Perturbation theory for light diffraction with surface-polariton resonances on a bigrating
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The diffraction of light of arbitrary polarization and arbitrary plane of incidence from a bigrating surface is described by an existing theory based on Rayleigh's method and the vectorial Kirchhoff integral. Its implementation requires solving large matrix equations (e.g., 162X162). This paper presents an approximation of that theory, to first order in the corrugation amplitude. It yields a 4X4 matrix equation--allowing one to determine the reflectance for any diffracted order, as well as the surface-field enhancement, when there are surface polarization resonant excitations. the theory retains all the nonresonant amplitudes (to renormalize the surface-polarization frequency) and is valid directly at--or away from-- the boundaries of the two-dimensional Brillouin zones defined by the surface periodicity. the complex dispersion relation, for a surface polariton which propagates in an arbitrary direction across the bigrating, is given by a simple algebraic expression in this perturbation theory.
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