The precession of vortex-beams in a rotating uniaxial crystal

We consider theoretically and experimentally the precession of the optical vortex in a singular beam propagating nearly perpendicular to the crystal optical axis, the beam and the crystal axis rotating with different angular velocities. The precession is a result of different scales along the major axes in a uniaxial crystal. Also we analyze the properties of the optical reducer consisting of two rotating crystals and a wave retarder between them permitting us to control the form of the vortex trajectory.