Single and multiple electromagnetic scattering by dielectric obstacles from a resonance perspective

Abstract

A new application of the singularity expansion method (SEM) is explored. This application combines the classical theory of wave propagation through a multiple scattering environment and the SEM. Since the SEM is generally considered a theory for surface currents on conducting scatterers, extensions are made which permit, under certain conditions, a singularity expansion representation of the electromagnetic field scattered by a dielectric scatterer. Application of this expansion is then made to the multiple scattering case using both single and multiple interactions. A resonance scattering tensor form is used for the SEM description which leads to an associated tensor form of the solution to the multiple scattering problem with each SEM pole effect appearing explicitly. The coherent field is determined for both spatial and SEM parameter random variations.

A numerical example for the case of an ensemble of lossy dielectric spheres is made. Accurate resonance expansions for the single scattering problem are derived, and resonance trajectories based on the Debye relaxation model for the refractive index are introduced. Application of the resonance expansions to the multiple scattering results for a slab containing a distribution of spheres with varying radii is made. Conditions are discussed for when the hybrid theory is appropriate.