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The small perturbations method has been extensively used for waves scatteringby rough surfaces. The standard method developped by Rice is difficult to applywhen we consider second and third order of scattered fields as a function ofthe surface height. Calculations can be greatly simplified with the use ofreduced Rayleigh equations, because one of the unknown fields can beeliminated. We derive a new set of four reduced equations for the scatteringamplitudes, which are applied to the cases of a rough conducting surface, andto a slab where one of the boundary is a rough surface. As in theone-dimensional case, numerical simulations show the appearance of enhancedbackscattering for these structures.Comment: RevTeX 4 style, 38 pages, 16 figures, added references and comments  on the satellites peak

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