Wave propagation in a one-dimensional random inhomogeneous medium

The problem of wave propagation in a medium with random one-dimensional inhomogeneities of dielectric permittivity is considered in the approximation of a Markov random diffusion process. The solution of the diffusion equation for the distribution function of the reflection coefficient from the inhomogeneous slab is obtained. Some statistical moments of the solution are investigated. It is shown that the reflection coefficient has equally probable distribution of phase if the regular reflection at the boundaries of the layer vanishes. For this reason there is no regular component in a random reflected wave. Expressions are obtained for the intensity of the transmitted and reflected waves. A sufficiently thick layer reflects the whole energy of an incident wave in the form of the random scattered field energy. Also found are the formulas for the mean field inside the layer and behind it and for the effective permittivity of a one-dimensional random inhomogeneous medium. The problem is considered for two limiting cases of a small-scale (kl ≪ 1) and a large-scale (kl ≫ 1) inhomogeneous medium.