A simple model is developed for the surface–plasmon polariton on a rough surface. Only plane-surface Maxwell boundary conditions are used, with the roughness entering through a single complex-valued parameter. The calculated dispersion relation for silver in air agrees well with published data over a useful frequency range. The model is extended to describe the corresponding nonradiating modes of a thin film with two rough surfaces. The resulting dispersion relation for silver films again corresponds closely to the available data. The complex roughness parameter can be calculated from published perturbation theories. The transmission of an ordinarily opaque metal film can be very large under kinematical conditions in which the internal excitation couples to radiation at both rough surfaces.
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Thomas C. Paulick (1988) studied this question.