Unified approach towards the dynamics of optical and electron vortex beams

TL;DR

This paper presents a unified geometric framework for understanding the dynamics of optical and electron vortex beams, highlighting their Hall effects and fractional orbital angular momentum states.

Contribution

It introduces a unified approach based on geometric phase to describe vortex beam dynamics, linking optical and electron beams through their spin and vortex structures.

Findings

Paraxial EVBs cause OAM Hall effect in electric fields.

Non-paraxial EVBs induce spin Hall effect with tilted vortices.

Both optical and electron vortex beams can have fractional OAM states.

Abstract

We have proposed a unified framework towards the dynamics of optical and electron vortex beams from the perspective of geometric phase and the associated Hall effects. The unification is attributed to the notion that the spin degrees of freedom of a relativistic particle, either massive or massless, is associated with a vortex line. %The formulation in cylindrical coordinates leads to a local vortex structure related to orbital angular momentum(OAM). Based on cylindrical corodinate formulation, which leads to a local vortex structure related to orbital angular momentum (OAM), it can be shown that when electron vortex beams (EVBs) move in an external electric field paraxial beams give rise to OAM Hall effect and non-paraxial beams with tilted vortices initiate spin Hall effect in free space as well as in an external field. A similar analysis reveals that the paraxial optical vortex beams(OVBs) in an inhomogeneous medium induce OAM Hall effect whereas non-paraxial beams with tilted vortices drive the spin Hall effect. Moreover, both OVBs and EVBs with tilted vortices give rise to OAM states with arbitrary fractional value.