CORRUGATED DIFFRACTION GRATINGS IN UNIAXIAL CRYSTALS

We present a rigorous electromagnetic approach to wave diffraction by corrugated gratings made of uniaxial crystals. The optic axis of the anisotropic medium is assumed to lie on the mean surface of the grating, inclined at an arbitrary angle with respect to the grooves. The diffraction problem is exactly analyzed as a two-medium boundary-value problem. We simplify the fully vectorial treatment by first writing the fields everywhere in terms of the components of the electric and magnetic fields along the groove direction. Then a coordinate transformation mapping the corrugated interface into a plane is used, and the transformed propagation equations are solved by means of a differential method. The theory is exemplified numerically for the case of gratings made of sodium nitrate, and the results are compared against those obtained with a simplified formalism invoking the Rayleigh hypothesis.