Showing papers on "Bessel function published in 2017"
TL;DR: Meta-axicons with high NA up to 0.9 capable of generating Bessel beams with full width at half maximum about as small as ~λ/3 (λ=405 nm) have transverse intensity profiles independent of wavelength across the visible spectrum.
Abstract: Bessel beams are of great interest due to their unique non-diffractive properties Using a conical prism or an objective paired with an annular aperture are two typical approaches for generating zeroth-order Bessel beams However, the former approach has a limited numerical aperture (NA), and the latter suffers from low efficiency, as most of the incident light is blocked by the aperture Furthermore, an additional phase-modulating element is needed to generate higher-order Bessel beams, which in turn adds complexity and bulkiness to the system We overcome these problems using dielectric metasurfaces to realize meta-axicons with additional functionalities not achievable with conventional means We demonstrate meta-axicons with high NA up to 09 capable of generating Bessel beams with full width at half maximum about as small as ~λ/3 (λ=405 nm) Importantly, these Bessel beams have transverse intensity profiles independent of wavelength across the visible spectrum These meta-axicons can enable advanced research and applications related to Bessel beams, such as laser fabrication, imaging and optical manipulation
186 citations
TL;DR: Experimental results indicate that the compensation scheme can effectively reduce the inter-channel crosstalk, improve the bit-error rate (BER) performance, and recuperate the nondiffracting property of Bessel beams.
Abstract: We present a scheme to realize obstruction- and turbulence-tolerant free-space orbital angular momentum (OAM) multiplexing link by using self-healing Bessel beams accompanied by adaptive compensation techniques. Compensation of multiple 16-ary quadrature amplitude modulation (16-QAM) data carrying Bessel beams through emulated atmospheric turbulence and obstructions is demonstrated. The obtained experimental results indicate that the compensation scheme can effectively reduce the inter-channel crosstalk, improve the bit-error rate (BER) performance, and recuperate the nondiffracting property of Bessel beams. The proposed scheme might be used in future high-capacity OAM links which are affected by atmospheric turbulence and obstructions.
110 citations
TL;DR: In this article, the 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.
Abstract: 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.
65 citations
TL;DR: In this article, a simple and efficient approach for multipole expansion of a circularly symmetric Bessel beam is derived, and the convergence and correctness of the beam shape coefficients are verified numerically in detail for both on-axis and off-axis cases.
64 citations
TL;DR: In this paper, the Laguerre and Jacobi versions of the one-body interaction terms are derived in terms of the eigenvalue PDF of certain random matrices with Gaussian entries.
Abstract: Muttalib–Borodin ensembles are characterised by the pair interaction term in the eigenvalue probability density function being of the form Q (Formula presented). We study the Laguerre and Jacobi versions of this model — so named by the form of the one-body interaction terms — and show that for θ ∈ ℤ+ they can be realised as the eigenvalue PDF of certain random matrices with Gaussian entries. For general θ > 0, realisations in terms of the eigenvalue PDF of ensembles involving triangular matrices are given. In the Laguerre case this is a recent result due to Cheliotis, although our derivation is different. We make use of a generalisation of a double contour integral formula for the correlation functions contained in a paper by Adler, van Moerbeke and Wang to analyse the global density (which we also analyse by studying characteristic polynomials), and the hard edge scaled correlation functions. For the global density functional equations for the corresponding resolvents are obtained; solving this gives the moments in terms of Fuss–Catalan numbers (Laguerre case — a known result) and particular binomial coefficients (Jacobi case). For θ ∈ ℤ+ the Laguerre and Jacobi cases are closely related to the squared singular values for products of θ standard Gaussian random matrices, and truncations of unitary matrices, respectively. At the hard edge the double contour integral formulas provide a double contour integral form of the scaled correlation kernel obtained by Borodin in terms of Wright’s Bessel function.
62 citations
TL;DR: In this article, the authors focused on heat transfer analysis in the unsteady flow of a generalized Maxwell fluid over an oscillating vertical flat plate with constant temperature, and obtained an exact solution of the dimensionless problem by using the Laplace transform.
Abstract: This article is focused on heat transfer analysis in the unsteady flow of a generalized Maxwell fluid over an oscillating vertical flat plate with constant temperature. The well-known equation of the Maxwell fluid with classical derivatives, describing the unidirectional and one-dimensional flow, has been generalized to a non-integer-order derivative, known as fractional derivative, with free convection term of buoyancy. A new definition of the fractional derivative introduced by Caputo and Fabrizio has been used in the mathematical formulation of the problem. Exact solution of the dimensionless problem has been obtained by using the Laplace transform. These solutions are expressed with complementary error and modified Bessel functions. Similar solutions for classical Maxwell and Newtonian fluids and generalized Newtonian fluid performing the same motion are obtained as limiting cases of our general results. Graphical illustrations show that the velocity profiles corresponding to a generalized Maxwell fluid are similar to those for an ordinary Maxwell fluid when the fraction order approaches 1. A comparison amongst four different types of fluids is also shown graphically.
61 citations
TL;DR: In this article, a high-order Bessel vortex beam carrying orbital angular momentum (OAM) is generated by using multilayer amplitude-phase-modulated surfaces (APMSs) at 10 GHz.
Abstract: 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.
61 citations
TL;DR: A new representation of solutions to the equation −y′′+q(x)y=ω2y is obtained that allows one to compute large sets of eigendata with a nondeteriorating accuracy.
57 citations
TL;DR: It is shown that, by appropriate spectral excitations, the three different types of conic sections can lead to optical waves of the Bessel, Airy, and modified Bessel types, respectively.
Abstract: We investigate the dynamics of spatiotemporal optical waves with one transverse dimension obtained as the intersections of the dispersion cone with a plane. We show that, by appropriate spectral excitations, the three different types of conic sections (elliptic, parabolic, and hyperbolic) can lead to optical waves of the Bessel, Airy, and modified Bessel types, respectively. We find closed form solutions that accurately describe the wave dynamics and unveil their fundamental properties.
56 citations
TL;DR: In this article, an eigenfunction-matching method was developed for linear water-wave scattering by a circular floating porous elastic plate, and a coupled boundary-element and finite-element method is developed for the problem in which the plate is of arbitrary shape.
54 citations
TL;DR: Both theoretical and experimental results reveal that high order Bessel beams are less influenced by the turbulent atmosphere and have an advantage of mitigating the beam wander in OAM multiplexing FSO communication.
Abstract: Optical beam wander is one of the most important issues for free-space optical (FSO) communication. We theoretically derive a beam wander model for Bessel beams propagating in turbulent atmosphere. The calculated beam wander of high order Bessel beams with different turbulence strengths are consistent with experimental measurements. Both theoretical and experimental results reveal that high order Bessel beams are less influenced by the turbulent atmosphere. We also demonstrate the Bessel beams based orbital angular momentum (OAM) multiplexing/demultiplexing in FSO communication with atmospheric turbulence. Under the same atmospheric turbulence condition, the bit error rates of transmitted signals carried by high order Bessel beams show smaller values and fluctuations, which indicates that the high order Bessel beams have an advantage of mitigating the beam wander in OAM multiplexing FSO communication.
TL;DR: In this paper, the angular power spectrum and bispectrum of cosmological observables are computed using an FFTlog algorithm to decompose the momentum-space statistics onto a basis of power-law functions.
Abstract: Angular statistics of cosmological observables are hard to compute. The main difficulty is due to the presence of highly-oscillatory Bessel functions which need to be integrated over. In this paper, we provide a simple and fast method to compute the angular power spectrum and bispectrum of any observable. The method is based on using an FFTlog algorithm to decompose the momentum-space statistics onto a basis of power-law functions. For each power law, the integrals over Bessel functions have a simple analytical solution. This allows us to efficiently evaluate these integrals, independently of the value of the multipole $\ell$. In particular, this method significantly speeds up the evaluation of the angular bispectrum compared to existing methods. To illustrate our algorithm, we compute the galaxy, lensing and CMB temperature angular power spectrum and bispectrum.
TL;DR: In this paper, a general class of linear viscoelastic models whose creep and relaxation memory functions are expressed in Laplace domain by suitable ratios of modified Bessel functions of contiguous order is investigated.
Abstract: In this paper we investigate a general class of linear viscoelastic models whose creep and relaxation memory functions are expressed in Laplace domain by suitable ratios of modified Bessel functions of contiguous order. In time domain these functions are shown to be expressed by Dirichlet series (that is infinite Prony series). It follows that the corresponding creep compliance and relaxation modulus turn out to be characterized by infinite discrete spectra of retardation and relaxation time respectively. As a matter of fact, we get a class of viscoelastic models depending on a real parameter $$
u > -1$$
. Such models exhibit rheological properties akin to those of a fractional Maxwell model (of order 1/2) for short times and of a standard Maxwell model for long times.
TL;DR: In this article, the primordial power spectra of scalar and tensor perturbations during slow-roll inflation were calculated with the method of Bessel function approximation, and the numerical results were compared with the analytical results derived from the Bessel functions.
Abstract: The primordial power spectra of scalar and tensor perturbations during slow-roll inflation are usually calculated with the method of Bessel function approximation. For constant-roll or ultra slow-roll inflation, the method of Bessel function approximation may be invalid. We compare the numerical results with the analytical results derived from the Bessel function approximation, and we find that they differ significantly on super-horizon scales if the constant slow-roll parameter $\eta_H$ is not small. More accurate method is needed for calculating the primordial power spectrum for constant-roll inflation.
TL;DR: In this paper, the authors have performed experimental, analytical, and numerical studies of beams with topological charges of $mmode\pm\else\textpm\fi{}1$ and $ifmmode \pm \else \textpm \fa{}2$ formed by silicon binary phase axicons (BPAs) with spiral zone structures.
Abstract: In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of $\ifmmode\pm\else\textpm\fi{}1$ and $\ifmmode\pm\else\textpm\fi{}2$ 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 $L/r\ensuremath{\approx}190$ 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 $\ensuremath{\pi}$, 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 $\ensuremath{\mu}\mathrm{m}$ in our case), the BPAs can form the beams at incident radiation with any wavelength, albeit with a reduced diffraction efficiency, and their cross section is the same for any wavelength.
TL;DR: In this article, it was shown that a higher order Bessel beam with azimuthal phase variation can be generated in the near field by synthesizing an inward cylindrical traveling-wave distribution over a finite aperture antenna.
Abstract: In this communication, it is shown that a nondiffracting vortex beam (i.e., a higher order Bessel beam with azimuthal phase variation) can be generated in the near field by synthesizing an inward cylindrical traveling-wave distribution over a finite aperture antenna. A radial line slot array (RLSA) is then designed to prove the concept. The collimated vortex beam is excited in the proximity of the RLSA, within a region properly defined by the nondiffracting range of the generated beam. The radial dependence of the longitudinal electric field of the vortex-beam magnitude follows a first-order Bessel function, and its phase presents a linear azimuthal variation. Full-wave results validate the generation of the nondiffractive higher order Bessel beam within the radiative near field of the launcher.
TL;DR: In this article, an analytical solution to predict axisymmetric consolidation in unsaturated soil deposits subjected to different time-dependent loadings is presented, which uses the separation of variables and Laplace transformation methods to obtain the final solution.
Abstract: This paper presents an analytical solution to predict the axisymmetric consolidation in unsaturated soil deposits subjected to different time-dependent loadings The mathematical procedure uses the separation of variables and Laplace transformation methods to obtain the final solution A set of polar governing equations of flow are obtained and presented under the partial differential equations (PDEs), and then the variable separation technique is used to alter the PDEs to ordinary differential equations (ODEs) consisting of distinctive variables Fourier Bessel and sine series are used to present functions of radial and vertical flows, respectively, and the Laplace transformation is used to obtain a function of time Four primary time-dependent loading functions, including ramping, asymptotic, sinusoid, and damped sine wave, are mathematically simulated and incorporated into the proposed solutions This study investigates changes in excess pore-air and pore-water pressures as well as consolidatio
TL;DR: In this article, a general description of transverse mode Bessel beams is proposed based on an analysis of polarized Bessel beam using the Hertz vector potentials and the angular spectrum representation (ASR).
Abstract: 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.
TL;DR: In this article, the beam shape coefficients of on-axis zeroth-order Bessel beams are evaluated using localized approximation procedures for small axicon angles, and it is shown that these procedures are valid only for small Bessel angles.
Abstract: 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.
TL;DR: In this article, the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium is discussed, and an analytic expression for the long-time behavior of the response function of the material is provided by means of the Tauberian theorems for the Laplace transform.
Abstract: 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.
TL;DR: In this article, the authors studied the problem of finding necessary and sufficient conditions under which a bounded normal operator A in a Hilbert space and a fixed vector x ∈ N constitutes a Bessel sequence.
TL;DR: A theoretical framework to analyze the performance of the AF cooperative systems with an MRC receiver is provided and accurate and simple analytical expressions for the outage probability, the bit error probability, and the ergodic capacity are obtained.
Abstract: A statistical model is derived for the equivalent signal-to-noise ratio of the Source-to-Relay-to-Destination (S-R-D) link for Amplify-and-Forward (AF) relaying systems that are subject to block Rayleigh-fading. The probability density function and the cumulated density function of the S-R-D link SNR involve modified Bessel functions of the second kind. Using fractional-calculus mathematics, a novel approach is introduced to rewrite those Bessel functions (and the statistical model of the S-R-D link SNR) in series form using simple elementary functions. Moreover, a statistical characterization of the total receive-SNR at the destination, corresponding to the S-R-D and the S-D link SNR, is provided for a more general relaying scenario in which the destination receives signals from both the relay and the source and processes them using maximum ratio combining (MRC). Using the novel statistical model for the total receive SNR at the destination, accurate and simple analytical expressions for the outage probability, the bit error probability, and the ergodic capacity are obtained. The analytical results presented in this paper provide a theoretical framework to analyze the performance of the AF cooperative systems with an MRC receiver.
TL;DR: In this paper, a new method is developed to obtain explicit and integral expressions for the kernel of the ( κ, a ) -generalized Fourier transform for dihedral groups.
TL;DR: In this Letter, continuous Bessel theory is manipulated to formulate the phase and amplitude conditions necessary for generating free-space-propagating Bessel-Gauss beams using on-chip optical phased arrays.
Abstract: Integrated optical phased arrays for generating quasi-Bessel beams are proposed and experimentally demonstrated in a CMOS-compatible platform. Owing to their elongated central beams, Bessel beams have applications in a range of fields, including multiparticle trapping and laser lithography. In this Letter, continuous Bessel theory is manipulated to formulate the phase and amplitude conditions necessary for generating free-space-propagating Bessel–Gauss beams using on-chip optical phased arrays. Discussion of the effects of select phased array parameters on the generated beam’s figures of merit is included. A one-dimensional splitter-tree-based phased array architecture is modified to enable arbitrary passive control of the array’s element phase and amplitude distributions. This architecture is used to experimentally demonstrate on-chip quasi-Bessel-beam generation with a ∼14 mm Bessel length and ∼30 μm power full width at half maximum.
TL;DR: In this paper, the radius of uniform convexity for three kinds of normalized Bessel functions of the first kind was determined and necessary and sufficient conditions were given for the parameters of the three normalized functions such that they were uniformly convex in the open unit disk.
TL;DR: In this paper, the authors developed fractional kinetic equations involving generalized k-Bessel function via Sumudu transform, and the graphical interpretation of the solutions by employing MATLAB is given.
Abstract: Principle aim of the present study is to develop fractional kinetic equations involving generalized k-Bessel function via Sumudu transform. Also, the graphical interpretation of the solutions by employing MATLAB is given.
TL;DR: In this paper, the authors obtained tight lower and upper bounds for the radius of univalence of some normalized Bessel, Struve and Lommel functions via Euler-Rayleigh inequalities.
Abstract: Tight lower and upper bounds for the radius of univalence of some normalized Bessel, Struve and Lommel functions of the first kind are obtained via Euler-Rayleigh inequalities. It is shown also that the radius of univalence of the Struve functions is greater than the corresponding radius of univalence of Bessel functions. Moreover, by using the idea of Kreyszig and Todd, and Wilf it is proved that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. The Laguerre-Polya class of entire functions plays an important role in our study.
TL;DR: This work helps in elucidating that ILA provides adequate beam shape coefficients and descriptions of ideal scalar BBs up to certain limits and, even when it fails to do so, reliable information on the physical optical properties of interest can still be inferred, depending on specific geometric and electromagnetic aspects of the scatterer.
Abstract: In this paper we investigate the integral version of the localized approximation (ILA)—a powerful technique for evaluating the beam shape coefficients in the framework of the generalized Lorenz–Mie theory—as applied to ideal scalar Bessel beams (BBs). Originally conceived for arbitrary shaped beams with a propagating factor exp(±ikz), it has recently been shown that care must be taken when applying the ILA for the case of ideal scalar BBs, since they carry a propagating factor exp(±ikz cos α), with α being the axicon angle, which cannot be smoothly accommodated into its mathematical formalism. Comparisons are established between the beam shape coefficients calculated from both ILA and exact approaches, assuming paraxial approximation and both on- and off-axis beams. Particular simulations of radiation pressure forces are provided based on the existing data in the literature. This work helps us in elucidating that ILA provides adequate beam shape coefficients and descriptions of ideal scalar BBs up to certain limits and, even when it fails to do so, reliable information on the physical optical properties of interest can still be inferred, depending on specific geometric and electromagnetic aspects of the scatterer.
TL;DR: In this article, a generalized Lorenz-Mie theory and other light scattering theories such as the Extended Boundary Condition Method are described in terms of beam shape coefficients, allowing one to establish whether the beam intensity is zero on an axis or not.
Abstract: Within the framework of generalized Lorenz–Mie theories and other light scattering theories such as the Extended Boundary Condition Method, the illuminating electromagnetic beam is described in terms of beam shape coefficients. We establish a darkness theorem in terms of the shape coefficients, allowing one to establish whether the beam intensity is zero on an axis (i.e. dark) or not. This theorem allows one to predict the existence of higher-order nonvortex Bessel beams. A proposal for similar studies concerning other types of beams is provided, as a possible extension of the present work.
TL;DR: Zero-order terahertz Bessel beams with linear and circular polarizations are generated by using a THz quarter wave plate and Teflon axicons with different opening angles and the vectorial Rayleigh diffraction integral is used to accurately reproduce the amplitude, phase, and non-diffractive feature of each polarization component.
Abstract: As a kind of special beams, Bessel beams are always a research hot spot in optics due to its non-diffractive and self-healing properties. Here, zero-order terahertz (THz) Bessel beams with linear and circular polarizations are generated by using a THz quarter wave plate and Teflon axicons with different opening angles. By applying a THz digital holographic imaging system, the evolutions of the transverse (E x , E y ) and longitudinal (E z ) electric fields are coherently measured and analyzed during the propagation processes of the THz Bessel beams. The vectorial Rayleigh diffraction integral is used to accurately reproduce the amplitude, phase, and non-diffractive feature of each polarization component for the THz Bessel beams. With varying opening angles of the axicons, the focal spots, diffraction-free ranges, and Gouy phase shifts of the THz Bessel beams are compared and discussed. The experiment and simulation results provide a comprehensive view for exactly understanding peculiar features of THz Bessel beams.