Reflection and Transmission of a Polarized Vortex Beam by an Inhomogeneous Anisotropic Plane Layer

We consider oblique incidence of a vortex polarized beam on an inhomogeneous anisotropic plane layer of an artificial metamaterial. A matrix model of beam reflection from the layer boundaries and of its propagation in an inhomogeneous anisotropic medium is developed on the basis of the classical equations of electrodynamics. Using the forward Fourier transform, the beam is represented as a set of plane monochromatic waves, which have different directions of the wave vector and different directions and amplitudes of the electric fields. The obtained matrix solution allows one to calculate projections of the vectors of the electromagnetic wave inside an inhomogeneous anisotropic medium. The reflection and transmission matrices for an inhomogeneous anisotropic layer are found for the plane waves which have different propagation directions and constitute the beam. The reflected beam is reconstructed by means of the inverse Fourier transform. The distributions of the components of the electric field over the cross section of the reflected beam at oblique incidence and the phases of these components are calculated. The cross correlation functions are calculated for the components of the electric field of the beam. The Fourier series of the cross correlation function shows that components with a variation of the topological charge by ±1 appear in the reflected beam.