Showing papers on "Bessel function published in 2019"
TL;DR: Owing to the isotropy of the unit cells and the rotational symmetry of the arrangements, the proposed metasurfaces are polarization insensitive, providing a promising avenue for achieving such wave manipulations with any linear or circular polarization.
Abstract: We present a generic approach for the generation of pseudo non-diffracting Bessel beams using polarization insensitive metasurfaces with high efficiency. Cascaded unit cells, which are fully symmetric, are designed for the complete 2π phase control in the transmission mode. Based on the topological arrangements of such unit cells, two metasurfaces for the generation of zero-order (i.e., single phase profile) and first-order (i.e., merger of two distinct phase profiles) Bessel beams are designed and characterized. Both numerical simulations and experimental measurements are in agreement with each other, confirming the electromagnetic characteristics of the reported Bessel beams. Owing to the isotropy of the unit cells and the rotational symmetry of the arrangements, the proposed metasurfaces are polarization insensitive, providing a promising avenue for achieving such wave manipulations with any linear or circular polarization.
78 citations
TL;DR: This work experimentally, numerically and theoretically report acoustic truncated Bessel beams of flat-intensity along their axis in the ultrasound regime using phase-only holograms, which may have potential applications in ultrasonic imaging, biomedical ultrasound and particle manipulation applications using passive lenses.
Abstract: We report zero-th and high-order acoustic Bessel beams with broad depth-of-field generated using acoustic holograms. While the transverse field distribution of Bessel beams generated using traditional passive methods is correctly described by a Bessel function, these methods present a common drawback: the axial distribution of the field is not constant, as required for ideal Bessel beams. In this work, we experimentally, numerically and theoretically report acoustic truncated Bessel beams of flat-intensity along their axis in the ultrasound regime using phase-only holograms. In particular, the beams present a uniform field distribution showing an elongated focal length of about 40 wavelengths, while the transverse width of the beam remains smaller than 0.7 wavelengths. The proposed acoustic holograms were compared with 3D-printed fraxicons, a blazed version of axicons. The performance of both phase-only holograms and fraxicons is studied and we found that both lenses produce Bessel beams in a wide range of frequencies. In addition, high-order Bessel beam were generated. We report first order Bessel beams that show a clear phase dislocation along their axis and a vortex with single topological charge. The proposed method may have potential applications in ultrasonic imaging, biomedical ultrasound and particle manipulation applications using passive lenses.
61 citations
TL;DR: A new kind of POV, termed as double-ring POV (DR-POV), whose diameters of the two rings are independent of topological charge is reported, theoretically demonstrating that such a vortex is the Fourier transform of an azimuthally polarized Bessel beam.
Abstract: The perfect optical vortex (POV), the ring size being independent of its topological charge, has found potential applications in optical tweezers and optical communications. In this Letter, we report a new kind of POV, termed as double-ring POV (DR-POV), whose diameters of the two rings are independent of topological charge. We theoretically demonstrate that such a vortex is the Fourier transform of an azimuthally polarized Bessel beam. Experimental results agree well with theoretical prediction. We further investigate the vortex nature of the DR-POV through an interferometric method, showing that the two rings of the vortex have the same topological charge value (magnitude and sign). The specular properties of the DR-POV may find application in optical tweezers, such as trapping and rotating of low-refractive-index particles in the dark region between the two rings.
38 citations
TL;DR: In this article, the Kirchhoff law in one dimension in the form of the Schr\"odinger equation is reformulated as a quantum walk in electric circuits and the time evolution of one-dimensional quantum walks is exactly solvable with the use of the generating function made of the Bessel functions.
Abstract: Recent progress has witnessed that various topological physics can be simulated by electric circuits under alternating current. However, it is still a nontrivial problem if it is possible to simulate the dynamics subject to the Schr\"odinger equation based on electric circuits. In this work, we reformulate the Kirchhoff law in one dimension in the form of the Schr\"odinger equation. As a typical example, we investigate quantum walks in $LC$ circuits. We also investigate how quantum walks are different in topological and trivial phases by simulating the Su-Schrieffer-Heeger model in electric circuits. We then generalize them to include dissipation and nonreciprocity by introducing resistors, which produce non-Hermitian effects. We point out that the time evolution of one-dimensional quantum walks is exactly solvable with the use of the generating function made of the Bessel functions.
34 citations
TL;DR: A new inequality called Bessel–Laguerre integral inequality is proposed, which can be applied to stability analysis of linear systems with infinite distributed delays and with general kernels, which derives a set of sufficient stability conditions that is parameterized by the degree of the polynomials.
33 citations
TL;DR: In this paper, an alternative decomposition scheme for the bath correlation function based on Chebyshev polynomials and Bessel functions was proposed to derive a hierarchical equations of motion (HEOM) approach up to an arbitrary order in the environmental coupling.
Abstract: The time evolution in open quantum systems, such as a molecular aggregate in contact with a thermal bath, still poses a complex and challenging problem. The influence of the thermal noise can be treated using a plethora of schemes, several of which decompose the corresponding correlation functions in terms of weighted sums of exponential functions. One such scheme is based on the hierarchical equations of motion (HEOM), which is built using only certain forms of bath correlation functions. In the case where the environment is described by a complex spectral density or is at a very low temperature, approaches utilizing the exponential decomposition become very inefficient. Here, we utilize an alternative decomposition scheme for the bath correlation function based on Chebyshev polynomials and Bessel functions to derive a HEOM approach up to an arbitrary order in the environmental coupling. These hierarchical equations are similar in structure to the popular exponential HEOM scheme, but are formulated using the derivatives of the Bessel functions. The proposed scheme is tested up to the fourth order in perturbation theory for a two-level system and compared to benchmark calculations for the case of zero-temperature quantum Ohmic and super-Ohmic noise. Furthermore, the benefits and shortcomings of the present Chebyshev-based hierarchical equations are discussed.
30 citations
TL;DR: In this article, standing waves appear at the surface of a spherical viscous liquid drop subjected to radial parametric oscillation, which is the spherical analogue of the Faraday instability.
Abstract: Standing waves appear at the surface of a spherical viscous liquid drop subjected to radial parametric oscillation. This is the spherical analogue of the Faraday instability. Modifying the Kumar & Tuckerman (1994) planar solution to a spherical interface, we linearize the governing equations about the state of rest and solve the resulting equations by using a spherical harmonic decomposition for the angular dependence, spherical Bessel functions for the radial dependence, and a Floquet form for the temporal dependence. Although the inviscid problem can, like the planar case, be mapped exactly onto the Mathieu equation, the spherical geometry introduces additional terms into the analysis. The dependence of the threshold on viscosity is studied and scaling laws are found. It is shown that the spherical thresholds are similar to the planar infinite-depth thresholds, even for small wavenumbers for which the curvature is high. A representative time-dependent Floquet mode is displayed.
29 citations
TL;DR: This work utilizes an alternative decomposition scheme for the bath correlation function based on Chebyshev polynomials and Bessel functions to derive a HEOM approach up to an arbitrary order in the environmental coupling.
Abstract: The time evolution in open quantum systems, such as a molecular aggregate in contact with a thermal bath, still poses a complex and challenging problem. The influence of the thermal noise can be treated using a plethora of schemes, several of which decompose the corresponding correlation functions in terms of weighted sums of exponential functions. One such scheme is based on the hierarchical equations of motion (HEOM), which is built using only certain forms of bath correlation functions. In the case where the environment is described by a complex spectral density or is at a very low temperature, approaches utilizing the exponential decomposition become very inefficient. Here we utilize an alternative decomposition scheme for the bath correlation function based on Chebyshev polynomials and Bessel functions to derive a hierarchical equations of motion approach up to an arbitrary order in the environmental coupling. These hierarchical equations are similar in structure to the popular exponential HEOM scheme, but are formulated using the derivatives of the Bessel functions. The proposed scheme is tested up to the fourth order in perturbation theory for a two-level system and compared to benchmark calculations for the case of zero-temperature quantum Ohmic and super-Ohmic noise. Furthermore, the benefits and shortcomings of the present Chebyshev-based hierarchical equations are discussed.
29 citations
TL;DR: In this paper, the authors consider an inverse scattering problem to identify the locations or shapes of unknown anomalies from scattering parameter data collected by a small number of dipole antennas and design an imaging function with and without diagonal elements of the so-called scattering matrix, based on the Born approximation and the physical interpretation of the measurement data when the locations of the transducer and receiver are the same and different.
28 citations
TL;DR: Li et al. as mentioned in this paper derived a gyrokinetic linearized exact (not model) Landau collision operator by transforming the symmetric and conservative Landau form, which preserves the symmetry between test-particle and fieldparticle contributions, and enables discretization with a finite-volume or spectral method to preserve the conservation properties numerically, independent of resolution.
Abstract: A gyrokinetic linearized exact (not model) Landau collision operator is derived by transforming the symmetric and conservative Landau form. The formulation obtains the velocity-space flux density and preserves the operator's conservative form as the divergence of this flux density. The operator contains both test-particle and field-particle contributions, and finite Larmor radius effects are evaluated in either Bessel function series or gyrophase integrals. While equivalent to the gyrokinetic Fokker-Planck form with Rosenbluth potentials [B. Li and D. R. Ernst, Phys. Rev. Lett. 106, 195002 (2011)10.1103/PhysRevLett.106.195002], the gyrokinetic conservative Landau form explicitly preserves the symmetry between test-particle and field-particle contributions, which underlies the conservation laws and the H theorem, and enables discretization with a finite-volume or spectral method to preserve the conservation properties numerically, independent of resolution. The form of the exact linearized field-particle terms differs from those of widely used model operators. We show the finite Larmor radius corrections to the field-particle terms in the exact linearized operator involve Bessel functions of all orders, while present model field-particle terms involve only the first two Bessel functions. This new symmetric and conservative formulation enables the gyrokinetic exact linearized Landau operator to be implemented in gyrokinetic turbulence codes for comparison with present model operators using similar numerical methods.
26 citations
TL;DR: In this article, the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large, was studied.
Abstract: We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm determinants of integral operators associated to kernels built out of Meijer $G$-functions or Wright's generalized Bessel functions. They generalize in a natural way the hard edge Bessel kernel Fredholm determinant. We express the logarithmic derivatives of the Fredholm determinants identically in terms of a $2\times 2$ Riemann-Hilbert problem, and use this representation to obtain the so-called large gap asymptotics.
TL;DR: In this paper, the free flexural vibration behavior of a range of tapered beams is investigated by making use of the exact solutions of the governing differential equations and then imposing the necessary boundary conditions.
TL;DR: In this paper, the authors used SDEs to derive corresponding limit laws for starting points of the form k ⋅ x for k → ∞ with x in the interior of the corresponding Weyl chambers.
TL;DR: The side lobes of Bessel beam will create significant out-of-focus background when scanned in light-sheet fluorescence microscopy (LSFM), limiting the axial resolution of the imaging system, so this work proposes to overcome this issue by scanning the sample twice with zeroth-order Besselbeam and another type of propagation-invariant beam, complementary to the zerOTH- order Bessel beams.
Abstract: The side lobes of Bessel beam will create significant out-of-focus background when scanned in light-sheet fluorescence microscopy (LSFM), limiting the axial resolution of the imaging system. Here, we propose to overcome this issue by scanning the sample twice with zeroth-order Bessel beam and another type of propagation-invariant beam, complementary to the zeroth-order Bessel beam, which greatly reduces the out-of-focus background created in the first scan. The axial resolution can be improved from 1.68 μm of the Bessel light-sheet to 1.07 μm by subtraction of the two scanned images across a whole field-of-view of up to 300 μm × 200 μm × 200 μm. The optimization procedure to create the complementary beam is described in detail and it is experimentally generated with a spatial light modulator. The imaging performance is validated experimentally with fluorescent beads as well as eGFP-labeled mouse brain neurons.
TL;DR: In this article, the Bessel kernel was used to analyze the fluctuations of the spin current for the one dimensional XX spin chain starting from the domain wall initial condition, and an exact analytical expression for the large deviation function was obtained by applying the Coulomb gas method.
Abstract: We investigate the fluctuations of the spin current for the one dimensional XX spin chain starting from the domain wall initial condition. The generating function of the current is shown to be written as a determinant with the Bessel kernel. An exact analytical expression for the large deviation function is obtained by applying the Coulomb gas method. Our results are also compared with DMRG calculations.
TL;DR: Applicability of the DSM is theoretically demonstrated by proving that its indicator function can be represented in terms of an infinite series of Bessel functions of integer order, Hankel function of order zero, and the antenna configurations.
TL;DR: In this article, partial wave series method (PWSM) and T matrix method (TMM) are employed to investigate the three-dimensional radiation torque of both spherical and nonspherical objects in a single Bessel beam over broader frequencies (from Rayleigh scattering to geometric-optics regimes), with emphasis on the parametric conditions for torque reversal and corresponding physical mechanisms.
Abstract: Acoustic radiation torque (ART) plays an important role in the subject of acoustophoresis, which could induce the spinning rotation of particles on their own axes. The partial wave series method (PWSM) and T matrix method (TMM) are employed to investigate the three-dimensional radiation torques of both spherical and nonspherical objects in a single Bessel beam over broader frequencies (from Rayleigh scattering to geometric-optics regimes), with emphasis on the parametric conditions for torque reversal and the corresponding physical mechanisms. For elastic objects, the dipole, quadrupole, and even several higherscattering modes are dominant to induce the axial ARTs beyond the Rayleigh limit with a relatively large offset from the particle centroid to the beam axis in Bessel beams. The reversals appear with parametric conditions (including wave number, cone angle, and offset) for the extrema or null values of the corresponding cylindrical Bessel functions. The reversal of transverse ART from a rigid nonspherical particle is also investigated in an ordinary Bessel beam and the geometrical surface roughness is briefly studied for the effect on the radiation torques. This suggests the possibility of acoustic tweezers controlling the spinning motion of particles within and beyond the Rayleigh limit.
TL;DR: In this paper, the local converse conjecture of Jacquet over p-adic fields for GL(n) using Bessel functions was shown to hold for GL n with respect to GL n.
Abstract: In this paper, we prove the local converse conjecture of Jacquet over p-adic fields for GL(n) using Bessel functions.
TL;DR: Numerical computations for the dimensionless radiation force function for a perfect electromagnetic conductor (PEMC) cylinder are performed with emphasis on its dimensionless size parameter and source distance, which clearly draw attention to the contribution of the cross-polarized scattered waves (resulting from the rotary polarization effect) to the total force.
Abstract: The optical radiation force experienced by a cylinder material of circular cross section exhibiting circular dichroism (known also as rotary polarization) in an electric line source illumination is considered. An exact analytical expression for the radiation force (per length) valid for any frequency range is derived assuming an electric line source radiating cylindrically diverging TM-polarized waves without any approximations. The partial-wave series expansion method in cylindrical coordinates utilizing standard Bessel and Hankel functions is used to derive the electric and magnetic field expressions and a dimensionless radiation force function (or efficiency), which depends on the scattering coefficient of the cylinder as well as the distance from the radiating source. To illustrate the analysis, numerical computations for the dimensionless radiation force function for a perfect electromagnetic conductor (PEMC) cylinder are performed with emphasis on its dimensionless size parameter and source distance, which clearly draw attention to the contribution of the cross-polarized scattered waves (resulting from the rotary polarization effect) to the total force. The numerical predictions demonstrate the possibility to pull a circular-shaped cylinder material with rotary polarization toward the illuminating electric line source with TM-polarized waves using a curved wavefront depending on the PEMC material admittance, distance to the source, and size of the cylinder.
26 Jul 2019
TL;DR: In this article, the joint probability generating function for k occupancy numbers on disjoint intervals in the Bessel point process was studied and the generating function can be expressed as a Fredholm determinant.
Abstract: We study the joint probability generating function for k occupancy numbers on disjoint intervals in the Bessel point process. This generating function can be expressed as a Fredholm determinant. We...
TL;DR: In this article, the authors considered the real-time dynamics of noninteracting fermions in d = 1 and showed that the Wigner function for large n is uniform in phase space inside the Fermi volume, and vanishes at the fermi surf over a scale e n being described by a universal scaling function related to the Airy function.
Abstract: We consider the real-time dynamics of N noninteracting fermions in d = 1. They evolve in a trapping potential V(x), starting from the equilibrium state in a potential V 0(x). We study the time evolution of the Wigner function W(x, p, t) in the phase space (x, p), and the associated kernel which encodes all correlation functions. At t = 0 the Wigner function for large N is uniform in phase space inside the Fermi volume, and vanishes at the Fermi surf over a scale e N being described by a universal scaling function related to the Airy function. We obtain exact solutions for the Wigner function, the density, and the correlations in the case of harmonic and inverse square potentials, for several V 0(x). In the large-N limit, near the edges where the density vanishes, we obtain limiting kernels (of the Airy or Bessel types) that retain the form found in equilibrium, up to a time-dependent rescaling. For nonharmonic traps the evolution of the Fermi volume is more complex. Nevertheless we show that, for intermediate times, the Fermi surf is still described by the same equilibrium scaling function, with a nontrivial time- and space-dependent width which we compute analytically. We discuss the multi-time correlations and obtain their explicit scaling forms valid near the edge for the harmonic oscillator. Finally, we address the large-time limit where relaxation to the Generalized Gibbs Ensemble (GGE) was found to occur in the “classical” regime . Using the diagonal ensemble we compute the Wigner function in the quantum case (large N, fixed ℏ ) and show that it agrees with the GGE. We also obtain the higher order (nonlocal) correlations in the diagonal ensemble.
15 Feb 2019
TL;DR: In this article, the authors developed a semi-analytical model using the modal expansion method in cylindrical coordinates to calculate the optical/electromagnetic (EM) radiation force-per-length experienced by an infinitely long electrically-conducting elliptical cylinder having a smooth or wavy/corrugated surface in EM plane progressive waves with different polarizations.
Abstract: The aim of this work is to develop a formal semi-analytical model using the modal expansion method in cylindrical coordinates to calculate the optical/electromagnetic (EM) radiation force-per-length experienced by an infinitely long electrically-conducting elliptical cylinder having a smooth or wavy/corrugated surface in EM plane progressive waves with different polarizations. In this analysis, one of the semi-axes of the elliptical cylinder coincides with the direction of the incident field. Initially, the modal matching method is used to determine the scattering coefficients by imposing appropriate boundary conditions and solving numerically a linear system of equations by matrix inversion. In this method, standard cylindrical (Bessel and Hankel) wave functions are used. Subsequently, simplified expressions leading to exact series expansions for the optical/EM radiation forces assuming either electric (TM) or magnetic (TE) plane wave incidences are provided without any approximations, in addition to integral equations demonstrating the direct relationship of the radiation force with the square of the scattered field magnitude. An important application of these integral equations concerns the accurate determination of the radiation force from the measurement of the scattered field by any 2D non-absorptive object of arbitrary shape in plane waves. Numerical computations for the non-dimensional radiation force function are performed for electrically conducting elliptic and circular cylinders having a smooth or ribbed/corrugated surface. Adequate convergence plots confirm the validity and correctness of the method to evaluate the radiation force with no limitation to a particular frequency range (i.e. Rayleigh, Mie, or geometrical optics regimes). Particular emphases are given on the aspect ratio, the non-dimensional size of the cylinder, the corrugation characteristic of its surface, and the polarization of the incident field. The results are particularly relevant in optical tweezers and other related applications in fluid dynamics, where the shape and stability of a cylindrical drop stressed by a uniform external electric/magnetic field are altered. Furthermore, a direct analogy with the acoustical counterpart is noted and discussed.
TL;DR: In this article, the authors investigated the differences in the derivation procedures applying each one to both Bessel and Laguerre-Gauss profiles, and showed that the electromagnetic fields thus derived differ in the relative strength of electric and magnetic contributions.
Abstract: The electromagnetic field of optical vortices is in most cases derived from vector and scalar potentials using either a procedure based on the Lorenz or the Coulomb gauge. The former procedure has been typically used to derive paraxial solutions with Laguerre-Gauss radial profiles, while the latter procedure has been used to derive full solutions of the wave equation with Bessel radial profiles. We investigate the differences in the derivation procedures applying each one to both Bessel and Laguerre-Gauss profiles. We show that the electromagnetic fields thus derived differ in the relative strength of electric and magnetic contributions. The new solution that arises from the Lorenz procedure in the case of Bessel beams restores a field symmetry that previous work failed to resolve. Our procedure is further generalized and we find a spectrum of fields beyond the Lorenz and Coulomb gauge types. Finally, we describe a possible experiment to test our findings.
TL;DR: It is observed that semi analytical technique and exact technique are approximately the same and satisfy imposed boundary conditions and satisfying all the imposed physical conditions.
Abstract: In this paper, semi analytical solutions for velocity field and tangential stress correspond to fractional Oldroyd-B fluid, in an annulus, are acquired by Laplace transforms and modified Bessel equation. In the beginning, cylinders are stationary, motion is produced after t = 0 when both cylinders start rotating about their common axis. The governing equations solved for velocity field and shear stress by using the Laplace transform technique. The inverse Laplace transform is alternately calculated by Stehfest's algorithm using “MATHCAD” numerically. The numerically obtained solutions are in the form of modified Bessel's equations of first and second kind and satisfying all the imposed physical conditions. Finally, there is a comparison between exact and obtained solutions. It is observed that semi analytical technique and exact technique are approximately the same and satisfy imposed boundary conditions. Through graphs, the impact of physical parameters (relaxation time, retardation time kinematic viscosity, and dynamic viscosity) and fractional parameters on both velocity and shear stress is observed.
TL;DR: In this article, a novel diffractive elements are presented to produce zero-order Bessel beams in the terahertz (THz) band by using phase plates to change the direction of the incident Gaussian beam.
Abstract: Novel diffractive elements are presented to produce zero-order Bessel beams in the terahertz (THz) band. First, diffractive elements are designed as phase plates to change the direction of the incident Gaussian beam. Then, they are fabricated by the emerging three-dimensional printing technology. Last, zero-order Bessel beams are generated by the diffractive elements at 0.3 THz. To verify the feasibility of this approach, the generated zero-order Bessel beams are monitored and compared with the ones generated by the axicons. The comparison confirms that the diffractive elements can produce Bessel beam effectively and efficiently. In addition, the diffractive elements are applied to introduce zero-order Bessel beam to a THz reflection imaging system. A resolution test phantom is imaged by the THz reflection imaging system with zero-order Bessel beam and a conventional THz reflection imaging system. The results indicate that the THz reflection imaging system with Bessel beam offers a significantly extended depth of field and high anti-interference capability.
TL;DR: In this article, the authors extend the CLT in the A-case from start in 0 to arbitrary starting distributions by using a limit result for the corresponding Bessel functions, and determine the eigenvalues and eigenvectors of the covariance matrices of the Gaussian limits.
TL;DR: In this paper, the authors studied the MFS using Bessel and Neumann functions and derived the bounds of errors for bounded simply-connected domains and condition number for disk domains.
TL;DR: In this article, the exact beam shape coefficients of a specific and promising class of nondiffracting light waves for optical trapping and micro-manipulation known as continuous vector frozen waves (CVFWs) were theoretically investigated.
Abstract: In this paper we theoretically investigate the exact beam shape coefficients (BSCs) of a specific and promising class of nondiffracting light waves for optical trapping and micro-manipulation known as continuous vector frozen waves (CVFWs). CVFWs are constructed from vector Bessel beams in terms of a continuous superposition (integral) over the longitudinal wavenumber, the final longitudinal intensity pattern being determined through the specification of a given spectrum S(kz). The incorporation of such highly confined and micro-structured fields into the theoretical framework of the generalized Lorenz–Mie theory (GLMT) is a first step toward the integration of such beams with optical tweezers systems as potential laser beams for the multiple manipulation of micro-particles and nano-particles along their optical axis and in multiple transverse planes. Linear, azimuthal, and radial polarizations are considered, the BSCs being calculated using three distinct approaches. The results extend and complete previous works on discrete frozen waves for light scattering problems with the aid of the GLMT.
TL;DR: In this paper, the authors focus on parameter management for the inscription of efficient BGWs using the point-by-point method employing Bessel beams, achieving a high value of 34dB for 8mm length.
Abstract: Ultrashort pulsed Bessel beams with intrinsic nondiffractive character and potential strong excitation confinement down to 100 nm can show a series of advantages over Gaussian beams in fabricating efficient Bragg grating waveguides (BGWs). In this work, we focus on parameter management for the inscription of efficient BGWs using the point-by-point method employing Bessel beams. Due to their high aspect ratio, the resulting one-dimensional void-like structures can section the waveguides and interact efficiently with the optical modes. Effective first-order BGWs with low birefringence can then be fabricated in bulk fused silica. By controlling the size and the relative location of grating voids via the Bessel pulse energy and scan velocities, the resonant behaviors of BGWs can be well regulated. A high value of 34 dB for 8 mm length is achieved. A simple predictive model for BGWs is proposed for analyzing the influences of processing parameters on the performance of BGWs. The technique permits multiplexing several gratings in the same waveguide. Up to eight grating traces were straightforwardly inscribed into the waveguide in a parallel-serial combined mode, forming the multiplex BGWs. As an application, the multiplex BGW sensor with two resonant peaks is proposed and fabricated for improving the reliability of temperature detection.