Evolution of orbital angular momentum in three-dimensional structured light

TL;DR

This paper demonstrates how three-dimensional structured light beams can exhibit local variations in orbital angular momentum during propagation, revealing complex topological dynamics while conserving total OAM.

Contribution

The study introduces a method to engineer 3D structured light with controllable local OAM variations, advancing understanding of topological charge dynamics in free-space propagation.

Findings

Local OAM can change sign and magnitude along the beam axis.

Topological charge transitions involve vortex creation, movement, and annihilation.

Global OAM remains conserved despite local variations.

Abstract

Light beams with an azimuthal phase dependency of $e^{i\ell\phi}$ have helical phase fronts and thus carry orbital angular momentum (OAM), a strictly conserved quantity with propagation. Here, we engineer quasi three-dimensional (3D) structured light fields and demonstrate unusual scenarios in which OAM can vary locally in both sign and magnitude along the beam's axis, in a controlled manner, under free-space propagation. To reveal the underlying mechanisms of this phenomenon, we perform full modal decomposition and reconstruction of the generated beams to describe the evolution of their intrinsic OAM and topological charge with propagation. We show that topological transition and the associated variation in local OAM rely on the creation, movement, and annihilation of local vortex charges without disturbing the global net charge of the beam, thus conserving the global OAM while varying it locally. Our results may be perceived as an experimental demonstration of the Hilbert Hotel paradox, while advancing our understanding of topological deformations in general.