. The Bessel beam has, however, an infinite energy in the cross-section perpendicular to the direction of propagation and, because of this fact, its realizability is sceptical. To remedy this problem, a new beam is introduced, which has a series from with a Gaussian envelope function and tested for diffraction on propagation by a computer simulation. Compared with the Bessel-Gauss beam, this new beam shows much less diffraction. While, by using a scraper mirror in an Nd:YAG laser with a ring resonator, an annular output beam is obtained. This annular beam is focused by a Fourier Transformation lens to produce a diffraction-free beam. This diffraction-free beam dose not show any noticible diffraction on propagation over the distance of 16 m, which is determined by the scraper mirror and the Fourier transformation lens. This achievement provides a profound basis for the generation of diffraction-free beams over much longer distances. The developed technique will provide a stable and precise communication method in remote controlling system, remote sensing through atmosphere, and information transfer using the optical fiber. 30 refs., 22 figs. (author)
International Nuclear Information System (INIS)
Yang, Yang; Li, Jiafang; Li, Zhi-Yuan; Chen, Yue-Gang
2015-01-01
In this paper, through a vector-spherical harmonics approach, we investigate the optical spectra of plasmonic Au nanoparticles excited by two special accelerating beams: a non-paraxial Airy beam and a Bessel beam. We systematically analyze the impacts of the beam profile, phase, and helical wave front of the electromagnetic fields on the optical spectrum and the excitation of the surface plasmon resonance (SPR). We find that the high-order phase in the Airy beam would result in strong plasmonic oscillations in the optical spectra, while the cone angle and orbital angular momentum carried by the Bessel beam could be employed to engineer the plasmon modes excited in Au nanoparticles. Furthermore, the optical spectrum excited by a combined Airy–Bessel–Gauss beam is discussed. The study could help to deeply explore new ways to manipulate SPR in metal nanoparticles via the wave front engineering of optical beams for enhancing light–matter interaction and optical sensing performance. (paper)
On numerical Bessel transformation
International Nuclear Information System (INIS)
Sommer, B.; Zabolitzky, J.G.
1979-01-01
The authors present a computer program to calculate the three dimensional Fourier or Bessel transforms and definite integrals with Bessel functions. Numerical integration of systems containing Bessel functions occurs in many physical problems, e.g. electromagnetic form factor of nuclei, all transitions involving multipole expansions at high momenta. Filon's integration rule is extended to spherical Bessel functions. The numerical error is of the order of the Simpson error term of the function which has to be transformed. Thus one gets a stable integral even at large arguments of the transformed function. (Auth.)
Resonator with Bessel-Gauss transverse mode distribution
CSIR Research Space (South Africa)
Litvin, IA
2006-07-01
Full Text Available Slide 4 © CSIR 2006 www.csir.co.za F R1 R0 L1 L0 rdrqrJrfqF n R n )(),(),( 0 0 ∫= ϕϕ )exp()/exp()(),( 22 ϕϕ inwrqrAJrf n −= -15 -10 -5 0 5 10 15 0 0.2 0.4 0.6 0.8 1 ∫ −= 0 0 2 2 2 )exp()()exp(),( R nn rdr..., R1=0.95 R0, λ=0.53 10-6м 1.44 1.46 1.48 1.5 radius of mirror L1, ´ 10- 4 m e d u t i l p m a , r . u . 1 3 5 7 9 0 6 0.2 0.25 0.3 0.35 0.4 n o i t c a r f f i d s e s s o l 0 2 4 6 8 10 12 14 16 18 20...
Mode structure analysis of a Bessel-Gauss resonator
CSIR Research Space (South Africa)
Litvin, IA
2006-08-01
Full Text Available for helpful discussions. REFERENCES 1. Durnin J. Opt. Soc. Am. A., 4, 651 (1987). 2. Durnin J., Meceli J.J and Eberly J.H., Phys. Rev. Lett., 58, 1499 (1987). 3. Bouchal Z. J. Mod. Opt., 40, 1325 (1993). 4. Bouchal Z., Olivik M., J. Mod. Opt., 42...
The Generation Mechanism of Airy—Bessel Wave Packets in Free Space
International Nuclear Information System (INIS)
Ren Zhi-Jun; Ying Chao-Fu; Fan Chang-Jiang; Wu Qiong
2012-01-01
Localized optical Airy—Bessel configuration wave packets were first generated on the basis of a grating-telescope combination [Nat. Photon. 4(2010) 103]. By studying the spatially induced group velocity dispersion effect of ultrashort pulsed Bessel beams during propagation, we find the universal physical foundation of generating Airy—Bessel wave packets (ABWs) in free space. The research results are expected to open up more common channels for generating stable linear localized ABWs
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.
Indian Academy of Sciences (India)
was born into the family of Gebhard Dietrich Gauss, a bricklayer at the German town of ... Duke Carl Wilhelm Ferdinand of Brunswick to demonstrate .... the asteroid Ceres. For about ... impossibility of making constant scale maps of the Earth.
Entangled Bessel-Gaussian beams
CSIR Research Space (South Africa)
McLaren, M
2012-10-01
Full Text Available by performing a Bell-type experiment and showing a violation of the Clauser-Horne-Shimony-Holt inequality. In addition, we use quantum state tomography to indicate higher-dimensional entanglement in terms of BG modes....
Efficient sorting of Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2013-01-01
Full Text Available of both freeform optics. An initial radial spacing of ?kr will result in a vertical spread in the signal plane, ?u, given by ,2 r r kdu kpi ?? = (5) and thus the minimum resolvable feature, ?, constrains the resolvable wavevectors to 2 .r rk kd...
Bessel–Gauss resonator with internal amplitude filter
CSIR Research Space (South Africa)
Litvin, IA
2008-05-01
Full Text Available The authors investigate a conventional resonator configuration, using only spherical curvature optical elements, for the generation of Bessel–Gauss beams. This is achieved through the deployment of a suitable amplitude filter at a Fourier plane...
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.
Two-photon optics of Bessel-Gaussian modes
CSIR Research Space (South Africa)
McLaren, M
2013-09-01
Full Text Available In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum...
Bessel light sheet structured illumination microscopy
Noshirvani Allahabadi, Golchehr
Biomedical study researchers using animals to model disease and treatment need fast, deep, noninvasive, and inexpensive multi-channel imaging methods. Traditional fluorescence microscopy meets those criteria to an extent. Specifically, two-photon and confocal microscopy, the two most commonly used methods, are limited in penetration depth, cost, resolution, and field of view. In addition, two-photon microscopy has limited ability in multi-channel imaging. Light sheet microscopy, a fast developing 3D fluorescence imaging method, offers attractive advantages over traditional two-photon and confocal microscopy. Light sheet microscopy is much more applicable for in vivo 3D time-lapsed imaging, owing to its selective illumination of tissue layer, superior speed, low light exposure, high penetration depth, and low levels of photobleaching. However, standard light sheet microscopy using Gaussian beam excitation has two main disadvantages: 1) the field of view (FOV) of light sheet microscopy is limited by the depth of focus of the Gaussian beam. 2) Light-sheet images can be degraded by scattering, which limits the penetration of the excitation beam and blurs emission images in deep tissue layers. While two-sided sheet illumination, which doubles the field of view by illuminating the sample from opposite sides, offers a potential solution, the technique adds complexity and cost to the imaging system. We investigate a new technique to address these limitations: Bessel light sheet microscopy in combination with incoherent nonlinear Structured Illumination Microscopy (SIM). Results demonstrate that, at visible wavelengths, Bessel excitation penetrates up to 250 microns deep in the scattering media with single-side illumination. Bessel light sheet microscope achieves confocal level resolution at a lateral resolution of 0.3 micron and an axial resolution of 1 micron. Incoherent nonlinear SIM further reduces the diffused background in Bessel light sheet images, resulting in
Computation of hyperspherical Bessel functions
Tram, Thomas
2013-01-01
In this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of large order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed so far due to the lack of a backwards recurrence. We solved this problem by establishing a relation to Gegenbauer polynomials. All our algorithms are written in C and are publicly available at Github [https://github.com/lesgourg/class_public]. A Python wrapp...
Directory of Open Access Journals (Sweden)
Mohammed Larbi Labbi
2007-12-01
Full Text Available The $(2k$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k = 1$. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos gravity. In this paper we present various aspects of these curvature invariants and review their variational properties. In particular, we discuss natural generalizations of the Yamabe problem, Einstein metrics and minimal submanifolds.
International Nuclear Information System (INIS)
Bouferguene, Ahmed
2005-01-01
When computing multicentre integrals over Slater-type orbitals (STOs) by means of the Shavitt and Karplus Gaussian integral transforms (Shavitt and Karplus 1962 J. Chem. Phys. 36 550), one usually ends up with a multiple integral of the form ∫ 0 1 du ∫ 0 1 dv ...∫ 0 ∞ dz F(u, v, ..., z) (Shavitt and Karplus 1965 J. Chem. Phys. 43 398) in which all the integrals are inter-related. The most widely used approach for computing such an integral is to apply a product of Gauss-Legendre quadratures for the integrals over [0, 1] while the semi-infinite term is evaluated by a special procedure. Although numerous approaches have been developed to accurately perform the integration over [0, ∞) efficiently, it is the aim of this work to add a new tool that could be of some benefit in carrying out the hard task of multicentre integrals over STOs. The new approach relies on a special Gauss quadrature referred to as Gauss-Bessel to accurately evaluate the semi-infinite integral of interest. In this work, emphasis is put on accuracy rather than efficiency since its aim is essentially to bring a proof of concept showing that Gauss-Bessel quadrature can successfully be applied in the context of multicentre integrals over STOs. The obtained accuracy is comparable to that obtained with other methods available in the literature
Student difficulties with Gauss' law
Kanim, Stephen
2000-09-01
Many students in introductory courses have difficulty solving Gauss' law problems. Through interviews with students and analysis of solutions to homework and examination questions we have identified some specific conceptual difficulties that often contribute to students' inability to solve quantitative Gauss' law problems. We give examples of common difficulties and discuss instructional implications.
Extension of Oppenheim's Problem to Bessel Functions
Directory of Open Access Journals (Sweden)
Zhu Ling
2007-01-01
Full Text Available Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we deduce the hyperbolic analogue of these trigonometric inequalities, and we extend these inequalities to modified Bessel functions.
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.
Bessel functions: parallel display and processing.
Lohmann, A W; Ojeda-Castañeda, J; Serrano-Heredia, A
1994-01-01
We present an optical setup that converts planar binary curves into two-dimensional amplitude distributions, which are proportional, along one axis, to the Bessel function of order n, whereas along the other axis the order n increases. This Bessel displayer can be used for parallel Bessel transformation of a signal. Experimental verifications are included.
Topological setting of Bessel functions
International Nuclear Information System (INIS)
Mekhfi, M.
1995-11-01
We start from the topology of the punctured plane encoded within its homotopy group which is isomorphic to the set of integers Z. We then realize group elements Π(n), n is an element of Z as differential operators on the space of analytic functions. Using plausible physical arguments we select a subset of functions which we identify with integer orders reduced Bessel functions. On the other hand we propose a unifying new formula of topological origin, generating real orders Bessel functions out of integers orders ones, the generator being an operator built entirely out of the Π s . We thus have shown that the topology (of the puntured plane) is underlying the inner structure of Bessel functions, in addition it unifies them independently of the orders being integers or reals. (author). 4 refs
The AGS Ggamma Meter and Calibrating the Gauss Clock
Energy Technology Data Exchange (ETDEWEB)
Ahrens, Leif [Brookhaven National Laboratory (BNL), Upton, NY (United States). Collider-Accelerator Dept.
2014-03-31
During AGS Polarized Proton acceleration periods, one output from the AGS Ggamma Meter, namely the energy (or Ggamma) calculated from the magnetic field in the AGS main magnets and the beam radius- both measured in particular instant, is used to figure out the times in the AGS magnet acceleration cycle when the beam passes through a particular set of depolarizing resonances. The resonance set occur whenever a particle’s Ggamma (energy*(G/m) becomes nearly equal to n*Qx (i.e. any integer multiplied by the horizontal betatron tune). This deliverable is why the machinery is referred to as the ''Ggamma Meter'' rather than the AGS energy meter. The Ggamma Meter takes as inputs a set of measurements of frequency (F(t)), radius (r(t)), and gauss clock counts (GCC(t)). The other energy (GgammaBr) assumes the field when the gauss clock starts counting is known. The change in field to time t is given by the measured accumulated gauss clock counts multiplied by the gauss clock calibration (gauss/GCC). In order to deal with experimental data, this calibration factor gets an added ad hoc complication, namely a correction dependent on the rate of change the counting rate. The Ggamma meter takes GCC(t) and together with the past history for this cycle calculates B(t).
The AGS Ggamma Meter and Calibrating the Gauss Clock
International Nuclear Information System (INIS)
Ahrens, Leif
2014-01-01
During AGS Polarized Proton acceleration periods, one output from the AGS Ggamma Meter, namely the energy (or Ggamma) calculated from the magnetic field in the AGS main magnets and the beam radius- both measured in particular instant, is used to figure out the times in the AGS magnet acceleration cycle when the beam passes through a particular set of depolarizing resonances. The resonance set occur whenever a particle's Ggamma (energy*(G/m) becomes nearly equal to n*Qx (i.e. any integer multiplied by the horizontal betatron tune). This deliverable is why the machinery is referred to as the ''Ggamma Meter'' rather than the AGS energy meter. The Ggamma Meter takes as inputs a set of measurements of frequency (F(t)), radius (r(t)), and gauss clock counts (GCC(t)). The other energy (GgammaBr) assumes the field when the gauss clock starts counting is known. The change in field to time t is given by the measured accumulated gauss clock counts multiplied by the gauss clock calibration (gauss/GCC). In order to deal with experimental data, this calibration factor gets an added ad hoc complication, namely a correction dependent on the rate of change the counting rate. The Ggamma meter takes GCC(t) and together with the past history for this cycle calculates B(t).
Sellahi, Mohamed; Seghilani, Mohamed Seghir; Sagnes, Isabelle; Beaudoin, Gregoire; Lafosse, Xavier; Legratiet, Luc; Lalanne, Philippe; Myara, Mikhal; Garnache, Arnaud
2017-11-01
Since years, the VeCSEL concept is pointed out as a technology of choice for beyond-state-of-the-art laser light sources. The targeted coherent state in CW is typically the common gaussian TEM00, single frequency, linearly polarized lightstate. In this work, we take advantage of the VeCSEL technology for the generation of other kinds of coherent states, thanks to the insertion of intracavity functions, such as low-loss intensity and phase filters integrated on a semiconductor chip. This technological development permitted to demonstrate very pure high-order Laguerre-Gauss mode, both degenerate and non-degenerate(vortex)modes, preserving the coherence properties of usual TEM00 VeCSELs. This technology paves the way for the generation of other coherences (Bessel beams) or new functionnalities (wavelength filtering, etc.). We also explore new time domain coherence : owing to a high gain semiconductor chip design and the insertion of intracavity AOM, we demonstrated the first Frequecy-Shifted-Feedback VeCSEL, with a broadband coherence state as wide as 300 GHz.
Research on atmospheric transmission distortion of Gauss laser using multiple phase screen method
Zhang, Yizhuo; Wang, Qiushi; Gu, Haidong
2018-02-01
The laser beam is attenuated, broadened, defocused and may even be deflected from its initial propagation direction as it propagates through the atmosphere. It leads to the decrease of the laser intensity of the receiving surface. Gauss beam is the fundamental components of all possible laser waveforms. Therefore, research on the transmission of the Gauss laser has far-reaching consequences in optical communication, weaponry, target designation, ranging, remote sensing and other applications that require transmission of laser beams through the atmosphere. In this paper, we propose a laboratory simulation method using multi-phase screen to calculate the effects of atmospheric turbulence. Theoretical analysis of Gauss laser transmission in the atmosphere is given. By calculating the propagation of the Gauss beam TEM00, the far field intensity and phase distribution is shown. By the given method, the optical setup is presented and used for optimizing the adaptive optics algorithm.
Theory of generalized Bessel functions
International Nuclear Information System (INIS)
Dattoli, G.; Giannessi, L.; Mezi, L.; Torre, A.
1990-01-01
In this paper it is discussed the theory of generalized Bessel functions which are of noticeable importance in the analysis of scattering processes for which the dipole approximation cannot be used. These functions have been introduced in their standard form and their modified version. The relevant generating functions and Graf-type addition theorems have been stated. The usefulness of the results to construct a fast algorithm for their quantitative computation is also devised. It is commented on the possibility of getting two-index generalized Bessel functions in e.g. the study of sum rules of the type Σ n=-∞ ∞ t n J n 3 (x), where J n is the cylindrical Bessel function of the first kind. The usefulness of the results for problems of practical interest is finally commented on. It is shown that a modified Anger function can be advantageously introduced to get an almost straightforward computation of the Bernstein sum rule in the theory of ion waves
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
International Nuclear Information System (INIS)
Gorbachev, D V; Ivanov, V I
2015-01-01
Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles
Improved fixation quality provided by a Bessel beacon in an adaptive optics system.
Lambert, Andrew J; Daly, Elizabeth M; Dainty, Christopher J
2013-07-01
We investigate whether a structured probe beam that creates the beacon for use in a retinal imaging adaptive optics system can provide useful side effects. In particular we investigate whether a Bessel beam that is seen by the subject as a set of concentric rings has a dampening effect on fixation variations of the subject under observation. This calming effect would allow longer periods of observation, particularly for patients with abnormal fixation. An experimental adaptive optics system developed for retinal imaging is used to monitor the fluctuations in aberrations for artificial and human subjects. The probe beam is alternated between a traditional beacon and one provided by a Bessel beam created by SLM. Time-frequency analysis is used to indicate the differences in power and time variation during fixation depending on whether the Bessel beam or the traditional beacon is employed. Comparison is made with the response for an artificial eye to discount systemic variations. Significant evidence is accrued to indicate the reduced fluctuations in fixation when the Bessel beam is employed to create the beacon. © 2013 The Authors Ophthalmic & Physiological Optics © 2013 The College of Optometrists.
Colon Cancer Risk Assessment - Gauss Program
An executable file (in GAUSS) that projects absolute colon cancer risk (with confidence intervals) according to NCI’s Colorectal Cancer Risk Assessment Tool (CCRAT) algorithm. GAUSS is not needed to run the program.
Covariant Gauss law commutator anomaly
International Nuclear Information System (INIS)
Dunne, G.V.; Trugenberger, C.A.; Massachusetts Inst. of Tech., Cambridge
1990-01-01
Using a (fixed-time) hamiltonian formalism we derive a covariant form for the anomaly in the commutator algebra of Gauss law generators for chiral fermions interacting with a dynamical non-abelian gauge field in 3+1 dimensions. (orig.)
Poisson processes and a Bessel function integral
Steutel, F.W.
1985-01-01
The probability of winning a simple game of competing Poisson processes turns out to be equal to the well-known Bessel function integral J(x, y) (cf. Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill, New York, 1962). Several properties of J, some of which seem to be new, follow quite easily
The Bessel polynomials and their differential operators
International Nuclear Information System (INIS)
Onyango Otieno, V.P.
1987-10-01
Differential operators associated with the ordinary and the generalized Bessel polynomials are defined. In each case the commutator bracket is constructed and shows that the differential operators associated with the Bessel polynomials and their generalized form are not commutative. Some applications of these operators to linear differential equations are also discussed. (author). 4 refs
Generating and measuring nondiffracting vector Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2013-09-01
Full Text Available (2006). 12. W. Han, W. Cheng, and Q. Zhan, Opt. Lett. 36, 1605 (2011). 13. F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, Appl. Opt. 51, C1 (2012). 14. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte...
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.
Directory of Open Access Journals (Sweden)
Zoran Gojković
2017-01-01
Full Text Available The physical surface of the earth has irregular shape which is not mathematically defined, therefore the shape of the Earth is approximated with mathematically defined surfaces such as ellipsoid and sphere. The developing of a global positioning systems, thus and modern navigation systems, as effect produce large amounts of data which contain the problem of homogeneity. This problem could be exceed if all the data are store in the same coordinate system. Hence the need for data transformation from local coordinate systems to the global coordinate systems. Global level implies WGS84 ellipsoid and UTM projection while national coordinate system of Republic Serbia is Gauss-Kruger with Bessel ellipsoid. This coordinate system of Republic Serbia on a global level has a local character. Applying appropriate mathematical models and functions it is possible to transform coordinates from one system to another and vice versa. The paper describes coordinate transformations from Gauss-Kruger coordinate system ellipsoid Bessel to UTM projection WGS84 ellipsoid and vice versa, and also an application which provides transformation of its kind that is made using open source environment. Name of the application is TRANS7_GK_UTM_GK and it can be found and used on the web page of the faculty for Mining and Geology under the link http://gk2utm.rgf.bg.ac.rs with a user guide.
Gaussian vs. Bessel light-sheets: performance analysis in live large sample imaging
Reidt, Sascha L.; Correia, Ricardo B. C.; Donnachie, Mark; Weijer, Cornelis J.; MacDonald, Michael P.
2017-08-01
Lightsheet fluorescence microscopy (LSFM) has rapidly progressed in the past decade from an emerging technology into an established methodology. This progress has largely been driven by its suitability to developmental biology, where it is able to give excellent spatial-temporal resolution over relatively large fields of view with good contrast and low phototoxicity. In many respects it is superseding confocal microscopy. However, it is no magic bullet and still struggles to image deeply in more highly scattering samples. Many solutions to this challenge have been presented, including, Airy and Bessel illumination, 2-photon operation and deconvolution techniques. In this work, we show a comparison between a simple but effective Gaussian beam illumination and Bessel illumination for imaging in chicken embryos. Whilst Bessel illumination is shown to be of benefit when a greater depth of field is required, it is not possible to see any benefits for imaging into the highly scattering tissue of the chick embryo.
Computer program for Bessel and Hankel functions
Kreider, Kevin L.; Saule, Arthur V.; Rice, Edward J.; Clark, Bruce J.
1991-01-01
A set of FORTRAN subroutines for calculating Bessel and Hankel functions is presented. The routines calculate Bessel and Hankel functions of the first and second kinds, as well as their derivatives, for wide ranges of integer order and real or complex argument in single or double precision. Depending on the order and argument, one of three evaluation methods is used: the power series definition, an Airy function expansion, or an asymptotic expansion. Routines to calculate Airy functions and their derivatives are also included.
Inequalities for the Modified k-Bessel Function
Directory of Open Access Journals (Sweden)
Saiful Rahman Mondal
2017-07-01
Full Text Available The article considers the generalized k-Bessel functions and represents it as Wright functions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel functions, and the ratio of the k-Bessel and the k-Bessel functions. The log-convexity with respect to the order of the k-Bessel also given. An investigation regarding the monotonicity of the ratio of the k-Bessel and k-confluent hypergeometric functions are discussed.
Gauss Sum Factorization with Cold Atoms
International Nuclear Information System (INIS)
Gilowski, M.; Wendrich, T.; Mueller, T.; Ertmer, W.; Rasel, E. M.; Jentsch, Ch.; Schleich, W. P.
2008-01-01
We report the first implementation of a Gauss sum factorization algorithm by an internal state Ramsey interferometer using cold atoms. A sequence of appropriately designed light pulses interacts with an ensemble of cold rubidium atoms. The final population in the involved atomic levels determines a Gauss sum. With this technique we factor the number N=263193
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....
Generating bessel functions in mie scattering calculations using continued fractions.
Lentz, W J
1976-03-01
A new method of generating the Bessel functions and ratios of Bessel functions necessary for Mie calculations is presented. Accuracy is improved while eliminating the need for extended precision word lengths or large storage capability. The algorithm uses a new technique of evaluating continued fractions that starts at the beginning rather than the tail and has a built-in error check. The continued fraction representations for both spherical Bessel functions and ratios of Bessel functions of consecutive order are presented.
A Determinant Expression for the Generalized Bessel Polynomials
Directory of Open Access Journals (Sweden)
Sheng-liang Yang
2013-01-01
Full Text Available Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented as determinant the entries of which involve Catalan numbers.
Generalized Bessel functions in tunnelling ionization
International Nuclear Information System (INIS)
Reiss, H R; Krainov, V P
2003-01-01
We develop two new approximations for the generalized Bessel function that frequently arises in the analytical treatment of strong-field processes, especially in non-perturbative multiphoton ionization theories. Both these new forms are applicable to the tunnelling environment in atomic ionization, and are analytically much simpler than the currently used low-frequency asymptotic approximation for the generalized Bessel function. The second of the new forms is an approximation to the first, and it is the second new form that exhibits the well-known tunnelling exponential
Nonextensive entropies derived from Gauss' principle
International Nuclear Information System (INIS)
Wada, Tatsuaki
2011-01-01
Gauss' principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles. - Highlights: → Nonextensive entropies are derived from Gauss' principle and ensemble equivalence. → Gauss' principle is generalized for a q-exponential distribution. → I have found the condition for satisfying Greene-Callen principle. → The associated statistical q-entropy is found to be normalized Tsallis entropy.
Spherical Bessel transform via exponential sum approximation of spherical Bessel function
Ikeno, Hidekazu
2018-02-01
A new algorithm for numerical evaluation of spherical Bessel transform is proposed in this paper. In this method, the spherical Bessel function is approximately represented as an exponential sum with complex parameters. This is obtained by expressing an integral representation of spherical Bessel function in complex plane, and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double-exponential transformation. The number of terms in the expression is reduced using the modified balanced truncation method. The residual part of integrand is also expanded by exponential functions using Prony-like method. The spherical Bessel transform can be evaluated analytically on arbitrary points in half-open interval.
The modified Gauss diagonalization of polynomial matrices
International Nuclear Information System (INIS)
Saeed, K.
1982-10-01
The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)
Large degree asymptotics of generalized Bessel polynomials
J.L. López; N.M. Temme (Nico)
2011-01-01
textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the
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.
Monotonicity and bounds on Bessel functions
Directory of Open Access Journals (Sweden)
Larry Landau
2000-07-01
Full Text Available survey my recent results on monotonicity with respect to order of general Bessel functions, which follow from a new identity and lead to best possible uniform bounds. Application may be made to the "spreading of the wave packet" for a free quantum particle on a lattice and to estimates for perturbative expansions.
Holographic Superconductivity with Gauss-Bonnet gravity
Gregory, Ruth
2010-01-01
I review recent work on holographic superconductivity with Einstein-Gauss-Bonnet gravity, and show how the critical temperature of the superconductor depends on both gravitational backreaction and the Gauss-Bonnet parameter, using both analytic and numerical arguments. I also review computations of the conductivity, finding the energy gap, and demonstrating that there is no universal gap ratio, $\\omega_g/T_c$, for these superconductors.
Chen, J; Yuan, X-C; Zhao, X; Fang, Z L; Zhu, S W
2009-11-01
We propose a generalized approach to producing optical vortices with suppressed sidelobes using a variable Bessel-like function added to the conventional spiral phase plate. Experimental verifications are implemented by a phase-only spatial light modulator. It is demonstrated that the method is valid for optical vortex beams with arbitrary topological charges and without changing the primary ring size as a unique property among the existing techniques.
Walk-off reduction, using an external optical plate and Bessel-Gaussian interaction
Masoume, Mansouri; Mohsen, Askarbioki; Saeed Ghavami, Sabouri; Alireza, Khorsandi
2015-02-01
To reduce the walk-off angle of the extraordinary third-harmonic ultraviolet wave at 355 nm generated by type II KTiOPO4 and type I β-BaB2O4 optical crystals, and the Gaussian output beam of a Q-switched Nd:YAG laser, a simple theoretical model was developed based on a rotatable BK7 plate of variable thickness. By rotating the plate up to 35° along the beam direction, we reduced the walk-off angle up to ˜ 13%. The same phenomenon is predicted by the model, confirming the performance of the model. It is found that, due to the walk-off effect, the intensity profile of the third-harmonic generation beam is slightly degraded. To compensate for the observed phenomena and further reduce the walk-off, we used a combination of a convex lens and an axicon to transform the beam profile of the interacting fundamental and second-harmonic generation waves to the zero-order Bessel-Gaussian form. As a result, the walk-off is decreased to ˜48.81 mrad, providing ˜30% relative reduction. By using the same BK7 plate rotated up to 35° along the third-harmonic beam direction, the walk-off angle is further reduced to 38.9 mrad. Moreover, it is observed that the beam profile of the emerged Bessel-Gaussian third-harmonic generation beam remains unchanged with no degradation.
Generating and analyzing non-diffracting vector vortex beams
CSIR Research Space (South Africa)
Li, Y
2013-08-01
Full Text Available single order Bessel beam and superposition cases are studied. The polarization and the azimuthal modes of the generated beams are analyzed. The results of modal decompositions on polarization components are in good agreement with theory. We demonstrate...
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....
Galileo, Gauss, and the Green Monster
Kalman, Dan; Teague, Daniel J.
2013-01-01
Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…
Metaoptics for Spectral and Spatial Beam Manipulation
Raghu Srimathi, Indumathi
Laser beam combining and beam shaping are two important areas with applications in optical communications, high power lasers, and atmospheric propagation studies. In this dissertation, metaoptical elements have been developed for spectral and spatial beam shaping, and multiplexing. Beams carrying orbital angular momentum (OAM), referred to as optical vortices, have unique propagation properties. Optical vortex beams carrying different topological charges are orthogonal to each other and have low inter-modal crosstalk which allows for them to be (de)multiplexed. Efficient spatial (de)multiplexing of these beams have been carried out by using diffractive optical geometrical coordinate transformation elements. The spatial beam combining technique shown here is advantageous because the efficiency of the system is not dependent on the number of OAM states being combined. The system is capable of generating coaxially propagating beams in the far-field and the beams generated can either be incoherently or coherently multiplexed with applications in power scaling and dynamic intensity profile manipulations. Spectral beam combining can also be achieved with the coordinate transformation elements. The different wavelengths emitted by fiber sources can be spatially overlapped in the far-field plane and the generated beams are Bessel-Gauss in nature with enhanced depth of focus properties. Unique system responses and beam shapes in the far-field can be realized by controlling amplitude, phase, and polarization at the micro-scale. This has been achieved by spatially varying the structural parameters at the subwavelength scale and is analogous to local modification of material properties. With advancements in fabrication technology, it is possible to control not just the lithographic process, but also the deposition process. In this work, a unique combination of spatial structure variations in conjunction with the conformal coating properties of an atomic layer deposition tool
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...
Approximation of Analytic Functions by Bessel's Functions of Fractional Order
Directory of Open Access Journals (Sweden)
Soon-Mo Jung
2011-01-01
Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.
Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
Hale, Nicholas
2013-03-06
An efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton\\'s root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100. © 2013 Society for Industrial and Applied Mathematics.
Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
Hale, Nicholas; Townsend, Alex
2013-01-01
An efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton's root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100. © 2013 Society for Industrial and Applied Mathematics.
Zernike vs. Bessel circular functions in visual optics.
Trevino, Juan P; Gómez-Correa, Jesus E; Iskander, D Robert; Chávez-Cerda, Sabino
2013-07-01
We propose the Bessel Circular Functions as alternatives of the Zernike Circle Polynomials to represent relevant circular ophthalmic surfaces. We assess the fitting capabilities of the orthogonal Bessel Circular Functions by comparing them to Zernike Circle Polynomials for approximating a variety of computationally generated surfaces which can represent ophthalmic surfaces. The Bessel Circular Functions showed better modelling capabilities for surfaces with abrupt variations such as the anterior eye surface at the limbus region, and influence functions. From our studies we find that the Bessel Circular Functions can be more suitable for studying particular features of post surgical corneal surfaces. We show that given their boundary conditions and free oscillating properties, the Bessel Circular Functions are an alternative for representing specific wavefronts and can be better than the Zernike Circle Polynomials for some important cases of corneal surfaces, influence functions and the complete anterior corneal surface. © 2013 The Authors Ophthalmic & Physiological Optics © 2013 The College of Optometrists.
Theory of generalized Bessel functions: Pt. 2
International Nuclear Information System (INIS)
Dattoli, G.; Torre, A.; Chiccoli, C.
1991-01-01
In this paper the systematic study of the generalized Bessel functions (GBF), recently introduced and often encountered in problems of scattering for which the dipole approximation is inadequate, is continuated. The relations among different GBF are analysed and their importance for the solution of differential finite-difference equation of the Raman-Nath type is discussed. Numerical results for the first-kind cylinder GBF in the preasymptotic region and also a preliminary analysis of the asymptotic properties of the modified GBF are presented
On Sensitivity of Gauss-Christoffel Quadrature
Czech Academy of Sciences Publication Activity Database
O'Leary, D.P.; Strakoš, Zdeněk; Tichý, Petr
2007-01-01
Roč. 107, č. 1 (2007), s. 147-174 ISSN 0029-599X R&D Projects: GA AV ČR 1ET400300415 Grant - others:NSF(US) CCR -0204084; NSF(US) CCF-0514213 Institutional research plan: CEZ:AV0Z10300504 Keywords : Gauss-Christoffel quadrature * sensitivity * moments Subject RIV: BA - General Mathematics Impact factor: 1.376, year: 2007
All-optical 3D atomic loops generated with Bessel light fields
International Nuclear Information System (INIS)
Volke-Sepulveda, Karen; Jauregui, RocIo
2009-01-01
The propagation invariance of Bessel beams as well as their transversal structure is used to perform a comparative analysis of their effect on cold atoms for four different configurations and combinations thereof. We show that, even at temperatures for which the classical description of the atom's centre-of-mass motion is valid, the interchange of momentum, energy and orbital angular momentum between light and atoms yields efficient tools for all-optical trapping, transporting and, in general, manipulating the state of motion of cold atoms.
Bessel collocation approach for approximate solutions of Hantavirus infection model
Directory of Open Access Journals (Sweden)
Suayip Yuzbasi
2017-11-01
Full Text Available In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.
A simple derivation of new sum rules of Bessel functions
International Nuclear Information System (INIS)
Ciocci, F.; Dattoli, G.; Dipace, A.
1985-01-01
In this note it is exploited a recently suggested technique to get simple expressions for a class of sum rules of Bessel functions appearing in plasma physics; their relevance to the numerical evaluation of the Turkin function is also discussed
Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering
International Nuclear Information System (INIS)
Boer, D.; Gamberg, L.; Musch, B.U.; Prokudin, A.
2011-01-01
The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.
Fourier expansions and multivariable Bessel functions concerning radiation programmes
International Nuclear Information System (INIS)
Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.
1996-01-01
The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)
International Nuclear Information System (INIS)
Doha, E H; Ahmed, H M
2004-01-01
A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed
Power-Scalable Blue-Green Bessel Beams
2016-02-23
building system to achieve emission at the desired blue colours , was, however, abandoned due to lack of funds relative to the original anticipated award...Chen, P. Steinvurzel, K. Rottwitt, S. Ramachandran, “High-energy Fiber Lasers at Non-traditional Colours , via Intermodal Nonlinearities,” CTu3M.6
Intracavity generation of longitudinal dependant Bessel like beams
CSIR Research Space (South Africa)
Litvin, IA
2009-08-01
Full Text Available is based on doublet of axicon and axicon-lens. For both resonator systems the LDBLB is output of fundamental mode, but the spectral properties of obtaining LDBLBs are different....
From stationary annular rings to rotating Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2012-04-01
Full Text Available contributions from the two ring-slits completely overlap (evident in Fig. 1), the angular rotation is non-zero and the entire field at P3 experiences the rotation. 3. EXPERIMENTAL METHODOLOGY The experimental setup used to generate superpositions of higher...) as a ?petal?-field. The field at the ring-slit hologram (i.e., the field at plane P1), we will term the ?singularity?-field and that formed at plane P2 (a distance of 2f from lens L4) will be termed as the ?spiral?-field. 4. RESULTS AND DISCUSSION...
GaussStudio: designing seamless tangible interactions on portable displays
Liang, R.-H.; Kuo, H.-C.; Bruns Alonso, M.; Chen, B.-Y.
2016-01-01
The analog Hall-sensor grid, GaussSense, is a thin-form magnetic-field camera technology for designing expressive occlusion-free, near-surface tangible interactions on conventional portable displays. The studio will provide hands-on experiences that combine physical designs and the GaussSense
Parallel multigrid smoothing: polynomial versus Gauss-Seidel
International Nuclear Information System (INIS)
Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray
2003-01-01
Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines
Parallel multigrid smoothing: polynomial versus Gauss-Seidel
Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray
2003-07-01
Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.
Filtered Bessel functions in computerized tomography
International Nuclear Information System (INIS)
Rathore, R.K.S.; Munshi, P.; Bhatia, V.K.; Pandimani, S.
1988-01-01
Computer Aided Tomography (CAT) is widely used in the medical imaging area for the detection of cancerous tissues. It has also proved to be a good technique for measuring point-density (void-fraction) in two-phase flow systems. The present day CAT-scanners employ alogorithms which are essentially a discrete implementation of the Radon Inversion Formulae. These methods of reconstructing density distributions are fast and easy to implement. The present work is an attempt to simplify (and consequently to speed-up) the existing algorithms for the cases of radially symmetric density distribution. The method uses Radon Inversion Formulae and involves Bessels's Function of Fourier frequency. The algorithm was tested on some known distributions and the reconstruction is excellent. Data for bubbly-flow was also processed to obtain a point density distribution. The range of investigation was 0.6 ≤ ≤ 0.9 g/cm 3 , where ' ' denotes average cross-sectional value. The values of CT > are within ±0.03 g/cm 3 of the true values , for the data sets considered. The results are comparable with another simple method involving radial polynominals. It is observed that the simplified Radon Inversion Formulae for the radially symmetric case gives good results and can be implemented with ease. (orig.)
Generation and propagation of high-order Bessel vortices in linear and non-linear crystals
CSIR Research Space (South Africa)
Belyi, VN
2009-08-01
Full Text Available E⊥ of the electric field for these beams are given by the following expressions: ( ))2exp()()( )( )exp( 20 1 10 ϕρρ iqJqJ qw zikA i zoo −+⊥ += eeE , (1) с Uniaxial crystal θs Bs2ω(ρ) Bsω(ρ) Figure 1: Geometry of SHG when wave vectors cone of Bessel... beam at fundamental )(ρωBs and second harmonic frequencies )(2 ρωBs coincides with phase-matching cone of uniaxial crystal. Proc. of SPIE Vol. 7430 74300F-2 ( ))2exp()()()cos( )( )exp( 20 1 1 ϕρργ iqJqJ qw zikA i e zee e −+⊥ −= ee...
Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term
Deruelle, Nathalie; Merino, Nelson; Olea, Rodrigo
2018-05-01
We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which uses the Chern-Weil theorem plus a dimensional continuation process, such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The boundary term constructed in this paper allows to deal with a general background and is not equivalent to the Gibbons-Hawking-Myers boundary term. However, we show that they coincide if one replaces the background of the Katz procedure by a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients, the expected mass of the Boulware-Deser black hole.
International Nuclear Information System (INIS)
Fan Hongyi; Wang Yong
2006-01-01
With the help of Bose operator identities and entangled state representation and based on our previous work [Phys. Lett. A 325 (2004) 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.
Intra–cavity generation of Bessel–like beams with longitudinally dependent cone angles
CSIR Research Space (South Africa)
Litvin, IA
2010-02-01
Full Text Available The authors report on two resonator systems for producing Bessel–like beams with longitudinally dependent cone angles (LDBLBs). Such beams have extended propagation distances as compared to conventional Bessel– Gauss beams, with a far field pattern...
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.
Series of Bessel and Kummer-type functions
Baricz, Arpad; Pogány, Tibor K
2017-01-01
This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.
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.
Scalar field collapse in Gauss-Bonnet gravity
Banerjee, Narayan; Paul, Tanmoy
2018-02-01
We consider a "scalar-Einstein-Gauss-Bonnet" theory in four dimension, where the scalar field couples non-minimally with the Gauss-Bonnet (GB) term. This coupling with the scalar field ensures the non-topological character of the GB term. In this scenario, we examine the possibility for collapsing of the scalar field. Our result reveals that such a collapse is possible in the presence of Gauss-Bonnet gravity for suitable choices of parametric regions. The singularity formed as a result of the collapse is found to be a curvature singularity which is hidden from the exterior by an apparent horizon.
Scalar field collapse in Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Narayan [Indian Institute of Science Education and Research Kolkata, Department of Physical Sciences, Nadia, West Bengal (India); Paul, Tanmoy [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)
2018-02-15
We consider a ''scalar-Einstein-Gauss-Bonnet'' theory in four dimension, where the scalar field couples non-minimally with the Gauss-Bonnet (GB) term. This coupling with the scalar field ensures the non-topological character of the GB term. In this scenario, we examine the possibility for collapsing of the scalar field. Our result reveals that such a collapse is possible in the presence of Gauss-Bonnet gravity for suitable choices of parametric regions. The singularity formed as a result of the collapse is found to be a curvature singularity which is hidden from the exterior by an apparent horizon. (orig.)
Modified Bessel P-integrals and P-derivatives and their properties
International Nuclear Information System (INIS)
Volosivets, S S
2014-01-01
We study the modified Bessel P-integral, whose properties are similar to those of the Bessel potential, and the modified Bessel P-derivative. These operators are inverse to each other. We prove analogues of the embedding theorems of Hardy, Littlewood, Stein, Zygmund and Lizorkin concerning the images of L p (R) under the action of Bessel potentials. We give applications of the Bessel integral and derivative to the integrability of the P-adic Fourier transform and to approximation theory (an embedding theorem of Ul'yanov type)
FUNPACK-2, Subroutine Library, Bessel Function, Elliptical Integrals, Min-max Approximation
International Nuclear Information System (INIS)
Cody, W.J.; Garbow, Burton S.
1975-01-01
1 - Description of problem or function: FUNPACK is a collection of FORTRAN subroutines to evaluate certain special functions. The individual subroutines are (Identification/Description): NATSI0 F2I0 Bessel function I 0 ; NATSI1 F2I1 Bessel function I 1 ; NATSJ0 F2J0 Bessel function J 0 ; NATSJ1 F2J1 Bessel function J 1 ; NATSK0 F2K0 Bessel function K 0 ; NATSK1 F2K1 Bessel function K 1 ; NATSBESY F2BY Bessel function Y ν ; DAW F1DW Dawson's integral; DELIPK F1EK Complete elliptic integral of the first kind; DELIPE F1EE Complete elliptic integral of the second kind; DEI F1EI Exponential integrals; NATSPSI F2PS Psi (logarithmic derivative of gamma function); MONERR F1MO Error monitoring package . 2 - Method of solution: FUNPACK uses evaluation of min-max approximations
Cosmology of modified Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Li Baojiu; Barrow, John D.; Mota, David F.
2007-01-01
We consider the cosmology where some function f(G) of the Gauss-Bonnet term G is added to the gravitational action to account for the late-time accelerating expansion of the universe. The covariant and gauge invariant perturbation equations are derived with a method which could also be applied to general f(R,R ab R ab ,R abcd R abcd ) gravitational theories. It is pointed out that, despite their fourth-order character, such f(G) gravity models generally cannot reproduce arbitrary background cosmic evolutions; for example, the standard ΛCDM paradigm with Ω DE =0.76 cannot be realized in f(G) gravity theories unless f is a true cosmological constant because it imposes exclusionary constraints on the form of f(G). We analyze the perturbation equations and find that, as in the f(R) model, the stability of early-time perturbation growth puts some constraints on the functional form of f(G), in this case ∂ 2 f/∂G 2 <0. Furthermore, the stability of small-scale perturbations also requires that f not deviate significantly from a constant. These analyses are illustrated by numerically propagating the perturbation equations with a specific model reproducing a representative ΛCDM cosmic history. Our results show how the f(G) models are highly constrained by cosmological data
Ricci-Gauss-Bonnet holographic dark energy
Saridakis, Emmanuel N.
2018-03-01
We present a model of holographic dark energy in which the infrared cutoff is determined by both the Ricci and the Gauss-Bonnet invariants. Such a construction has the significant advantage that the infrared cutoff, and consequently the holographic dark energy density, does not depend on the future or the past evolution of the universe, but only on its current features, and moreover it is determined by invariants, whose role is fundamental in gravitational theories. We extract analytical solutions for the behavior of the dark energy density and equation-of-state parameters as functions of the redshift. These reveal the usual thermal history of the universe, with the sequence of radiation, matter and dark energy epochs, resulting in the future to a complete dark energy domination. The corresponding dark energy equation-of-state parameter can lie in the quintessence or phantom regime, or experience the phantom-divide crossing during the cosmological evolution, and its asymptotic value can be quintessencelike, phantomlike, or be exactly equal to the cosmological-constant value. Finally, we extract the constraints on the model parameters that arise from big bang nucleosynthesis.
Gauss-Bonnet actions and their dimensionally reduced descendants
International Nuclear Information System (INIS)
Mueller-Hoissen, F.
1989-01-01
A brief introduction to Gauss-Bonnet type generalizations of the Einstein-Hilbert gravity action in more than four dimensions is given and the structure of associated (effective) theories obtained by dimensional reduction is discussed. (author)
The Gauss-Seidel Numerical Procedure for Markov Stochastic Games
National Research Council Canada - National Science Library
Kushner, Harold J
2004-01-01
.... The convergence of the Gauss-Seidel form of this procedure is shown for both the discounted and ergodic cost problems, under appropriate conditions, with extensions to problems where one stops...
The Gauss-Bonnet identity in quartic gravitation theories
International Nuclear Information System (INIS)
Gomes, M.
1989-01-01
The possible modifications in Gauss-Bonnet relation due to quantum oscillations are studied. The introduction of quantum operator correspondent in the function of two points, in space without singularities is calculated. (M.C.K.)
Composite Gauss-Legendre Quadrature with Error Control
Prentice, J. S. C.
2011-01-01
We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)
GigaGauss solenoidal magnetic field inside bubbles excited in under-dense plasma
Lécz, Zs.; Konoplev, I. V.; Seryi, A.; Andreev, A.
2016-10-01
This paper proposes a novel and effective method for generating GigaGauss level, solenoidal quasi-static magnetic fields in under-dense plasma using screw-shaped high intensity laser pulses. This method produces large solenoidal fields that move with the driving laser pulse and are collinear with the accelerated electrons. This is in contrast with already known techniques which rely on interactions with over-dense or solid targets and generates radial or toroidal magnetic field localized at the stationary target. The solenoidal field is quasi-stationary in the reference frame of the laser pulse and can be used for guiding electron beams. It can also provide synchrotron radiation beam emittance cooling for laser-plasma accelerated electron and positron beams, opening up novel opportunities for designs of the light sources, free electron lasers, and high energy colliders based on laser plasma acceleration.
Quasi-fractional approximation to the Bessel functions
International Nuclear Information System (INIS)
Guerrero, P.M.L.
1989-01-01
In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions J ν (x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4
On functions defined by sums of products of Bessel functions
International Nuclear Information System (INIS)
Martin, P A
2008-01-01
Various functions, defined as infinite series of products of Bessel functions of the first kind, are studied. Integral representations are obtained, and then used to deduce asymptotic approximations. Although several methods have been investigated (including power series expansions and integral transforms), methods based on Fourier series emerge as the most useful
Superiority of Bessel function over Zernicke polynomial as base ...
Indian Academy of Sciences (India)
Abstract. Here we describe the superiority of Bessel function as base function for radial expan- sion over Zernicke polynomial in the tomographic reconstruction technique. The causes for the superiority have been described in detail. The superiority has been shown both with simulated data for Kadomtsev's model for ...
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.
On a family of Bessel type functions: Estimations, series, overconvergence
Paneva-Konovska, Jordanka
2017-12-01
A family of the Bessel-Maitland functions are considered in this paper and some useful estimations are obtained for them. Series defined by means of these functions are considered and their behaviour on the boundaries of the convergence domains is discussed. Using the obtained estimations, necessary and sufficient conditions for the series overconvergence, as well as Hadamard type theorem are proposed.
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.
Asymmetric skew Bessel processes and their applications to finance
Decamps, M.; Goovaerts, M.J.; Schoutens, W.
2006-01-01
In this paper, we extend the Harrison and Shepp's construction of the skew Brownian motion (1981) and we obtain a diffusion similar to the two-dimensional Bessel process with speed and scale densities discontinuous at one point. Natural generalizations to multi-dimensional and fractional order
Heat kernel analysis for Bessel operators on symmetric cones
DEFF Research Database (Denmark)
Möllers, Jan
2014-01-01
. The heat kernel is explicitly given in terms of a multivariable $I$-Bessel function on $Ω$. Its corresponding heat kernel transform defines a continuous linear operator between $L^p$-spaces. The unitary image of the $L^2$-space under the heat kernel transform is characterized as a weighted Bergmann space...
Resonant and hollow beam generation of plasma channels
International Nuclear Information System (INIS)
Alexeev, I.; Kim, K.Y.; Fan, J.; Parra, E.; Milchberg, H.M.; Margolin, L.Ya.; Pyatnitskii, L.N.
2001-01-01
We report two variations on plasma channel generation using the propagation of intense Bessel beams. In the first experiment, the propagation of a high intensity Bessel beam in neutral gas is observed to give rise to resonantly enhanced plasma channel generation, resulting from resonant self-trapping of the beam and enhanced laser-plasma heating. In the second experiment, a high power, hollow Bessel beam (J 5 ) is produced and the optical breakdown of a gas target and the generation of a tubular plasma channel with such a beam is realized for the first time. Hydrodynamic simulations of the laser-plasma interaction of are in good agreement with the results of both experiments
Gauss-Bonnet black holes in dS spaces
International Nuclear Information System (INIS)
Cai Ronggen; Guo Qi
2004-01-01
We study the thermodynamic properties associated with the black hole horizon and cosmological horizon for the Gauss-Bonnet solution in de Sitter space. When the Gauss-Bonnet coefficient is positive, a locally stable small black hole appears in the case of spacetime dimension d=5, the stable small black hole disappears, and the Gauss-Bonnet black hole is always unstable quantum mechanically when d≥6. On the other hand, the cosmological horizon is found to be always locally stable independent of the spacetime dimension. But the solution is not globally preferred; instead, the pure de Sitter space is globally preferred. When the Gauss-Bonnet coefficient is negative, there is a constraint on the value of the coefficient, beyond which the gravity theory is not well defined. As a result, there is not only an upper bound on the size of black hole horizon radius at which the black hole horizon and cosmological horizon coincide with each other, but also a lower bound depending on the Gauss-Bonnet coefficient and spacetime dimension. Within the physical phase space, the black hole horizon is always thermodynamically unstable and the cosmological horizon is always stable; furthermore, as in the case of the positive coefficient, the pure de Sitter space is still globally preferred. This result is consistent with the argument that the pure de Sitter space corresponds to an UV fixed point of dual field theory
Further 'comment on 'Generalized Bessel functions in tunnelling ionization''
International Nuclear Information System (INIS)
Reiss, H R; Krainov, V P
2005-01-01
J Bauer, in commenting on our tunnelling approximation for the generalized Bessel function, points out that when the approximation is applied to strong-field ionization, it is suitable only for the lowest-energy part of an ionization spectrum. We do not disagree. We point out several things: the results of Bauer are to be expected; linear polarization results are dominated by the lowest part of the multiphoton spectrum; and we do not recommend practical use of this tunnelling approximation, since the asymptotic approximation is so much better. We show comparisons of momentum distributions calculated with the tunnelling approximation and those with the complete strong-field approximation, which show in more detail than spectrum comparisons that the tunnelling approximation to the generalized Bessel function is applicable only to the low-momentum part of the distribution, and neglects altogether the high-momentum portion. (reply)
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.
Compact and continuous embeddings of logarithmic Bessel potential spaces
Czech Academy of Sciences Publication Activity Database
Edmunds, D. E.; Gurka, P.; Opic, Bohumír
2005-01-01
Roč. 168, č. 3 (2005), s. 229-250 ISSN 0039-3223 R&D Projects: GA ČR(CZ) GA201/01/0333 Institutional research plan: CEZ:AV0Z10190503 Keywords : Bessel potential spaces * spaces of Hölder-continuous functions * Lorentz-Zygmund spaces Subject RIV: BA - General Mathematics Impact factor: 0.538, year: 2005
Stability of cylindrical plasma in the Bessel function model
International Nuclear Information System (INIS)
Yamagishi, T.; Gimblett, C.G.
1988-01-01
The stability of free boundary ideal and tearing modes in a cylindrical plasma is studied by examining the discontinuity (Δ') of the helical flux function given by the force free Bessel function model at the singular surface. The m = O and m = 1 free boundary tearing modes become strongly unstable when the singular surface is just inside the plasma boundary for a wide range of longitudinal wave numbers. (author)
Extensions of Bessel sequences to dual pairs of frames
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2013-01-01
Tight frames in Hilbert spaces have been studied intensively for the past years. In this paper we demonstrate that it often is an advantage to use pairs of dual frames rather than tight frames. We show that in any separable Hilbert space, any pairs of Bessel sequences can be extended to a pair of...... be extended to a pair of dual frames. © 2012 Elsevier Inc. All rights reserved....
Gauss-Bonnet chameleon mechanism of dark energy
International Nuclear Information System (INIS)
Ito, Yusaku; Nojiri, Shin'ichi
2009-01-01
As a model of the current accelerated expansion of the Universe, we consider a model of the scalar-Einstein-Gauss-Bonnet gravity. This model includes the propagating scalar modes, which might give a large correction to the Newton law. In order to avoid this problem, we propose an extension of the chameleon mechanism where the scalar mode becomes massive due to the coupling with the Gauss-Bonnet term. Since the Gauss-Bonnet invariant does not vanish near the Earth or in the Solar System, even in the vacuum, the scalar mode is massive even in the vacuum and the correction to the Newton law could be small. We also discuss the possibility that the model could describe simultaneously the inflation in the early Universe, in addition to the current accelerated expansion.
Gravitational perfect fluid collapse in Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Abbas, G.; Tahir, M. [The Islamia University of Bahawalpur, Department of Mathematics, Bahawalpur (Pakistan)
2017-08-15
The Einstein Gauss-Bonnet theory of gravity is the low-energy limit of heterotic super-symmetric string theory. This paper deals with gravitational collapse of a perfect fluid in Einstein-Gauss-Bonnet gravity by considering the Lemaitre-Tolman-Bondi metric. For this purpose, the closed form of the exact solution of the equations of motion has been determined by using the conservation of the stress-energy tensor and the condition of marginally bound shells. It has been investigated that the presence of a Gauss-Bonnet coupling term α > 0 and the pressure of the fluid modifies the structure and time formation of singularity. In this analysis a singularity forms earlier than a horizon, so the end state of the collapse is a naked singularity depending on the initial data. But this singularity is weak and timelike, which goes against the investigation of general relativity. (orig.)
The Bessel functions J0 and J1 of complex argument
International Nuclear Information System (INIS)
Ardill, R.W.B.; Moriarty, K.J.M.
1977-01-01
The Bessel function appears in a wide range of physical applications. The package Bessel contains complex function routines to calculate J 0 (z) and J 1 (z) for complex z. Bessel functions of higher order n 0 (z) and J 1 (z) for all values of mod(z) up to machine overflow. For mod(z) 10, the results diverge quite rapidly from their actual values. The accuracy for mod(z)<=10 is sufficient for most physical applications, and the polynomial approximations provide a quicker calculation of Bessel functions than the use of the ascending series formula used previously, particularly for values of mod(z) near 10. (Auth.)
Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory.
Kleihaus, Burkhard; Kunz, Jutta; Radu, Eugen
2011-04-15
We construct generalizations of the Kerr black holes by including higher-curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. We show that the domain of existence of these Einstein-Gauss-Bonnet-dilaton (EGBD) black holes is bounded by the Kerr black holes, the critical EGBD black holes, and the singular extremal EGBD solutions. The angular momentum of the EGBD black holes can exceed the Kerr bound. The EGBD black holes satisfy a generalized Smarr relation. We also compare their innermost stable circular orbits with those of the Kerr black holes and show the existence of differences which might be observable in astrophysical systems.
Large parameter cases of the Gauss hypergeometric function
N.M. Temme (Nico)
2002-01-01
textabstractWe consider the asymptotic behaviour of the Gauss hypergeometric function when several of the parameters {it a, b, c} are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Meixner, Krawtchouk, etc.), which results are already available and
Understanding Gauss's Law Using Spreadsheets
Baird, William H.
2013-01-01
Some of the results from the electrostatics portion of introductory physics are particularly difficult for students to understand and/or believe. For students who have yet to take vector calculus, Gauss's law is far from obvious and may seem more difficult than Coulomb's. When these same students are told that the minimum potential…
Composite Gauss-Legendre Formulas for Solving Fuzzy Integration
Directory of Open Access Journals (Sweden)
Xiaobin Guo
2014-01-01
Full Text Available Two numerical integration rules based on composition of Gauss-Legendre formulas for solving integration of fuzzy numbers-valued functions are investigated in this paper. The methods' constructions are presented and the corresponding convergence theorems are shown in detail. Two numerical examples are given to illustrate the proposed algorithms finally.
Gauss law constraints on Debye–Hückel screening
Indian Academy of Sciences (India)
We demand that the Gauss law at the edge must be obeyed by the electric potential () generated within a neutral plasma/electrolyte of strictly ﬁnite size by the introduction of a test charge b. Our proposal has the nice features that total ionic numbers are conserved, the point-Coulomb behaviour of () is guaranteed at ...
Maximum entropy estimation via Gauss-LP quadratures
Thély, Maxime; Sutter, Tobias; Mohajerin Esfahani, P.; Lygeros, John; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
2017-01-01
We present an approximation method to a class of parametric integration problems that naturally appear when solving the dual of the maximum entropy estimation problem. Our method builds up on a recent generalization of Gauss quadratures via an infinite-dimensional linear program, and utilizes a
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.
Bessel equation as an operator identity's matrix element in quantum mechanics
International Nuclear Information System (INIS)
Fan Hongyi; Li Chao
2004-01-01
We study the well-known Bessel equation itself in the framework of quantum mechanics. We show that the Bessel equation is a spontaneous result of an operator identity's matrix element in some definite entangled state representations, which is a fresh look. Application of this operator formalism in the Hankel transform of Laplace equation is presented
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.
Kerimov, M. K.
2018-01-01
This paper is the fourth in a series of survey articles concerning zeros of Bessel functions and methods for their computation. Various inequalities, estimates, expansions, etc. for positive zeros are analyzed, and some results are described in detail with proofs.
Conversion of isotropic fluorescence into a long-range non-diverging beam
Zhang, Douguo; Zhu, Liangfu; Chen, Junxue; Wang, Ruxue; Wang, Pei; Ming, Hai; Badugu, Ramachandram; Rosenfeld, Mary; Zhan, Qiwen; Kuang, Cuifang; Liu, Xu; Lakowicz, Joseph R.
2018-04-01
Fluorescent samples typically emit isotropically in all directions. Large lenses and other optical components are needed to capture a significant fraction of the emission, and complex confocal microscopes are required for high resolution focal-plane imaging. It is known that Bessel beams have remarkable properties of being able to travel over long distances, over 1000 times the wavelength, without diverging, and hence are called non-diffracting beams. In previous reports the Bessel beams were formed by an incident light source, typically with plane-wave illumination on a circular aperture. It was not known if Bessel beams could form from fluorescent light sources. We demonstrate transformation of the emission from fluorescent polystyrene spheres (FPS) into non-diverging beams which propagate up to 130 mm (13 cm) along the optical axis with a constant diameter. This is accomplished using a planar metal film, with no nanoscale features in the X-Y plane, using surface plasmon-coupled emission. Using samples which contain many FPS in the field-of-view, we demonstrate that an independent Bessel beam can be generated from any location on the metal film. The extremely long non-diffracted propagation distances, and self-healing properties of Bessel beams, offer new opportunities in fluorescence sensing and imaging.
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].
Energy Technology Data Exchange (ETDEWEB)
Balakin, A. A., E-mail: balakin.alexey@yandex.ru; Mironov, V. A.; Skobelev, S. A., E-mail: sk.sa1981@gmail.com [Russian Academy of Sciences, Institute of Applied Physics (Russian Federation)
2017-01-15
The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.
Computation of bessel functions in light scattering studies.
Ross, W D
1972-09-01
Computations of light scattering require finding Bessel functions of a series of orders. These are found most easily by recurrence, but excessive rounding errors may accumulate. Satisfactory procedures for cylinder and sphere functions are described. If argument z is real, find Y(n)(z) by recurrence to high orders. From two high orders of Y(n)(z) estimate J(n)(z). Use backward recurrence to maximum J(n)(z). Correct by forward recurrence to maximum. If z is complex, estimate high orders of J(n)(z) without Y(n)(z) and use backward recurrence.
Handling of the Generation of Primary Events in Gauss, the LHCb Simulation Framework
Corti, G; Brambach, T; Brook, N H; Gauvin, N; Harrison, K; Harrison, P; He, J; Ilten, P J; Jones, C R; Lieng, M H; Manca, G; Miglioranzi, S; Robbe, P; Vagnoni, V; Whitehead, M; Wishahi, J
2010-01-01
The LHCb simulation application, Gauss, consists of two independent phases, the generation of the primary event and the tracking of particles produced in the experimental setup. For the LHCb experimental program it is particularly important to model B meson decays: the EvtGen code developed in CLEO and BaBar has been chosen and customized for non coherent B production as occuring in pp collisions at the LHC. The initial proton-proton collision is provided by a different generator engine, currently Pythia 6 for massive production of signal and generic pp collisions events. Beam gas events, background events originating from proton halo, cosmics and calibration events for different detectors can be generated in addition to pp collisions. Different generator packages are available in the physics community or specifically developed in LHCb, and are used for the different purposes. Running conditions affecting the events generated such as the size of the luminous region, the number of collisions occuring in a bunc...
Noether symmetries in Gauss-Bonnet-teleparallel cosmology.
Capozziello, Salvatore; De Laurentis, Mariafelicia; Dialektopoulos, Konstantinos F
2016-01-01
A generalized teleparallel cosmological model, [Formula: see text], containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant [Formula: see text], is studied in the framework of the Noether symmetry approach. As [Formula: see text] gravity, where [Formula: see text] is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, [Formula: see text] contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function [Formula: see text] and to derive exact cosmological solutions.
Grassmannians and Gauss maps in piecewise-linear topology
Levitt, Norman
1989-01-01
The book explores the possibility of extending the notions of "Grassmannian" and "Gauss map" to the PL category. They are distinguished from "classifying space" and "classifying map" which are essentially homotopy-theoretic notions. The analogs of Grassmannian and Gauss map defined incorporate geometric and combinatorial information. Principal applications involve characteristic class theory, smoothing theory, and the existence of immersion satifying certain geometric criteria, e.g. curvature conditions. The book assumes knowledge of basic differential topology and bundle theory, including Hirsch-Gromov-Phillips theory, as well as the analogous theories for the PL category. The work should be of interest to mathematicians concerned with geometric topology, PL and PD aspects of differential geometry and the geometry of polyhedra.
Robust structural optimization using Gauss-type quadrature formula
International Nuclear Information System (INIS)
Lee, Sang Hoon; Seo, Ki Seog; Chen, Shikui; Chen, Wei
2009-01-01
In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the Tensor Product Quadrature (TPQ) formula and the Univariate Dimension Reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.
Robust structural optimization using Gauss-type quadrature formula
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Hoon; Seo, Ki Seog [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Chen, Shikui; Chen, Wei [Northwestern University, Illinois (United States)
2009-07-01
In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the Tensor Product Quadrature (TPQ) formula and the Univariate Dimension Reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.
Robust Structural Optimization Using Gauss-type Quadrature Formula
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Hoon; Seo, Ki Seog; Chen, Shikui; Chen, Wei [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2009-08-15
In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the tensor product quadrature (TPQ) formula and the univariate dimension reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.
Robust Structural Optimization Using Gauss-type Quadrature Formula
International Nuclear Information System (INIS)
Lee, Sang Hoon; Seo, Ki Seog; Chen, Shikui; Chen, Wei
2009-01-01
In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the tensor product quadrature (TPQ) formula and the univariate dimension reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty
Fate of black branes in Einstein-Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Suranyi, P.; Wijewardhana, L. C. R.; Vaz, C.
2009-01-01
Black branes are studied in Einstein-Gauss-Bonnet gravity. Evaporation drives black branes toward one of two singularities depending on the sign of α, the Gauss-Bonnet coupling. For positive α and sufficiently large ratio √(α)/L, where L/2π is the radius of compactification, black branes avoid the Gregory-Laflamme (GL) instability before reaching a critical state. No black branes with the radius of horizon smaller than the critical value can exist. Approaching the critical state branes have a nonzero Hawking temperature. For negative α all black branes encounter the GL instability. No black branes may exist outside of the interval of the critical values 0≤β h 2 and r h is the radius of horizon of the black brane. The first order phase transition line of GL transitions ends in a second order phase transition point at β=0.
Noether symmetries in Gauss-Bonnet-teleparallel cosmology
Energy Technology Data Exchange (ETDEWEB)
Capozziello, Salvatore [Universita' di Napoli' ' Federico II' ' , Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica ' ' E. Pancini' ' , Napoli (Italy); INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli (Italy); Gran Sasso Science Institute (INFN), L' Aquila (Italy); Tomsk State Pedagogical University, Tomsk (Russian Federation); De Laurentis, Mariafelicia [INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli (Italy); Tomsk State Pedagogical University, Tomsk (Russian Federation); Goethe University, Institute for Theoretical Physics, Frankfurt (Germany); Laboratory of Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), Tomsk (Russian Federation); Dialektopoulos, Konstantinos F. [Universita' di Napoli' ' Federico II' ' , Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica ' ' E. Pancini' ' , Napoli (Italy); INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli (Italy)
2016-11-15
A generalized teleparallel cosmological model, f(T{sub G},T), containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant T{sub G}, is studied in the framework of the Noether symmetry approach. As f(G, R) gravity, where G is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, f(T{sub G},T) contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function f(T{sub G},T) and to derive exact cosmological solutions. (orig.)
The block Gauss-Seidel method in sound transmission problems
Poblet-Puig, Jordi; Rodríguez Ferran, Antonio
2009-01-01
Sound transmission through partitions can be modelled as an acoustic fluid-elastic structure interaction problem. The block Gauss-Seidel iterative method is used in order to solve the finite element linear system of equations. The blocks are defined in a natural way, respecting the fluid and structural domains. The convergence criterion (spectral radius of iteration matrix smaller than one) is analysed and interpreted in physical terms by means of simple one-dimensional problems. This anal...
Resurgence and hydrodynamic attractors in Gauss-Bonnet holography
Casalderrey-Solana, Jorge; Gushterov, Nikola I.; Meiring, Ben
2018-04-01
We study the convergence of the hydrodynamic series in the gravity dual of Gauss-Bonnet gravity in five dimensions with negative cosmological constant via holography. By imposing boost invariance symmetry, we find a solution to the Gauss-Bonnet equation of motion in inverse powers of the proper time, from which we can extract high order corrections to Bjorken flow for different values of the Gauss-Bonnet parameter λGB. As in all other known examples the gradient expansion is, at most, an asymptotic series which can be understood through applying the techniques of Borel-Padé summation. As expected from the behaviour of the quasi-normal modes in the theory, we observe that the singularities in the Borel plane of this series show qualitative features that interpolate between the infinitely strong coupling limit of N=4 Super Yang Mills theory and the expectation from kinetic theory. We further perform the Borel resummation to constrain the behaviour of hydrodynamic attractors beyond leading order in the hydrodynamic expansion. We find that for all values of λGB considered, the convergence of different initial conditions to the resummation and its hydrodynamization occur at large and comparable values of the pressure anisotropy.
International Nuclear Information System (INIS)
Li Shun; Zhang Sijiong
2014-01-01
A numerical model is presented to simulate the influence function of deformable mirror actuators. The numerical model is formed by Bessel Fourier orthogonal functions, which are constituted of Bessel orthogonal functions and a Fourier basis. A detailed comparison is presented between the new Bessel Fourier model, the Zernike model, the Gaussian influence function and the modified Gaussian influence function. Numerical experiments indicate that the new numerical model is easy to use and more accurate compared with other numerical models. The new numerical model can be used for describing deformable mirror performances and numerical simulations of adaptive optics systems. (research papers)
Comment on 'Analytical results for a Bessel function times Legendre polynomials class integrals'
International Nuclear Information System (INIS)
Cregg, P J; Svedlindh, P
2007-01-01
A result is obtained, stemming from Gegenbauer, where the products of certain Bessel functions and exponentials are expressed in terms of an infinite series of spherical Bessel functions and products of associated Legendre functions. Closed form solutions for integrals involving Bessel functions times associated Legendre functions times exponentials, recently elucidated by Neves et al (J. Phys. A: Math. Gen. 39 L293), are then shown to result directly from the orthogonality properties of the associated Legendre functions. This result offers greater flexibility in the treatment of classical Heisenberg chains and may do so in other problems such as occur in electromagnetic diffraction theory. (comment)
Three-dimensional Bessel light bullets in self-focusing Kerr media
International Nuclear Information System (INIS)
Zhong Weiping; Belic, Milivoj; Huang Tingwen
2010-01-01
We study three-dimensional (3D) Bessel light-bullet solutions of the nonlinear Schroedinger equation with a photonic lattice potential in the form of squared Bessel functions in polar coordinates, both analytically and numerically. Analytical solutions are obtained by the Hartree approximation, and numerical simulations are performed, to compare with the analytical solutions and to confirm the stability of localized solutions. The 3D spatial wave packets are built by the products of hyperbolic secant and Bessel functions. These solitons appear in different forms, such as 3D vortex solitons and multipole solitons.
Bessel-function analysis of the optimized star coupler for uniform power splitting.
Song, G Hugh; Park, Mahn Yong
2004-08-01
An optimized N x N planar optic star coupler that utilizes directional coupling of arrayed waveguides for uniform power splitting is analyzed on the basis of special properties of the involved Bessel-function series. The analysis has provided a remarkably simple, novel basic design formula for such a device with much needed physical insights into the unique diffraction properties. For the analysis of diffraction from the end of directionally coupled arrayed waveguides, many useful formulas around the Bessel functions, such as the addition theorem and the Kepler-Bessel series, have been given in new forms.
A Limit Relation for Dunkl-Bessel Functions of Type A and B
Directory of Open Access Journals (Sweden)
Margit Rösler
2008-12-01
Full Text Available We prove a limit relation for the Dunkl-Bessel function of type BN with multiplicity parameters k_1 on the roots ±ei and k_2 on ±e_i±e_j where k_1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkl-type Bessel function of type A_{N−1} with multiplicity k_2. For certain values of k_2 an improved estimate is obtained from a corresponding limit relation for Bessel functions on matrix cones.
Self-reconstruction of diffraction-free and accelerating laser beams in scattering media
International Nuclear Information System (INIS)
Ersoy, T.; Yalizay, B.; Akturk, S.
2012-01-01
We experimentally investigate propagation of laser beams with different intensity profiles in highly scattering media. We generate transverse laser amplitude profiles with Gaussian, Bessel and Airy function envelopes. We then propagate these beams through optical phantoms formed with variable density intralipid solutions. At the sample exit, we compare change in maximum intensities, as well as beam profile reconstruction. We show that self-reconstruction properties of Bessel and Airy beams bring about slower decrease in maximum intensity with increasing scatterer density. On the other hand, the beam profiles deteriorate faster, as compared to reference Gaussian beams. Slower decrease in the intensity can be attributed to the wavevector spectra providing a continuous flow of energy to the beam center, while beam deterioration is linked to total beam volume in the scattering medium. These results show that beam shaping methods can significantly enhance delivery of intense light deeper into turbid media, but this enhancement is compromised by stronger speckling of beam profiles. -- Highlights: ► We experimentally investigate propagation of shaped laser beams in turbid media. ► Peak intensity of Bessel and Airy beams decrease slower with increasing scatterer. ► Shaped beam profiles deteriorate faster, as compared to reference Gaussian beams. ► Shaped beam profiles can enhance applications of lasers inscattering media.
Beams made of twisted atoms: A theoretical analysis
Energy Technology Data Exchange (ETDEWEB)
Hayrapetyan, Armen [Physikalisches Institut, Ruprecht-Karls-Universitaet Heidelberg, 69120 Heidelberg (Germany); Matula, Oliver [Physikalisches Institut, Ruprecht-Karls-Universitaet Heidelberg, 69120 Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung, 64291 Darmstadt (Germany); Surzhykov, Andrey [Helmholtz-Institut Jena, 07743 Jena (Germany); Fritzsche, Stephan [Helmholtz-Institut Jena, 07743 Jena (Germany); Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet Jena, 07743 Jena (Germany)
2014-07-01
We have analyzed Bessel beams of two-level atoms that are driven by a linearly polarized laser light. Based on the Schroedinger equation for two-level systems, we first determine the states of two-level atoms in a plane-wave field by taking into account propagation directions both of the atom and the field. For such laser-driven two-level atoms, we construct Bessel beams by going beyond the typical paraxial approximation. In particular, we show that the probability density of these atomic beams exhibits a non-trivial, Bessel-squared-type behavior. The profile of such twisted atoms is affected by atom and laser parameters, such as the nuclear charge, atom velocity, laser frequency, and propagation geometry of the atom and laser beams. Moreover, we spatially and temporally characterize the beam of hydrogen and selected (neutral) alkali-metal atoms that carry non-zero orbital angular momentum (OAM). The proposed spatiotemporal Bessel states (i) are able to describe twisted states of any two-level system which is driven by the radiation field and (ii) have potential applications in atomic and nuclear processes as well as in quantum communication.
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
Roots of two transcendental equations involving spherical bessel functions
International Nuclear Information System (INIS)
Pexton, R.L.; Steiger, A.D.
1977-01-01
Roots of the transcendental equations j/sub l/(αlambda) y/sub l/(lambda) =j/sub l/(lambda) y/sub l/(αlambda) and [xj/sub l/(x)]'/sub x alphaeta yl-italic/(x)]'/sub x eta/=xj/sub l/(x)]'/sub x eta yl-italic/(x)]'/sub x alphaeta/for the spherical Bessel functions of the first and second kind, j/sub l/(z) and y/sub l/(z), have been computed. The ranges for the parameter α, the order l and the root index n are: α=0.1(0.1)0.7,l=1(1)15,n=1(1)30
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.
Precise analytic approximations for the Bessel function J1 (x)
Maass, Fernando; Martin, Pablo
2018-03-01
Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.
Semi-analytical solution to arbitrarily shaped beam scattering
Wang, Wenjie; Zhang, Huayong; Sun, Yufa
2017-07-01
Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.
Bessel smoothing filter for spectral-element mesh
Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.
2017-06-01
Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the
Elliptic integral evaluations of Bessel moments and applications
International Nuclear Information System (INIS)
Bailey, David H; Borwein, Jonathan M; Broadhurst, David; Glasser, M L
2008-01-01
We record and substantially extend what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. In particular, we develop formulae for integrals of products of six or fewer Bessel functions. In consequence, we are able to discover and prove closed forms for c n,k := ∫ ∞ 0 t k K n 0 (t) dt with integers n 1, 2, 3, 4 and k ≥ 0, obtaining new results for the even moments c 3,2k and c 4,2k . We also derive new closed forms for the odd moments s n,2k+1 := ∫ ∞ 0 t 2k+1 I 0 (t)K n-1 0 (t) dt with n = 3, 4 and for t n,2k+1 :∫ ∞ 0 t 2k+1 I 2 0 (t)K n-2 0 (t) dt with n = 5, relating the latter to Green functions on hexagonal, diamond and cubic lattices. We conjecture the values of s 5,2k+1 , make substantial progress on the evaluation of c 5,2k+1 , s 6,2k+1 and t 6,2k+1 and report more limited progress regarding c 5,2k , c 6,2k+1 and c 6,2k . In the process, we obtain eight conjectural evaluations, each of which has been checked to 1200 decimal places. One of these lies deep in four-dimensional quantum field theory and two are probably provable by delicate combinatorics. There remains a hard core of five conjectures whose proofs would be most instructive, to mathematicians and physicists alike
Application of a non-integer Bessel uniform approximation to inelastic molecular collisions
International Nuclear Information System (INIS)
Connor, J.N.L.; Mayne, H.R.
1979-01-01
A non-integer Bessel uniform approximation has been used to calculate transition probabilities for collinear atom-oscillator collisions. The collision systems used are a harmonic oscillator interacting via a Lennard-Jones potential and a Morse oscillator interacting via an exponential potential. Both classically allowed and classically forbidden transitions have been treated. The order of the Bessel function is chosen by a physical argument that makes use of information contained in the final-action initial-angle plot. Limitations of this procedure are discussed. It is shown that the non-integer Bessel approximation is accurate for elastic 0 → 0 collisions at high collision energies, where the integer Bessel approximation is inaccurate or inapplicable. (author)
Semi-Inclusive Deep Inelastic Scattering and Bessel-Weighted Asymmetries
International Nuclear Information System (INIS)
Gamberg, Leonard; Boer, Daniel; Musch, Bernhard; Prokudin, Alexei
2012-01-01
We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.
Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions.
Ziener, Christian H; Kurz, Felix T; Buschle, Lukas R; Kampf, Thomas
2015-01-01
The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval [Formula: see text] with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function [Formula: see text] or linear combinations of the spherical Bessel functions [Formula: see text]. The orthogonality relations with analytical expressions for the normalization constant are given. Explicit expressions for the Lommel integrals in terms of Lommel functions are derived. The cross product zeros [Formula: see text] and [Formula: see text] are considered in the complex plane for real as well as complex values of the index [Formula: see text] and approximations for the exceptional zero [Formula: see text] are obtained. A numerical scheme based on the discretization of the two-dimensional and three-dimensional Laplace operator with Neumann boundary conditions is presented. Explicit representations of the radial part of the Laplace operator in form of a tridiagonal matrix allow the simple computation of the cross product zeros.
Bessel harmonic analysis and approximation of functions on the half-line
International Nuclear Information System (INIS)
Platonov, Sergei S
2007-01-01
We study problems of approximation of functions on [0,+∞) in the metric of L p with power weight using generalized Bessel shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Bessel shifts. We establish the equivalence of the modulus of smoothness and the K-functional. We define function spaces of Nikol'skii-Besov type and describe them in terms of best approximations. As a tool for approximation, we use a certain class of entire functions of exponential type. In this class, we prove analogues of Bernstein's inequality and others for the Bessel differential operator and its fractional powers. The main tool we use to solve these problems is Bessel harmonic analysis
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_\
On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind
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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.
q-Sumudu transforms of q-analogues of Bessel functions.
Uçar, Faruk
2014-01-01
The main purpose of this paper is to evaluate q-Sumudu transforms of a product of q-Bessel functions. Interesting special cases of theorems are also discussed. Further, the results proved in this paper may find certain applications of q-Sumudu transforms to the solutions of the q-integrodifferential equations involving q-Bessel functions. The results may help to extend the q-theory of orthogonal functions.
Symbolic methods for the evaluation of sum rules of Bessel functions
International Nuclear Information System (INIS)
Babusci, D.; Dattoli, G.; Górska, K.; Penson, K. A.
2013-01-01
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics
On sharp estimates of the convergence of double Fourier-Bessel series
Abilov, V. A.; Abilova, F. V.; Kerimov, M. K.
2017-11-01
The problem of approximation of a differentiable function of two variables by partial sums of a double Fourier-Bessel series is considered. Sharp estimates of the rate of convergence of the double Fourier-Bessel series on the class of differentiable functions of two variables characterized by a generalized modulus of continuity are obtained. The proofs of four theorems on this issue, which can be directly applied to solving particular problems of mathematical physics, approximation theory, etc., are presented.
Expansion of infinite series containing modified Bessel functions of the second kind
International Nuclear Information System (INIS)
Fucci, Guglielmo; Kirsten, Klaus
2015-01-01
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the parameters in the argument of the modified Bessel function of the second kind is small compared to the others. We apply the results obtained for the asymptotic expansion to specific problems that arise in the ambit of quantum field theory. (paper)
On the Computation and Applications of Bessel Functions with Pure Imaginary Indices
Matyshev, A. A.; Fohtung, E.
2009-01-01
Bessel functions with pure imaginary index (order) play an important role in corpuscular optics where they govern the dynamics of charged particles in isotrajectory quadrupoles. Recently they were found to be of great importance in semiconductor material characterization as they are manifested in the strain state of crystalline material. A new algorithm which can be used for the computation of the normal and modifed Bessel functions with pure imaginary index is proposed. The developed algorit...
Reduction of quantum systems and the local Gauss law
Stienstra, Ruben; van Suijlekom, Walter D.
2018-05-01
We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796-1808, 2002; J Math Phys 46:032303, 2004).
Colliding scalar pulses in the Einstein-Gauss-Bonnet gravity
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Shinkai Hisaaki
2018-01-01
Full Text Available We numerically investigated how the nonlinear dynamics depends on the dimensionality and on the higher-order curvature corrections in the form of Gauss-Bonnet (GB terms, with a model of colliding scalar pulses in plane-symmetric space-time. We observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude depends on αGB. The normal corrections (αGB > 0 work for avoiding the appearance of singularity, although it is inevitable.
Non-paraxial beam to push and pull microparticles
DEFF Research Database (Denmark)
Novitsky, Andrey; Qiu, C.-W.
2011-01-01
We discuss a feasibility of the pulling (backward) force acting on a spherical microparticle in a non-paraxial Bessel beam. The effect can be explained by the strong interaction of particle's multipoles or by the conservation of momentum in the system “photons-particle.” It is remarkable that the...
Energy conditions in modified Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Garcia, Nadiezhda Montelongo; Harko, Tiberiu; Lobo, Francisco S. N.; Mimoso, Jose P.
2011-01-01
In considering alternative higher-order gravity theories, one is liable to be motivated in pursuing models consistent and inspired by several candidates of a fundamental theory of quantum gravity. Indeed, motivations from string/M theory predict that scalar field couplings with the Gauss-Bonnet invariant, G, are important in the appearance of nonsingular early time cosmologies. In this work, we discuss the viability of an interesting alternative gravitational theory, namely, modified Gauss-Bonnet gravity or f(G) gravity. We consider specific realistic forms of f(G) analyzed in the literature that account for the late-time cosmic acceleration and that have been found to cure the finite-time future singularities present in the dark energy models. We present the general inequalities imposed by the energy conditions and use the recent estimated values of the Hubble, deceleration, jerk and snap parameters to examine the viability of the above-mentioned forms of f(G) imposed by the weak energy condition.
Phase space of modified Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Carloni, Sante [Universidade de Lisboa-UL, Centro Multidisciplinar de Astrofisica-CENTRA, Instituto Superior Tecnico-IST, Lisbon (Portugal); Mimoso, Jose P. [Instituto de Astrofisica e Ciencias do Espaco, Universidade de Lisboa, Departamento de Fisica, Faculdade de Ciencias, Lisbon (Portugal)
2017-08-15
We investigate the evolution of non-vacuum Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f(R) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations. (orig.)
A note on the viability of Gauss-Bonnet cosmology
International Nuclear Information System (INIS)
Chingangbam, R.; Sami, M.; Tretyakov, P.V.; Toporensky, A.V.
2008-01-01
In this Letter, we analyze the viability of a vacuum Gauss-Bonnet cosmology by examining the dynamics of the homogeneous and anisotropic background in 4+1 dimensions. The trajectories of the system either originate from the standard singularity or from non-standard type, the later is characterized by the divergence of time derivative of the Hubble parameters for its finite value. At the onset, the system should relax to Einstein phase at late times as the effect of Gauss-Bonnet term becomes negligible in the low energy regime. However, we find that most of the trajectories emerging from the standard big-bang singularity lead to future re-collapse whereas the system beginning its evolution from the non-standard singularity enters the Kasner regime at late times. This leads to the conclusion that the measure of trajectories giving rise to a smooth evolution from a standard singularity to the Einstein phase is negligibly small for generic initial conditions
Reduction of entanglement degradation in Einstein-Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Nasr Esfahani, B.; Shamirzaie, M.; Soltani, M.
2011-01-01
Bipartite entanglement for states of a noninteracting bosonic or fermionic field in the spacetime of a spherically symmetric black hole of Einstein-Gauss-Bonnet gravity is investigated. Although the initial state is chosen to be maximally entangled as the Bell states, the Hawking-Unruh effect causes the state to be mixed and the entanglement degrades, but with different asymptotic behaviors for the fermionic and bosonic fields. The Gauss-Bonnet term with positive α can play an antigravitation role and so this causes a decrease in the Hawking-Unruh effect and consequently reduces the entanglement degradation. On the other hand, the suggested higher dimensions for the spacetime lead to increased entanglement degradation by increasing the dimension. There is a dramatic difference between the behaviors of the entanglement in terms of the radius of the horizon for a five-dimensional black hole and that for higher dimensional black holes. Both bosonic and fermionic fields entanglements are treated beyond the single-mode approximation. Also, the cases where the accelerating observers located at regions near and far from the event horizon of black hole are studied separately.
A line scanned light-sheet microscope with phase shaped self-reconstructing beams.
Fahrbach, Florian O; Rohrbach, Alexander
2010-11-08
We recently demonstrated that Microscopy with Self-Reconstructing Beams (MISERB) increases both image quality and penetration depth of illumination beams in strongly scattering media. Based on the concept of line scanned light-sheet microscopy, we present an add-on module to a standard inverted microscope using a scanned beam that is shaped in phase and amplitude by a spatial light modulator. We explain technical details of the setup as well as of the holograms for the creation, positioning and scaling of static light-sheets, Gaussian beams and Bessel beams. The comparison of images from identical sample areas illuminated by different beams allows a precise assessment of the interconnection between beam shape and image quality. The superior propagation ability of Bessel beams through inhomogeneous media is demonstrated by measurements on various scattering media.
Vectorial analysis of the collimated beam of a small Gaussian source
Cao, Changqing; Wang, Ting; Zeng, Xiaodong; Feng, Zhejun; Zhang, Wenrui; Zhang, Xiaobing; Chen, Kun
2018-03-01
A vectorial analysis method to describe the collimated beam is proposed, the formulas of the intensity distribution and divergence angles represented in terms of Bessel functions are derived, and the propagation properties such as the vectorial structure of the collimated field and the shape of the beam spot are discussed in detail. Omitting the vectorial nature of the collimated beam can cause an error of 7.6% in determining the intensity distribution on the optical axis of the collimated beam.
A New Sum Analogous to Gauss Sums and Its Fourth Power Mean
Directory of Open Access Journals (Sweden)
Shaofeng Ru
2014-01-01
Full Text Available The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.
International Nuclear Information System (INIS)
Qin Hong; Phillips, Cynthia K.; Davidson, Ronald C.
2007-01-01
The susceptibility tensor of a hot, magnetized plasma is conventionally expressed in terms of infinite sums of products of Bessel functions. For applications where the particle's gyroradius is larger than the wavelength, such as alpha particle dynamics interacting with lower-hybrid waves, and the focusing of charged particle beams using a solenoidal field, the infinite sums converge slowly. In this paper, a new derivation of the plasma susceptibility tensor is presented which exploits a symmetry in the particle's orbit to simplify the integration along the unperturbed trajectories. As a consequence, the infinite sums appearing in the conventional expression are replaced by definite double integrals over one gyroperiod, and the cyclotron resonances of all orders are captured by a single term. Furthermore, the double integrals can be carried out and expressed in terms of Bessel functions of complex order, in agreement with expressions deduced previously using the Newburger sum rule. From this new formulation, it is straightforward to derive the asymptotic form of the full hot plasma susceptibility tensor for a gyrotropic but otherwise arbitrary plasma distribution in the large gyroradius limit. These results are of more general importance in the numerical evaluation of the plasma susceptibility tensor. Instead of using the infinite sums occurring in the conventional expression, it is only necessary to evaluate the Bessel functions once according to the new expression, which has significant advantages, especially when the particle's gyroradius is large and the conventional infinite sums converge slowly. Depending on the size of the gyroradius, the computational saving enabled by this representation can be several orders-of-magnitude
Higher order Riesz transforms associated with Bessel operators
Betancor, Jorge J.; Fariña, Juan C.; Martinez, Teresa; Rodríguez-Mesa, Lourdes
2008-10-01
In this paper we investigate Riesz transforms R μ ( k) of order k≥1 related to the Bessel operator Δμ f( x)=- f”( x)-((2μ+1)/ x) f’( x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We obtain that for every k≥1, R μ ( k) is a principal value operator of strong type ( p, p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ( x)= x 2μ+1 dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R μ ( k) maps L p (ω) into itself and L 1(ω) into L 1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class mathcal{A}p^μ of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman.
Anisotropic resonator analysis using the Fourier-Bessel mode solver
Gauthier, Robert C.
2018-03-01
A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday's and Ampere's laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier-Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.
The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
Directory of Open Access Journals (Sweden)
Shuguo Shi
2008-03-01
Full Text Available In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1. Particularly, we discuss the surfaces with conformal normal Gauss map in H³ and S³1, and prove a duality property. We give a Weierstrass representation formula for space-like surfaces in S³1 with conformal normal Gauss map. We also state the similar results for time-like surfaces in S³1. Some examples of surfaces in S³1 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère type for the graphs in S³1 with conformal normal Gauss map is derived.Neste artigo, introduzimos a quarta forma fundamental de uma hipersuperfície em Hn+1 de uma hipersuperfície tipo-espaço em S1n+1, e discutimos a conformalidade da aplicação normal de Gauss de tais hipersuperfícies. Em particular, investigamos o caso de superfícies com aplicação normal de Gauss conforme em H³ e S³1, e provamos um teorema de dualidade. Apresentamos uma representação de Weierstrass para superfícies tipo-espaço em S³1 com aplicação de Gauss conforme. Enunciamos também resultados semelhantes para superfícies tipo-tempo em S³1. São dados alguns exemplos de superfícies em S³1 com aplicações de Gauss conformes, e é deduzida uma equação totalmente não-linear do tipo Monge-Ampère para gráficos em S³1 com aplicações de Gauss conformes.
Instability of black holes with a Gauss-Bonnet term
International Nuclear Information System (INIS)
Ahn, Wha-Keun; Gwak, Bogeun; Lee, Wonwoo; Lee, Bum-Hoon
2015-01-01
We investigate the fragmentation instability of hairy black holes in the theory with a Gauss-Bonnet (GB) term in asymptotically flat spacetime. Our approach is through the non-perturbative fragmentation instability. By this approach, we investigate whether the initial black hole can be broken into two black holes by comparing the entropy of the initial black hole with the sum of those of two fragmented black holes. The relation between the black hole instability and the GB coupling with dilaton hair are presented. We describe the phase diagrams with respect to the mass of the black hole solutions and coupling constants. We find that a perturbatively stable black hole can be unstable under fragmentation. (orig.)
Gauss-Manin Connection in Disguise: Calabi-Yau Threefolds
Alim, Murad; Movasati, Hossein; Scheidegger, Emanuel; Yau, Shing-Tung
2016-06-01
We describe a Lie Algebra on the moduli space of non-rigid compact Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions {{F}g^alg, g ≥ 1}, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.
Gauss decomposition, Wakimoto realisation and gauged WZNW models
International Nuclear Information System (INIS)
Arfaei, H.; Mohammedi, N.
1993-10-01
The implications of gauging the Wess-Zumino-Novikov-Witten (WZNW) model using the Gauss decomposition of the group elements are explored. We show that, contrary to standard gauging of WZNW models, this gauging is carried out by minimally coupling the gauge fields. We find that this gauging, in the case of gauging an abelian vector subgroup, differs from the standard one by terms proportional to the field strength of the gauge fields. We prove that gauging an abelian vector subgroup does not have a nonlinear sigma model interpretation. This is because the target-space metric resulting from the integration over the gauge fields is degenerate. We demonstrate, however, that this kind of gauging has a natural interpretation in terms of Wakimoto variables. (orig.)
The Cousins of Stuxnet: Duqu, Flame, and Gauss
Directory of Open Access Journals (Sweden)
Márk Félegyházi
2012-11-01
Full Text Available Stuxnet was the first targeted malware that received worldwide attention forcausing physical damage in an industrial infrastructure seemingly isolated from the onlineworld. Stuxnet was a powerful targeted cyber-attack, and soon other malware samples were discovered that belong to this family. In this paper, we will first present our analysis of Duqu, an information-collecting malware sharing striking similarities with Stuxnet. Wedescribe our contributions in the investigation ranging from the original detection of Duquvia finding the dropper file to the design of a Duqu detector toolkit. We then continue with the analysis of the Flame advanced information-gathering malware. Flame is unique in thesense that it used advanced cryptographic techniques to masquerade as a legitimate proxyfor the Windows Update service. We also present the newest member of the family, called Gauss, whose unique feature is that one of its modules is encrypted such that it can onlybe decrypted on its target system; hence, the research community has not yet been able to analyze this module. For this particular malware, we designed a Gauss detector serviceand we are currently collecting intelligence information to be able to break its very specialencryption mechanism. Besides explaining the operation of these pieces of malware, wealso examine if and how they could have been detected by vigilant system administrators manually or in a semi-automated manner using available tools. Finally, we discuss lessonsthat the community can learn from these incidents. We focus on technical issues, and avoidspeculations on the origin of these threats and other geopolitical questions.
F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements
Karney, C. F. F.; Deakin, R. E.
2010-08-01
Issue No. 86 (1825 October) of the Astronomische Nachrichten was largely devoted to a single paper by F. W. Bessel on the solution of the direct geodesic problem (see the first sentences of the paper). For the most part, the paper stands on its own and needs little introduction. However, a few words are in order to place this paper in its historical context. First of all, it should be no surprise that a paper on this subject appeared in an astronomical journal. At the time, the disciplines of astronomy, navigation, and surveying were inextricably linked -- the methods and, in many cases, the practitioners (in particular, Bessel) were the same. Prior to Bessel's paper, the solution of the geodesic problem had been the subject of several studies by Clairaut, Euler, du Séjour, Legendre, Oriani, and others. The interest in the subject was twofold. It combined several new fields of mathematics: the calculus of variations, the theory of elliptic functions, and the differential geometry of curved surfaces. It also addressed very practical needs: the determination of the figure of the earth, the requirements of large scale surveys, and the construction of map projections. With the papers of Legendre and of Oriani in 1806, the framework for the mathematical solution for an ellipsoid of revolution had been established. However, Bessel was firmly in the practical camp; he carried out the East Prussian survey that connected the West European and Russian triangulation networks and later he made the first accurate estimate of the figure of the Earth, the ``Bessel ellipsoid''. He lays out his goal for this paper in its first section: to simplify the numerical solution of the geodesic problem. In Sects. \\ref{sec2}--\\ref{sec4}, Bessel gives a clear and concise summary of the previous work on the problem. In the remaining sections, he develops series for the distance and longitude integrals and constructs the tables which allow geodesics to be calculated to an accuracy of about 3
Lötstedt, Erik; Jentschura, Ulrich D
2009-02-01
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.
Approximate solutions of the hyperchaotic Rössler system by using the Bessel collocation scheme
Directory of Open Access Journals (Sweden)
Şuayip Yüzbaşı
2015-02-01
Full Text Available The purpose of this study is to give a Bessel polynomial approximation for the solutions of the hyperchaotic Rössler system. For this purpose, the Bessel collocation method applied to different problems is developed for the mentioned system. This method is based on taking the truncated Bessel expansions of the functions in the hyperchaotic Rössler systems. The suggested secheme converts the problem into a system of nonlinear algebraic equations by means of the matrix operations and collocation points, The accuracy and efficiency of the proposed approach are demonstrated by numerical applications and performed with the help of a computer code written in Maple. Also, comparison between our method and the differential transformation method is made with the accuracy of solutions.
Fractional Fourier transform for confluent hypergeometric beams
International Nuclear Information System (INIS)
Tang, Bin; Jiang, Chun; Zhu, Haibin
2012-01-01
Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.
International Nuclear Information System (INIS)
Dattoli, G.; Torre, A.; Mancho, A.M.
2000-01-01
The theory of generalized Bessel functions has found significant applications in the analysis of radiation phenomena, associated with charges moving in magnetic devices. In this paper we exploit the monomiality principle to discuss the theory of two-variable Laguerre polynomials and introduce the associated Laguerre-Bessel functions. We study their properties (addition and multiplication theorems, generating function, recurrence relations and so on) and discuss the link with the ordinary case. The usefulness of the obtained results to treat problems relevant to the paraxial propagation of electromagnetic waves is also discussed.
Generalized coherent states related to the associated Bessel functions and Morse potential
International Nuclear Information System (INIS)
Mojaveri, B; Amiri Faseghandis, S
2014-01-01
Using the associated Bessel functions, a shape-invariant Lie algebra spanned by ladder operators plus the identity operator, is realized. The Hilbert space of the associated Bessel functions, representing the Lie algebra, are established and two kinds of generalized coherent states as an appropriate superposition of these functions are constructed. By implying appropriate similarity transformation on the constructed coherent states, the generalized coherent states for the Morse potential are obtained. By considering some statistical characteristics, it is revealed that the constructed coherent states indeed possess nonclassical features, such as squeezing and sub-Poissonian statistics. (paper)
Studies on the zeros of Bessel functions and methods for their computation
Kerimov, M. K.
2014-09-01
The zeros of Bessel functions play an important role in computational mathematics, mathematical physics, and other areas of natural sciences. Studies addressing these zeros (their properties, computational methods) can be found in various sources. This paper offers a detailed overview of the results concerning the real zeros of the Bessel functions of the first and second kinds and general cylinder functions. The author intends to publish several overviews on this subject. In this first publication, works dealing with real zeros are analyzed. Primary emphasis is placed on classical results, which are still important. Some of the most recent publications are also discussed.
Aksenov, Valerii P; Kolosov, Valeriy V; Pogutsa, Cheslav E
2014-06-10
The propagation of laser beams having orbital angular momenta (OAM) in the turbulent atmosphere is studied numerically. The variance of random wandering of these beams is investigated with the use of the Monte Carlo technique. It is found that, among various types of vortex laser beams, such as the Laguerre-Gaussian (LG) beam, modified Bessel-Gaussian beam, and hypergeometric Gaussian beam, having identical initial effective radii and OAM, the LG beam occupying the largest effective volume in space is the most stable one.
Uniform Gauss-Weight Quadratures for Discrete Ordinate Transport Calculations
International Nuclear Information System (INIS)
Carew, John F.; Hu, Kai; Zamonsky, Gabriel
2000-01-01
Recently, a uniform equal-weight quadrature set, UE n , and a uniform Gauss-weight quadrature set, UG n , have been derived. These quadratures have the advantage over the standard level-symmetric LQ n quadrature sets in that the weights are positive for all orders,and the transport solution may be systematically converged by increasing the order of the quadrature set. As the order of the quadrature is increased,the points approach a uniform continuous distribution on the unit sphere,and the quadrature is invariant with respect to spatial rotations. The numerical integrals converge for continuous functions as the order of the quadrature is increased.The numerical characteristics of the UE n quadrature set have been investigated previously. In this paper, numerical calculations are performed to evaluate the application of the UG n quadrature set in typical transport analyses. A series of DORT transport calculations of the >1-MeV neutron flux have been performed for a set of pressure-vessel fluence benchmark problems. These calculations employed the UG n (n = 8, 12, 16, 24, and 32) quadratures and indicate that the UG n solutions have converged to within ∼0.25%. The converged UG n solutions are found to be comparable to the UE n results and are more accurate than the level-symmetric S 16 predictions
Regular black holes in Einstein-Gauss-Bonnet gravity
Ghosh, Sushant G.; Singh, Dharm Veer; Maharaj, Sunil D.
2018-05-01
Einstein-Gauss-Bonnet theory, a natural generalization of general relativity to a higher dimension, admits a static spherically symmetric black hole which was obtained by Boulware and Deser. This black hole is similar to its general relativity counterpart with a curvature singularity at r =0 . We present an exact 5D regular black hole metric, with parameter (k >0 ), that interpolates between the Boulware-Deser black hole (k =0 ) and the Wiltshire charged black hole (r ≫k ). Owing to the appearance of the exponential correction factor (e-k /r2), responsible for regularizing the metric, the thermodynamical quantities are modified, and it is demonstrated that the Hawking-Page phase transition is achievable. The heat capacity diverges at a critical radius r =rC, where incidentally the temperature is maximum. Thus, we have a regular black hole with Cauchy and event horizons, and evaporation leads to a thermodynamically stable double-horizon black hole remnant with vanishing temperature. The entropy does not satisfy the usual exact horizon area result of general relativity.
Gravity in the Einstein-Gauss-Bonnet theory with the Randall-Sundrum background
International Nuclear Information System (INIS)
Kim, Jihn E.; Lee, Hyun Min
2001-01-01
We obtain the full 5D graviton propagator in the Randall-Sundrum model with the Gauss-Bonnet interaction. From the decomposition of the graviton propagator on the brane, we show that localization of gravity arises in the presence of the Gauss-Bonnet term. We also obtain the metric perturbation for observers on the brane with considering the brane bending and compute the amplitude of one massless graviton exchange. For the positive definite amplitude or no ghost states, the sign of the Gauss-Bonnet term should be negative in our convention, which is compatible with string amplitude computations. In that case, the ghost-free condition is sufficient for obtaining the Newtonian gravity. For a vanishing Gauss-Bonnet coefficient, the brane bending allows us to reproduce the correct graviton polarizations for the effective 4D Einstein gravity
Automatic Fourier transform and self-Fourier beams due to parabolic potential
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)
2015-12-15
We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.
A Derandomized Algorithm for RP-ADMM with Symmetric Gauss-Seidel Method
Xu, Jinchao; Xu, Kailai; Ye, Yinyu
2017-01-01
For multi-block alternating direction method of multipliers(ADMM), where the objective function can be decomposed into multiple block components, we show that with block symmetric Gauss-Seidel iteration, the algorithm will converge quickly. The method will apply a block symmetric Gauss-Seidel iteration in the primal update and a linear correction that can be derived in view of Richard iteration. We also establish the linear convergence rate for linear systems.
Penyelesaian Persamaan Poisson 2D dengan Menggunakan Metode Gauss-Seidel dan Conjugate Gradien
Mahmudah, Dewi Erla; Naf'an, Muhammad Zidny
2017-01-01
In this paper we focus on solution of 2D Poisson equation numerically. 2D Poisson equation is a partial differential equation of second order elliptical type. This equation is a particular form or non-homogeneous form of the Laplace equation. The solution of 2D Poisson equation is performed numerically using Gauss Seidel method and Conjugate Gradient method. The result is the value using Gauss Seidel method and Conjugate Gradient method is same. But, consider the iteration process, the conver...
Note on inflation with a tachyon rolling on the Gauss-Bonnet brane
International Nuclear Information System (INIS)
Paul, B.C.; Sami, M.
2004-01-01
In this paper we study the tachyonic inflation in brane world cosmology with Gauss-Bonnet term in the bulk. We obtain the exact solution of slow roll equations in case of exponential potential. We attempt to implement the proposal of J. E. Lidsey and N. J. Nunes [Phys. Rev. D 67, 103510 (2003)] for the tachyon condensate rolling on the Gauss-Bonnet brane and discuss the difficulties associated with the proposal
Orbital angular momentum mode of Gaussian beam induced by atmospheric turbulence
Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Yan, Xu; Dong, Kangjun
2018-02-01
Superposition theory of the spiral harmonics is employed to numerical study the transmission property of the orbital angular momentum (OAM) mode of Gaussian beam induced by atmospheric turbulence. Results show that Gauss beam does not carry OAM at the source, but various OAM modes appear after affected by atmospheric turbulence. With the increase of atmospheric turbulence strength, the smaller order OAM modes appear firstly, followed by larger order OAM modes. The beam spreading of Gauss beams in the atmosphere enhance with the increasing topological charge of the OAM modes caused by atmospheric turbulence. The mode probability density of the OAM generated by atmospheric turbulence decreases, and peak position gradually deviate from the Gauss beam spot center with the increase of the topological charge. Our results may be useful for improving the performance of long distance laser digital spiral imaging system.
Algorithm 831: modified Bessel functions of imaginary order and positive argument
A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)
2004-01-01
textabstract77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions Kia (x), Lia (x) and their derivatives for real a and positive x; these functions are independent solutions of the differential equation x2w'' + xw' + (a2
Evaluating the Financial Flows of Bessel Processes by Using Spectral Analysis
Directory of Open Access Journals (Sweden)
Burtnyak Ivan V.
2017-07-01
Full Text Available The article solves the two-parameter task of evaluating the intensity of diffuse Bessel processes by the methods of spectral theory. In particular, barriers for cost of options, where the derivative of financial flows turns into zero, have been considered, and a task for the two-barrier option has been solved, which corresponds to Bessel process. A Green’s function has been built for the diffusion Bessel process of the two-barrier option, decomposed according to the first-type system of Bessel functions. The barriers are taken in such a way that the derivative of financial flow in terms of price is turned to zero, i.e. there are the points where flow can acquire extreme values. On the basis of Green’s function, the value of securities has been calculated. It is handier to use similar barriers when monitoring a stock market. The Green’s function for this task, which represents the probability of spreading the option price, is represented through the Fourier series. This provides an opportunity to evaluate the intensity of financial flows in stock markets.
Directory of Open Access Journals (Sweden)
Burtnyak Ivan V.
2017-06-01
Full Text Available In the paper we apply the spectral theory to find the price for derivatives of financial assets assuming that the processes described are Markov processes and such that can be considered in the Hilbert space L^2 using the Sturm-Liouville theory. Bessel diffusion processes are used in studying Asian options. We consider the financial flows generated by the Bessel diffusions by expressing them in terms of the system of Bessel functions of the first kind, provided that they take into account the linear combination of the flow and its spatial derivative. Such expression enables calculating the size of the market portfolio and provides a measure of the amount of internal volatility in the market at any given moment, allows investigating the dynamics of the equity market. The expansion of the Green function in terms of the system of Bessel functions is expressed by an analytic formula that is convenient in calculating the volume of financial flows. All assumptions are natural, result in analytic formulas that are consistent with the empirical data and, when applied in practice, adequately reflect the processes in equity markets.
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.
Dispersion relation for Bernstein waves using a new transformation for the modified Bessel function
International Nuclear Information System (INIS)
Sato, Masumi
1985-01-01
Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves. (author)
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…
Optimality of embeddings of Bessel-potential-type spaces into Lorentz-Karamata spaces
Czech Academy of Sciences Publication Activity Database
Gogatishvili, Amiran; Opic, Bohumír; Neves, J. S.
2004-01-01
Roč. 134, č. 6 (2004), s. 1127-1147 ISSN 0308-2105 R&D Projects: GA ČR GA201/01/0333 Institutional research plan: CEZ:AV0Z1019905 Keywords : slowly varying functions * Lorentz-Karamata spaces * Bessel potentials Subject RIV: BA - General Mathematics Impact factor: 0.487, year: 2004
Spherical Bessel functions jsub(n) and ysub(n) of integer order and real argument
International Nuclear Information System (INIS)
Ardill, R.W.B.; Moriarty, K.J.M.
1978-01-01
The spherical Bessel function appears in a variety of physical applications, and especially in phase shift analysis. The package SPHBES contains a subroutine to calculate jsub(n)(x) and ysub(n)(x) for any integer order n and real argument x. The functions jsub(n)(x) and ysub(n)(x) are produced simultaneously and efficiently. (Auth.)
Design of Extended Depth-of-Focus Laser Beams Using Orthogonal Beam Expansions
Directory of Open Access Journals (Sweden)
Leonard Bergstein
2005-06-01
Full Text Available Laser beams with extended depth of focus have many practical applications, such as scanning printed bar codes. Previous work has concentrated on synthesizing such beams by approximating the nondiffracting Bessel beam solution to the wave equation. In this paper, we introduce an alternate novel synthesis method that is based on maintaining a minimum MTF value (contrast over the largest possible distance. To achieve this, the coefficients of an orthogonal beam expansion are sequentially optimized to this criterion. One of the main advantages of this method is that it can be easily generalized to noncircularly symmetrical beams by the appropriate choice of the beam expansion basis functions. This approach is found to be very useful for applications that involve scanning of the laser beam.
Dynamic behaviour of non-uniform Bernoulli-Euler beams subjected ...
African Journals Online (AJOL)
This paper investigates the dynamics behaviour of non-uniform Bernoulli-Euler beams subjected to concentrated loads ravelling at variable velocities. The solution technique is based on the Generalized Galerkin Method and the use of the generating function of the Bessel function type. The results show that, for all the ...
Effect of ABCD transformations on beam paraxiality.
Vaveliuk, Pablo; Martinez-Matos, Oscar
2011-12-19
The limits of the paraxial approximation for a laser beam under ABCD transformations is established through the relationship between a parameter concerning the beam paraxiality, the paraxial estimator, and the beam second-order moments. The applicability of such an estimator is extended to an optical system composed by optical elements as mirrors and lenses and sections of free space, what completes the analysis early performed for free-space propagation solely. As an example, the paraxiality of a system composed by free space and a spherical thin lens under the propagation of Hermite-Gauss and Laguerre-Gauss modes is established. The results show that the the paraxial approximation fails for a certain feasible range of values of main parameters. In this sense, the paraxial estimator is an useful tool to monitor the limits of the paraxial optics theory under ABCD transformations.
CSIR Research Space (South Africa)
Milione, G
2015-02-01
Full Text Available , 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 experimentally measured using Stokes polarimetry as they propagated through two...
Measuring the orbital angular momentum density for a superposition of Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2012-01-01
Full Text Available and amplitude gratings,? Opt. Commun. 284(1), 48?51 (2011). [8] Mair, A., Vaziri, A., Weihs, G., and Zeilinger, A., ?Entanglement of the orbital angular momentum states of photons,? Nature 412(6844), 313?316 (2001). [9] Gibson, G., Courtial, J., Padgett, M...
Affects of binary and continuous phase modulations on the structure of Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2010-09-01
Full Text Available The authors implement a novel technique to operate a phase-only spatial light modulator (SLM) in amplitude mode, allowing them to reproduce Durnin’s ring slit on a liquid crystal display (LCD). The affects of binary and continuous phase modulations...
P-T phase diagram of a holographic s+p model from Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Nie, Zhang-Yu; Zeng, Hui
2015-01-01
In this paper, we study the holographic s+p model in 5-dimensional bulk gravity with the Gauss-Bonnet term. We work in the probe limit and give the Δ-T phase diagrams at three different values of the Gauss-Bonnet coefficient to show the effect of the Gauss-Bonnet term. We also construct the P-T phase diagrams for the holographic system using two different definitions of the pressure and compare the results.
Occupation times and exact asymptotics of small deviations of Bessel processes for Lp-norms with p>0
International Nuclear Information System (INIS)
Fatalov, V R
2007-01-01
We prove theorems on exact asymptotics of the distributions of integral functionals of the occupation time of Bessel processes. Using these results, we obtain exact asymptotics of small deviations for Bessel processes in the L p -norm. We use Laplace's method for the occupation times of Markov processes with continuous time. Computations are carried out for p=2 and p=1. We also solve extremal problems for the action functional
Kerimov, M. K.
2016-07-01
This work continues the study of real zeros of first- and second-kind Bessel functions and Bessel general functions with real variables and orders begun in the first part of this paper (see M.K. Kerimov, Comput. Math. Math. Phys. 54 (9), 1337-1388 (2014)). Some new results concerning such zeros are described and analyzed. Special attention is given to the monotonicity, convexity, and concavity of zeros with respect to their ranks and other parameters.
International Nuclear Information System (INIS)
Cho, Seog Je; Jeong, Hyun Jo
1999-01-01
The wave propagation problem in anisotropic media is modeled by the Gauss-Hermite beam and tile finite element method and their results are compared. Gauss-Hermite mettled is computationally fast and simple, and explicitly incorporates beam spreading. In the 2-D model problem chosen, the ultrasonic beam leaves a transducer, propagates through a layer of ferritic steel and through a planar interface into a region of columnar cast stainless steel with two directions. After propagation to a reference plane, comparison .if made of the time-domain waveforms predicted by tile two models. The predictions of the two models are found to be in good agreement near the center of the beam, with deviations developing as one moves away from tile central ray. These are interpreted to be a consequence of the Fresnel approximation, made in the Gauss-Hermite model.
A symmetric integral identity for Bessel functions with applications to integral geometry
Salman, Yehonatan
2017-12-01
In the article of Kunyansky (Inverse Probl 23(1):373-383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in Rn . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in R2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates.
Construction of normal-regular decisions of Bessel typed special system
Tasmambetov, Zhaksylyk N.; Talipova, Meiramgul Zh.
2017-09-01
Studying a special system of differential equations in the separate production of the second order is solved by the degenerate hypergeometric function reducing to the Bessel functions of two variables. To construct a solution of this system near regular and irregular singularities, we use the method of Frobenius-Latysheva applying the concepts of rank and antirank. There is proved the basic theorem that establishes the existence of four linearly independent solutions of studying system type of Bessel. To prove the existence of normal-regular solutions we establish necessary conditions for the existence of such solutions. The existence and convergence of a normally regular solution are shown using the notion of rank and antirank.
Polarization holograms allow highly efficient generation of complex light beams.
Ruiz, U; Pagliusi, P; Provenzano, C; Volke-Sepúlveda, K; Cipparrone, Gabriella
2013-03-25
We report a viable method to generate complex beams, such as the non-diffracting Bessel and Weber beams, which relies on the encoding of amplitude information, in addition to phase and polarization, using polarization holography. The holograms are recorded in polarization sensitive films by the interference of a reference plane wave with a tailored complex beam, having orthogonal circular polarizations. The high efficiency, the intrinsic achromaticity and the simplicity of use of the polarization holograms make them competitive with respect to existing methods and attractive for several applications. Theoretical analysis, based on the Jones formalism, and experimental results are shown.
Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum
International Nuclear Information System (INIS)
Dotti, Gustavo; Oliva, Julio; Troncoso, Ricardo
2010-01-01
The classification of a certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in d≥5 dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of the real line and an arbitrary base manifold. It is shown that for a generic value of the Gauss-Bonnet coupling, the base manifold must be necessarily Einstein, with an additional restriction on its Weyl tensor for d>5. The boundary admits a wider class of geometries only in the special case when the Gauss-Bonnet coupling is such that the theory admits a unique maximally symmetric solution. The additional freedom in the boundary metric enlarges the class of allowed geometries in the bulk, which are classified within three main branches, containing new black holes and wormholes in vacuum.
Collapsing spherical star in Scalar-Einstein-Gauss-Bonnet gravity with a quadratic coupling
Chakrabarti, Soumya
2018-04-01
We study the evolution of a self interacting scalar field in Einstein-Gauss-Bonnet theory in four dimension where the scalar field couples non minimally with the Gauss-Bonnet term. Considering a polynomial coupling of the scalar field with the Gauss-Bonnet term, a self-interaction potential and an additional perfect fluid distribution alongwith the scalar field, we investigate different possibilities regarding the outcome of the collapsing scalar field. The strength of the coupling and choice of the self-interaction potential serves as the pivotal initial conditions of the models presented. The high degree of non-linearity in the equation system is taken care off by using a method of invertibe point transformation of anharmonic oscillator equation, which has proven itself very useful in recent past while investigating dynamics of minimally coupled scalar fields.
Effects of backreaction on power-Maxwell holographic superconductors in Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Salahi, Hamid Reza; Montakhab, Afshin [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Sheykhi, Ahmad [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P.O. Box 55134-441, Maragha (Iran, Islamic Republic of)
2016-10-15
We analytically and numerically investigate the properties of s-wave holographic superconductors by considering the effects of scalar and gauge fields on the background geometry in five-dimensional Einstein-Gauss-Bonnet gravity. We assume the gauge field to be in the form of the power-Maxwell nonlinear electrodynamics. We employ the Sturm-Liouville eigenvalue problem for analytical calculation of the critical temperature and the shooting method for the numerical investigation. Our numerical and analytical results indicate that higher curvature corrections affect condensation of the holographic superconductors with backreaction. We observe that the backreaction can decrease the critical temperature of the holographic superconductors, while the power-Maxwell electrodynamics and Gauss-Bonnet coefficient term may increase the critical temperature of the holographic superconductors. We find that the critical exponent has the mean-field value β = 1/2, regardless of the values of Gauss-Bonnet coefficient, backreaction and power-Maxwell parameters. (orig.)
Multi-grid Beam and Warming scheme for the simulation of unsteady ...
African Journals Online (AJOL)
In this paper, a multi-grid algorithm is applied to a large-scale block matrix that is produced from a Beam and Warming scheme. The Beam and Warming scheme is used in the simulation of unsteady flow in an open channel. The Gauss-Seidel block-wise iteration method is used for a smoothing process with a few iterations.
CMB in a box: Causal structure and the Fourier-Bessel expansion
International Nuclear Information System (INIS)
Abramo, L. Raul; Reimberg, Paulo H.; Xavier, Henrique S.
2010-01-01
This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility γ=e -μ , where μ is the optical depth to Thomson scattering. We show that the contributions of order γ N to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z>>10 3 , effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position x-vector=0 and time t 0 . Hence, for each multipole l there is a discrete tower of momenta k il (not a continuum) which can affect physical observables, with the smallest momenta being k 1l ∼l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.
Asymptotic formulae for the Lommel and Bessel functions and their derivatives.
Aleksandrova, N I
2014-10-01
We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for what values of the parameters our representations have reasonable accuracy.
Factorization of products of discontinuous functions applied to Fourier-Bessel basis.
Popov, Evgeny; Nevière, Michel; Bonod, Nicolas
2004-01-01
The factorization rules of Li [J. Opt. Soc. Am. A 13, 1870 (1996)] are generalized to a cylindrical geometry requiring the use of a Bessel function basis. A theoretical study confirms the validity of the Laurent rule when a product of two continuous functions or of one continuous and one discontinuous function is factorized. The necessity of applying the so-called inverse rule in factorizing a continuous product of two discontinuous functions in a truncated basis is demonstrated theoretically and numerically.
Analytic approximation for the modified Bessel function I -2/3(x)
Martin, Pablo; Olivares, Jorge; Maass, Fernando
2017-12-01
In the present work an analytic approximation to modified Bessel function of negative fractional order I -2/3(x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and assymptotic expansions are simultaneously used to obtain the approximation.
Certain new unified integrals associated with the product of generalized Bessel functions
Directory of Open Access Journals (Sweden)
Praveen Agarwal
2016-02-01
Full Text Available Our focus to presenting two very general integral formulas whose integrands are the integrand given in the Oberhettinger's integral formula and a finite product of the generalized Bessel function of the first kind, which are expressed in terms of the generalized Lauricella functions. Among a large number of interesting and potentially useful special cases of our main results, some integral formulas involving such elementary functions are also considered.
The application of a Bessel transform to the determination of stellar rotational velocities
International Nuclear Information System (INIS)
Deeming, T.J.
1977-01-01
A method for analysing line profiles by means of a transform using Bessel functions is described. This yields the stellar rotational velocity γ sin i, to an accuracy of about +-1 km s -1 for rotational velocities greater than about 5 km s -1 , provided that rotation is the major source of line broadening. The theory of the method is a special case of a general theory of linear transforms in data analysis, which is outlined in an appendix. (Auth.)
Fourier Bessel transform method for efficiently calculating the magnetic field of solenoids
International Nuclear Information System (INIS)
Nachamkin, J.; Maggiore, C.J.
1980-01-01
A numerical procedure for calculating the magnetic field of a selenoid is derived. Based on the properties of Bessel functions, the procedure is shown to be convergent everywhere, including within the windings of the solenoid. The most critical part of the procedure is detailed in the main text. A simple method is used to ensure numerical significance while allowing economical computational times. In the appendix the procedure is generalized to universal convergence by appropriate partitioning of the solenoid windings
A note on a hyper-cubic Mahler measure and associated Bessel integral
International Nuclear Information System (INIS)
Glasser, M L
2012-01-01
The Mahler measure for the n-variable polynomial k + ∑(x j + 1/x j ) is reduced to a single integral of the n-th power of the modified Bessel function I 0 . Several special cases are examined in detail. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday. (paper)
A generalization for the infinite integral over three spherical Bessel functions
International Nuclear Information System (INIS)
Mehrem, R; Hohenegger, A
2010-01-01
A new formula is derived that generalizes an earlier result for the infinite integral over three spherical Bessel functions. The analytical result involves a finite sum over associated Legendre functions, P m l (x) of degree l and order m. The sum allows for the values of |m| that are greater than l. A generalization for the associated Legendre functions to allow for any rational m for a specific l is also shown.
Multidimensional digital image representations using generalized Kaiser-Bessel window functions.
Lewitt, R M
1990-10-01
Inverse problems that require the solution of integral equations are inherent in a number of indirect imaging applications, such as computerized tomography. Numerical solutions based on discretization of the mathematical model of the imaging process, or on discretization of analytic formulas for iterative inversion of the integral equations, require a discrete representation of an underlying continuous image. This paper describes discrete image representations, in n-dimensional space, that are constructed by the superposition of shifted copies of a rotationally symmetric basis function. The basis function is constructed using a generalization of the Kaiser-Bessel window function of digital signal processing. The generalization of the window function involves going from one dimension to a rotationally symmetric function in n dimensions and going from the zero-order modified Bessel function of the standard window to a function involving the modified Bessel function of order m. Three methods are given for the construction, in n-dimensional space, of basis functions having a specified (finite) number of continuous derivatives, and formulas are derived for the Fourier transform, the x-ray transform, the gradient, and the Laplacian of these basis functions. Properties of the new image representations using these basis functions are discussed, primarily in the context of two-dimensional and three-dimensional image reconstruction from line-integral data by iterative inversion of the x-ray transform. Potential applications to three-dimensional image display are also mentioned.
The nonlocal problem for a hyperbolic equation with Bessel operator in a rectangular domain
Directory of Open Access Journals (Sweden)
Natalya V. Zaitseva
2016-12-01
Full Text Available We consider a boundary value problem for a hyperbolic equation with Bessel differential operator in a rectangular domain with integral nonlocal boundary value condition of the first kind. The equivalence between boundary value problem with integral nonlocal condition of the first kind and a local boundary value problem with mixed boundary conditions of the first and third kinds is proved. The existence and uniqueness of solution of the equivalent problem are established by means of the spectral method. At the uniqueness proof the completeness of the eigenfunction system of the spectral problem is used . At the existence proof the assessment of coefficients of series, the asymptotic formula for Bessel function of the first kind and asymptotic formula for eigenvalues are used. Sufficient conditions on the functions defining initial data of the problem are received. The solution of the problem is obtained in explicit form. The solution is obtained in the form of the Fourier–Bessel series. Its convergence is proved in the class of regular solutions.
International Nuclear Information System (INIS)
Herr, W; Pieloni, T
2014-01-01
One of the most severe limitations in high-intensity particle colliders is the beam-beam interaction, i.e. the perturbation of the beams as they cross the opposing beams. This introduction to beam-beam effects concentrates on a description of the phenomena that are present in modern colliding beam facilities
The Gauss and Ampere laws: different laws but similar difficulties for student learning
International Nuclear Information System (INIS)
Guisasola, Jenaro; AlmudI, Jose M; Zuza, Kristina; Ceberio, Mikel; Salinas, Julia
2008-01-01
This study aims to analyse university students' reasoning regarding two laws of electromagnetism: Gauss's law and Ampere's law. It has been supposed that the problems seen in understanding and applying both laws do not spring from students' misconceptions. Students habitually use reasoning known in the literature as 'common sense' methodology that leads to incorrect forms of reasoning. To test our hypothesis, questionnaires were designed emphasizing explanations. The results obtained show the low level of students' reasoning in both electricity and magnetism in terms of Gauss's and Ampere's laws
Convergence and Applications of a Gossip-Based Gauss-Newton Algorithm
Li, Xiao; Scaglione, Anna
2013-11-01
The Gauss-Newton algorithm is a popular and efficient centralized method for solving non-linear least squares problems. In this paper, we propose a multi-agent distributed version of this algorithm, named Gossip-based Gauss-Newton (GGN) algorithm, which can be applied in general problems with non-convex objectives. Furthermore, we analyze and present sufficient conditions for its convergence and show numerically that the GGN algorithm achieves performance comparable to the centralized algorithm, with graceful degradation in case of network failures. More importantly, the GGN algorithm provides significant performance gains compared to other distributed first order methods.
Gauss: La revolución de las matemáticas del siglo XIX
Gutierrez, Santiago
2005-01-01
Hace 150 años, el 23 de febrero de 1855, moría, en Gotinga, a la edad de setenta y siete años, Johan Friedrich Carl Gauss o, simplemente, Carl Friedrich Gauss, como él mismo quiso ser llamado. Eran tiempos de revolución y progreso: comenzaba la revolución industrial en Inglaterra, en Estados Unidos se perforaba el primer pozo de petróleo (1859), la economía estaba dominada por las teorías liberales de Adam Smith mientras se gestaba la creación de la Internacional Socialista, Darwin publicaba ...
Charged Rényi entropies in CFTs with Einstein-Gauss-Bonnet holographic duals
Pastras, Georgios; Manolopoulos, Dimitrios
2014-11-01
We calculate the Rényi entropy S q ( μ, λ), for spherical entangling surfaces in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals. Rényi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings λ, larger than specific value, but still allowed by causality, we observe a violation of the inequality , which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. Moreover, we find an interesting distinction of the behaviour of the analytic continuation of S q ( μ, λ) for imaginary chemical potential, between negative and non-negative λ.
A new look at the free electromagnetic field. The Gauss law as a hamiltonian equation of motion
International Nuclear Information System (INIS)
Aldaya, V.; Navarro-Salas, J.
1992-01-01
A new canonical formalism for the free electromagnetic field is proposed in terms of an infinite-dimensional Lie group. The Gauss law is derived as a hamiltonian equation of motion and the quantum theory is obtained by constructing the irreducible representation of the group. The quantum Gauss law thus appears as an additional polarization equation and not as a constraint equation. (orig.)
On Gauss-Green theorem and boundaries of a class of Hölder domains
Lyons, TJ; Yam, PSC
2006-01-01
The purpose of this paper is to show that, if α > 1/3 and ε > 0, the boundary of an α-Hölder domain is a 1 α + ε geometric rough path; and as a direct application, we extend the classical Green-Gauss' formula to this class of fractal domains. © 2005 Elsevier SAS. All rights reserved.
An Alternative Method to Gauss-Jordan Elimination: Minimizing Fraction Arithmetic
Smith, Luke; Powell, Joan
2011-01-01
When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…
Time-domain incomplete Gauss-Newton full-waveform inversion of Gulf of Mexico data
AlTheyab, Abdullah; Wang, Xin; Schuster, Gerard T.
2013-01-01
We apply the incomplete Gauss-Newton full-waveform inversion (TDIGN-FWI) to Gulf of Mexico (GOM) data in the space-time domain. In our application, iterative least-squares reverse-time migration (LSRTM) is used to estimate the model update at each
5D black hole solution in Einstein-Yang-Mills-Gauss-Bonnet theory
International Nuclear Information System (INIS)
Mazharimousavi, S. Habib; Halilsoy, M.
2007-01-01
By adopting the 5D version of the Wu-Yang ansatz we present in closed form a black hole solution in the Einstein-Yang-Mills-Gauss-Bonnet theory. In the Einstein-Yang-Mills limit, we recover the 5D black hole solution already known
Horizons of radiating black holes in Einstein-Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Ghosh, S. G.; Deshkar, D. W.
2008-01-01
A Vaidya-based model of a radiating black hole is studied in a 5-dimensional Einstein gravity with Gauss-Bonnet contribution of quadratic curvature terms. The structure and locations of the apparent and event horizons of the radiating black hole are determined
New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term
Butter, D.; de Wit, B.; Kuzenko, S.M.; Lodato, I.|info:eu-repo/dai/nl/357520890
2013-01-01
A new class of N = 2 locally supersymmetric higher-derivative invariants is constructed based on logarithms of conformal primary chiral superfields. They characteristically involve a coupling to Rμν 2 − 1 3 R2, which equals the non-conformal part of the Gauss-Bonnet term. Upon combining one such
Directory of Open Access Journals (Sweden)
Mika Tanda
2015-01-01
Full Text Available We compute alien derivatives of the WKB solutions of the Gauss hypergeometric differential equation with a large parameter and discuss the singularity structures of the Borel transforms of the WKB solution expressed in terms of its alien derivatives.
Nonlinear space charge effect of bunched beam in linac
International Nuclear Information System (INIS)
Chen Yinbao
1992-02-01
The nonlinear space charge effect due to the nonuniform particle density distribution in bunched beam of a linac is discussed. The formulae of nonlinear space charge effect and nonlinear focusing forces were derived for the bunched beam with Kapchinskij-Vladimirskij (K-V) distribution, waterbag (WB) distribution, parabolic (PA) distribution, and Gauss (GA) distribution in both of the space charge disk model and space charge cylinder model in the waveguide of a linac
Gravitational quasinormal modes of static Einstein-Gauss-Bonnet anti-de Sitter black holes
Ma, Hong; Li, Jin
2018-04-01
In this paper, we describe quasinormal modes (QNMs) for gravitational perturbations of Einstein-Gauss-Bonnet black holes (BHs) in higher dimensional spacetimes, and derive the corresponding parameters of such black holes in three types of spacetime (flat, de Sitter (dS) and anti-de Sitter (AdS)). Our attention is concentrated on discussing the (in)stability of Einstein-Gauss-Bonnet AdS BHs through the temporal evolution of all types of gravitational perturbation fields (tensor, vector and scalar). It is concluded that the potential functions in vector and scalar gravitational perturbations have negative regions, which suppress quasinormal ringing. Furthermore, the influences of the Gauss-Bonnet coupling parameter α, the number of dimensions n and the angular momentum quantum number l on the Einstein-Gauss-Bonnet AdS BHs quasinormal spectrum are analyzed. The QNM frequencies have greater oscillation and lower damping rate with the growth of α. This indicates that QNM frequencies become increasingly unstable with large α. Meanwhile, the dynamic evolutions of the perturbation field are compliant with the results of computation from the Horowitz and Hubeny method. Because the number of extra dimensions is connected with the string scale, the relationship between α and properties of Einstein-Gauss-Bonnet AdS BHs might be beneficial for the exploitation of string theory and extra-dimensional brane worlds. Supported by FAPESP (2012/08934-0), National Natural Science Foundation of China (11205254, 11178018, 11375279, 11605015), the Natural Science Foundation Project of CQ CSTC (2011BB0052), and the Fundamental Research Funds for the Central Universities (106112016CDJXY300002, 106112017CDJXFLX0014, CDJRC10300003)
Measurements of the temporal onset of mega-Gauss magnetic fields in a laser-driven solenoid
Goyon, Clement; Polllock, B. B.; Turnbull, D. T.; Hazi, A.; Ross, J. S.; Mariscal, D. A.; Patankar, S.; Williams, G. J.; Farmer, W. A.; Moody, J. D.; Fujioka, S.; Law, K. F. F.
2016-10-01
We report on experimental results obtained at Omega EP showing a nearly linear increase of the B-field up to about 2 mega-Gauss in 0.75 ns in a 1 mm3 region. The field is generated using 1 TW of 351 nm laser power ( 8*1015 W/cm2) incident on a laser-driven solenoid target. The coil target converts about 1% of the laser energy into the B-field measured both inside and outside the coil using proton deflectometry with a grid and Faraday rotation of probe beam through SiO2 glass. Proton data indicates a current rise up to hundreds of kA with a spatial distribution in the Au solenoid conductor evolving in time. These results give insight into the generating mechanism of the current between the plates and the time behavior of the field. These experiments are motivated by recent efforts to understand and utilize High Energy Density (HED) plasmas in the presence of external magnetic fields in areas of research from Astrophysics to Inertial Confinement Fusion. We will describe the experimental results and scale them to a NIF hohlraum size. This work was performed under the auspices of the U.S. Department of Energy by LLNL under Contract DE-AC52-07NA27344.
Kerimov, M. K.
2016-12-01
This paper continues the study of real zeros of Bessel functions begun in the previous parts of this work (see M. K. Kerimov, Comput. Math. Math. Phys. 54 (9), 1337-1388 (2014); 56 (7), 1175-1208 (2016)). Some new results regarding the monotonicity, convexity, concavity, and other properties of zeros are described. Additionally, the zeros of q-Bessel functions are investigated.
Sherstyukov, V. B.; Sumin, E. V.
2017-12-01
Modified Bessel functions of the first kind Iv (z) (Infeld functions) where v > -1 are considered. Due to the constraint on the parameter v, all zeros of the function Iv (z) except z = 0 are simple, located on the imaginary axis by symmetric pairs and form an infinite countable set. On the basis on previous research of the authors dealing with general Bessel functions of the first kind Jv (z), a question about reciprocal expansion 1/Iv (z) in series of simple fractions of a certain structure (Krein’s series) is studied. The general formulas to calculate of special infinite sums containing degrees of Infeld function zeros are an important consequence of obtained expansion in simple fractions of the value 1/Iv (z) with any v > -1. The possibility of concrete definition of established summation relationships at different values of parameters and their connection with analogous relationships for the Bessel functions of the first kind Jv (z) is discussed.
Zheng, Guo; Wang, Jue; Wang, Lin; Zhou, Muchun; Xin, Yu; Song, Minmin
2017-11-15
The general formulae for second-order moments of Schell-model beams with various correlation functions in atmospheric turbulence are derived and validated by the Bessel-Gaussian Schell-model beams and cosine-Gaussian-correlated Schell-model beams. Our finding shows that the second-order moments of partially coherent Schell-model beams are related to the second-order partial derivatives of source spectral degree of coherence at the origin. The formulae we provide are much more convenient to analyze and research propagation problems in turbulence.
Gohn-Kreuz, Cristian; Rohrbach, Alexander
2016-03-21
Self-reconstruction of Bessel beams in inhomogeneous media is beneficial in light-sheet based microscopy. Although the beam's ring system enables propagation stability, the resulting image contrast is reduced. Here, we show that by a combination of two self-reconstructing beams with different orbital angular momenta it is possible to inhibit fluorescence from the ring system by using stimulated emission depletion (STED) even in strongly scattering media. Our theoretical study shows that the remaining fluorescence γ depends non-linearly on the beams' relative radial and orbital angular momenta. For various scattering media we demonstrate that γ remains remarkably stable over long beam propagation distances.
Exponential and Bessel fitting methods for the numerical solution of the Schroedinger equation
International Nuclear Information System (INIS)
Raptis, A.D.; Cash, J.R.
1987-01-01
A new method is developed for the numerical integration of the one dimensional radial Schroedinger equation. This method involves using different integration formulae in different parts of the range of integration rather than using the same integration formula throughout. Two new integration formulae are derived, one which integrates Bessel and Neumann functions exactly and another which exactly integrates certain exponential functions. It is shown that, for large r, these new formulae are much more accurate than standard integration methods for the Schroedinger equation. The benefit of using this new approach is demonstrated by considering some numerical examples based on the Lennard-Jones potential. (orig.)
Directory of Open Access Journals (Sweden)
Fatima G. Khushtova
2016-03-01
Full Text Available In this paper Cauchy problem for a parabolic equation with Bessel operator and with Riemann–Liouville partial derivative is considered. The representation of the solution is obtained in terms of integral transform with Wright function in the kernel. It is shown that when this equation becomes the fractional diffusion equation, obtained solution becomes the solution of Cauchy problem for the corresponding equation. The uniqueness of the solution in the class of functions that satisfy the analogue of Tikhonov condition is proved.
International Nuclear Information System (INIS)
Poquerusse, A.; Alexiou, S.
1999-01-01
In this work we review the status of the standard line broadening theory for plasmas and fill in the existing gap, i.e., the partially overlapping case for ions lines, by deriving expressions as well as fast and accurate numerical approximations for the relevant functions, namely the modified Bessel function of imaginary order and its derivative with respect to argument. These functions also arise in the context of the theory of Coulomb excitation. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
A theorem regarding roots of the zero-order Bessel function of the first kind
Lin, X.-A.; Agrawal, O. P.
1993-01-01
This paper investigates a problem on the steady-state, conduction-convection heat transfer process in cylindrical porous heat exchangers. The governing partial differential equations for the system are obtained using the energy conservation law. Solution of these equations and the concept of enthalpy lead to a new approach to prove a theorem that the sum of inverse squares of all the positive roots of the zero order Bessel function of the first kind equals to one-forth. As a corollary, it is shown that the sum of one over pth power (p greater than or equal to 2) of the roots converges to some constant.
On the propagation of transient waves in a viscoelastic Bessel medium
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
2017-06-01
In this paper, we discuss the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium. First, we provide the analytic expression for the response function of the material as we approach the wave front. To do so, we take profit of a revisited version of the so called Buchen-Mainardi algorithm. Secondly, we provide an analytic expression for the long-time behavior of the response function of the material. This result is obtained by means of the Tauberian theorems for the Laplace transform. Finally, we relate the obtained results to a peculiar model for fluid-filled elastic tubes.
Certain fractional integral formulas involving the product of generalized Bessel functions.
Baleanu, D; Agarwal, P; Purohit, S D
2013-01-01
We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.
Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions
Baleanu, D.; Agarwal, P.; Purohit, S. D.
2013-01-01
We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions. PMID:24379745
Bessel Plasmon-Polaritons at the Boundaries of Metamaterials with Near-Zero Dielectric Constants
Kurilkina, S. N.; Belyi, V. N.; Kazak, N. S.; Binhussain, M. A.
2015-07-01
The conditions for and features of the excitation of Bessel plasmon-polaritons (BPP) are examined at the boundary of a hyperbolic metamaterial with a near-zero dielectric constant made of a dielectric matrix with metal nanorods embedded in it normal to its surface. This material is compared with BPP that have traditional surface plasmons. The effect of the absorption of the metamaterial on the excitation of BPP is studied. The possibility of changes in the direction of the radial energy fl ows in BPP excited at the surface of an isotropic medium, a hyperbolic metamaterial, is demonstrated and the conditions for these changes are determined.
Directory of Open Access Journals (Sweden)
Ali H. Bhrawy
2014-01-01
Full Text Available The modified generalized Laguerre-Gauss collocation (MGLC method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.
Dadhich, Naresh; Pons, Josep M
We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with the topology of the product of two spheres, [Formula: see text], in higher dimensions. There is an unusual new feature of the Gauss-Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of [Formula: see text]. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for [Formula: see text] is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature.
Reconstruction of the Scalar Field Potential in Inflationary Models with a Gauss-Bonnet term
Koh, Seoktae; Lee, Bum-Hoon; Tumurtushaa, Gansukh
2017-06-01
We consider inflationary models with a Gauss-Bonnet term to reconstruct the scalar-field potentials and the Gauss-Bonnet coupling functions. Both expressions are derived from the observationally favored configurations of ns and r . Our result implies that, for the reconstructed potentials and coupling functions, the blue tilt of inflationary tensor fluctuations can be realized. To achieve a blue tilt for the inflationary tensor fluctuations, a scalar field must climb up its potential before rolling down. We further investigate the properties of propagation of the perturbation modes in Friedmann-Robertson-Walker spacetime. For the reconstructed configurations that give rise to the blue tilt for the inflationary tensor fluctuations, we show that the ghosts and instabilities are absent with the superluminal propagation speeds for the scalar perturbation modes, whereas the propagation speeds of the tensor perturbations are subluminal.
The effect of the Gauss-Bonnet term on Hawking radiation from arbitrary dimensional black brane
Energy Technology Data Exchange (ETDEWEB)
Kuang, Xiao-Mei [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Valparaiso (Chile); Yangzhou University, Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou (China); Saavedra, Joel [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Valparaiso (Chile); Oevguen, Ali [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Valparaiso (Chile); Eastern Mediterranean University, Physics Department, Famagusta, Northern Cyprus (Country Unknown)
2017-09-15
We investigate the probabilities of the tunneling and the radiation spectra of massive spin-1 particles from arbitrary dimensional Gauss-Bonnet-Axions (GBA) Anti-de Sitter (AdS) black branes, via using the WKB approximation to the Proca spin-1 field equation. The tunneling probabilities and Hawking temperature of the arbitrary dimensional GBA AdS black brane is calculated via the Hamilton-Jacobi approach. We also compute the Hawking temperature via the Parikh-Wilczek tunneling approach. The results obtained from the two methods are consistent. In our setup, the Gauss-Bonnet (GB) coupling affects the Hawking temperature if and only if the momentum of the axion fields is non-vanishing. (orig.)
Two new modified Gauss-Seidel methods for linear system with M-matrices
Zheng, Bing; Miao, Shu-Xin
2009-12-01
In 2002, H. Kotakemori et al. proposed the modified Gauss-Seidel (MGS) method for solving the linear system with the preconditioner [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner () J. Comput. Appl. Math. 145 (2002) 373-378]. Since this preconditioner is constructed by only the largest element on each row of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the nth row. In the present paper, to deal with this drawback, we propose two new preconditioners. The convergence and comparison theorems of the modified Gauss-Seidel methods with these two preconditioners for solving the linear system are established. The convergence rates of the new proposed preconditioned methods are compared. In addition, numerical experiments are used to show the effectiveness of the new MGS methods.
The preconditioned Gauss-Seidel method faster than the SOR method
Niki, Hiroshi; Kohno, Toshiyuki; Morimoto, Munenori
2008-09-01
In recent years, a number of preconditioners have been applied to linear systems [A.D. Gunawardena, S.K. Jain, L. Snyder, Modified iterative methods for consistent linear systems, Linear Algebra Appl. 154-156 (1991) 123-143; T. Kohno, H. Kotakemori, H. Niki, M. Usui, Improving modified Gauss-Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997) 113-123; H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner (I+Smax), J. Comput. Appl. Math. 145 (2002) 373-378; H. Kotakemori, H. Niki, N. Okamoto, Accelerated iteration method for Z-matrices, J. Comput. Appl. Math. 75 (1996) 87-97; M. Usui, H. Niki, T.Kohno, Adaptive Gauss-Seidel method for linear systems, Internat. J. Comput. Math. 51(1994)119-125 [10
Capacity of a bosonic memory channel with Gauss-Markov noise
International Nuclear Information System (INIS)
Schaefer, Joachim; Daems, David; Karpov, Evgueni; Cerf, Nicolas J.
2009-01-01
We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a 'quantum water-filling' solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit of an infinite number of modes. The method can also be applied to a more general noise environment which is constructed by a stationary Gauss process. The extension of our results to the case of broadband bosonic channels with colored Gaussian noise should also be straightforward.
The effect of the Gauss-Bonnet term on Hawking radiation from arbitrary dimensional black brane
International Nuclear Information System (INIS)
Kuang, Xiao-Mei; Saavedra, Joel; Oevguen, Ali
2017-01-01
We investigate the probabilities of the tunneling and the radiation spectra of massive spin-1 particles from arbitrary dimensional Gauss-Bonnet-Axions (GBA) Anti-de Sitter (AdS) black branes, via using the WKB approximation to the Proca spin-1 field equation. The tunneling probabilities and Hawking temperature of the arbitrary dimensional GBA AdS black brane is calculated via the Hamilton-Jacobi approach. We also compute the Hawking temperature via the Parikh-Wilczek tunneling approach. The results obtained from the two methods are consistent. In our setup, the Gauss-Bonnet (GB) coupling affects the Hawking temperature if and only if the momentum of the axion fields is non-vanishing. (orig.)
Quintessence background for 5D Einstein-Gauss-Bonnet black holes
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Sushant G. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa); Centre for Theoretical Physics, New Delhi (India); Amir, Muhammed [Centre for Theoretical Physics, New Delhi (India); Maharaj, Sunil D. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)
2017-08-15
As we know that the Lovelock theory is an extension of the general relativity to the higher-dimensions, in this theory the first- and the second-order terms correspond to general relativity and the Einstein-Gauss-Bonnet gravity, respectively. We obtain a 5D black hole solution in Einstein-Gauss-Bonnet gravity surrounded by the quintessence matter, and we also analyze their thermodynamical properties. Owing to the quintessence corrected black hole, the thermodynamic quantities have also been corrected except for the black hole entropy, and a phase transition is achievable. The phase transition for the thermodynamic stability is characterized by a discontinuity in the specific heat at r = r{sub C}, with the stable (unstable) branch for r < (>) r{sub C}. (orig.)
History of cosmic evolution with modified Gauss-Bonnet-dilatonic coupled term
International Nuclear Information System (INIS)
Debnath, Subhra; Sanyal, Abhik Kumar; Ruz, Soumendra Nath; Mandal, Ranajit
2017-01-01
Gauss-Bonnet-dilatonic coupling in four dimensions plays an important role to explain late-time cosmic evolution. However, this term is an outcome of the low energy string effective action and thus ought to be important in the early universe too. Unfortunately, a phase-space formulation of such a theory does not exist in the literature due to branching. We therefore consider a modified theory of gravity, which contains a nonminimally coupled scalar-tensor sector in addition to a higher-order scalar curvature invariant term with Gauss-Bonnet-dilatonic coupling. Such an action unifies early inflation with late-time cosmic acceleration. The quantum version of the theory is also well behaved. (orig.)
History of cosmic evolution with modified Gauss-Bonnet-dilatonic coupled term
Energy Technology Data Exchange (ETDEWEB)
Debnath, Subhra; Sanyal, Abhik Kumar [Jangipur College, Department of Physics, Murshidabad (India); Ruz, Soumendra Nath [Ramananda Centenary College, Department of Physics, Purulia (India); Mandal, Ranajit [University of Kalyani, Department of Physics, Nadia (India)
2017-05-15
Gauss-Bonnet-dilatonic coupling in four dimensions plays an important role to explain late-time cosmic evolution. However, this term is an outcome of the low energy string effective action and thus ought to be important in the early universe too. Unfortunately, a phase-space formulation of such a theory does not exist in the literature due to branching. We therefore consider a modified theory of gravity, which contains a nonminimally coupled scalar-tensor sector in addition to a higher-order scalar curvature invariant term with Gauss-Bonnet-dilatonic coupling. Such an action unifies early inflation with late-time cosmic acceleration. The quantum version of the theory is also well behaved. (orig.)
Quintessence background for 5D Einstein-Gauss-Bonnet black holes
Ghosh, Sushant G.; Amir, Muhammed; Maharaj, Sunil D.
2017-08-01
As we know that the Lovelock theory is an extension of the general relativity to the higher-dimensions, in this theory the first- and the second-order terms correspond to general relativity and the Einstein-Gauss-Bonnet gravity, respectively. We obtain a 5D black hole solution in Einstein-Gauss-Bonnet gravity surrounded by the quintessence matter, and we also analyze their thermodynamical properties. Owing to the quintessence corrected black hole, the thermodynamic quantities have also been corrected except for the black hole entropy, and a phase transition is achievable. The phase transition for the thermodynamic stability is characterized by a discontinuity in the specific heat at r=r_C, with the stable (unstable) branch for r ) r_C.
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.
Numerical evaluation of integrals containing a spherical Bessel function by product integration
International Nuclear Information System (INIS)
Lehman, D.R.; Parke, W.C.; Maximon, L.C.
1981-01-01
A method is developed for numerical evaluation of integrals with k-integration range from 0 to infinity that contain a spherical Bessel function j/sub l/(kr) explicitly. The required quadrature weights are easily calculated and the rate of convergence is rapid: only a relatively small number of quadrature points is needed: for an accurate evaluation even when r is large. The quadrature rule is obtained by the method of product integration. With the abscissas chosen to be those of Clenshaw--Curtis and the Chebyshev polynomials as the interpolating polynomials, quadrature weights are obtained that depend on the spherical Bessel function. An inhomogenous recurrence relation is derived from which the weights can be calculated without accumulation of roundoff error. The procedure is summarized as an easily implementable algorithm. Questions of convergence are discussed and the rate of convergence demonstrated for several test integrals. Alternative procedures are given for generating the integration weights and an error analysis of the method is presented
Eikonal instability of Gauss-Bonnet-(anti-)-de Sitter black holes
Konoplya, R. A.; Zhidenko, A.
2017-05-01
Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of space-time in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in Grozdanov, Kaplis, and Starinets, [J. High Energy Phys. 07 (2016) 151, 10.1007/JHEP07(2016)151] for the higher curvature corrected black hole with the planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of the Gauss-Bonnet term, it was shown [Deppe et al, Phys. Rev. Lett. 114, 071102 (2015), 10.1103/PhysRevLett.114.071102], that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories [Frolov, Phys. Rev. Lett. 115, 051102 (2015), 10.1103/PhysRevLett.115.051102]. The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, dS and asymptotically flat black holes may explain the existing mass gaps in their formation.
Rotational hypersurfaces with $L_r$-pointwise 1-type Gauss map
Directory of Open Access Journals (Sweden)
Akram Mohammadpouri
2018-07-01
Full Text Available In this paper, we study hypersurfaces in $\\E^{n+1}$ which Gauss map $G$ satisfies the equation $L_rG = f(G + C$ for a smooth function $f$ and a constant vector $C$, where $L_r$ is the linearized operator of the $(r + 1$th mean curvature of the hypersurface, i.e., $L_r(f=tr(P_r\\circ\
Simple compactifications and black p-branes in Gauss-Bonnet and Lovelock theories
International Nuclear Information System (INIS)
Giribet, Gaston; Oliva, Julio; Troncoso, Ricardo
2006-01-01
We look for the existence of asymptotically flat simple compactifications of the form M D-p x T p in D-dimensional gravity theories with higher powers of the curvature. Assuming the manifold M D-p to be spherically symmetric, it is shown that the Einstein-Gauss-Bonnet theory admits this class of solutions only for the pure Einstein-Hilbert or Gauss-Bonnet Lagrangians, but not for an arbitrary linear combination of them. Once these special cases have been selected, the requirement of spherical symmetry is no longer relevant since actually any solution of the pure Einstein or pure Gauss-Bonnet theories can then be toroidally extended to higher dimensions. Depending on p and the spacetime dimension, the metric on M D-p may describe a black hole or a spacetime with a conical singularity, so that the whole spacetime describes a black or a cosmic p-brane, respectively. For the purely Gauss-Bonnet theory it is shown that, if M D-p is four-dimensional, a new exotic class of black hole solutions exists, for which spherical symmetry can be relaxed. Under the same assumptions, it is also shown that simple compactifications acquire a similar structure for a wide class of theories among the Lovelock family which accepts this toroidal extension. The thermodynamics of black p-branes is also discussed, and it is shown that a thermodynamical analogue of the Gregory-Laflamme transition always occurs regardless the spacetime dimension or the theory considered, hence not only for General Relativity. Relaxing the asymptotically flat behavior, it is also shown that exact black brane solutions exist within a very special class of Lovelock theories
Spontaneous Scalarization of Black Holes and Compact Stars from a Gauss-Bonnet Coupling.
Silva, Hector O; Sakstein, Jeremy; Gualtieri, Leonardo; Sotiriou, Thomas P; Berti, Emanuele
2018-03-30
We identify a class of scalar-tensor theories with coupling between the scalar and the Gauss-Bonnet invariant that exhibit spontaneous scalarization for both black holes and compact stars. In particular, these theories formally admit all of the stationary solutions of general relativity, but these are not dynamically preferred if certain conditions are satisfied. Remarkably, black holes exhibit scalarization if their mass lies within one of many narrow bands. We find evidence that scalarization can occur in neutron stars as well.
Projected Gauss-Seidel subspace minimization method for interactive rigid body dynamics
DEFF Research Database (Denmark)
Silcowitz-Hansen, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny
2010-01-01
artifacts such as viscous or damped contact response. In this paper, we present a new approach to contact force determination. We formulate the contact force problem as a nonlinear complementarity problem, and discretize the problem to derive the Projected Gauss–Seidel method. We combine the Projected Gauss......–Seidel method with a subspace minimization method. Our new method shows improved qualities and superior convergence properties for specific configurations....
Application of Quantum Gauss-Jordan Elimination Code to Quantum Secret Sharing Code
Diep, Do Ngoc; Giang, Do Hoang; Phu, Phan Huy
2018-03-01
The QSS codes associated with a MSP code are based on finding an invertible matrix V, solving the system vATMB (s a)=s. We propose a quantum Gauss-Jordan Elimination Procedure to produce such a pivotal matrix V by using the Grover search code. The complexity of solving is of square-root order of the cardinal number of the unauthorized set √ {2^{|B|}}.
On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere
Arnlind, Joakim; Wilson, Mitsuru
2017-01-01
We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.
Extremal dyonic black holes in D=4 Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Chen, C.-M.; Gal'tsov, Dmitri V.; Orlov, Dmitry G.
2008-01-01
We investigate extremal dyon black holes in the Einstein-Maxwell-dilaton theory with higher curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. In the same theory without the Gauss-Bonnet term the extremal dyon solutions exist only for discrete values of the dilaton coupling constant a. We show that the Gauss-Bonnet term acts as a dyon hair tonic enlarging the allowed values of a to continuous domains in the plane (a,q m ) where q m is the magnetic charge. In the limit of the vanishing curvature coupling (a large magnetic charge) the dyon solutions obtained tend to the Reissner-Nordstroem solution but not to the extremal dyons of the Einstein-Maxwell-dilaton theory. Both solutions have the same dependence of the horizon radius in terms of charges. The entropy of new dyonic black holes interpolates between the Bekenstein-Hawking value in the limit of the large magnetic charge (equivalent to the vanishing Gauss-Bonnet coupling) and twice this value for the vanishing magnetic charge. Although an expression for the entropy can be obtained analytically using purely local near-horizon solutions, its interpretation as the black hole entropy is legitimate only once the global black hole solution is known to exist, and we obtain numerically the corresponding conditions on the parameters. Thus, a purely local analysis is insufficient to fully understand the entropy of the curvature-corrected black holes. We also find dyon solutions which are not asymptotically flat, but approach the linear dilaton background at infinity. They describe magnetic black holes on the electric linear dilaton background.
On the Gauss Map of Surfaces of Revolution with Lightlike Axis in Minkowski 3-Space
Directory of Open Access Journals (Sweden)
Minghao Jin
2013-01-01
Full Text Available By studying the Gauss map G and Laplace operator Δh of the second fundamental form h, we will classify surfaces of revolution with a lightlike axis in 3-dimensional Minkowski space and also obtain the surface of Enneper of the 2nd kind, the surface of Enneper of the 3rd kind, the de Sitter pseudosphere, and the hyperbolic pseudosphere that satisfy condition ΔhG=ΛG, Λ being a 3×3 real matrix.
Clinical Profile of Statin Intolerance in the Phase 3 GAUSS-2 Study.
Cho, Leslie; Rocco, Michael; Colquhoun, David; Sullivan, David; Rosenson, Robert S; Dent, Ricardo; Xue, Allen; Scott, Rob; Wasserman, Scott M; Stroes, Erik
2016-06-01
Recent evidence suggests that statin intolerance may be more common than reported in randomized trials. However, the statin-intolerant population is not well characterized. The goal of this report is to characterize the population enrolled in the phase 3 Goal Achievement after Utilizing an anti-PCSK9 antibody in Statin Intolerant Subjects Study (GAUSS-2; NCT 01763905). GAUSS-2 compared evolocumab, a fully human monoclonal antibody to proprotein convertase subtilisin/kexin type 9 (PCSK9) to ezetimibe in hypercholesterolemic patients who discontinued statin therapy due to statin-associated muscle symptoms (SAMS). GAUSS-2 was a 12-week, double-blind, placebo-controlled, randomized study that enrolled patients with elevated LDL-C who were either not on a statin or able to tolerate only a low-dose due to SAMS. Patients had received ≥2 statins and were unable to tolerate any statin dose or increase in dose above a specified weekly dose due to SAMS. Three hundred seven patients (mean [SD] age, 62 [10] years; 54 % males) were randomized 2:1 (evolocumab:ezetimibe). Mean (SD) LDL-C was 4.99 (1.51) mmol/L. Patients had used ≥2 (100 %), ≥3 (55 %), or ≥4 (21 %) statins. Coronary artery disease was present in 29 % of patients. Statin-intolerant symptoms were myalgia in 80 % of patients, weakness in 39 %, and more serious complications in 20 %. In 98 % of patients, SAMS interfered with normal daily activity; in 52 %, symptoms precluded moderate exertion. Evaluation of the GAUSS-2 trial population of statin-intolerant patients demonstrates that most patients were high risk with severely elevated LDL-C and many had statin-associated muscle symptoms that interfered with their quality of life.
Scalar hair around charged black holes in Einstein-Gauss-Bonnet gravity
Grandi, Nicolás; Landea, Ignacio Salazar
2018-02-01
We explore charged black hole solutions in Einstein-Gauss-Bonnet gravity in five dimensions, with a charged scalar hair. We interpret such hairy black holes as the final state of the superradiant instability previously reported for this system. We explore the relation of the hairy black hole solutions with the nonbackreacting quasibound states and scalar clouds, as well as with the boson star solutions.
Directory of Open Access Journals (Sweden)
Junesang Choi
2014-01-01
Full Text Available A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving the Fp(α,β(·. In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functions Fp(α,β,m(·. Some interesting special cases of our main results are also considered.
Increasing reliability of Gauss-Kronrod quadrature by Eratosthenes' sieve method
Adam, Gh.; Adam, S.
2001-04-01
The reliability of the local error estimates returned by the Gauss-Kronrod quadrature rules can be raised up to the theoretical 100% rate of success, under error estimate sharpening, provided a number of natural validating conditions are required. The self-validating scheme of the local error estimates, which is easy to implement and adds little supplementary computing effort, strengthens considerably the correctness of the decisions within the automatic adaptive quadrature.
Error bounds on block Gauss-Seidel solutions of coupled multiphysics problems
Whiteley, J. P.
2011-05-09
Mathematical models in many fields often consist of coupled sub-models, each of which describes a different physical process. For many applications, the quantity of interest from these models may be written as a linear functional of the solution to the governing equations. Mature numerical solution techniques for the individual sub-models often exist. Rather than derive a numerical solution technique for the full coupled model, it is therefore natural to investigate whether these techniques may be used by coupling in a block Gauss-Seidel fashion. In this study, we derive two a posteriori bounds for such linear functionals. These bounds may be used on each Gauss-Seidel iteration to estimate the error in the linear functional computed using the single physics solvers, without actually solving the full, coupled problem. We demonstrate the use of the bound first by using a model problem from linear algebra, and then a linear ordinary differential equation example. We then investigate the effectiveness of the bound using a non-linear coupled fluid-temperature problem. One of the bounds derived is very sharp for most linear functionals considered, allowing us to predict very accurately when to terminate our block Gauss-Seidel iteration. © 2011 John Wiley & Sons, Ltd.
Einstein-Gauss-Bonnet metrics: black holes, black strings and a staticity theorem
International Nuclear Information System (INIS)
Bogdanos, C.; Charmousis, C.; Gouteraux, B.; Zegers, R.
2009-01-01
We find the general solution of the 6-dimensional Einstein-Gauss-Bonnet equations in a large class of space and time-dependent warped geometries. Several distinct families of solutions are found, some of which include black string metrics, space and time-dependent solutions and black holes with exotic horizons. Among these, some are shown to verify a Birkhoff type staticity theorem, although here, the usual assumption of maximal symmetry on the horizon is relaxed, allowing exotic horizon geometries. We provide explicit examples of such static exotic black holes, including ones whose horizon geometry is that of a Bergman space. We find that the situation is very different from higher-dimensional general relativity, where Einstein spaces are admissible black hole horizons and the associated black hole potential is not even affected. In Einstein-Gauss-Bonnet theory, on the contrary, the non-trivial Weyl tensor of such exotic horizons is exposed to the bulk dynamics through the higher order Gauss-Bonnet term, severely constraining the allowed horizon geometries and adding a novel charge-like parameter to the black hole potential. The latter is related to the Euler characteristic of the four-dimensional horizon and provides, in some cases, additional black hole horizons.
Solving radiative transfer with line overlaps using Gauss-Seidel algorithms
Daniel, F.; Cernicharo, J.
2008-09-01
Context: The improvement in observational facilities requires refining the modelling of the geometrical structures of astrophysical objects. Nevertheless, for complex problems such as line overlap in molecules showing hyperfine structure, a detailed analysis still requires a large amount of computing time and thus, misinterpretation cannot be dismissed due to an undersampling of the whole space of parameters. Aims: We extend the discussion of the implementation of the Gauss-Seidel algorithm in spherical geometry and include the case of hyperfine line overlap. Methods: We first review the basics of the short characteristics method that is used to solve the radiative transfer equations. Details are given on the determination of the Lambda operator in spherical geometry. The Gauss-Seidel algorithm is then described and, by analogy to the plan-parallel case, we see how to introduce it in spherical geometry. Doing so requires some approximations in order to keep the algorithm competitive. Finally, line overlap effects are included. Results: The convergence speed of the algorithm is compared to the usual Jacobi iterative schemes. The gain in the number of iterations is typically factors of 2 and 4 for the two implementations made of the Gauss-Seidel algorithm. This is obtained despite the introduction of approximations in the algorithm. A comparison of results obtained with and without line overlaps for N2H^+, HCN, and HNC shows that the J=3-2 line intensities are significantly underestimated in models where line overlap is neglected.
Error bounds on block Gauss-Seidel solutions of coupled multiphysics problems
Whiteley, J. P.; Gillow, K.; Tavener, S. J.; Walter, A. C.
2011-01-01
Mathematical models in many fields often consist of coupled sub-models, each of which describes a different physical process. For many applications, the quantity of interest from these models may be written as a linear functional of the solution to the governing equations. Mature numerical solution techniques for the individual sub-models often exist. Rather than derive a numerical solution technique for the full coupled model, it is therefore natural to investigate whether these techniques may be used by coupling in a block Gauss-Seidel fashion. In this study, we derive two a posteriori bounds for such linear functionals. These bounds may be used on each Gauss-Seidel iteration to estimate the error in the linear functional computed using the single physics solvers, without actually solving the full, coupled problem. We demonstrate the use of the bound first by using a model problem from linear algebra, and then a linear ordinary differential equation example. We then investigate the effectiveness of the bound using a non-linear coupled fluid-temperature problem. One of the bounds derived is very sharp for most linear functionals considered, allowing us to predict very accurately when to terminate our block Gauss-Seidel iteration. © 2011 John Wiley & Sons, Ltd.
State space orderings for Gauss-Seidel in Markov chains revisited
Energy Technology Data Exchange (ETDEWEB)
Dayar, T. [Bilkent Univ., Ankara (Turkey)
1996-12-31
Symmetric state space orderings of a Markov chain may be used to reduce the magnitude of the subdominant eigenvalue of the (Gauss-Seidel) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the dominant term of the Gauss-Seidel splitting (that is, the term approximating the coefficient matrix) do not necessarily converge faster. An ordering of a Markov chain that satisfies Property-R is semi-convergent. On the other hand, there are semi-convergent symmetric state space orderings that do not satisfy Property-R. For a given ordering, a simple approach for checking Property-R is shown. An algorithm that orders the states of a Markov chain so as to increase the likelihood of satisfying Property-R is presented. The computational complexity of the ordering algorithm is less than that of a single Gauss-Seidel iteration (for sparse matrices). In doing all this, the aim is to gain an insight for faster converging orderings. Results from a variety of applications improve the confidence in the algorithm.
Theory and experiment of Fourier-Bessel field calculation and tuning of a pulsed wave annular array
DEFF Research Database (Denmark)
Fox, Paul D.; Jiqi, Cheng; Jian-yu, Lu
2003-01-01
A one-dimensional (1D) Fourier-Bessel series method for computing and tuning (beamforming) the linear lossless field of flat pulsed wave annular arrays is developed and supported with both numerical simulation and experimental verification. The technique represents a new method for modeling and t...
A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Nash, Patrick L.
2008-01-01
Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation Δ perpendicular FDA of 1/r (∂)/(∂r) r(∂)/(∂r) that possesses an associated exact unitary representation of e i/2λΔ perpendicular FDA . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium
Guo, Jian; Wei, Zhongchao; Liu, Yuebo; Huang, Aili
2015-02-01
Two amplitude modulation methods, including modified Bessel-like function modulation structure and trapezoid annulus structure, for suppressing sidelobes of optical vortices are studied. In the former approach, we propose that the order of the Bessel-like function can be an additional parameter to modulate diffraction patterns of optical vortices motivated by the idea of conventional annulus structures. Furthermore, new Bessel-like modulation functions are introduced to solve the problem of low diffraction efficiency of the original one. Trapezoid annulus structure is proposed as a compromise structure between the modified Bessel-like modulation structure and the conventional annulus one, and has advantages of both. It is demonstrated that these two approaches can achieve high-quality optical vortices with suppressed sidelobes effectively, and the relative structures behave as more flexible and applicable structures for producing optical vortices with large coverage of topological charges, which suggests great potential in simplifying the structure designing procedure. These reliable and generalized structures for generating high-quality optical vortices will help to promote the development of future optical communication and optical manipulation significantly.
A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)
2002-01-01
textabstractThe use of a uniform Airy-type asymptotic expansion for the computation of the modified Bessel functions of the third kind of imaginary orders ($K_{ia}(x)$) near the transition point $x=a$, is discussed. In [2], an algorithm for the evaluation of $K_{ia}(x)$ was presented, which made use
Beam shaping to provide round and square-shaped beams in optical systems of high-power lasers
Laskin, Alexander; Laskin, Vadim
2016-05-01
Optical systems of modern high-power lasers require control of irradiance distribution: round or square-shaped flat-top or super-Gaussian irradiance profiles are optimum for amplification in MOPA lasers and for thermal load management while pumping of crystals of solid-state ultra-short pulse lasers to control heat and minimize its impact on the laser power and beam quality while maximizing overall laser efficiency, variable profiles are also important in irradiating of photocathode of Free Electron lasers (FEL). It is suggested to solve the task of irradiance re-distribution using field mapping refractive beam shapers like piShaper. The operational principle of these devices presumes transformation of laser beam intensity from Gaussian to flat-top one with high flatness of output wavefront, saving of beam consistency, providing collimated output beam of low divergence, high transmittance, extended depth of field, negligible residual wave aberration, and achromatic design provides capability to work with ultra-short pulse lasers having broad spectrum. Using the same piShaper device it is possible to realize beams with flat-top, inverse Gauss or super Gauss irradiance distribution by simple variation of input beam diameter, and the beam shape can be round or square with soft edges. This paper will describe some design basics of refractive beam shapers of the field mapping type and optical layouts of their applying in optical systems of high-power lasers. Examples of real implementations and experimental results will be presented as well.
Generation of spirally polarized propagation-invariant beam using fiber microaxicon.
Philip, Geo M; Viswanathan, Nirmal K
2011-10-01
We present here a fiber microaxicon (MA)based method to generate spirally polarized propagation-invariant optical beam. MA chemically etched in the tip of a two-mode fiber efficiently converts the generic cylindrically polarized vortex fiber mode into a spirally polarized propagation-invariant (Bessel-type) beam via radial dependence of polarization rotation angle. The combined roles of helico-conical phase and nonparaxial propagation in the generation and characteristics of the output beam from the fiber MA are discussed. © 2011 Optical Society of America
Light beam tracing for multi-bounce specular and glossy transport paths
CSIR Research Space (South Africa)
Duvenhage, B
2014-09-01
Full Text Available This paper describes a new extension to light beam tracing that includes glossy multi-bounce transport paths for more realistic rendering of caustics. A spherical Gaussian approximation of the glossy scatter distribution as well as Gauss' divergence...
Laser-plasma interactions with a Fourier-Bessel particle-in-cell method
Energy Technology Data Exchange (ETDEWEB)
Andriyash, Igor A., E-mail: igor.andriyash@gmail.com [Synchrotron SOLEIL, L' Orme des Merisiers, Saint Aubin, 91192 Gif-sur-Yvette (France); LOA, ENSTA ParisTech, CNRS, Ecole polytechnique, Université Paris-Saclay, 828 bd des Maréchaux, 91762 Palaiseau cedex (France); Lehe, Remi [Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Lifschitz, Agustin [LOA, ENSTA ParisTech, CNRS, Ecole polytechnique, Université Paris-Saclay, 828 bd des Maréchaux, 91762 Palaiseau cedex (France)
2016-03-15
A new spectral particle-in-cell (PIC) method for plasma modeling is presented and discussed. In the proposed scheme, the Fourier-Bessel transform is used to translate the Maxwell equations to the quasi-cylindrical spectral domain. In this domain, the equations are solved analytically in time, and the spatial derivatives are approximated with high accuracy. In contrast to the finite-difference time domain (FDTD) methods, that are used commonly in PIC, the developed method does not produce numerical dispersion and does not involve grid staggering for the electric and magnetic fields. These features are especially valuable in modeling the wakefield acceleration of particles in plasmas. The proposed algorithm is implemented in the code PLARES-PIC, and the test simulations of laser plasma interactions are compared to the ones done with the quasi-cylindrical FDTD PIC code CALDER-CIRC.
On the evaluation of the integral over the product of two spherical Bessel functions
International Nuclear Information System (INIS)
Maximon, L.C.
1991-01-01
The integral I l,l' (k,k')=∫ ∞ 0 j l (kr)j l' (k'r)r 2 dr, in which the spherical Bessel functions j l (kr) are the radial eigenfunctions of the three-dimensional wave equation in spherical coordinates, is evaluated in terms of distributions, in particular, step functions and delta functions. It will be shown that the behavior of I l,l' is very different in the cases l-l' even (0, ±2, ±4, ...) and l-l' odd (±1, ±3, ...). For l-l' even it is expressed in terms of the delta function, step functions, and Legendre polynomials. For l-l' odd it is expressed in terms of Legendre functions of the second kind and step functions; no delta functions appear
Pupil filter design by using a Bessel functions basis at the image plane.
Canales, Vidal F; Cagigal, Manuel P
2006-10-30
Many applications can benefit from the use of pupil filters for controlling the light intensity distribution near the focus of an optical system. Most of the design methods for such filters are based on a second-order expansion of the Point Spread Function (PSF). Here, we present a new procedure for designing radially-symmetric pupil filters. It is more precise than previous procedures as it considers the exact expression of the PSF, expanded as a function of first-order Bessel functions. Furthermore, this new method presents other advantages: the height of the side lobes can be easily controlled, it allows the design of amplitude-only, phase-only or hybrid filters, and the coefficients of the PSF expansion can be directly related to filter parameters. Finally, our procedure allows the design of filters with very different behaviours and optimal performance.
Monotonicity of the ratio of modified Bessel functions of the first kind with applications.
Yang, Zhen-Hang; Zheng, Shen-Zhou
2018-01-01
Let [Formula: see text] with [Formula: see text] be the modified Bessel functions of the first kind of order v . In this paper, we prove the monotonicity of the function [Formula: see text] on [Formula: see text] for different values of parameter p with [Formula: see text]. As applications, we deduce some new Simpson-Spector-type inequalities for [Formula: see text] and derive a new type of bounds [Formula: see text] ([Formula: see text]) for [Formula: see text]. In particular, we show that the upper bound [Formula: see text] for [Formula: see text] is the minimum over all upper bounds [Formula: see text], where [Formula: see text] and is not comparable with other sharpest upper bounds. We also find such type of upper bounds for [Formula: see text] with [Formula: see text] and for [Formula: see text] with [Formula: see text].
Spherical space Bessel-Legendre-Fourier mode solver for Maxwell's wave equations
Alzahrani, Mohammed A.; Gauthier, Robert C.
2015-02-01
For spherically symmetric dielectric structures, a basis set composed of Bessel, Legendre and Fourier functions, BLF, are used to cast Maxwell's wave equations into an eigenvalue problem from which the localized modes can be determined. The steps leading to the eigenmatrix are reviewed and techniques used to reduce the order of matrix and tune the computations for particular mode types are detailed. The BLF basis functions are used to expand the electric and magnetic fields as well as the inverse relative dielectric profile. Similar to the common plane wave expansion technique, the BLF matrix returns the eigen-frequencies and eigenvectors, but in BLF only steady states, non-propagated, are obtained. The technique is first applied to a air filled spherical structure with perfectly conducting outer surface and then to a spherical microsphere located in air. Results are compared published values were possible.
VizieR Online Data Catalog: Bessel (1825) calculation for geodesic measurements (Karney+, 2010)
Karney, C. F. F.; Deakin, R. E.
2010-06-01
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. Included here are the tables that accompanied Bessel's paper (with corrections). The tables were crafted by Bessel to be minimize the labor of hand calculations. To this end, he adjusted the intervals in the tables, the number of terms included in the series, and the number of significant digits given so that the final results are accurate to about 8 places. For that reason, the most useful form of the tables is as the PDF file which provides the tables in a layout close to the original. Also provided is the LaTeX source file for the PDF file. Finally, the data has been put into a format so that it can be read easily by computer programs. All the logarithms are in base 10 (common logarithms). The characteristic and the mantissa should be read separately (indicated as x.c and x.m in the file description). Thus the first entry in the table, -4.4, should be parsed as "-4" (the characteristic) and ".4" (the mantissa); the anti-log for this entry is 10(-4+0.4)=2.5e-4. The "Delta" columns give the first difference of the preceding column, i.e., the difference of the preceding column in the next row and the preceding column in the current row. In the printed tables these are expressed as "units in the last place" and the differences are of the rounded representations in the preceding columns (to minimize interpolation errors). In table1.dat these are given scaled to a match the format used for the preceding column, as indicated by the units given for these columns. The unit log(") (in the description within square brackets [arcsec]) means the logarithm of a quantity expressed in arcseconds. (3 data files).
X-ray section topographs under various coherence properties of the primary beam
International Nuclear Information System (INIS)
Borowski, J.; Gronkowski, J.
2001-01-01
The aim of this work is to study to what extent a typical section-topography setup can supply information about the degree of coherence of the incident x-ray beam. In real experiments, the incident beam is partially coherent, with the degree of coherence described by the shape of the correlation function. In this paper the correlation functions for the outgoing beam are calculated by solving the Takagi-Taupin equations, assuming a truncated Gauss correlation function for the incident beam with the correlation length determined by the van Cittert-Zernike theorem. Its influence on the measured intensity of the diffracted beam in section topography is investigated. (author)
Konoplya, R. A.; Zhidenko, A.
2017-09-01
Here we shall show that there is no other instability for the Einstein-Gauss-Bonnet-anti-de Sitter (AdS) black holes, than the eikonal one and consider the features of the quasinormal spectrum in the stability sector in detail. The obtained quasinormal spectrum consists from the two essentially different types of modes: perturbative and non-perturbative in the Gauss-Bonnet coupling α. The sound and hydrodynamic modes of the perturbative branch can be expressed through their Schwazrschild-AdS limits by adding a linear in α correction to the damping rates: ω≈Re ω SAdS -Im ω SAdS(1- α·(( D+1)( D-4) /2 R 2)) i, where R is the AdS radius. The non-perturbative branch of modes consists of purely imaginary modes, whose damping rates unboundedly increase when α goes to zero. When the black hole radius is much larger than the anti-de Sitter radius R, the regime of the black hole with planar horizon (black brane) is reproduced. If the Gauss-Bonnet coupling α (or used in holography λGB) is not small enough, then the black holes and branes suffer from the instability, so that the holographic interpretation of perturbation of such black holes becomes questionable, as, for example, the claimed viscosity bound violation in the higher derivative gravity. For example, D = 5 black brane is unstable at |λGB| > 1 /8 and has anomalously large relaxation time when approaching the threshold of instability.
General aspects of Gauss-Bonnet models without potential in dimension four
Energy Technology Data Exchange (ETDEWEB)
Santillán, Osvaldo P., E-mail: firenzecita@hotmail.com [Departamento de Matemáticas Luis Santaló (IMAS), Buenos Aires (Argentina)
2017-07-01
In the present work, the isotropic and homogenous solutions with spatial curvature k =0 of four dimensional Gauss-Bonnet models are characterized. The main assumption is that the scalar field φ which is coupled to the Gauss-Bonnet term has no potential [1]–[2]. Some singular and some eternal solutions are described. The evolution of the universe is given in terms of a curve γ=( H (φ), φ) which is the solution of a polynomial equation P ( H {sup 2}, φ)=0 with φ dependent coefficients. In addition, it is shown that the initial conditions in these models put several restrictions on the evolution. For instance, an universe initially contracting will be contracting always for future times and an universe that is expanding was always expanding at past times. Thus, there are no cyclic cosmological solutions for this model. These results are universal, that is, independent on the form of the coupling f (φ) between the scalar field and the Gauss-Bonnet term. In addition, a proof that at a turning point φ-dot →0 a singularity necessarily emerges is presented, except for some specific choices of the coupling. This is valid unless the Hubble constant H → 0 at this point. This proof is based on the Raychaudhuri equation for the model. The description presented here is in part inspired in the works [3]–[4]. However, the mathematical methods that are implemented are complementary of those in these references, and they may be helpful for study more complicated situations in a future.
Unfocused beam patterns in nonattenuating and attenuating fluids
International Nuclear Information System (INIS)
Goldstein, Albert
2004-01-01
The most important aspect of an ultrasound measuring system is knowledge of the transducer beam pattern. At all depths accurate single integral equations have been derived for the full beam pattern of steady state unfocused circular flat piston sources radiating into nonattenuating and attenuating fluids. The axial depth of the beginning of the unattenuated beam pattern far field is found to be at 6.41Y 0 . The unattenuated single integral equations are identical to a Jinc function directivity term at this and deeper depths. For attenuating fluids values of α and z are found that permit the attenuated axial pressure to be represented by a plane wave multiplicative exponential attenuation factor. This knowledge will aid in the experimental design of highly accurate attenuation measurements. Accurate single integral equations for the attenuated full beam pattern are derived using complex Bessel functions
Bayesian model comparison using Gauss approximation on multicomponent mass spectra from CH4 plasma
International Nuclear Information System (INIS)
Kang, H.D.; Dose, V.
2004-01-01
We performed Bayesian model comparison on mass spectra from CH4 rf process plasmas to detect radicals produced in the plasma. The key ingredient for its implementation is the high-dimensional evidence integral. We apply Gauss approximation to evaluate the evidence. The results were compared with those calculated by the thermodynamic integration method using Markov Chain Monte Carlo technique. In spite of very large difference in the computation time between two methods a very good agreement was obtained. Alternatively, a Monte Carlo integration method based on the approximated Gaussian posterior density is presented. Its applicability to the problem of mass spectrometry is discussed
Energetics and optical properties of 6-dimensional rotating black hole in pure Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Abdujabbarov, Ahmadjon; Ahmedov, Bobomurat; Atamurotov, Farruh; Dadhich, Naresh; Stuchlik, Zdenek
2015-01-01
We study physical processes around a rotating black hole in pure Gauss-Bonnet (GB) gravity. In pure GB gravity, the gravitational potential has a slower fall-off as compared to the corresponding Einstein potential in the same dimension. It is therefore expected that the energetics of a pure GB black hole would be weaker, and our analysis bears out that the efficiency of energy extraction by the Penroseprocess is increased to 25.8 % and the particle acceleration is increased to 55.28 %; the optical shadow of the black hole is decreased. These are in principle distinguishing observable features of a pure GB black hole. (orig.)
Spacetime structure of static solutions in Gauss-Bonnet gravity: Neutral case
International Nuclear Information System (INIS)
Torii, Takashi; Maeda, Hideki
2005-01-01
We study the spacetime structures of the static solutions in the n-dimensional Einstein-Gauss-Bonnet-Λ system systematically. We assume the Gauss-Bonnet coefficient α is non-negative and a cosmological constant is either positive, zero, or negative. The solutions have the (n-2)-dimensional Euclidean submanifold, which is the Einstein manifold with the curvature k=1, 0, and -1. We also assume 4α-tilde/l 2 ≤1, where l is the curvature radius, in order for the sourceless solution (M=0) to be defined. The general solutions are classified into plus and minus branches. The structures of the center, horizons, infinity, and the singular point depend on the parameters α, l 2 , k, M, and branches complicatedly so that a variety of global structures for the solutions are found. In our analysis, the M-tilde-r diagram is used, which makes our consideration clear and enables easy understanding by visual effects. In the plus branch, all the solutions have the same asymptotic structure at infinity as that in general relativity with a negative cosmological constant. For the negative-mass parameter, a new type of singularity called the branch singularity appears at nonzero finite radius r=r b >0. The divergent behavior around the singularity in Gauss-Bonnet gravity is milder than that around the central singularity in general relativity. There are three types of horizons: inner, black hole, and cosmological. In the k=1,0 cases, the plus-branch solutions do not have any horizon. In the k=-1 case, the radius of the horizon is restricted as r h h >√(2α-tilde)) in the plus (minus) branch. The black hole solution with zero or negative mass exists in the plus branch even for the zero or positive cosmological constant. There is also the extreme black hole solution with positive mass. We briefly discuss the effect of the Gauss-Bonnet corrections on black hole formation in a collider and the possibility of the violation of the third law of the black hole thermodynamics
Some exact solutions with torsion in 5D Einstein-Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Canfora, F.; Giacomini, A.; Willison, S.
2007-01-01
Exact solutions with torsion in Einstein-Gauss-Bonnet gravity are derived. These solutions have a cross product structure of two constant curvature manifolds. The equations of motion give a relation for the coupling constants of the theory in order to have solutions with nontrivial torsion. This relation is not the Chern-Simons combination. One of the solutions has an AdS 2 xS 3 structure and is so the purely gravitational analogue of the Bertotti-Robinson space-time where the torsion can be seen as the dual of the covariantly constant electromagnetic field
International Nuclear Information System (INIS)
Watanabe, Shuichi; Kudo, Hiroyuki; Saito, Tsuneo
1993-01-01
In this paper, we propose a new reconstruction algorithm based on MAP (maximum a posteriori probability) estimation principle for emission tomography. To improve noise suppression properties of the conventional ML-EM (maximum likelihood expectation maximization) algorithm, direct three-dimensional reconstruction that utilizes intensity correlations between adjacent transaxial slices is introduced. Moreover, to avoid oversmoothing of edges, a priori knowledge of RI (radioisotope) distribution is represented by using a doubly-stochastic image model called the compound Gauss-Markov random field. The a posteriori probability is maximized by using the iterative GEM (generalized EM) algorithm. Computer simulation results are shown to demonstrate validity of the proposed algorithm. (author)
Decentralized Gauss-Newton method for nonlinear least squares on wide area network
Liu, Lanchao; Ling, Qing; Han, Zhu
2014-10-01
This paper presents a decentralized approach of Gauss-Newton (GN) method for nonlinear least squares (NLLS) on wide area network (WAN). In a multi-agent system, a centralized GN for NLLS requires the global GN Hessian matrix available at a central computing unit, which may incur large communication overhead. In the proposed decentralized alternative, each agent only needs local GN Hessian matrix to update iterates with the cooperation of neighbors. The detail formulation of decentralized NLLS on WAN is given, and the iteration at each agent is defined. The convergence property of the decentralized approach is analyzed, and numerical results validate the effectiveness of the proposed algorithm.
Dataset for petroleum based stock markets and GAUSS codes for SAMEM
Directory of Open Access Journals (Sweden)
Ahmed A.A. Khalifa
2017-02-01
Full Text Available This article includes a unique data set of a balanced daily (Monday, Tuesday and Wednesday for oil and natural gas volatility and the oil rich economies’ stock markets for Saudi Arabia, Qatar, Kuwait, Abu Dhabi, Dubai, Bahrain and Oman, using daily data over the period spanning Oct. 18, 2006–July 30, 2015. Additionally, we have included unique GAUSS codes for estimating the spillover asymmetric multiplicative error model (SAMEM with application to Petroleum-Based Stock Market. The data, the model and the codes have many applications in business and social science.
Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation
Energy Technology Data Exchange (ETDEWEB)
Bu, Yanyan; Lublinsky, Michael; Sharon, Amir [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)
2015-06-24
Relativistic hydrodynamics dual to Einstein-Gauss-Bonnet gravity in asymptotic AdS{sub 5} space is under study. To linear order in the amplitude of the fluid velocity and temperature, we derive the fluid’s stress-energy tensor via an all-order resummation of the derivative terms. Each order is accompanied by new transport coefficients, which all together could be compactly absorbed into two functions of momenta, referred to as viscosity functions. Via inverse Fourier transform, these viscosities appear as memory functions in the constitutive relation between components of the stress-energy tensor.
Kink-antikink, trapping bags and five-dimensional Gauss-Bonnet gravity
Giovannini, Massimo
2006-01-01
Five-dimensional Gauss-Bonnet gravity, with one warped extra-dimension, allows classes of solutions where two scalar fields combine either in a kink-antikink system or in a trapping bag configuration. While the kink-antikink system can be interpreted as a pair of gravitating domain walls with opposite topological charges, the trapping bag solution consists of a domain wall supplemented by a non-topological defect. In both classes of solutions, for large absolute values of the bulk coordinate (i.e. far from the core of the defects), the geometry is given by five-dimensional anti-de Sitter space.
Kink-antikink, trapping bags and five-dimensional Gauss-Bonnet gravity
Giovannini, Massimo
2006-01-01
Five-dimensional Gauss-Bonnet gravity, with one warped extra-dimension, allows classes of solutions where two scalar fields combine either in a kink-antikink system or in a trapping bag configuration. While the kink-antikink system can be interpreted as a pair of gravitating domain walls with opposite topological charges, the trapping bag solution consists of a domain wall supplemented by a non-topological defect. In both classes of solutions, for large absolute values of the bulk coordinate ...
Dataset for petroleum based stock markets and GAUSS codes for SAMEM.
Khalifa, Ahmed A A; Bertuccelli, Pietro; Otranto, Edoardo
2017-02-01
This article includes a unique data set of a balanced daily (Monday, Tuesday and Wednesday) for oil and natural gas volatility and the oil rich economies' stock markets for Saudi Arabia, Qatar, Kuwait, Abu Dhabi, Dubai, Bahrain and Oman, using daily data over the period spanning Oct. 18, 2006-July 30, 2015. Additionally, we have included unique GAUSS codes for estimating the spillover asymmetric multiplicative error model (SAMEM) with application to Petroleum-Based Stock Market. The data, the model and the codes have many applications in business and social science.
Fast large-scale clustering of protein structures using Gauss integrals
DEFF Research Database (Denmark)
Harder, Tim; Borg, Mikael; Boomsma, Wouter
2011-01-01
trajectories. Results: We present Pleiades, a novel approach to clustering protein structures with a rigorous mathematical underpinning. The method approximates clustering based on the root mean square deviation by rst mapping structures to Gauss integral vectors – which were introduced by Røgen and co......-workers – and subsequently performing K-means clustering. Conclusions: Compared to current methods, Pleiades dramatically improves on the time needed to perform clustering, and can cluster a signicantly larger number of structures, while providing state-ofthe- art results. The number of low energy structures generated...
GPU-accelerated Modeling and Element-free Reverse-time Migration with Gauss Points Partition
Zhen, Z.; Jia, X.
2014-12-01
Element-free method (EFM) has been applied to seismic modeling and migration. Compared with finite element method (FEM) and finite difference method (FDM), it is much cheaper and more flexible because only the information of the nodes and the boundary of the study area are required in computation. In the EFM, the number of Gauss points should be consistent with the number of model nodes; otherwise the accuracy of the intermediate coefficient matrices would be harmed. Thus when we increase the nodes of velocity model in order to obtain higher resolution, we find that the size of the computer's memory will be a bottleneck. The original EFM can deal with at most 81×81 nodes in the case of 2G memory, as tested by Jia and Hu (2006). In order to solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition (GPP), and utilize the GPUs to improve the computation efficiency. Considering the characteristics of the Gaussian points, the GPP method doesn't influence the propagation of seismic wave in the velocity model. To overcome the time-consuming computation of the stiffness matrix (K) and the mass matrix (M), we also use the GPUs in our computation program. We employ the compressed sparse row (CSR) format to compress the intermediate sparse matrices and try to simplify the operations by solving the linear equations with the CULA Sparse's Conjugate Gradient (CG) solver instead of the linear sparse solver 'PARDISO'. It is observed that our strategy can significantly reduce the computational time of K and Mcompared with the algorithm based on CPU. The model tested is Marmousi model. The length of the model is 7425m and the depth is 2990m. We discretize the model with 595x298 nodes, 300x300 Gauss cells and 3x3 Gauss points in each cell. In contrast to the computational time of the conventional EFM, the GPUs-GPP approach can substantially improve the efficiency. The speedup ratio of time consumption of computing K, M is 120 and the
Phantom-like behavior of a DGP-inspired Scalar-Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Nozari, Kourosh; Azizi, Tahereh; Setare, M.R.
2009-01-01
We study the phantom-like behavior of a DGP-inspired braneworld scenario where curvature correction on the brane is taken into account. We include a possible modification of the induced gravity on the brane by incorporating higher order curvature terms of Gauss-Bonnet type. We investigate the cosmological implications of the model and we show that the normal branch of the scenario self-accelerates in this modified scenario without introducing any dark energy component. Also, a phantom-like behavior can be realized in this model without introducing any phantom field that suffers from serious difficulties such as violation of the null energy condition
Field computation for two-dimensional array transducers with limited diffraction array beams.
Lu, Jian-Yu; Cheng, Jiqi
2005-10-01
A method is developed for calculating fields produced with a two-dimensional (2D) array transducer. This method decomposes an arbitrary 2D aperture weighting function into a set of limited diffraction array beams. Using the analytical expressions of limited diffraction beams, arbitrary continuous wave (cw) or pulse wave (pw) fields of 2D arrays can be obtained with a simple superposition of these beams. In addition, this method can be simplified and applied to a 1D array transducer of a finite or infinite elevation height. For beams produced with axially symmetric aperture weighting functions, this method can be reduced to the Fourier-Bessel method studied previously where an annular array transducer can be used. The advantage of the method is that it is accurate and computationally efficient, especially in regions that are not far from the surface of the transducer (near field), where it is important for medical imaging. Both computer simulations and a synthetic array experiment are carried out to verify the method. Results (Bessel beam, focused Gaussian beam, X wave and asymmetric array beams) show that the method is accurate as compared to that using the Rayleigh-Sommerfeld diffraction formula and agrees well with the experiment.
International Nuclear Information System (INIS)
Rutt, H.N.
2003-01-01
The modified Bessel functions of the second kind and fractional order K 1/3 (x) and K 2/3 (x) are of importance in the calculation of the frequency spectrum of synchrotron radiation. The parameter range of interest is typically 10 -6 x10. Recently, there has been particular interest in the generation of 'terahertz' radiation, which can be coherently enhanced by many orders of magnitude when the electron bunch length is shorter than the terahertz wavelength. This requires evaluation of the Bessel functions for small values of the argument. It is shown that the series commonly used to evaluate these functions has poor convergence properties under these conditions. An alternative series is derived which has much better convergence for x1
Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko
2017-07-10
This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.
Calculation of photoionization differential cross sections using complex Gauss-type orbitals.
Matsuzaki, Rei; Yabushita, Satoshi
2017-09-05
Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss-type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so-called two-potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth-order final continuum state and the first-order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss-type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular-frame photoelectron angular distributions of H2+ and H2 . In the calculations of H2 , the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.