An overview of the methods for deriving recurrence relations for T-matrix calculation

Abstract

In this paper, we present a consistent analysis of the methods dealing with the derivation of recurrence relations for calculation of the T-matrix. Central and forward recurrence relations are obtained in the framework of the invariant embedding T-matrix method, the matrix Riccati equation method, and the superposition T-matrix method. The accuracies and efficiencies of the central and forward recurrence schemes are analyzed, and some implementation issues related to the improvement of the numerical accuracy and to the problem of overcoming of overflow errors are discussed.

Calculation of the electromagnetic scattering by non-spherical particles based on the volume integral equation in the spherical wave function basis

“…The named excessive inversion is not omitted in the method of [6], though the possibility of formulating a procedure with only one matrix inversion per step is noted in [11]. An operator transforming the external field amplitudes to the scattered field for the considered spherical shell amplitudes can be rewritten in the matrix form:…”

“…Such algorithm was formulated in [6] using the invariant imbedding method. It is derived below by means of some intuitive observations analogous to the superposition T-matrix method given by [10,11].…”

“…(25) decompositions of the permittivity functions into the spherical harmonics should be done for twice larger maximum harmonic degree 2N than the one used in the methods. Functions (47) are also simplified since indices m = q (for further simplification of the method based on the rotational symmetry, see [11]). In case of a general polyhedron particle the following approach can be applied (see Fig.…”

“…This approach was considered in [6] within the rationale of the invariant imbedding technique, and further applied in [7,8,9] for analysis of atmospheric ice particle light scattering features. The equivalence between the invariant imbedding procedure and the integral-matrix approaches was outlined in [10,11]. The method represents an interesting alternative to the previously well-developed volume integral methods.…”

Theory of perturbation of electric potential by a 3D object made of an anisotropic dielectric material

“…In addition, bases have been numerically synthesized for certain gyrotropic dielectric-magnetic mediums [7][8][9]. The EBCM literature continues to expand as time marches on [3,[10][11][12] Historically, the situation has been markedly different in electrostatics. Green's second identity yields an expression [13,14] that was used by Farafonov [15] in 2014 to formulate the EBCM for the perturbation (i.e., "scattering") of a source electric potential (the electrostatic counterpart of an incident time-harmonic electromagnetic field) by a 3D object composed of a homogeneous isotropic medium.…”