Light scattering from rough surfaces: General incidence angle and polarization

The amplitudes of the diffracted fields from a rough surface, for light of general polarization and incidence angle, are found by the classical method of Rayleigh and Fano. Explicit formulas are then obtained for the differential reflected intensity of $P$- and $S$-polarized light as well as for the decrease in reflection coefficient of $S$, $P$, and circularly polarized light due to the excitation of surface plasmons. The results are valid to first order in the surface roughness and are confirmed by additional calculations based on other perturbative methods, both classical and quantum mechanical. The discrepanies found in some cases with the recent results of Maradudin and Mills are analyzed and explained.