Polarized light in a weakly inhomogeneous anisotropic media with amplification

The problem of the propagation of linearly polarized light in an optically inhomogeneous anisotropic media with amplification (twist-oriented nematic liquid crystal with pleochroic dye) is considered theoretically. The existence of an exact analytical solution of the system of complex equations in this geometry is proven to be related to the deformation of the dielectric constant and gain tensor do not violate the coincidence of their principal axes. The latter is a direct consequence of the guest-host effect known in a liquid crystal. The influence of gain anisotropy on the spatial dynamics of the propagation of ordinary and extraordinary waves in the medium is determined