T-matrix computations for light scattering by penetrable particles with large aspect ratios

Abstract

Using extensive numerical computations for several benchmark geometries, we demonstrate the physical correctness and numerical stability of a two-step algorithm for computing the electromagnetic-scattering T-matrix of homogeneous penetrable three-dimensional scatterers with smooth boundaries. Our numerical results show that the T-matrices computed with our algorithm have high accuracy, even at size parameters and aspect ratios exceeding the upper limits that can be tackled using the current state-of-the-art algorithm, the Extended Boundary Condition Method. The two-step algorithm is an extension to penetrable scatterers of the algorithm introduced in Ganesh and Hawkins (2010) for perfect conductors. The numerical stability of the T-matrix algorithm stems from the application of an efficient new high-order method in the first step, and a stable fully-discrete Laplace–Fourier transform in the second step. The high-order method is based on a recently established surface integral equation formulation for electromagnetic scattering by bounded penetrable media, for which stability at all-frequencies has been proven.