Transition matrix of a nonspherical layered particle in the non-local optical response theory

Abstract

In this paper, we derive the transition matrix of a nonspherical layered particle, consisting in a dielectric core and a metallic shell, in the non-local optical response theory. The key point in our analysis is the separation of the internal field within the shell into a transverse and a longitudinal field. The approach uses the null-field equations for the total field inside the particle and the transverse and longitudinal fields outside the metallic shell, the integral representation for the scattered field, the conventional boundary conditions for the transverse fields, and the additional boundary conditions for the normal components of the fields. Depending on the way in which the additional boundary conditions are treated, three methods for computing the transition matrix are proposed. When the non-local effects are neglected, the transition matrix becomes the transition matrix in the local optical response theory, and for a homogeneous particle, the transition matrix simplifies to that derived in a previous paper.