Effective ray equations for vortex light and their application in an optical waveguide

Beyond its spin, light can also carry intrinsic orbital angular momentum (IOAM), termed as vortex light. In this study, we derive effective ray equations for vortex light by applying the WKB approximation to the covariant Maxwell equations. According to these equations, the propagation of vortex light can be significantly affected by its IOAM, as suggested by numerous studies. To examine the effects of IOAM, we solve the effective ray equations for vortex light and investigate its ray trajectory within a specific optical waveguide. Our findings indicate that the ray trajectory of vortex light exhibits a divergence perpendicular to the normal propagation plane, akin to the spin Hall effect in light. This divergence, termed as the orbital Hall effect, stems from the IOAM of the light. In this study, the effective ray equations are derived by modeling the interaction between light and media as light's free fall in a curved spacetime. Therefore, observing the orbital Hall effect could not only enhance our understanding of light's spin and IOAM, but also offer novel insights into the coupling between light and gravitational fields.