Density-of-States Calculations and Multiple-Scattering Theory for Photons

TL;DR

This paper develops a comprehensive multiple-scattering theory for photons, expressing the density of states as a sum of individual scatterer contributions and multiple scattering effects, applicable to arbitrary-shaped scatterers in three dimensions.

Contribution

It introduces a general three-dimensional multiple-scattering framework for electromagnetic waves with arbitrary-shaped scatterers, including vector structure constants and photon analogs of KKR equations.

Findings

Derived vector structure constants from scalar ones.

Formulated the photon KKR equations.

Presented a general theory applicable to arbitrary scatterer shapes.

Abstract

The density of states for a finite or an infinite cluster of scatterers in the case of both electrons and photons can be represented in a general form as the sum over all Krein-Friedel contributions of individual scatterers and a contribution due to the presence of multiple scatterers. The latter is given by the sum over all periodic orbits between different scatterers. General three dimensional multiple-scattering theory for electromagnetic waves in the presence of scatterers of arbitrary shape is presented. Vector structure constants are calculated and general rules for obtaining them from known scalar structure constants are given. The analog of the Korringa-Kohn-Rostocker equations for photons is explicitly written down. PACS numbers: 41.20.Jb, 41.20.Bt, 05.40.+j, 05.45.+b