The T-matrix method is one of the most versatile and efficient direct computer solvers of the macroscopic Maxwell equations and is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper is the seventh update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2013. It also lists a number of earlier publications overlooked previously.

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Comprehensive thematic T-matrix reference database: A 2014–2015 update

This paper is the sixth update to the comprehensive thematic database of peer-reviewed T -matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2013 It also lists several earlier publications not incorporated in the original database and previous updates

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Comprehensive Thematic T-matrix Reference Database: a 2013-2014 Update

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

The description of an electromagnetic beam for use in light scattering theories may be carried out by using an expansion over vector spherical wave functions with expansion coefficients expressed in terms of Beam Shape Coefficients (BSCs). A celebrated method to evaluate these BSCs has been the use of localized approximations (with several existing variants). We recently established that the use of any existing localized approximation is of limited validity in the case of Bessel and Mathieu beams. In the present paper, we address a warning against the use of any existing localized approximation in the case of helical beams. More specifically, we demonstrate that a procedure used to validate any existing localized approximation fails in the case of helical beams. Numerical computations in a companion paper will confirm that existing localized approximations are of limited validity in the case of helical beams.

On the validity of the use of a localized approximation for helical beams. I. Formal aspects

When using some analytical and semi-analytical scattering theories such as Generalized Lorenz–Mie Theories (GLMTs) and Extended Boundary Condition Method (EBCM) for structured beams, electromagnetic fields, expanded over a set of vector wave functions, may be encoded in some coefficients known as Beam Shape Coefficients (BSCs). In the case of Laguerre–Gauss beams freely propagating, the evaluation of BSCs by using numerical quadratures is time-consuming while localized approximations have been shown to be of limited validity. The present paper therefore establishes finite series expressions to evaluate the BSCs of Laguerre–Gauss beams freely propagating in a rigorous framework, which has the known advantage of speeding up computations with respect to the use of a numerical quadrature technique.

Finite series expressions to evaluate the beam shape coefficients of a Laguerre–Gauss beam freely propagating.

A solution for light scattering from an optically anisotropic particle illuminated by an arbitrary shaped beam is proposed in this paper, which is implemented using a combination of a recent developed T-matrix approach for anisotropic particles and the description of arbitrary shaped beam originally derived in the generalized Lorenz–Mie theory (GLMT). The internal fields inside anisotropic particle are expanded in terms of a series of quasi-spherical vector wave functions (qSVWFs) which are derived using an inverse Fourier transform operation, and the incident shaped beam is expanded in terms of the regular spherical vector wave functions (SVWFs), then the scattering transition matrix of an anisotropic particle is obtained using the extended boundary condition method (EBCM) technique. Verification computations are implemented for a uniaxial anisotropic particle illuminated by a focused Gaussian beam. Comparisons are made between the results obtained using the presented method and those calculated using other methods. Furthermore, numerical calculations are performed to study the influences of shaped beam parameters (beam waist radius, incident angles) and of particle parameters on the scattering properties.

Light scattering from an optically anisotropic particle illuminated by an arbitrary shaped 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.

An Tao Chen

Papers

Light scattering from an optically anisotropic particle illuminated by an arbitrary shaped beam

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