Diffraction of light by a bigrating: Surface polariton resonances and electric field enhancements

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.