In order to describe and predict the optical properties of a medium consisting different phases, one should consider structural geometry and aggregate topology of the medium which will make the model derivation a challenging issue. To solve this problem, these systems can be took into account as an optically quasi-homogeneous effective-medium materials. The main idea of such an assumption is to replace the inhomogeneous composite by a homogeneous material with specific dielectric function and consequently calculation of optical properties such as reflectance and transmittance as a linear response of this structure.
Precisely, to introduce a model for determining the dielectric function of a medium first we should start by examining the case of homogeneous media. In this case, one can describe the dielectric function by classical Clausius-Mossotti equation
Where α is the linear microscopic polarizability, ℵ is density of microscopic constituents and ε is dielectric coefficient of medium. Furthermore, for a two-phase media, Clausius-Mossotti equation can be extended to a first order effective medium approximation where the polarizabilities of component a is a and polarizabilities of component b is b. In this case we can
rewrite the Clausius-Mossotti equation as:
Finally we can write:
Where f is the volume fraction of the component i within the matrix.
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