The Hall effects of vortex light in optical materials

Abstract: 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 might differ from the orbital Hall effect as light propagates through optical materials. In this paper, we model optical materials as curved space-time and investigate light propagation in two specific materials by solving the covariant Maxwell equations. We find that the trajectory of light with spin $\sigma$ and intrinsic orbital angular momentum $\ell$ 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 $\sigma$ to angle $\theta_{\sigma,\ell}$ is twice that of the intrinsic orbital angular momentum $\ell$, highlighting their differing effects on light propagation in optical materials. Furthermore, this angle $\theta_{\sigma,\ell}$ could potentially be observed experimentally, enhancing our understanding of the role of angular momentum in light propagation.