Diffraction from corrugated gratings made with biaxial crystals: Rayleigh methods

We apply the Rayleigh hypothesis to study the diffraction of electromagnetic waves at corrugated gratings made of biaxial crystals with arbitrary orientations of their optic axes. The method is valid for gratings made of shallow grooves of any shape, with arbitrary orientation of the plane of incidence with respect to the main section of the cylindrical corrugation (conical mounting). We solve the dispersion equation to find the propagation constants and the polarization of the plane waves involved in Rayleigh expansions. These expansions are used to impose Maxwell boundary conditions at the grating interface. This leads to a linear system of equations with the amplitudes of the diffracted fields as unknowns, which is solved numerically. As examples of application of this procedure, we calculate the co- and cross-polarized components in the specularly diffracted order when the periodically corrugated biaxial crystal is illuminated from an isotropic medium by s and p polarized plane waves, and we study the excitation of surface plasmons for incidence from the biaxial crystal onto a metal surface.