The matrix solution of the 4x4 problem by the Wentzel-Kramers-Brillouin method for a planar inhomogeneous anisotropic layer

Using methods of classical electrodynamics, we consider the oblique incidence of a plane electromagnetic wave on a twisted planar anisotropic inhomogeneous layer, in which the optical axis changes direction with respect to the plane of incidence. We consider the general case when all components of the permittivity tensor of the medium are nonzero functions of the transverse coordinate in the layer. Using the Wentzel-Kramers-Brillouin method, we obtain in the initial approximation a 4x4-matrix solution for the projections of the fields of an electromagnetic wave in an inhomogeneous anisotropic medium. The matrix reflection coefficients are calculated and shown to depend on the torsion angle of the medium.