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 ten sor along the longitudinal direction. On the basis of these equations we determine the scattering matrix and the corresponding grating effic iencies. The conditions for electromagnetic energy conservation are de rived 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 t he electromagnetic field inside the grating, we discuss the polarizati on properties of the diffracted beams in chiral C smectics in the phas e-grating configuration and in the periodic structures induced in cert ain nematic liquid crystals by the application of static magnetic or e lectric fields.