Transformation of a vortex polarized beam in an anisotropic medium

We consider a vector cylindrical polarized beam having a symmetric transverse distribution of the amplitude of the electric field vector relative to the axis, incident on planar inhomogeneous anisotropic layer. The beam is presented in the form of a set of plane polarized waves. For each of the waves, based on Maxwell's equations, a matrix solution is obtained for a wave propagating in a gyrotropic medium, as well as a reflection and transmission matrix. The transmitted and reflected beams are restored by the inverse Fourier transform.