An Improved Method for T-Matrix Calculations of Light Scattering by Spheroidal Particles

Abstract

The modeling of light scattering by particles has a long history, starting with the case of spheres (Mishchenko and Travis LD, Bull Am Meteorol Soc 89:1853–1861, 2008). Spheres however provide a constrained shape to model particles, and the extension to spheroids allows the modeling of many more systems. However, the modeling of light scattering by spheroids remains a more challenging problem than for spheres. One common semi-analytic technique to model spheroids is the Extended Boundary-Condition Method (EBCM) to compute the Transition-matrix (T-matrix) (Waterman, Proc IEEE 53:805–812, 1965), which may be thought of as an extension of Lorenz-Mie theory to particles of arbitrary shape. The T-matrix method allows the calculation of near-and far-field optical properties, as well as the easy calculation of orientation-averaged scattering properties, as well as considering scattering by collections of particles. It is thus an attractive method for the modeling of light scattering in plasmonics and other fields (Boyack and Le Ru, Phys Chem Chem Phys 11:7398–7405, 2009). However, in the case of spheroids, there are problems in most implementations of the EBCM that limit the parameter space that the method is useful for. The EBCM consists of populating a matrix with surface integrals over the surface of the particle being modeled, followed by the inversion of the system, to obtain the T-matrix.