High-frequency dielectric constant of a two-dimensionally disordered model medium

An exact solution is derived for the two-dimensional two-phase model of a disordered medium proposed by Morozovskii and Snarskii [Ukr. Fiz. Zh. (Russ. Ed.) 28, 1230 (1983)] that arises because of hierarchical mixing of phases with different dielectric constants. The problem reduces to a nonlinear recurrence relation for the dielectric constants. It is found that the expressions for the dielectric constants at the nth stage of the iteration process can be expressed in terms of elementary functions. It is also found that in the absence of absorption the high-frequency dielectric constant of a composite material with different signs of the initial dielectric constants ε does not converge to a limit and is an oscillatory function of the frequency and n. Finally, for massive and thin-film samples, the local plasmon frequencies in the medium are established. Zh. éksp. Teor. Fiz. 114, 669–675 (August 1998)