Optical spin-orbit Hall effect in a focused field from the Poincaré sphere perspective

The optical Hall effect, which manifests as angular momentum separation resulting from the spin-orbit interaction in photonics, has attracted tremendous interest due to its practical and potential applications. Traditionally, the optical Hall effect only expresses the angular momentum separation of the spin term or the orbital term. Recently, a novel optical Hall effect called the spin-orbit Hall effect has been proposed. This effect exhibits a separation between the spin and orbital angular momentums. Here, we prove numerically that the spin-orbit Hall effect can occur in the tightly focused first-order Poincaré sphere vortex beams. Specifically, the spatial separation of the spin and orbital angular momentum parts appears in the focal plane when the polarization states located at the equator of the first-order Poincaré sphere and the vortex charges are equal to ±1 and when the polarization states located at the surface of the northern hemisphere and the vortex charges are equal to -1, as well as when the polarization states located at the surface of the southern hemisphere and the vortex charges are equal to 1. These findings can be useful in applications such as optical manipulation and sensing.