Theory of Brillouin scattering on a surface grating: Role of surface polaritons

In a recent paper [W. M. Robertson et al., Phys. Rev. B 41, 4986 (1990)] an empirical and unexplained selection rule governing light scattering by surface acoustic waves on corrugated metal surfaces has been found experimentally, whenever a surface polariton acts as an intermediate state giving rise to a Rayleigh wave replica in the spectra. The replica occurs only when the scattered light is s polarized, independently of the incident polarization. In this paper the Brillouin cross section for a corrugated surface is evaluated theoretically within the extinction-theorem formalism and the above-mentioned selection rule is shown to be valid in the limit of large dielectric constant.