Group Representation of Waves in Gyrotropic Crystals

A new group (linear) representation of the propagation of waves in properly and naturally gyrotropic crystals in the general case where the nonreciprocity effect takes place has been developed. Simple expressions of the dependence of ray (group) velocities and polarization vectors of isonormal waves on the complex vector of principal velocities dual to the unitary tensor by which the optical properties of crystals are directly characterized have been obtained. The relationship between gyrotropy and anisotropy and the dipole moment and displacement current induced by the radiation in the crystal has been established. It is shown that the presence of gyrotropy and nonlinear polarization of radiation together with the elimination of conical points entails a phase ambiguity of the ray velocity of the quantummechanical type and a smearing and layering of the wave surface, as well as a discreteness of the spectrum of velocity values of isonormal waves.