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Perturbation theory for light diffraction with surface-polariton resonances on a bigrating

1987; American Physical Society; Volume: 35; Issue: 6 Linguagem: Inglês

10.1103/physrevb.35.2647

1095-3795

Nina E. Glass,

Photonic and Optical Devices

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., 162\ifmmode\times\else\texttimes\fi{}162). This paper presents an approximation of that theory, to first order in the corrugation amplitude. It yields a 4\ifmmode\times\else\texttimes\fi{}4 matrix equation---allowing one to determine the reflectance for any diffracted order, as well as the surface-field enhancement, when there are surface-polariton resonant excitations. The theory retains all the nonresonant amplitudes (to renormalize the surface-polariton 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.