Understanding of transverse spin angular momentum in tightly focused linearly polarized vortex beams.

Spin angular momentum (SAM) is widely used in spin-dependent unidirectional optical interfaces, optical manipulation, integrated optical signal processing, laser structuring and other fields, but its physical mechanism has not been fully understood so far. In this work, we investigate the three-dimensional (3D) SAM in tightly focused x-polarized first-order vortex beams from the perspectives of light field itself, phase distribution, and focusing propagation. It is shown that the distribution of three orthogonal components of SAM at the focal plane has pseudo two-fold rotational symmetry, because the cycloidal rotation of the electric field of the tightly focused vortex beam is opposite. The 3D SAM distribution in the focal region is visualized by mapping the 3D distribution of state of polarization (SoP). In addition, a principle experimental method for identifying the transverse SAM by using the direction of particle's rotation axis in optical tweezers is proposed.