Geometric spin Hall effect of a laser beam beyond the paraxial approximation

Abstract

An intriguing spin-orbital angular momentum interaction, called the geometric spin Hall effect of light (GSHEL), has aroused much interest and manifests itself as a transverse shift. The GSHEL of the classical optical field is independent of the beam size. In this paper the GSHELs of the vortex vector continuous wave (VVCW) and vortex ultrashort pulsed beam (VUPB) are systematically analyzed beyond the paraxial approximation. The analytical expression of the transverse shift of the VVCW is obtained. Evidently, the magnitude of the transverse shift depends on the ratio of the beam waist to the wavelength. The transverse shift can be effectively enlarged by narrowing the beam waist even to the order of more than $10\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\text{m}$. This intriguing phenomenon is caused by the stronger spin-orbital interaction induced energy flow in the nonparaxial regime. Furthermore, the GSHEL of the VUPB is also explored. The pulse duration time strongly affects the distribution of the phase. The singularities play a crucial role in altering the orientation of the electric field. As a result, the VUPBs with different pulse duration time have different magnitudes of the GSHEL. These results may find significant applications in the investigation of the particle manipulation, microscopic imaging, and ultrashort optics.