Localization of surface plasmon waves on the surface of a random rough metallic grating with a narrow-band spectrum

Abstract The random wave fields on the surface of a random rough metallic grating are numerically calculated by the stochastic functional approach for the Bragg incidence, and the wave localization on the grating surface can be clearly observed from the spatial distributions of the random wave fields. The fields are expanded as the harmonics of the central spatial frequency of the grating with the stochastic amplitudes, instead of the Wiener-Ito expansion used in our previous work [Ogura and Wang, Phys. Rev. B 53 (1996) 10358], which could not give convergent results in the numerical calculation. There is no divergence problem for the harmonic expansion, but in the present its application is limited only for a rough grating with a very narrow-band spectrum.