Showing papers on "Bessel function published in 2016"
TL;DR: In this paper, the atmospheric turbulence effects on orbital angular momentum spectra of different kinds of vortex beams, including Laguerre-Gaussian (LG) beams and Bessel beams, numerically were investigated.
Abstract: We investigate the atmospheric turbulence effects on orbital angular momentum (OAM) spectra of different kinds of vortex beams, including Laguerre–Gaussian (LG) beams and Bessel beams, numerically. We generate the holograms of atmospheric turbulence with different structure constants of the refractive index. The OAM spectra of distorted single-mode or multiplexed LG beams and Bessel beams are analyzed. Compared with the OAM spectra of the two kinds of vortex beams, the spectrum of the Bessel beams is more dispersive. The results illustrate that Bessel beams suffer more from turbulent atmosphere than LG beams.
104 citations
TL;DR: This work theoretically design and experimentally demonstrate one kind of planar Bessel beam generators based on metasurfaces with analytical structures perforated in ultra-thin metallic screens and finds applications in future optical communication, nanofabrication and super-resolution imaging, etc.
Abstract: Non-diffracting Bessel beams, including zero-order and high-order Bessel Beams which carry orbital angular momentum (OAM), enable a variety of important applications in optical micromanipulation, sub-diffraction imaging, high speed photonics/quantum communication, etc. The commonly used ways to create Bessel beams, including an axicon or a digital hologram written to a spatial light modulator (SLM), have great challenges to operate at the nanoscale. Here we theoretically design and experimentally demonstrate one kind of planar Bessel beam generators based on metasurfaces with analytical structures perforated in ultra-thin metallic screens. Continuous phase modulation between 0 to 2π is realized with a single element. In addition, due to the dispersionless phase shift stemming from spin-orbit interaction, the proposed device can work in a wide wavelength range. The results may find applications in future optical communication, nanofabrication and super-resolution imaging, etc.
86 citations
TL;DR: High-order Bessel beams are formed by a passive acoustic device consisting of an Archimedes' spiral diffraction grating characterized by an azimuthal variation of the phase along its annular spectrum producing an acoustic vortex in the near field.
Abstract: The formation of high-order Bessel beams by a passive acoustic device consisting of an Archimedes' spiral diffraction grating is theoretically, numerically, and experimentally reported in this paper. These beams are propagation-invariant solutions of the Helmholtz equation and are characterized by an azimuthal variation of the phase along its annular spectrum producing an acoustic vortex in the near field. In our system, the scattering of plane acoustic waves by the spiral grating leads to the formation of the acoustic vortex with zero pressure on axis and the angular phase dislocations characterized by the spiral geometry. The order of the generated Bessel beam and, as a consequence, the size of the generated vortex can be fixed by the number of arms in the spiral diffraction grating. The obtained results allow for obtaining Bessel beams with controllable vorticity by a passive device, which has potential applications in low-cost acoustic tweezers and acoustic radiation force devices.
84 citations
TL;DR: The novel results on bulk modifications of soda-lime glass using a non-ideal axicon-generated Bessel beam are presented and the possibility to control the transverse crack propagation direction is demonstrated, which is crucial in the case of glass cutting applications.
Abstract: The extended focal depth of Bessel beams is a very attracting property for glass cutting applications. However, Bessel beam generation with a non-ideal conical lens induces beam pattern distortions. We present our novel results on bulk modifications of soda-lime glass using a non-ideal axicon-generated Bessel beam. Modelling of the Bessel beam pattern and experimental measurements indicated ellipticity of the central core diameter. That resulted in the formation of cracks in a transverse direction inside the bulk of glass. Furthermore, we demonstrate the possibility to control the transverse crack propagation direction, which is crucial in the case of glass cutting applications.
80 citations
TL;DR: In this paper, a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator is presented, where the effective Hamiltonian is non-Hermitian and interpolation parameter is obtained through minimizing the next residual in the projective hierarchy.
Abstract: We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wave function. In between, we interpolate using a single parameter. The effective Hamiltonian is non-Hermitian and this polynomial similarity transformation theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit, whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction strengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.
66 citations
TL;DR: This paper has proposed a method which can be used to generate a high-power Bessel beam and gives an innovative idea to form vortex phase by using discontinuous piston phase.
Abstract: Bessel beam is the important member of the family of non-diffracting beams and has many novel properties which can be used in many areas. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, based on the coherent combining technology, we have proposed a method which can be used to generate a high-power Bessel beam. Even more, we give an innovative idea to form vortex phase by using discontinuous piston phase. To confirm the validity of this method, the intensity evolution of the combined beam and the Bessel-Gaussian beam at different propagation distance have been studied and compared. Meanwhile, the experimental realization has been discussed from the existing experimental result related to the coherent combining technology.
66 citations
TL;DR: In this article, a general description of circularly symmetric Bessel beams of arbitrary order is derived by analyzing the relationship between different descriptions of polarized Bessel beam obtained using different approaches.
Abstract: A general description of circularly symmetric Bessel beams of arbitrary order is derived in this paper. This is achieved by analyzing the relationship between different descriptions of polarized Bessel beams obtained using different approaches. It is shown that a class of circularly symmetric Davis Bessel beams derived using the Hertz vector potentials possesses the same general functional dependence as the aplanatic Bessel beams generated using the angular spectrum representation (ASR). This result bridges the gap between different descriptions of Bessel beams and leads to a general description of circularly symmetric Bessel beams, such that the Davis Bessel beams and the aplanatic Bessel beams are merely the two simplest cases of an infinite number of possible circularly symmetric Bessel beams. Additionally, magnitude profiles of the electric and magnetic fields, the energy density and the Poynting vector are displayed for Bessel beams in both paraxial and nonparaxial cases. The results presented in this paper provide a fresh perspective on the description of Bessel beams and cast some insights into the light scattering and light-matter interactions problems in practice.
63 citations
TL;DR: In this article, a leaky radial waveguide consisting of a capacitive sheet over a ground plane that supports higher-order leaky modes is presented. But the authors do not specify the operating bandwidth of the Bessel-beam launch system.
Abstract: We present a Bessel-beam launcher based on a leaky radial waveguide consisting of a capacitive sheet over a ground plane that supports higher-order leaky modes. A propagating Bessel beam is generated above the radiating waveguide. The Bessel beam is transverse-magnetic (TM) polarized with a vertical component of electric field that is a zeroth-order Bessel function of the first kind. A higher-order leaky-wave mode is used to reduce losses at millimeter waves and, at the same time, avoid the thin dielectric layers used in previously proposed lower order leaky-wave Bessel launchers. Closed-form design equations are provided for the proposed structure. In addition, the operating bandwidth of the launcher is defined using dispersion analysis. Near-field measurements of a prototype operating in the frequency range 38–39.5 GHz validate the concept. The measured launcher generates a Bessel beam with a stable spot size of about 4.3 mm ( $0.57\,\lambda$ ) over a nondiffractive range of about 16.4 mm ( $2.2\,\lambda$ ), within about a 4% fractional bandwidth.
53 citations
TL;DR: This work proposes a formal analytical theory using the partial-wave series expansion (PWSE) method in cylindrical coordinates, to calculate the acoustic backscattering form function as well as the radiation force-per-length on an infinitely long elliptical (non-circular) cylinder in plane progressive waves.
51 citations
TL;DR: In this paper, the existence of doubly connected V-state for generalized SQG equations with α ∈]0, 1[.7096, 2015 was proved and the authors showed that these V-states can be described by countable branches bifurcating from the annulus at some explicit eigenvalues related to Bessel functions of the first kind.
Abstract: In this paper, we prove the existence of doubly connected V-states for the generalized SQG equations with α ∈]0, 1[. They can be described by countable branches bifurcating from the annulus at some explicit “eigenvalues” related to Bessel functions of the first kind. Contrary to Euler equations Hmidi et al. (Doubly connected V-states for the planar Euler equations, arXiv:1409.7096, 2015), we find V-states rotating with positive and negative angular velocities. At the end of the paper we discuss some numerical experiments concerning the limiting V-states.
50 citations
TL;DR: In this article, the authors derived the solution of the fractional kinetic equation involving generalized Bessel function of first kind and generalized Struve function of the first kind in terms of a generalized Borschtein function.
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25 Aug 2016
TL;DR: The simulation results were shown to corroborate theoretical predictions, with the experiment being in agreement with theory and simulation.
Abstract: We derived exact analytical relationships to describe the complex amplitude of a perfect optical vortex generated by means of three different optical elements, namely, (i) an amplitude-phase element with a transmission function proportional to a Bessel function, (ii) an optimal phase element with a transmission equal to the sign function of a Bessel function, and (iii) a spiral axicon. The doughnut intensity was shown to be highest when using an optimal phase element. The spiral-axicon-aided diffraction ring was found to be twice as wide as when generated using two other elements. Thus, the optimal filter was shown to be best suited for generating a perfect optical vortex. The simulation results were shown to corroborate theoretical predictions, with the experiment being in agreement with theory and simulation.
Book•
11 Feb 2016
TL;DR: Schramm-Loewner Evolution (SLE) 2.3 Three Phases of SLE2.4 Cardy's Formula 2.5 SLE and Statistical Mechanics Models Exercises References 3 Dyson Model 3.5.
Abstract: 1 Bessel Process1.1 One-Dimensional BrownianMotion (BM) 1.2 Martingale Polynomials of BM 1.3 Drift Transform 1.4 Quadratic Variation 1.5 Stochastic Integration 1.6 Ito's Formula 1.7 Complex Brownian Motion and Conformal Invariance 1.8 Stochastic Differential Equation for Bessel Process 1.9 Kolmogorov Equation 1.10 BES(3) and Absorbing BM1.11 BES(1) and Reflecting BM 1.12 Critical Dimension Dc = 2 1.13 Bessel Flow and Another Critical Dimension Dc = 3/2 1.14 Hypergeometric Functions Representing Bessel Flow Exercises References 2 Schramm--Loewner Evolution (SLE) 2.1 Complexification of Bessel Flow2.2 Schwarz--Christoffel Formula and Loewner Chain 2.3 Three Phases of SLE2.4 Cardy's Formula 2.5 SLE and Statistical Mechanics Models Exercises References 3 Dyson Model 3.1 Multivariate Extension of Bessel Process 3.2 DysonModel as Eigenvalue Process 3.3 Dyson Model as Noncolliding Brownian Motion 3.4 Determinantal Martingale Representation (DMR) 3.5 Reducibility of DMR and Correlation Functions 3.5.1 Density Function rx(t, x) 3.5.2 Two-Time Correlation Function rx (s, x t, y) 3.6 Determinantal Process 3.7 Constant-Drift Transform of Dyson Model 3.8 Generalization for Initial Configuration with Multiple Points 3.9 Wigner's Semicircle Law and Scaling Limits 3.9.1 Wigner's Semicircle Law3.9.2 Bulk Scaling Limit and Homogeneous Infinite System <3.9.3 Soft-Edge Scaling Limit and Spatially Inhomogeneous Infinite System3.10 Entire Functions and Infinite Particle Systems 3.10.1 Nonequilibrium Sine Process 3.10.2 Nonequilibrium Airy Process 3.11 Tracy--Widom Distribution 3.11.1 Distribution Function of Maximum Position of Particles 3.11.2 Algebraic Calculation 3.11.3 System of Differential Equations 3.11.4 Nonlinear Third-Order Differential Equation 3.11.5 Soft-Edge Scaling Limit 3.11.6 Painleve II and Limit Theorem of Tracy and Widom 3.12 Beyond Determinantal Processes Exercises References Solutions Index
TL;DR: This work develops a non-iterative direct space beam shaping method to generate Bessel beams with high energy throughput from direct space with a single phase-only spatial light modulator for non-uniform input beams.
Abstract: Arbitrary shaping of the on-axis intensity of Bessel beams requires spatial modulation of both amplitude and phase. We develop a non-iterative direct space beam shaping method to generate Bessel beams with high energy throughput from direct space with a single phase-only spatial light modulator. For this purpose, we generalize the approach of Bolduc et al. to non-uniform input beams. We point out the physical limitations imposed on the on-axis intensity profile for unidirectional beams. Analytical, numerical and experimental results are provided.
TL;DR: The high-order polynomial method (p-FEM with Lobatto polynomials) and the wave-based discontinuous Galerkin method are compared for two-dimensional Helmholtz problems, indicating that the differences in performance, accuracy and conditioning are more nuanced than generally assumed.
01 Apr 2016
TL;DR: The main result of as discussed by the authors is that determinantal point processes with the Airy, the Bessel and the Gamma kernels are rigid, and the main step is the construction of a sequence of additive statistics with variance going to zero.
Abstract: A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main result of this paper is that determinantal point processes with the Airy, the Bessel and the Gamma kernels are rigid. The proof follows the scheme used by Ghosh, Ghosh and Peres: the main step is the construction of a sequence of additive statistics with variance going to zero.
TL;DR: In this article, a planar Bessel-beam launcher supporting multiple modes was analyzed and the energy-transfer characteristics of the coupled system were analyzed and discussed, and it was shown that the system can both transmit and receive Bessel beams.
Abstract: The generation of propagating Bessel beams is typically limited to optical frequencies with bulky experimental setups. Recent works have demonstrated Bessel-beam generation at microwave and millimeter-wave frequencies utilizing low-profile, planar, leaky-wave antennas. These studies have assumed a single leaky mode in the antenna. In this work, the rigorous analysis of a planar Bessel-beam launcher supporting multiple modes is presented. By employing the mode-matching technique, a complete electromagnetic solution of the structure, its supported modes, and radiated fields is obtained. Additionally, a coupled system of two planar Bessel launchers is analyzed, and it is shown that the system can both transmit and receive Bessel beams. The energy-transfer characteristics of the coupled system are analyzed and discussed. An analysis of the coupled system's even and odd modes of operation show that efficient power transfer is possible, and that an odd mode is preferred since it yields higher field confinement and power-transfer efficiency.
TL;DR: In this article, the authors present the analysis and design of Bessel beam launchers using a finite inward cylindrical traveling wave aperture field distribution, which radiates an electric field whose normal or longitudinal component takes the form of a zeroth-order Bessel function.
Abstract: The paper presents the analysis and design of Bessel beam launchers using a finite inward cylindrical traveling wave aperture field distribution. The launcher radiates an electric field whose normal or longitudinal component takes the form of a zeroth-order Bessel function. The nondiffractive behavior of the structure in a well-defined area close to the radiating aperture is analyzed by decomposing the radiated field in its geometrical optics (GO) and diffractive (D) contributions. A closed-form expression is provided for the GO contribution whereas an asymptotic approximation is provided for the diffractive part. Such theoretical analysis allows a precise definition of the nondiffractive region for the generated Bessel beam. At the same time, it also highlights and predicts the oscillating behavior of the longitudinal component of the electric field along the z -axis due to the diffraction from the edges of the aperture. The proposed analysis is validated by a prototype at 30 GHz made by a radial waveguide loaded with metallic gratings and centrally fed by a coaxial probe. Measurement results for the longitudinal component of the electric field are in excellent agreement with full-wave results. In addition, the nondiffractive behavior for the radiated beam is reported over a bandwidth larger than 6.5% around 30 GHz. This behavior is peculiar of the nonresonant first kind Hankel aperture field distribution used for the generation of the Bessel beam.
TL;DR: It is shown 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.
TL;DR: In this article, the authors deduce sufficient and necessary conditions for the close-to-convexity of Bessel, Struve, and Lommel functions of the first kind.
Abstract: In this paper our aim is to deduce some sufficient (and necessary) conditions for the close-to-convexity of some special functions and their derivatives, like Bessel functions, Struve functions, and a particular case of Lommel functions of the first kind, which can be expressed in terms of the hypergeometric function \({}_1F_2\). The key tool in our proofs is a result of Shah and Trimble about transcendental entire functions with univalent derivatives. Moreover, a known result of Polya on entire functions, the infinite product representations and some results on zeros of Bessel, Struve, and Lommel functions of the first kind are used in order to achieve the main results of the paper.
TL;DR: In this paper, it was demonstrated that care must be taken when constructing a localized approximation for a Bessel beam, namely a localized Besselbeam is satisfactorily close enough to the intended beam only when the axicon angle is small enough.
Abstract: 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.
TL;DR: It is shown that such an aperture distribution generates a non-diffractive Bessel beam whose transverse component (with respect to the normal of the radiating aperture) of the electric field takes the form of a zero-th order Bessel function.
Abstract: In this paper the focusing capability of a radiating aperture implementing an inward cylindrical traveling wave tangential electric field distribution directed along a fixed polarization unit vector is investigated In particular, it is shown that such an aperture distribution generates a non-diffractive Bessel beam whose transverse component (with respect to the normal of the radiating aperture) of the electric field takes the form of a zero-th order Bessel function As a practical implementation of the theoretical analysis, a circular-polarized Bessel beam launcher, made by a radial parallel plate waveguide loaded with several slot pairs, arranged on a spiral pattern, is designed and optimized The proposed launcher performance agrees with the theoretical model and exhibits an excellent polarization purity
TL;DR: In this article, the authors investigated the non-axisymmetric wave propagation in an infinite incompressible soft electroactive hollow cylinder under biasing fields, including an axial pre-stretch and a radial stretch in the plane perpendicular to the axis of the cylinder.
TL;DR: In this article, the Riccati equation is used to obtain bounds for modified Bessel functions of consecutive orders, and a procedure is considered in which the bounds obtained from the analysis of the RCE are used to define a new function satisfying a new RCE, which yields sharper bounds.
TL;DR: In this article, an identity on series involving the zeros of Bessel functions of the first kind is derived by an alternative method based on Laplace transforms, which leads to a Bernstein function of time, expressed by Dirichlet series, that allows to recover the Rayleigh-Sneddon sum.
Abstract: A relevant result independently obtained by Rayleigh and Sneddon on an identity on series involving the zeros of Bessel functions of the first kind is derived by an alternative method based on Laplace transforms. Our method leads to a Bernstein function of time, expressed by Dirichlet series, that allows us to recover the Rayleigh-Sneddon sum. We also consider another method arriving at the same result based on a relevant formula by Calogero. Moreover, we also provide an electrical example in which this sum results to be extremely useful in order to recover the analytical expression for the response of the system to a certain external input.
TL;DR: 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.
TL;DR: Characteristics of nondiffracting nonparaxial Bessel fractional vortex beams of progressive waves open new capabilities in optical tractor beam tweezers, optical spanners, invisibility cloaks, optically engineered metamaterials, and other applications.
Abstract: Energy and angular momentum flux density characteristics of an optical nondiffracting nonparaxial vector Bessel vortex beam of fractional order are examined based on the dual-field method for the generation of symmetric electric and magnetic fields. Should some conditions determined by the polarization state, the half-cone angle as well as the beam-order (or topological charge) be met, the axial energy and angular momentum flux densities vanish (representing Poynting singularities), before they become negative. These negative counterintuitive properties suggest retrograde (negative) propagation as well as a rotation reversal of the angular momentum with respect to the beam handedness. These characteristics of nondiffracting nonparaxial Bessel fractional vortex beams of progressive waves open new capabilities in optical tractor beam tweezers, optical spanners, invisibility cloaks, optically engineered metamaterials, and other applications.
TL;DR: In this article, the geometric properties of the Jackson and Hahn-Exton q-Bessel functions are studied and three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane.
TL;DR: In this paper, an absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque and the axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field.
Abstract: 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