Effective medium models for the optical properties of inhomogeneous materials

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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–Al2O3 cermets.