New approach in crystal optics

The orthogonal representation of wave propagation in magnetic crystals of triclinic and monoclinic systems is developed and generalized for magnetoelectrics. It is shown that, after introduction of principal velocities inversed to principal refraction indexes, Maxwell equations determine reciprocal tensors of velocities and indexes which depend linearly on directions and are similar to a angular momentum tensor. In the general case, when the non-reciprocity phenomenon takes place the 2-nd order characteristic equations are obtained for determination of phase velocities instead of the 4-th order equation. The two-dimensional representation of wave propagation is considered. It is established, that if gyrotropy takes place the introduced tensors are unitary ones. The simple expressions for dependence of ray (group) velocities, which directly define phase velocities and polarization of waves, on principal velocities in nongyrotropic crystals are adduced. Their generalization on purely and naturally gyrotropic crystals is discussed.