Spin splitting of reflected vortex-beam off hyperbolic-crystal surface

Abstract

We present a theoretical study on the spin-splitting of reflected linearly-polarized vortex beam light beam on the hyperbolic-crystal surface. We use two geometries with the optical axis of hyperbolic crystal in the surface plane, or the geometry-I with the optical axis in the incident plane and the geometry-II with the optical axis vertical to the incident plane. We analytically find that the in-plane or out-plane spin-splitting distance is composed of two parts for any polarization-orientation of the incident beam, i.e., one part originates from the optical-vortex (the intrinsic orbit angular momentum, IOAM) contribution and the other is not related to the optical vortex. The in-plane spin-splitting and out-plane spin-splitting have different responses to the IOAM. For the s-incidence or p-incidence, the in-plane spin-splitting is contributed by only the optical vortex, but the vortex does not support the out-plane spin-splitting. The direction of IOAM determines the sign of the spin-splitting distance. At the critical or Brewster angles, the in-plane or out-plane spin-splitting distance exhibits abnormity, which can have a very large value. For the mixed polarized incidence (containing the s- and p-incidences), the incident IOAM evidently influences on the in-plane and out-plane spin-splitting distances. In some specific orientations of incident beam and at the Brewster angles, the maximum of the spin-splitting distances can touch the amplitude order of 104λ0. Our results are useful for the manipulation of infrared radiations and infrared optical detection.