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Showing papers on "Bessel function published in 2015"


Journal ArticleDOI
TL;DR: In this article, a new technique for analysis of transverse momentum dependent parton distribution functions, based on the Bessel weighting formalism, is presented. But it is only applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering.
Abstract: In this paper we present a new technique for analysis of transverse momentum dependent parton distribution functions, based on the Bessel weighting formalism. The procedure is applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. Using a fully differential cross section for the process, the effect of four momentum conservation is analyzed using various input models for transverse momentum distributions and fragmentation functions. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations, which is due to the limitations imposed by the energy and momentum conservation at the given energy/ Q 2 . 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.

263 citations


Journal ArticleDOI
TL;DR: This 3D-printing-based Bessel beam generation technique is useful not only for THz imaging systems with zero-order Bessel beams but also for future orbital-angular-momentum-based THz free-space communication with higher-orderBessel beams.
Abstract: We present the generation of arbitrary order Bessel beams at 0.3 THz through the implementation of suitably designed axicons based on 3D printing technology. The helical axicons, which possess thickness gradients in both radial and azimuthal directions, can convert the incident Gaussian beam into a high-order Bessel beam with spiral phase structure. The evolution of the generated Bessel beams are characterized experimentally with a three-dimensional field scanner. Moreover, the topological charges carried by the high-order Bessel beams are determined by the fork-like interferograms. This 3D-printing-based Bessel beam generation technique is useful not only for THz imaging systems with zero-order Bessel beams but also for future orbital-angular-momentum-based THz free-space communication with higher-order Bessel beams.

105 citations


Journal ArticleDOI
TL;DR: It is shown that LGBs can propagate quasi-nondiffracting beams within the same region of space where the corresponding BBs do and are more robust in the sense that they can propagate further than BBs under similar initial conditions.
Abstract: We present for the first time a comparison under similar circumstances between Laguerre-Gauss beams (LGBs) and Bessel beams (BB), and show that the former can be a better option for many applications in which BBs are currently used. By solving the Laguerre-Gauss differential equation in the asymptotic limit of a large radial index, we find the parameters to perform a peer comparison, showing that LGBs can propagate quasi-nondiffracting beams within the same region of space where the corresponding BBs do. We also demonstrate that LGBs, which have the property of self-healing, are more robust in the sense that they can propagate further than BBs under similar initial conditions.

95 citations


Journal ArticleDOI
TL;DR: Using the OAM and nondiffracting characteristics of Bessel beams, 12 m distance obstruction-free optical m-ary coding/decoding is experimentally demonstrated using visible Bessel beam in a free-space optical communication system and the bit error rate (BER) performance of hexadecimal and 32-ary codes based on Besselbeam with different topological numbers is studied.
Abstract: Bessel beams carrying orbital angular momentum (OAM) with helical phase fronts exp(ilφ)(l=0;±1;±2;…), where φ is the azimuthal angle and l corresponds to the topological number, are orthogonal with each other. This feature of Bessel beams provides a new dimension to code/decode data information on the OAM state of light, and the theoretical infinity of topological number enables possible high-dimensional structured light coding/decoding for free-space optical communications. Moreover, Bessel beams are nondiffracting beams having the ability to recover by themselves in the face of obstructions, which is important for free-space optical communications relying on line-of-sight operation. By utilizing the OAM and nondiffracting characteristics of Bessel beams, we experimentally demonstrate 12 m distance obstruction-free optical m-ary coding/decoding using visible Bessel beams in a free-space optical communication system. We also study the bit error rate (BER) performance of hexadecimal and 32-ary coding/decoding based on Bessel beams with different topological numbers. After receiving 500 symbols at the receiver side, a zero BER of hexadecimal coding/decoding is observed when the obstruction is placed along the propagation path of light.

90 citations


Journal ArticleDOI
Ben Geng Cai1, Yun Bo Li1, Wei Xiang Jiang1, Qiang Cheng1, Tie Jun Cui1 
TL;DR: Backward radiations of leaky waves supported by a holographic metasurface are used to produce spatial Bessel beams in the microwave frequency regime, which may be useful in imaging applications or wireless power transmissions with the dynamic focal-depth controls.
Abstract: We propose to use backward radiations of leaky waves supported by a holographic metasurface to produce spatial Bessel beams in the microwave frequency regime. The holographic metasurface consists of a grounded dielectric slab and a series of metal patches. By changing the size of metal patches, the surface-impedance distribution of the holographic metasurface can be modulated, and hence the radiation properties of the leaky waves can be designed to realize Bessel beams. Both numerical simulations and experiments verify the features of spatial Bessel beams, which may be useful in imaging applications or wireless power transmissions with the dynamic focal-depth controls.

82 citations


Journal ArticleDOI
TL;DR: In this paper, the authors apply the truncated Bessel series approximation by using collocation scheme, for solving linear and nonlinear fractional optimal control problems (OCPs) indirectly, the necessary and sufficient optimality conditions are stated in a form of nonlinear (or linear) fractional two-point boundary value problem (TPBVP).

74 citations


Journal ArticleDOI
TL;DR: In this article, the authors experimentally measured the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams using a digital version of Durnin's method, using a spatial light modulator and a liquid crystal q-plate.
Abstract: We experimentally measured the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams. Radially and azimuthally polarized vector Bessel beams were experimentally generated via a digital version of Durnin's method, using a spatial light modulator in concert with a liquid crystal q-plate. As a proof of principle, their intensities and spatially inhomogeneous states of polarization were experimentally measured using Stokes polarimetry as they propagated through two disparate obstructions. It was found, similar to their intensities, that their spatially inhomogeneous states of polarization self-healed. The self-healing can be understood via geometric optics, i.e., the interference of the unobstructed conical rays in the shadow region of the obstruction, and may have applications in, for example, optical trapping.

70 citations


Journal ArticleDOI
TL;DR: This work uses a reflective geometry where a single parallel-aligned spatial light modulator device is used to spatially modulate two orthogonal linear polarizations with two axicon phase profiles to modulate the state of polarization along the line focus of the axicon.
Abstract: We generate nondiffracting Bessel beams whose polarization state varies with propagation distance. We use a reflective geometry where a single parallel-aligned spatial light modulator device is used to spatially modulate two orthogonal linear polarizations with two axicon phase profiles. Then, by adding an extra phase retardation radial profile between these linear states, we are able to modulate the state of polarization along the line focus of the axicon. We provide experimental results that demonstrate the polarization axial control with zero-order and higher order Bessel beams.

69 citations


Journal ArticleDOI
TL;DR: To overcome the diffraction limits the long-distance propagation of Bessel beams is considered and compared against Gaussian beam properties, which are shown to have a number of benefits over Gaussian beams when propagating through atmospheric turbulence.
Abstract: Free-space optical communication has the potential to transmit information with both high speed and security. However, since it is unguided it suffers from losses due to atmospheric turbulence and diffraction. To overcome the diffraction limits the long-distance propagation of Bessel beams is considered and compared against Gaussian beam properties. Bessel beams are shown to have a number of benefits over Gaussian beams when propagating through atmospheric turbulence.

67 citations


Journal ArticleDOI
TL;DR: In this paper, an azimuthally invariant inward traveling wave distribution is defined over the aperture of a radial line slot array (RLSA) to launch a Bessel beam whose normal electric field component assumes a truncated, zeroth-order Bessel function.
Abstract: In this paper, we prove experimentally that nondiffractive Bessel beams can be generated by using inward cylindrical traveling wave aperture distributions. An azimuthally invariant inward traveling wave distribution is defined over the aperture of a radial line slot array (RLSA) to launch a Bessel beam whose normal electric-field component assumes a truncated, zeroth-order Bessel function. An optimization procedure based on a holographic approach is used for tuning the position and size of the slots of the RLSA. The antenna is centrally fed by a coaxial probe transition. The final structure operates at 12.5 GHz. Full-wave simulations and measurements of the vertical component of the electric field show that a non-diffractive radiation is obtained within a range larger than 12 wavelengths in front of the antenna. The generated Bessel beam presents a stable half-power beamwidth of about 20 mm within this range. The proposed system may open new opportunities for planar, low-profile Bessel beam generators at millimeter waves, Terahertz, and optics.

55 citations


Journal ArticleDOI
TL;DR: In this paper, an analysis of scattering of an electromagnetic linearly polarized plane wave by a multilayered sphere is presented, where the focus is on obtaining a computational form of the Mie coefficients for the scattered field.
Abstract: An analysis is presented of scattering of an electromagnetic linearly polarized plane wave by a multilayered sphere. The focus is on obtaining a computational form of the Mie coefficients for the scattered field. A central role is played by ratios of spherical Bessel functions that can be calculated easily, rapidly, and accurately by recurrence relations whose stabilities are demonstrated. Logarithmic derivatives are not employed. A detailed outline is given of a carefully tested computer program for implementing and validating the analysis. Numerous comparisons are given of numerical results obtained with this program with corresponding results in the literature. Important properties of the Mie coefficients and aspects of the scattered field are discussed including the loci of the Mie coefficients in the complex plane; the resonances of the Mie coefficients; the extinction, scattering, and absorption efficiencies of the scattered field; radiation pressure; the Debye series, and the complex angular momentum (CAM) method.

Journal ArticleDOI
TL;DR: In this article, a complete description of vector Bessel (vortex) beams in the context of the generalized Lorenz-Mie theory (GLMT) for the electromagnetic resonance scattering by a dielectric sphere is presented, using the method of separation of variables and the subtraction of a non-resonant background (corresponding to a perfectly conducting sphere of the same size) from the standard Mie scattering coefficients.

Journal ArticleDOI
TL;DR: In this paper, a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind was developed, and the results obtained here are quite general in nature and capable of yielding a very large number of known and new results.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this paper, a parabolic Schauder-type estimate with respect to conical metrics has been shown for short-lived conical Kahler-Ricci flow, where the key is to establish the relevant heat kernel estimates, where they use the Weber formula on Bessel function of the second kind and Carslaw's heat kernel representation.

Journal ArticleDOI
TL;DR: The main purpose of this paper is to study the structure of the well-known noniterative MUltiple SIgnal Classification (MUSIC) algorithm for identifying the shape of extended electromagnetic inclusions of small thickness located in the two-dimensional homogeneous space.
Abstract: The main purpose of this paper is to study the structure of the well-known noniterative MUltiple SIgnal Classification (MUSIC) algorithm for identifying the shape of extended electromagnetic inclusions of small thickness located in the two-dimensional homogeneous space. We construct a relationship between a MUSIC-type imaging functional for thin inclusions and Bessel functions of integer order of the first kind. Our construction is based on the structure of left-singular vectors of a collected Multi-Static Response matrix whose elements are a measured far-field pattern and an asymptotic expansion formula of the existence of thin inclusions. Some numerical examples are shown to support the constructed structure of MUSIC.

Journal ArticleDOI
TL;DR: It is shown that twisted Gaussian Schell-model beams can be represented through an incoherent superposition of partially coherent beams carrying optical vortices and whose cross-spectral densities are expressed in terms of modified Bessel functions.
Abstract: We show that twisted Gaussian Schell-model (TGSM) beams can be represented through an incoherent superposition of partially coherent beams carrying optical vortices and whose cross-spectral densities are expressed in terms of modified Bessel functions. Moreover, starting from this result, we show that the modal expansion of the cross-spectral density of a TGSM source can be directly obtained through simple mathematics.

Journal ArticleDOI
TL;DR: In this paper, a theoretical analysis of the acoustic radiation force of a Bessel beam incident upon a rigid oblate or prolate spheroid, centered on its axis of wave propagation, is presented.

Journal ArticleDOI
TL;DR: In this paper, several expansions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the first kind were constructed.
Abstract: We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the first kind. The coefficients of different expansions obey four-, five-, or six-term recurrence relations that are reduced to ones involving less number of terms only in a few exceptional cases. The conditions for deriving finite-sum solutions via termination of the series are discussed.

Journal ArticleDOI
TL;DR: In this article, the beam-shape coefficients are computed within the framework of the generalized Lorenz-Mie theory and with the aid of integral localized approximation, and it is numerically shown that, under the paraxial regime, frozen waves could be designed to efficiently trap biological cells, viruses, bacteria, and so on, along multiple radial planes and at specific axial locations.
Abstract: Radiation pressure cross sections over arbitrary-sized spherical scatterers are evaluated considering, as wave fields, recently developed frozen waves, which are a suitable superposition of equal-frequency Bessel beams, of arbitrary order. The so-called beam-shape coefficients are computed within the framework of the generalized Lorenz–Mie theory and with the aid of integral localized approximation. It is numerically shown that, under the paraxial regime, frozen waves could be designed to efficiently trap biological cells, viruses, bacteria, and so on, along multiple radial planes and at specific axial locations. Our results reinforce frozen waves as potential laser beams in optical trapping and manipulation.

Journal ArticleDOI
TL;DR: In this paper, new tight Turan type inequalities for modified Bessel functions of the first and second kinds are deduced, motivated by some applications in applied mathematics, biology, chemistry, physics and engineering sciences.

Journal ArticleDOI
TL;DR: In this article, the radius of convexity of two normalized Bessel functions of the first kind was determined in the case when the order is between $-2$ and $-1.$.
Abstract: The radius of convexity of two normalized Bessel functions of the first kind are determined in the case when the order is between $-2$ and $-1.$ Our methods include the minimum principle for harmonic functions, the Hadamard factorization of some Dini functions, properties of the zeros of Dini functions via Lommel polynomials and some inequalities for complex and real numbers.


Journal ArticleDOI
TL;DR: In this paper, the generalized Zakharov equations were studied from the perspective of Lie symmetry analysis and conservation laws, and several reductions and numerous new exact solutions were obtained based on some subalgebras of symmetry.
Abstract: In this paper, the generalized Zakharov equations, which describe interactions between high- and low-frequency waves in plasma physics are studied from the perspective of Lie symmetry analysis and conservation laws. Based on some subalgebras of symmetries, several reductions and numerous new exact solutions are obtained. All of these solutions represent modified traveling waves. The obtained solutions include expressions involving Airy functions, Bessel functions, Whittaker functions, and generalized hypergeometric functions. Previously unknown conservation laws are constructed for the generalized Zakharov equations using the direct method. Profiles are presented for some of these new solutions.

Journal ArticleDOI
TL;DR: In this article, a planar structure is proposed for terahertz Bessel beamforming based on the concept of plasmonics, which 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 polaritons.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, a new formula for the heat kernel on regular trees in terms of classical $$I$$ -Bessel functions is established, and a proof is given through direct computation.
Abstract: We establish a new formula for the heat kernel on regular trees in terms of classical $$I$$ -Bessel functions. Although the formula is explicit, and a proof is given through direct computation, we also provide a conceptual viewpoint using the horocyclic transform on regular trees. From periodization, we then obtain a heat kernel expression on any regular graph. From spectral theory, one has another expression for the heat kernel as an integral transform of the spectral measure. By equating these two formulas and taking a certain integral transform, we obtain as application several generalized versions of the determinant formula for the Ihara zeta function associated to finite or infinite regular graphs. Our approach to the Ihara zeta function and determinant formula through heat kernel analysis follows a similar methodology which exists for quotients of rank one symmetric spaces.

Journal ArticleDOI
TL;DR: In this paper, the authors established inequalities, monotonicity, convexity, and unimodality for functions concerning the modified Bessel functions of the first kind and computed the completely monotonic degrees of differences between the exponential and trigamma functions.
Abstract: In the paper, the author establishes inequalities, monotonicity, convexity, and unimodality for functions concerning the modified Bessel functions of the first kind and compute the completely monotonic degrees of differences between the exponential and trigamma functions. Mathematics subject classification (2010): Primary 26A12; Secondary 26A48, 26A51, 26D15, 30D10, 30E20, 33B10, 33B15, 33C20, 42B10, 44A10.

Journal ArticleDOI
01 Nov 2015-EPL
TL;DR: In this paper, the authors demonstrate the emergence of a pulling force of attraction on non-spherical oblate and prolate rigid spheroidal particles centered on the beam's axis of wave propagation.
Abstract: The theoretical formalism for acoustical Bessel vortex (helicoidal) tractor beams and results presented here are the first to demonstrate the emergence of a pulling force of attraction on non-spherical oblate and prolate rigid spheroidal particles centered on the beam's axis of wave propagation. Numerical predictions for the axial acoustic radiation force illustrate the theory with particular emphasis on the aspect ratio of the spheroid, the half-cone angle and order of the beam, as well as the dimensionless size parameter. It is demonstrated here that the Bessel vortex beam parameters may be tailored in such a way that the spheroid is pulled against the forward linear momentum density flux associated with the incoming waves. Those results potentially suggest the use of Bessel vortex beams in the development of emergent technologies for non-contact remote sampling and particle characterization.

Posted Content
TL;DR: In this article, the authors 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 they also analyse by studying characteristic polynomials.
Abstract: Muttalib--Borodin ensembles are characterised by the pair interaction term in the eigenvalue probability density function being of the form $\prod_{1 \le j 0$, 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 $\theta \in \mathbb Z^+$ the Laguerre and Jacobi cases are closely related to the squared singular values for products of $\theta$ 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.

Journal ArticleDOI
TL;DR: In this article, a class of Grushin type operators P k where k ∈ N 0 defined in (1.1) was examined and the main purpose of the paper was to give an explicit expression of the fundamental solution of P k.

Journal ArticleDOI
TL;DR: In this article, it was shown that the nonparaxial laser modes propagating along the crystal axis are periodically oscillating owing to polarization conversion, and the oscillation period for Bessel beams is inversely proportional to the square of the spatial frequency of the laser mode and the difference between the dielectric constants of an anisotropic crystal.
Abstract: We compare nonparaxial propagation of Bessel and Laguerre–Gaussian modes along the axis of anisotropic media. It is analytically and numerically shown that the nonparaxial laser modes propagating along the crystal axis are periodically oscillating owing to polarization conversion. The oscillation period for Bessel beams is inversely proportional to the square of the spatial frequency of the laser mode and the difference between the dielectric constants of an anisotropic crystal. So, for higher spatial frequency of Bessel beams, we will get shorter period of oscillations. For a linearly polarized light, there is a periodic redistribution of the energy between the two transverse components, and for a beam with the circular polarization, the energy is transferred from the initial beam to a vortex beam and backward. Similar periodic behavior is observed for the high-order in radial index Laguerre–Gaussian beams. However, it is true only at short distances. As the distance increases, the frequency of periodici...