Anisotropic Surface Relief Diffraction Gratings under Arbitrary Plane Wave Incidence

A modal method is used for the analysis under oblique incidence of a diffraction grating made of anisotropic material. The problem is studied viewing the structure as the cascade of junctions between periodic arrays of anisotropic slab waveguides with the same period and different heights. This diffraction problem is formulated in terms of an integral equation that enforces the continuity of the transverse magnetic field at the junction. The unknown is the transverse electric field at the junction. It is possible to use also another formulation, where the role of the two fields is exchanged. The kernels of these equations are the relevant Green's functions, which are expressed in terms of eigenfunction expansions. The determination of the modes of the various regions composed of arrays of anisotropic dielectric slabs has been carried out by the method of spectral elements, whereby the field components are represented in a polynomial basis and the original differential eigenvalue problem is converted into an algebraic one. Thr integral equation is solved numerically by the method of moments and each junction is characterized by its generalized scattering matrix (GSM). Finally, the diffraction efficiencies of the grating are obtained by combining the various GSM's.