Application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces

The small perturbation method has been extensively used for wave scattering by rough surfaces. The standard method developed by Rice is difficult to apply when we consider second and third orders of scattered fields as functions of the surface height. Calculations can be greatly simplified with the use of reduced Rayleigh equations, because one of the unknown fields can be eliminated. We derive a set of four reduced equations for the scattering amplitudes, which are applied to cases of a rough conducting surface, and to a slab where one of the boundaries is a rough surface. As in the one-dimensional case, numerical simulations show the appearance of enhanced backscattering for these structures.