Past and present methods for computing the dielectric constant of lattices of spheres

The computation of the effective electromagnetic material parameters for a composite material is a complex and well-visited problem. For collections of spheres in a static field, the celebrated Clausius-Mossotti equation provides extremely good dielectric constant values when mutual interaction between particles is negligible. When mutual coupling is not negligible and identical spheres are arrayed on an infinite lattice, accurate values for the dielectric constant can be found using techniques described by Rayleigh and later refined by McPhedran and McKenzie (1978) and McKenzie et al. (1978). In this paper, we first provide a brief look at the effective dielectric constant methods developed for infinite lattices of identical particles. This is followed by developments in this area using a new T-matrix identity and subsequent extraction of the effective dielectric constant.