The Utility of an Impedance Boundary Condition in the Scattering of Light from One-Dimensional Randomly Rough Dielectric Surfaces

摘要

Local and nonlocal impedance boundary conditions have recently been obtained for p- and s-polarized electromagnetic fields at a one-dimensional, rough vacuum–metal interface defined by the equation x3 = (x1), when the plane of incidence is the x1x3-plane. The surface impedance appearing in these boundary conditions was obtained as an expansion in powers of the ratio of the optical skin depth of the metal at the frequency of the electromagnetic field to the local radius of curvature of the surface. In this paper, we apply these boundary conditions to computer simulation studies of the scattering of p- and s-polarized light from one-dimensional, randomly rough dielectric surfaces. These surfaces are characterized by dielectric constants that are real and positive rather than by complex dielectric constants with real parts that are negative and large in magnitude, as in the case of metal surfaces. Despite this difference, which leads to an “optical skin depth” that is now purely imaginary, comparisons of the results obtained by the use of these impedance boundary conditions with those obtained by formally exact computer simulation calculations show that the former are in very good quantitative agreement with the latter. Moreover, the computation time for such scattering calculations is reduced significantly by the use of an impedance boundary condition.