Electromagnetic scattering by two concentric spheres buried in a stratified material

Abstract

In this paper, a rigorous method to analyze the electromagnetic scattering of an elliptically polarized plane wave by two concentric spheres buried in a dielectric stratified medium is presented. The interaction of the electromagnetic radiation with the stratified material is taken into account by means of the transfer matrix approach, in this way we can consider the stratified medium as an effective single interface. All the electromagnetic fields are expanded in series of spherical vector harmonics. The transmitted field through the stratified medium is obtained by means of the effective transmission coefficient. This field is scattered by the two concentric spheres, and the scattered field interacts again with the stratified material. The scattered-reflected and scattered-transmitted fields by the layered medium are computed by exploiting the plane-wave spectrum of the scattered field, considering the reflection and transmission of each elementary plane wave by the effective interface. The boundary conditions imposition on the spheres' surfaces leads to a linear system that returns the unknown coefficients of the problem. A numerical code has been implemented to compute the field over all the space. In order to compute the scattered fields, a truncation criterion has been proposed for the numerical evaluation of the series. Finally, to validate the presented method, comparisons between the results of the proposed code and the results of simulations with a software based on the finite element method have been implemented, showing very good agreement.