The Mechanism of the Formation of the Spin Hall Effect in a Sharp Focus

Abstract

We have shown how the spin Hall effect is formed in a tight focus for two light fields with initial linear polarization. We have demonstrated that an even number of local subwavelength regions appear in which the sign of the longitudinal projection of the spin angular momentum (the third Stokes component) alternates. When an optical vortex with topological charge n and linear polarization passes through an ideal spherical lens, additional optical vortices with topological charges n + 2, n − 2, n + 1, and n − 1 with different amplitudes are formed in the converged beam. The first two of these vortices have left and right circular polarizations and the last two vortices have linear polarization. Since circularly polarized vortices have different amplitudes, their superposition will have elliptical polarization. The sign of this elliptical polarization (left or right) will change over the beam cross section with the change in the sign of the difference in the amplitudes of optical vortices with circular polarization. We also have shown that optical vortices with topological charges n + 2, n − 2 propagate in the opposite direction near the focal plane, and together with optical vortices with charges n + 1, n − 1, they form an azimuthal energy flow at the focus.

Keywords

• optical vortex
• optical Hall effect
• cylindrical vector beam
• Richards–Wolf formula