Conformal mapping method for electromagnetic scattering at the boundary of an uniaxial crystal and a periodically corrugated perfect conductor

A rigorous electromagnetic approach to wave scattering by one-dimensional, periodically corrugated interfaces between an uniaxial crystal and a perfect conductor is presented for the case of arbitrary orientations between the optic axis of the crystal and the mean interface. The fully vectorial treatment is first simplified by writing the total fields in terms of the components of the electric and magnetic fields along the grooves direction. Then a coordinate transformation that maps the corrugated interface into a plane is used and the transformed propagation equations are solved by means of a differential method. The method presented here could be regarded as the extension to uniaxial-perfectly conducting boundaries of the conformal mapping method proposed by Neviere et al. for isotropic-perfectly conducting boundaries [1]. The new method is applied to study the diffraction of ordinary and extraordinary modes at a perfectly conducting boundary with grooves of triangular shape.