  Propagation of gamma-beam in the anisotropic medium is considered. The
simpliest example of such a medium of the general type is a combination of the
two linearly polarized monochromatic laser waves with different frequencies
(dichromatic wave). The optical properties of this combination are described
with the use of the permittivity tensor. The refractive indices and
polarization characteristics of normal electromagnetic waves propagating in the
anisotropic medium are found. The relations, describing variations of
gamma-beam intensity and Stokes parameters as functions of propagation length
are obtained. The influence of laser wave intensity on the propagation process
are calculated.
  The gamma-beam intensity losses in the dichromatic wave depend on the initial
circular polarization of gamma-quanta. This effect is also applied to the
single crystals, which are oriented in some regions of coherent pair
production. In principle, the single crystal sensitivity to a circular
polarization can be used for determination of polarization of high energy (in
tens GeV and more) gamma-quanta and electrons.
