Differential formalism for multilayer diffraction gratings made with uniaxial materials

Abstract
We present a theoretical analysis for multilayer gratings of arbitrary shape containing uniaxial materials in which all optic axes lie in the plane of incidence, which itself is perpendicular to the grating grooves. The analysis is based on the differential method with internal boundary conditions imposed by means of a scattering matrix. Our development allows for layer interfaces of different shape, although they must all share the same periodicity.