The Hall effects of vortex light in optical materials

TL;DR

This paper models light propagation in optical materials as curved space-time, revealing that spin and orbital angular momentum cause distinct deviations in light trajectories, with potential for experimental observation.

Contribution

It introduces a covariant Maxwell equation approach to distinguish the effects of spin and orbital angular momentum on light's trajectory in optical materials.

Findings

Light with spin and orbital angular momentum deviates from zero angular momentum light.

Spin contributes twice as much as orbital angular momentum to the deviation angle.

The deviation angle could be observed experimentally.

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.