We analyze the effect of surface roughness on the attenuation length of surface polaritons in an unsupported film with randomly rough surfaces. With the consideration of the surface profile functions as stationary stochastic processes, an inhomogeneous matrix equation is established for the components of the mean electric field in the system. The surface polariton dispersion relation is obtained from the solvability conditions for this matrix equation. From the dispersion relation we obtain the effect of roughness on the attenuation length. The effect of roughness is found to be significant for thin films. Numerical results are obtained for parameters characteristic of a silver film.
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Farias et al. (1983) studied this question.
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