The Hall Effects of Vortex Light in Optical Materials

For light, its spin can be independent of the spatial distribution of its wave function, whereas its intrinsic orbital angular momentum does depend on this distribution. This difference suggests that the spin Hall effect may differ from the orbital Hall effect as light propagates through optical materials. Herein, optical materials are modeled as curved spacetime and light propagation in two specific materials by solving the covariant Maxwell equations is investigated. It is found that the trajectory of light with spin σ and intrinsic orbital angular momentum ℓ deviates from that of light without angular momentum ($\sigma =0$ and $\ell =0$) by an angle ${\theta }_{\sigma ,\ell }\propto 2\sigma +\ell$. In particular, the contribution of spin σ to angle ${\theta }_{\sigma ,\ell }$ is twice that of the intrinsic orbital angular momentum ℓ, highlighting their differing effects on light propagation in optical materials. Furthermore, angle ${\theta }_{\sigma ,\ell }$ can potentially be observed experimentally, enhancing the understanding of the role of angular momentum in light propagation.