Random-volume scattering: Boundary effects, cross sections, and enhanced backscattering.

Abstract

Assuming a scalar wave, the Bethe-Salpeter (BS) equation for a system of random medium with rough boundaries is first reviewed, together with the scattering matrices involved. Emphasis is placed on the optical condition of each scattering matrix, as well as that of a random layer with pronounced boundary effect as one scatterer. Their optical expressions are obtained in terms of the cross sections along with the respective optical conditions. The enhanced backscattering can be understood as a natural consequence of requiring coordinate-interchange invariance of the second-order Green's function, and the BS equation is rewritten as an equation for the function of the four coordinates involved, so that the invariance is immediately clear. With the solution, specific expressions of cross sections are obtained for a random layer to the approximation of using the boundary-value solution of the diffusion equation. Nevertheless, the angle distribution in the enhanced backscattering holds sufficient accuracy as long as the optical width of the layer is long enough, although not quite for the background term. Another method of using asymptotic evaluation of the cross sections under the diffusion condition is also discussed. A numerical example is shown for the enhanced backscattering.