Theory of optical and microwave properties of microscopically inhomogeneous materials

In this paper we present a theoretical study of the optical and microwave properties of microscopically inhomogeneous disordered materials. We derive an effective-medium theory (EMT) for the propagation of light in a heterogeneous system by means of a self-consistent extension of a multiple-scattering model. This approach is applicable when the correlation length for the fluctuation in the medium is much smaller than the optical wavelength. The Maxwell-Garnett theory is also shown to result from our model under less general circumstances. We present a scheme for the derivation of the macroscopic complex dielectric constant $\epsilon \left(\omega \right)$ through numerical simulations of the inhomogeneous medium, which can be viewed as a generalization of the numerical simulations of the electrical conductivity in resistor networks. On the basis of numerical simulations we assert that the EMT for $\epsilon \left(\omega \right)$ of a binary inhomogeneous medium is valid when the ratio $x\left(\omega \right)$ between the complex dielectric constants of the two components obeys the condition $0.05<\left|x\right(\omega \left)\right|<\mathrm{}20\mathrm{}$. Under more general conditions numerical simulations are more reliable than the EMT at the percolation transition region. The theory is applied to investigate the optical and microwave properties of some binary model systems. The results of this analysis are utilized to explain some optical and microwave properties of granular metallic films, metal-ammonia solutions, and amorphous germanium.