The calculations of the enhanced electric field near a randomly rough metal surface overcoated with a dielectric layer are presented. The enhancement is due to the roughness-induced resonant excitation of the surface-plasmon (SP) polariton by the incident photon. In calculating the coupling, the multiple scattering of the SP polariton from rough surface is included by solving the previously derived Bethe-Salpeter equation for the averaged two-polariton Green's function. This is found to be very important for the roughness parameters reported in most of the experiments. The presence of a thin dielectric overlayer shifts the polariton dispersion curves towards lower frequencies, which leads to the increase in coupling with the incident photon and hence large enhancement at lower frequencies. For bare aluminum, for which large enhancements are expected only in the ultraviolet region because of its large SP frequency ({~}10eV), it is found that by overcoating it with a thin dielectric (aluminum oxide) layer, one can also obtain large enhancements in or near the visible region.
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K. Arya (1984) studied this question.