Surface plasmons on a large-amplitude grating

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Abstract
Dispersion relations are obtained by two different methods for surface plasmons (in the nonretarded limit) propagating on the surface of a dielectric medium on which a large-amplitude grating has been ruled. The first method is based on the Rayleigh hypothesis; the second method is based on the extinction-theorem form of Green's theorem. It is found that there is an infinite number of branches of the surface-plasmon dispersion curve. Numerical solutions of the dispersion relations are obtained in the case that the dielectric medium is a free-electron metal for two surface profiles: a sinusoidal profile and a symmetric sawtooth profile. For the former profile, results are obtained for corrugation strengths far exceeding the value for which the Rayleigh hypothesis ceases to be valid.