SYMMETRY PROPERTIES OF ANISOTROPIC DIELECTRIC GRATINGS

We consider the exact equations, obtained by application of the Bloch-Floquet theorem, that describe the propagation of light in anisotropic dielectric gratings with an arbitrary variation of the dielectric tensor along the longitudinal direction. On the basis of these equations we determine the scattering matrix and the corresponding grating efficiencies. The conditions for electromagnetic energy conservation are derived and an energy representation for the field inside the grating is defined, thus permitting determination of reciprocity relations that give rise to particular symmetries of the grating efficiencies if one neglects the reflections at the boundaries. Finally, by exploiting the symmetry properties of the matrix that describes the propagation of the electromagnetic field inside the grating, we discuss the polarization properties of the diffracted beams in chiral C smectics in the phase-grating configuration and in the periodic structures induced in certain nematic liquid crystals by the application of static magnetic or electric fields.