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.

Shaping focal field by grafted polarization.

In this paper, we propose a novel (to our knowledge) vector beam by combining the radially polarized beams with the different polarization orders, which is called the grafted polarization vector beam (GPVB). Compared with the tight focusing of traditional cylindrical vector beams, GPVB can present more flexible focal field patterns by adjusting the polarization order of two (or more) grafted parts. Moreover, because the GPVB possesses the non-axisymmetrical polarization state distribution, which will lead to the spin-orbit coupling in its tight focusing, it can obtain the spatial separation of spin angular momentum (SAM) and orbital angular momentum (OAM) in the focal plane. The SAM and the OAM are well modulated by adjusting the polarization order of two (or more) grafted parts. Furthermore, we also find the on-axis energy flow in the tight focusing of the GPVB can be changed from positive to negative by adjusting its polarization order. Our results provide more modulation freedom and potential applications in optical tweezers and particles trapping.