Optical properties of randomly distributed particles

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Abstract
The optical properties of inhomogeneous media consisting of small metal particles in a dielectric host (cermet topology) are studied using the coherent-potential approximation in conjunction with a lattice-gas model. The theory includes the dipole fields of the randomly distributed particles and constitutes a self-consistent generalization of the Maxwell-Garnett model. It is shown that the disorder leads to a sizable red shift and broadening of absorption peaks. These effects are largest near filling fractions of about 10-20% in contrast to multipole-induced changes, which become important at higher particle concentrations. The composite dielectric function is shown to satisfy the rigorous bounds which hold for any two-component system. The disorder treatment is extended to multicomponent composites in order to illustrate the effect of nonuniform particle sizes. In the case of two-dimensional inhomogeneous systems, the disorder is shown to have a qualitatively different influence on the shift and broadening of the parallel and perpendicular collective modes. Several applications of the theory to real systems are given and compared with experimental absorption spectra.