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We present a theory of the diffraction of light of arbitrary polarization incident on a doubly periodic dielectric grating. We use Rayleigh's method together with the vectorial equivalent of Kirchhoff's integral. The amplitudes of the diffracted spectral orders are calculated for a sinusoidal bigrating and for a square lattice of hemiellipsoids on a flat surface, for Ag. The enhancement of the electric field on and near the surface is calculated and is found to reach values of about 300.
Glass et al. (1983) studied this question.