T-matrix methods for electromagnetic structured beams mainly encompass Generalized Lorenz-Mie Theories (GLMTs) which form a set of analytical approaches dealing with the interaction between electromagnetic structured beams and a class of particles possessing enough symmetries to allow one to use the method of separation of variables, and Extended Boundary Condition Method (EBCM) which is a semi-analytical method dealing in principle with arbitrary shaped particles. Both approaches, when dealing with structured beams (in principle in the case of GLMTs and occasionally in the case of EBCM) rely on the description of the illuminating beam in terms of Beam Shape Coefficients (BSCs). The present paper provides a commented reference database concerning GLMTs and EBCM for structured beams, and related topics for the period 2014–2018.

T-matrix methods for electromagnetic structured beams: A commented reference database for the period 2014–2018

We consider the simulation of electromagnetic scattering by single and multiple isotropic homogeneous dielectric particles using boundary integral equations Galerkin discretizations of the classical Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) boundary integral equation formulation provide accurate solutions for complex particle geometries, but are well-known to lead to ill-conditioned linear systems In this paper we carry out an experimental investigation into the performance of Calderon preconditioning techniques for single and multiple absorbing obstacles, which involve a squaring of the PMCHWT operator to produce a well-conditioned second-kind formulation For single-particle scattering configurations we find that Calderon preconditioning is actually often outperformed by simple “mass-matrix” preconditioning, ie working with the strong form of the discretized PMCHWT operator In the case of scattering by multiple particles we find that a significant saving in computational cost can be obtained by performing block-diagonal Calderon preconditioning in which only the self-interaction blocks are preconditioned Using the boundary element software library Bempp ( wwwbemppcom ) the numerical performance of the different methods is compared for a range of wavenumbers, particle geometries and complex refractive indices relevant to the scattering of light by atmospheric ice crystals

Calderón preconditioning of PMCHWT boundary integral equations for scattering by multiple absorbing dielectric particles

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.

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

Within the framework of the generalized multi-particle Mie (GMM) theory, analytical solution to electromagnetic scattering of two interacting homogeneous uniaxial anisotropic spheres by a Laguerre–Gaussian (LG) vortex beam is investigated. The particles with different size and dielectric parameter tensor elements are arbitrarily configured. Based on the continuous boundary conditions at each sphere surface, the interactive scattering coefficients are derived. The internal and near-surface field is investigated to describe the propagation of LG vortex beam through the NaCl crystal. In addition, the far fields of some typical anisotropic medium such as LiNbO3, TiO2 bispheres illuminated by an LG vortex beam are numerically presented in detail to analyze the influence of the anisotropic parameters, sphere positions, separation distance and topological charge etc. The results show that LG vortex beam has a better recovery after interacting with a spherical particle compared with Gaussian beam. The study in the paper are useful for the further research on the scattering and propagation characteristics of arbitrary vortex beam in anisotropic chains and periodic structure.

Scattering and propagation of a Laguerre–Gaussian vortex beam by uniaxial anisotropic bispheres

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Laser-light and Interactions with Particles (LIP), 2016

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.

Mei Ping Yu

Papers

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