Surface polaritons on large-amplitude gratings

Abstract

We present numerical studies of the dispersion relation for surface polaritons that propagate on the surface of a model free-electron metal upon which a periodic grating has been impressed. The calculations are based on the integral equation formulation of the boundary-value problem, as discussed earlier by Toigo, Marvin, Hill, Celli, and others. We employ the "extinction theorem" scheme, which yields convergent results for values of the ratio $\frac{{\ensuremath{\zeta}}_{0}}{a}$ far in excess of 0.072, where the Rayleigh-Fano method fails when applied to the scattering of a scalar wave from a hard wall with profile given by ${\ensuremath{\zeta}}_{0}cos(\frac{2\ensuremath{\pi}x}{a})$. We give results for the dispersion relation for two grating profiles, the sinusoidal and the symmetric sawtooth forms.