Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium

We have found the asymmetric splitting of a high-order circularly polarized vortex-beam in a uniaxial crystal. The l-order vortex-beam splits into the same one and the beam with the l−1 vortices at the beam axis while one optical vortex is shifted along the direction perpendicular to the inclination plane of the beam. Such a vortex displacement causes the transverse shift of the partial beam. We consider this effect both in terms of the conservation law of the angular-momentum flux and on the base of the solutions to the paraxial wave equation. We revealed that the transverse shift of the crystal-traveling beam depends on neither a magnitude nor a sign of the vortex topological charge being defined only by a handedness of the initial circular polarization and a sign of the inclination angle of the beam.