Effective medium models for the optical properties of inhomogeneous materials

TLDR

The authors derive Maxwell Garnett and Bruggeman effective medium theories for the average dielectric permeability of heterogeneous materials using a unified theoretical approach. They model two random unit cells representing distinct microstructures, enforce that they are electromagnetically invisible in an effective medium, and apply an extended optical theorem to set the forward scattering amplitude to zero, yielding the effective medium theories, which they then apply to numerical simulations of Co‑Al₂O₃ cermets. The higher‑order terms in the expansion give estimates of the approximations’ accuracy.

Abstract

The Maxwell Garnett and Bruggeman effective medium theories are derived for the average dielectric permeability of heterogeneous materials from a unified theoretical approach. It starts by specifying two random unit cells which represent different microstructures. Requiring that these cells should not be detectable by electromagnetic radiation when embedded in an effective medium, we show from an extended optical theorem that the forward scattering amplitude must vanish. Setting the leading term in the expansion series of this quantity equal to zero yields the effective medium theories pertaining to the two microstructures. The remaining terms provide estimates of the accuracy of the approximations. This approach is then used in numerical computations for Co-AI(2)O(3) cermets.