Reciprocity relations for uniaxial gratings

Starting from a formulation of the reciprocity theorem valid for uniaxial media, we derive symmetry properties for the co-polarized and cross-polarized efficiencies diffracted by a periodically corrugated surface that separates a uniaxial medium from a perfect conductor. These reciprocity relations are proved to be valid for arbitrary orientations of the optic axis of the crystal and for an arbitrary shape of the grating.