Optical spin Hall effect controlled by tunable orbital angular momentum structure

The broken symmetry of the optical beam's intrinsic structure can lead to the spin-orbit coupling and induce the optical spin Hall effect which displays the spin-dependent transverse deflection of the light. In this paper, we theoretically investigate the optical spin Hall effect in the tight focusing of the radially polarized beam with the trigonometric-function vortex phase, whose intrinsic orbital angular momentum (OAM) structure and the total OAM can be modulated by its trigonometric-function vortex phase. We show that, the broken symmetry of vortex phase structure will lead to the optical spin Hall effect in the focal field, which displays a decentered spatial separation of the different spin angular momentum (SAM) states. More interestingly, with the change of the initial phase of the trigonometric-function vortex phase, the decentered transverse deflection of the different SAM distributions rotates around the optical axis, and the periodic reversion between the positive and the negative SAM states occurs simultaneously. The is because that the total OAM and the intrinsic OAM structure are changed by modulating the parameters of the trigonometric-function vortex phase. Our results provide an effective modulation way of the optical spin Hall effect in the tight focusing of the vortex beams.