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.

On the Poincaré sphere the spatial evolution of the light’s polarization state has been studied quantitatively in the smoothly inhomogeneous anisotropic media with gyrotropy. The main features of the dependence on the sample’s thickness, the gyration vector and the azimuth of the polarization of the incident linearly polarized wave were revealed. An analytical solution of the system of coupled equations relative to Cartesian components of light's wave electric component obtained by transition to rotating coordinate system has been used for analysis.