Geometric optics of a twist-oriented nematic liquid crystal with anisotropic absorption

The spatial dynamics of polarized light in a smoothly inhomogeneous anisotropic medium mixed with an anisotropic absorbing dye is analyzed. As such a medium, a twist-oriented nematic liquid crystal with a pleochroic dye was considered. In the geometrical-optical approximation, a system of coupled shortened equations for the Cartesian components of the electric component of the light wave is obtained. A system of coupled complex equations was analytically solved and the behavior of a linearly polarized wave in such a medium was analyzed in the case of both absorption and amplification. An asymmetric effect of these two processes on the spatial dynamics of light propagation in the medium is found.