TMatrix for Electromagnetic Scattering from an Arbitrary Number of Scatterers and Representations of E(3)

Abstract

The $T$-matrix formulation of electromagnetic scattering given previously by Waterman for the case of one scatterer is extended to the case of an arbitrary number of scatterers. The resulting total $T$ matrix is expressed in terms of the individual $T$ matrices by an iterative procedure. The essential tools used in the extension are the expansions associated with a translation of the origin for the spherical-wave solutions of Helmholtz's equation. The connection between these expansions and the unitary irreducible representations and associated local representations of the three-dimensional Euclidean group E(3) is emphasized. Some applications to two spheres are given.