Vectorial spin Hall effect of light upon tight focusing

The spin Hall effect of light is a manifestation of angular momentum conservation in the process of spin-orbit interaction of light. This optical Hall effect is exhibited in tight focusing of a circularly polarized asymmetric input beam as a shift of the center of gravity of the focal spot in the transverse plane, perpendicular to the direction/axis of symmetry breaking. It is commonly established that the direction of this shift depends on the sign of the spin. Here we show, for the first time, to the best of our knowledge, both analytically and by numerical simulation, that different Cartesian components of an asymmetric circularly polarized focused beam shift in opposite directions by different amounts. Moreover, these shifts depend on the type and degree of the asymmetry and thus can be tuned/controlled. We show how these field components' shifts are related to spin and orbital angular momentum shifts. These findings shed new light on the spin optical Hall effect, facilitate new/simpler ways to measure it, and may broaden the gamut of its applications in manipulation and trapping of particles by light and precision metrology.