Surface-plasmon mode on a random rough metal surface: Enhanced backscattering and localization

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Abstract
The scattering of light by a silver film with a random rough surface and the excitation of surface-plasmon modes at the metal surface are studied by means of the stochastic functional approach, assuming that the random surface is a homogeneous Gaussian random field. The stochastic wave fields are represented in terms of the Wiener-Hermite orthogonal functionals, and the approximate solutions are obtained for the Wiener kernels. For the attenuated total reflection configuration considered in the paper, the angular distributions of incoherent scattering into both crystal and air are numerically calculated by using first- and second-order Wiener kernels for various combinations of the parameters. In the angular distributions of incoherent scattering into crystal, strong peaks can be observed corresponding to the excitation of forward- and backward-traveling plasmon modes, which are mainly described by the first-order Wiener kernel, and an enhanced scattering peak appears in the backward direction. In the angular distributions of incoherent scattering into air, an enhanced scattering peak also appears in a certain direction, related to the incident angle on the crystal side. The random wave fields at the resonant scattering on the surface of a random rough grating are also numerically calculated from the higher Wiener kernels with an iterative procedure. Localized modes can be clearly observed in the spatial distribution of the random wave fields. The enhanced scattering comes from the second-order Wiener kernel that describes the ‘‘double-scattering’’ processes of the ‘‘dressed’’ plasmon modes, and is due to the interference of the two double-scattering processes in the reciprocal directions, where the strongly excited plasmon modes take part in the intermediate scattering processes, while the wave localization is a result of ‘‘multiple’’ scattering of strongly excited dressed plasmon waves traveling in the ‘‘random media’’ created by the surface roughness. © 1996 The American Physical Society.