Spin Hall effect of fractional order radially polarized beam in its tight focusing

Abstract

Different from the traditional radially polarized beams, the fractional order radially polarized beam possess the symmetry broken structure of the polarization state distribution. The symmetry broken of the optical beams’ intrinsic structure can lead to the spin–orbit coupling of light. In this paper, we investigate the tight focusing of the fractional order radially polarized beam and show some interesting phenomena induced by the symmetry broken structure of the polarization state distribution. Firstly, the intensity and the spin angular momentum density are split in the focal plane, and the focal field intensity distribution can be controlled (split or focused) by modulating the initial phase of the polarization state. Furthermore, just like the spin angular momentum, the orbital angular momentum density also is split into two opposite parts (positive and negative). Though, the evolutions of the spin and the orbital angular momentum are different: as the change of the initial phase of the polarization state, the spin angular momentum distribution just is rotated slightly, yet the orbital angular momentum distribution is reversed. All these phenomena can be considered as the manifestations of the spin Hall effect of the fractional order radially polarized beam. Our results provide further potential applications of the vector beams in the focal field shaping.