Polarization helicity and the optical spin-orbit Hall effect.

The optical spin-orbit Hall effect manifests the separation of the spin angular momentum (SAM) and the orbital angular momentum (OAM), yet it can be obtained for the radially polarized light and well controlled by the initial phase of the polarization state which leads to the twist of its distribution. In this paper, we introduce the polarization helicity to characterize the effect of the initial phase of the polarization states in the optical spin-orbit Hall effect. We find the polarization helicity of the radial polarization state can be modulated by changing its initial phase, and the polarization helicity of the high-order polarization state always is zero. We show that the separation magnitude of the SAM and the OAM reach the maximum value when the initial phase of the radial polarization state equals π/4 (or -π/4). The sign of the SAM and the OAM are determined by the polarization helicity of incident light and the anisotropy of uniaxial crystal, and its evolution follows a sinusoidal function. Furthermore, the polarization state of the incident radially polarized light will evolve into the left-handed (or right-handed) elliptical polarization state as the change of the polarization helicity of incident light. Our studies further deepen the understanding of the spin-orbit coupling of the vector beams, and provide a potential technique for modulating the polarization state of the light in uniaxial crystal.