Renormalized polarizability in the Maxwell Garnett theory

Abstract

We develop a simple theory for the macroscopic dielectric function of a system of identical spheres embedded in a homogeneous matrix within the dipolar long-wavelength approximation. We obtained a relationship similar to the Clausius-Mossotti relation, but with a renormalized polarizability for the spheres instead of the bare polarizability. This renormalized polarizability obeys a second-order algebraic equation and it is given in terms of the bare polarizability, the volume fraction, and a functional of the two-particle correlation function of the spheres. We calculate the optical properties of metallic spheres within an insulating matrix and we compare our results with previous theories and with experiment.