Effective medium models for metal-dielectric composites:An analysis based on the spectral density theory

We study different effective medium theories for describing the optical behaviour of composites consisting of spherical metallic inclusions embedded in a dielectric matrix. The analysis is performed according to the Bergman spectral density theory. This theory establishes that any effective medium model has an integral representation in terms of a function (the spectral density) that depends on the geometry of the two-phase mixture and is independent of the optical constants of the composing materials. We review classical effective medium theories (Maxwell-Garnett and Bruggeman models) according to their spectral density. Furthermore, numerical simulations based in recent works allow studying the influence of different geometric parameters in the spectral density and compare the results with the classical theories.