High-order Bessel Vortex Beam Research Articles

Analysis on scattering and inner near-field characteristics of a uniaxial anisotropic sphere by an off-axis high-order Bessel (vortex) beam

Based on the generalized Lorenz–Mie theory (GLMT) and the Fourier transform method, a theoretical approach is introduced to study the scattering of a uniaxial anisotropic sphere illuminated by an off-axis high-order Bessel (vortex) beam (HOBVB). According to the orthogonality of the associated Legendre function and exponential function, a concise expression of the expansion coefficients of the off-axis HOBVB in terms of the spherical vector wave functions (SVWFs) is derived that can effectively reconstruct the HOBVB with all conical angles. The differences of scattering characteristics of a uniaxial anisotropic sphere illuminated by an on-axis and off-axis HOBVB and a plane wave are exhibited. Influences of the topological charge, conical angle, particle size, and off-axis distance on the angle distributions of the radar cross-section (RCS), scattering and extinction efficiencies, and asymmetric factor are analyzed in detail. The unique internal and near-field distributions of a uniaxial anisotropic spherical particle illuminated by an on-axis and off-axis HOBVB are demonstrated. The results provide insights into the scattering and Bessel beam–matter interactions and may find important applications in optical propagation and optical micromanipulation, microwave engineering, target shielding, and near-field measurement.

Optical pulling force on a uniaxial anisotropic sphere by a high-order Bessel (vortex) beam.

Based on the generalized Lorenz-Mie theory (GLMT) and the scattering theory of uniaxial spheres, a theoretical approach is introduced to study the axial radiation force (AOF) exerted on a uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel (vortex) beams (HOBVBs). Applying Maxwell's stress tensor, an analytical expression of the AOF on a uniaxial anisotropic sphere by the on-axis HOBVB is derived. The correctness of the theoretical and numerical results is verified by comparing the AOF on an isotropic sphere by a zero-order Bessel beam (ZOBB) with those results by a plane wave, Gaussian beam, and ZOBB. The focus of this study is to determine some conditions of the tractor beam, so as to realize the inverse motion of an anisotropic sphere through a Bessel beam. The range of optical pulling force (OPF) that can pull particles in reverse motion generated by zero-order and first-order Bessel beams is extended from isotropic spherical particles to anisotropic spherical particles. The effects of the sphere radius, conical angle, and especially electromagnetic anisotropy parameters on the OPF in water or a vacuum environment are discussed in detail. Moreover, the OPF exerted on the uniaxial anisotropic sphere illuminated by a HOBVB with l=2, 3, and 4 is also exhibited. It indicates that the HOBVB with l=2, 3 is also a good tractor beam for the uniaxial anisotropic sphere. The OPF generated by Bessel beams on uniaxial anisotropic spherical particles is not only affected by the conical angle and radius but is also significantly influenced by anisotropic parameters and topological charges. These properties of the OPF are different from those on an isotropic sphere. The theory and results are hopeful to provide an effective theoretical basis for the study of optical micromanipulation of biological and anisotropic complex particles by optical tractor (vortex) beams.

Light scattering of a uniform uniaxial anisotropic sphere by an on-axis high-order Bessel vortex beam.

Analytical solutions to the scattering of a uniform uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel vortex beam (HOBVB) are investigated. Using the vector wave theory, the expansion coefficients of the incident HOBVB in terms of the spherical vector wave functions (SVWFs) are obtained. According to the orthogonality of the associated Legendre function and exponential function, more concise expressions of the expansion coefficients are derived. It can reinterpret the incident HOBVB faster compared with the expansion coefficients of double integral forms. The internal fields of a uniform uniaxial anisotropic sphere are proposed in the integrating form of the SVWFs by introducing the Fourier transform. The differences of scattering characteristics of a uniaxial anisotropic sphere illuminated by a zero-order Bessel beam, Gaussian beam, and HOBVB are exhibited. Influences of the topological charge, conical angle, and particle size parameters on the angle distributions of the radar cross section are analyzed in detail. The scattering and extinction efficiencies varied with the particle radius, conical angle, permeability, and dielectric anisotropy are also discussed. The results provide insights into the scattering and light-matter interactions and may find important applications in optical propagation and optical micromanipulation of biological and anisotropic complex particles.

Terahertz quasi non-diffraction Bessel vortex beam generation using three lattice types reflective metasurface.

Bandwidth, orbital-angular momentum (OAM) divergence, and mode purity are the three critical issues for the practical terahertz orbital angular momentum manipulation, especially in the next sixth-generation (6G) communication system. Here we propose the broadband high-order Bessel vortex beam carrying multiple OAM modes reflective metasurface in the terahertz domain. The simulation results agree with the theoretical expectation, and the diffracting divergence of OAM vortex beam characteristics has been alleviated. The research on the relationship between the varieties of lattice type and mode purity is also relatively scarce. Henceforth, a comparison study has been conducted between three lattice types, i.e., square lattice, triangular lattice, and concentric ring lattice. And corresponding results of the relationship of mode purity with those lattice types show that the concentric ring lattice has the best performance.

A reflective metasurface for generating dual‐mode dual‐polarized high‐order Bessel vortex beams with equal divergence angle

A single-layer reflective metasurface is proposed in this study to generate dual-mode dual-polarized high-order Bessel vortex beams with equal divergence angle in Ka-band. The metasurface consists of two different subwavelength elements with different polarisations, which are located in the inner disk region and the outer ring region respectively. The inner element, composed of a square ring and a regular octagon, is proposed to achieve a phase response of 360°. The outer element, which consists of a microstrip line and a double W-shaped line, is designed to achieve the phase compensation and polarization conversion simultaneously. Equal divergence angle of different orbital angular momentum (OAM) modes is achieved by theoretically calculating the radii of the inner and outer regions. The metasurface prototype is fabricated and tested at 29 GHz, and the results show that the high-order Bessel beams with +1 mode of x-polarization and +2 mode of y-polarization are successfully generated. This work provides a simple and practical method to generate dual-mode dual-polarized high-order Bessel vortex beams for high-capacity OAM communications.

Generation and Measurement of a Bessel Vortex Beam Carrying Multiple Orbital-Angular-Momentum Modes through a Reflective Metasurface in the rf Domain

We discuss the generation and measurement of a Bessel vortex beam carrying multiple orbital-angular-momentum (OAM) modes in the radio-frequency domain. Considering that a high-order Bessel beam inherently has high-order OAM modes, in this paper, we propose to superpose these high-order Bessel vortex beams together, which can combine the advantages of the orthogonality of the vortex beam's multiple OAM modes and the Bessel beam's nondiffraction property. A theoretical formula and the basic design method are presented. A reflective metasurface is designed as the beam launcher to generate a deflected Bessel vortex beam that carries two OAM modes of $\ensuremath{\ell}=1$ and $\ensuremath{\ell}=2$ simultaneously. The corresponding reflective metasurface is designed, fabricated, and measured. The full-wave electromagnetic simulations and experimental measurements both verify the effectiveness of the design. The proposed method could further promote the application of a Bessel vortex beam in related near-field scenarios such as near-field wireless communication and radar detection and imaging.

Launcher of high-order Bessel vortex beam carrying orbital angular momentum by designing anisotropic holographic metasurface

In this paper, an ultra-low profile anisotropic holographic metasurface is proposed to generate a linearly polarized high-order Bessel vortex beam carrying orbital angular momentum with predesigned topological charge. Based on the leaky-wave theory and optical holographic principle, the anisotropic impedance pattern can be properly mapped by shaping the quasi-periodic metasurface with different meta-atom sizes. Compared with the prevalent spatial wave-modulated metasurface, this surface wave-modulated holographic metasurface effectively transforms a reference wave excited by a feeding source in a single point at the center of the antenna to a leaky high-order Bessel vortex beam without any extra air feeding, which enables a unique characteristic of error-free alignment between the air feeding and designed metasurface. The good agreement between the numerical simulation and the measured result demonstrates that the proposed approach can be employed to launch a linearly polarized high-order Bessel vortex beam with an arbitrary topological mode of interest.

Scattering of aerosol by a high-order Bessel vortex beam for multimedia information transmission in atmosphere

The essence of wireless communication and multimedia information transmission is the propagation of electromagnetic waves in the atmosphere. Within the framework of Generalized Lorenz Mie theory, and combining the vector wave theory with the generalized multi-spheres Mie theory, the analytical solution to the scattering of the high-order Bessel vortex beam (HOBVB) by aerosol aggregation in atmosphere is investigated. The angle distributions of the scattered field of soot, silicate and nitrate aerosol cluster particles illuminated by a HOBVB are numerically discussed. The examples are selected to illustrate the effects of aggregation configuration, mean value, particle number, topological charge and half-cone angle of the beam on the angle distribution of scattered field. It is noticed that the angle distribution of scattered field is sensitive to the configuration of the cluster for the multiple refraction and interactive scattering. The variation of the mean value of radius of the aerosol aggregation will result in different scattering characteristics and different transmission efficiency. The integration of the scattering algorithm and deep learning can be used in inversion of the shape and components of the aerosol clusters and in the improvement of transmission efficiency of multimedia information in atmosphere.

Realizing High-order Bessel Vortex Beams with High-level Phase Holograms

High-order Bessel beams are widely used in laser processing and precision measurement. For the realization of high-order Bessel beams, a spatial light modulator is used to load the high-order phase hologram instead of the real spiral phase plate and the axicon. The distribution of light field in two modes of axicon combination and phase superposition is analyzed theoretically. The beam modulation in two modes is designed and compared experimentally. The results show that the modulation effect of the phase superposition method is better than that of the axicon combination method. Meanwhile, the operation is flexible and the manufacture errors can be reduced. It is an effective method for realizing high-order Bessel beams.

Interactions of high-order Bessel vortex beam with a multilayered chiral sphere: Scattering and orbital angular momentum spectrum analysis

Analytical solution to the scattered field and near-surface field of a multilayered chiral sphere illuminated by a high-order Bessel vortex beam (HOBVB) are investigated. Using the vector wave theory, the expansion coefficients of a HOBVB in terms of spherical vector wave functions (SVWFs) are derived. Based on the fields expansion in each region and continuous boundary condition at each interface, the expansion coefficients of the sphere are solved by constructing the iterative form of the coefficients equations. Influences of the topological charge, half-cone angle and chirality on the scattering pattern of far region and near-surface field are analyzed in detail. In addition, the intensity and phase distributions at the transverse plane after interaction are presented for on- and off-axis incidences. Comparisons of orbital angular momentum (OAM) spectrum indicate that off-axis incidence results in topological charge shift from the incident case, and the farther from the axis and the more complex the particles, the more serious the phase distortion. The results provide insights into the scattering and light-matter interactions and may find important applications in optical propagation and multicasting optical communication.

Electromagnetic scattering by multiple dielectric particles under the illumination of unpolarized high-order Bessel vortex beam

This study investigates the electromagnetic scattering of a high-order Bessel vortex beam by multiple dielectric particles of arbitrary shape based on the surface integral equation (SIE) method. In Cartesian coordinates, the mathematical formulas are given for characterizing the electromagnetic field components of an arbitrarily incident high-order Bessel vortex beam. By using the SIE, a numerical scheme is formulated to find solutions for characterizing the electromagnetic scattering by multiple homogeneous particles of arbitrary shape and a home-made FORTRAN program is written. The presented theoretical derivations as well as the home-made program are validated by comparing to the scattering results of a Zero-Order Bessel Beam by the Generalized Lorenz-Mie theory. From our simulations, the beam’s order, half-cone angles, and the ways of particles’ arrangement have a great influence upon the differential scattering cross section (DSCS) for multiple particles. Furthermore, for a better understanding of the scattering characteristic in three dimension (3-D) space, the 3-D distribution of the DSCS for different cases is presented. It is anticipated that these results can be helpful to understand the scattering mechanisms of a high-order Bessel vortex beam on multiple dielectric particles of arbitrary shape.

Generation of high-order Bessel vortex beam carrying orbital angular momentum using multilayer amplitude-phase-modulated surfaces in radiofrequency domain

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.

Computation of radiation pressure force exerted on arbitrary shaped homogeneous particles by high-order Bessel vortex beams using MLFMA.

Due to special characteristics of nondiffraction and self reconstruction, the Bessel beams have attracted wide attention in optical trapping and appear to be a dramatic alternative to Gaussian beams. We present in this paper an efficient approach based on the surface integral equations (SIE) to compute the radiation pressure force (RPF) exerted on arbitrary shaped homogeneous particles by high-order Bessel vortex beam (HOBVB). The incident beam is described by vector expressions perfectly satisfy Maxwell's equations. The problem is formulated with the combined tangential formulation (CTF) and solved iteratively with the aid of the multilevel fast multipole algorithm (MLFMA). Then RPF is computed by vector flux of the Maxwell's stress tensor over a spherical surface tightly enclosing the particle and analytical expression for electromagnetic fields of incident beam in near region are used. The numerical predictions are compared with the results of the rigorous method for spherical particle to validate the accuracy of the approach. Some numerical results on relative large particles of complex shape, such as biconcave cell-like particles with different geometry parameters are given, showing powerful capability of our approach. These results are expected to provide useful insights into the RPF exerted on complex shaped particles by HOBVB.

Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves

The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto-fluidics would benefit from the results of the present investigation.

分数阶高阶贝塞尔涡旋光束的矢量波分析法研究

分数阶高阶贝塞尔涡旋光束的矢量波分析法研究

Multiple scattering of a zero-order Bessel beam with arbitrary incidence by an aggregate of uniaxial anisotropic spheres

Based on the generalized multiparticle Mie theory, multiple scattering of an aggregate of uniaxial anisotropic spheres illuminated by a zero-order Bessel beam (ZOBB) with arbitrary propagation direction is investigated. The particle size and configuration are arbitrary. The arbitrary incident Bessel beam is expanded in terms of spherical vector wave functions (SVWFs). Utilizing the vector addition theorem of SVWFs, interactive and total scattering coefficients are derived through the continuous boundary conditions on which the interaction of the particles is considered. The accuracy of the theory and codes are verified by comparing results with those obtained for arbitrary plane wave incidence by CST simulation, and for ZOBB incidence by a numerical method. The effects of angle of incidence, pseudo-polarization angle, half-conical angle, beam center position, and permittivity tensor elements on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres, such as a linear chain, a 4×4×4 cube-shaped array, and other periodical structures consisting of massive spheres, are numerically analyzed. Selected results on the properties of typical particles such as TiO2, SiO2, or other particle lattices are calculated. This investigation could provide an effective test for further research on the scattering characteristics of an aggregate of anisotropic spheres by a high-order Bessel vortex beam. The results have important application in optical tweezers and particle manipulation.

Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid

Partial-wave series representation of the acoustic scattering field of high-order Bessel vortex beams by rigid oblate and prolate spheroids using the modal matching method is developed. The method, which is applicable to slightly elongated objects at low-to-moderate frequencies, requires solving a system of linear equations which depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated partial-wave series expansions (PWSEs), and satisfying the Neumann boundary condition for a rigid immovable surface in the least-squares sense. This original semi-analytical approach developed for Bessel vortex beams is demonstrated for finite oblate and prolate spheroids, where the mathematical functions describing the spheroidal geometry are written in a form involving single angular (polar) integrals that are numerically computed. The transverse (θ=π/2) and 3D scattering directivity patterns are evaluated in the far-field for both prolate and oblate spheroids, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid) not exceeding 3:1, the half-cone angle β and order m of the Bessel vortex beam, as well as the dimensionless size parameter kr0. Periodic oscillations in the magnitude plots of the far-field scattering form function are observed, which result from the interference of the reflected waves with the circumferential (Franz’) waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the far-field scattering from the spheroid, that vanishes in the forward (θ=0) and backward (θ=π) directions. Particular applications in underwater acoustics and scattering, acoustic levitation and the detection of submerged elongated objects using Bessel vortex waves to name a few, would benefit from the results of the present investigation.

Acoustics of finite Bessel tractor beams

Surprises and counterintuitive effects occurring in physical phenomena rank high on the list of things that make science discoveries a source of perpetual excitement. Some examples illustrated here include, (i) the effects of attracting (i.e., pulling) a spherical particle placed in the field of a Bessel acoustical beam of progressive waves back towards the radiator’s surface [Mitri, “Single Bessel tractor-beam tweezers,” Wave Motion 51, no. 6, pp. 986–993, 2014], (ii) suppressing some of the sphere’s resonances [Mitri, “Near-field acoustic resonance scattering of a finite Bessel beam by an elastic sphere,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 61, no. 4, pp. 696–704, 2014], (iii) and the emergence of a “negative radiation torque,” meaning that an incoming high-order Bessel vortex beam with a positive topological charge (known also as the order of the beam) would rotate a viscoelastic sphere in the opposite sense of the beam handedness [Silva et al., “Radiation torque produced by an arbitrary acoustic wave,” Europhys. Lett., 97, art. no. 54003, 2012]. Results and numerical predictions illustrate the analysis and extensions to other geometries, such as rigid oblate and prolate spheroids [Mitri, “Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid,” http://arxiv.org/abs/1505.06754v3, ibid. "Acoustic radiation force on oblate and prolate spheroids in Bessel beams,” Wave Motion, 57, pp. 231–238, 2015] are also mentioned.

Light scattering of a non-diffracting zero-order Bessel beam by uniaxial anisotropic bispheres

Based on the generalized multi-particle Mie theory and the Fourier transformation approach, light scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes illuminated by a zero-order Bessel beam (ZOBB) is investigated. The size and configuration of the particles are arbitrary. The expansion expressions of the ZOBB are given in terms of the spherical vector wave functions (SVWFs) and the expansion coefficients are derived. Utilizing the vector addition theorem of the SVWFs, the interactive scattering coefficients are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. The effects of the conical angle, beam centre position, sphere separation distance, and anisotropic parameters on the far-region field distributions are numerically analyzed in detail. Some results are compared with those results for a Gaussian beam incidence. Selected results of bispheres consisting of typical medium such as TiO2, SiO2, Silicon, water are exhibited. This investigation could provide an effective test for further research on the scattering characteristic of an aggregate of anisotropic spheres by a high-order Bessel vortex beam and radiation forces, which are important in optical tweezers and particle manipulation applications.

Counterpropagating nondiffracting vortex beams with linear and angular momenta

Closed-form analytical expressions for the electric and magnetic (EM) field components of a high-order Bessel vortex beam of fractional type \ensuremath{\alpha} (HOBVB-F\ensuremath{\alpha}) are derived based on the axial polarization of the vector potentials [denoted by ($z,\ensuremath{-}z$)]. The fields' components correspond to the most generalized case of quasi-standing-waves that reduce to perfect (i.e., equiamplitude) standing waves or progressive waves with appropriate choice of the quasi-standing-wave coefficient $0\ensuremath{\le}\ensuremath{\Upsilon}\ensuremath{\le}1$. The beam components are exact solutions of the vector wave equation (Helmholtz equation) and Maxwell's equations. Moreover, computations of the EM components and comparison with the results obtained from a transverse polarization scheme [denoted by (x,\ensuremath{-}y)] illustrate the analysis. In addition, the time-averaged angular momentum density and flux are evaluated with particular emphasis on the axial and transverse polarization states of the vector potentials. It is found that the quasi-standing-wave effect does not influence the spatial distributions of the EM components in the transverse polarization scheme (x,\ensuremath{-}y); however, it affects the transverse EM field components in the axial polarization (z,\ensuremath{-}z). Moreover, both the linear and angular momenta density fluxes are shown to reverse sign for a particular value of the half-cone angle \ensuremath{\beta}. These phenomena anticipate the production of a ``tractor'' beam where particulate matter may be pulled back toward the source, and a spinning reversal effect in which particulate matter may rotate with opposite handedness to a HOBVB-F\ensuremath{\alpha}. The results are particularly useful in applications involving optical laser tweezers, tractor beams, optical spanners, arbitrary scattering, radiation force, angular momentum, and torque.