The small perturbations method has been extensively used for waves scattering
by rough surfaces. The standard method developped by Rice is difficult to apply
when we consider second and third order of scattered fields as a function 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 new set of four reduced equations for the scattering
amplitudes, which are applied to the cases of a rough conducting surface, and
to a slab where one of the boundary is a rough surface. As in the
one-dimensional case, numerical simulations show the appearance of enhanced
backscattering for these structures.Comment: RevTeX 4 style, 38 pages, 16 figures, added references and comments
on the satellites peak
