The angular distribution of the mean diffuse intensity scattered from a metal surface with one-dimensional roughness is studied with perturbation theory. From an approach based on the reduced Rayleigh equations in <i>p</i> polarization, exact perturbation terms up to eighth order in the height parameter are developed for surface roughness consistent with a stationary Gaussian process. The theory is evaluated for a number of cases in which surface plasmon polariton excitation is significant and produces effects such as backscattering enhancement. For surface roughness having a wide Gaussian power spectrum, it is found that the high-order terms lead to roughness-induced broadening of the backscattering peak. For rectangular spectra, two cases are studied in which backscattering effects are due to sixth- and eighth-order terms; both cases provide good comparisons with previously unexplained experimental results. Further, because of an eighth-order term, the diffuse intensity is shown to contain a specular peak that also relies on polariton excitation. This new effect is studied in detail and is found to arise from the constructive interference of contributions produced by multiple-scattering processes, although the time-reversed paths that produce backscattering enhancement are not essential to the specular effect.
© 2001 Optical Society of America
K. A. O’Donnell, "High-order perturbation theory for light scattering from a rough metal surface," J. Opt. Soc. Am. A 18, 1507-1518 (2001)