Theory of Light Scattering from a Rough Surface with an Inhomogeneous Dielectric Permittivity

Abstract

First-order perturbation theory is used to calculate the scattering of a plane wave from the surface of a semi-infinite medium; the surface is slightly rough and the scattering medium is isotropic but has optical constants which vary as a function of position over the surface, i.e., the material has an inhomogeneous dielectric permittivity. Both the roughness and dielectric permittivity perturbations, which are treated as random variables, can independently cause scattering, and there is generally interference between the two scattered fields. The scattering depends on the autocovariance functions for the surface roughness and dielectric fluctuations and their cross correlation properties. Thus, the polarization ratio between the p and s angle-resolved scattering components is found to be a variable that depends on the autocovariance functions and cross-correlation between the surface roughness and dielectric fluctuations. This result is unlike predicted scattering caused by roughness or dielectric perturbations alone; in these cases the polarization ratios do not depend on the statistical properties of the perturbation.