ar X iv : h ep - p h / 97 10 20 2 v 1 1 O ct 1 99 7 γ - beam propagation in the anisotropic medium

Propagation of γ-beam in the anisotropic medium is considered. The simplest 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 per-mittivity tensor. The refractive indices and polarization characteristics of normal electromagnetic waves propagating in the anisotropic medium are found. The relations , describing variations of γ-beam intensity and Stokes parameters as functions of the propagation length, are obtained. The influence of laser wave intensity on the propagation process is calculated. The γ-beam intensity losses in the dichromatic wave depend on the initial circular polarization of γ-quanta. This effect is also applied to 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) γ-quanta and electrons. 1 Introduction Polarization effects [1, 2] arising from the visible light propagation in the anisotropic or gyrotropic medium are well-known. The theory [3] makes prediction about the analogous effects for γ-quanta with energy > 1 GeV propagating in single crystals, which present the anisotropic medium. The main absorption process of γ-quanta in the single crystals is the electron-positron pair production. The cross section of this process depends on the linear polarization of γ-beam with respect to crystallographic planes. As a result, the monochromatic linearly polarized γ-beam may be presented as a superposition of two electromagnetic waves with different refractive indices due to which the transformation of linear (circular) polarization to circular (linear) one takes place. On the other hand, the process of e + e −-pair production in single crystals is similar to the same process in a linearly polarized laser wave [4]. A possibility to use a bunch of linearly polarized laser photons as a " single crystal " is pointed in [5], but the concrete calculations of this possibility are not given. In the recent paper [6] it has been shown that the polarization effects such as birefrin-gence and rotation of polarization plane for γ-beams with energies of tens GeV or more take place for short (about some picoseconds) laser bunches and parameters of lasers, which may be provided by real techniques. In the cited paper the differential equations which determine the variation of Stokes parameters and …