Theory of surface-polariton resonances and field enhancements in light scattering from bigratings

Abstract

A theory is presented of the diffraction of light of arbitrary polarization incident upon a doubly periodic grating on the surface of a dielectric medium characterized by a complex dielectric constant ∊(ω). We use Rayleigh’s method, together with the vectorial equivalent of Kirchhoff’s integral and the extinction theorem, to eliminate the field in the dielectric, thereby halving the size of the matrix to be inverted. The amplitudes of the diffracted orders have been calculated for a sinusoidal bigrating and for a square lattice of hemiellipsoids on a planar surface when the dielectric medium is silver. For a fixed wavelength (5145 A) of p-polarized incident light, the angles of incidence (polar and azimuthal) and grating parameters that maximize the coupling to surface polaritons and the electric-field enhancement are calculated. The enhancement of the square of the total field, calculated on and near the surface, is found to reach values of about 300.