Symmetry peculiarities of dielectric tensor in incommensurately modulated crystal phases

The dielectric permittivity tensor for incommensurately modulated phases in insulating crystals is considered. The main attention is paid to the spati al dispersion giving rise to optical gyration effects and the influence of the modulation phase on those effects. General properties of the dielectric tensor are analysed in relation to the lattice and incommensurate superlat tice periodicity requirements, the Onsager principle and the condition of a bsence of the radiation losses in the optical medium. The structure of the microscopic components of the tensor and a macroscopic averaging procedure for the plane-wave modulation region are discussed. The possibility of exis tence of an and-Hermitian part in the dielectric tensor of lossless incomme nsurate crystals originating from the modulation-induced spatial dispersion is revealed. The performed analysis shows a necessity for introduction int o the constitutive equation of the term including spatial derivatives of th e optical activity tensor.