The influence of the antisymmetric part of the gyration pseudotensor on the characteristics of reflected and transmitted light has been considered for crystals of classes 3, 4, and 6. The results are compared with the corresponding data for crystals of classes 32, 422, and 622 with a symmetric gyration pseudotensor. Specific features of the optical activity in crystals of classes 3m, 4mm, and 6mm with an antisymmetric gyration pseudotensor have been studied. Crystals of classes \(\bar 42m\) and \(\bar 4\) with the symmetric gyration pseudotensor of an unusual form have been considered. The polarization azimuth and ellipticity of the reflected and transmitted light are calculated for these crystals at different angles of incidence.

The influence of the antisymmetric part of gyration pseudotensor on the characteristics of transmitted light have been investigated for biaxial crystals. Analytical expressions for the optical rotation in the direction of optical axis are obtained with allowance for both the symmetric and antisymmetric parts of gyration pseudotensor. The polarization azimuth and transmitted light ellipticity have been calculated at different angles of incidence.

The paper presents of review of some methods for study optical properties of crystals possessing the optical activity (gyrotropy), the birefringence and the dichroism simultaneously which were elaborated by the authors during last several years. Two main approaches are considered: one making use of the measurement of the azimuth of transmitted light as a function of the incident light azimuth, the other one is based on the measurement of the light intensity transmitted through the sample placed between two polarizers. The intensity change is measured and analyzed depending on the rotation angle of the sample with crossed and parallel polarizers. The theoretical basis of this approach for the general case of nonorthogonal eigen waves is developed. The consideration is based on Muller matrix formalism.Analytical expressions were obtained for optical crystal parameters calculation in mentioned above methods. Theoretical considerations are illustrated by some results of experimental of different gyrotropic birefringent absorbing crystals.

Transmission and reflection matrices are obtained for low-symmetric absorbing gyrotropic crystal plates where eigenwave ellipticities can be different. Multiple reflections are taken into account. The eigenwave irreversibility is properly taken into account. The matrices are represented as the sums of four matrices, and each of them has its own physical meaning.