Conservation of transverse orbital angular momentum for spatiotemporal optical vortices

TL;DR

This paper shows that the transverse orbital angular momentum of spatiotemporal optical vortices is conserved during propagation when standard definitions are used and common approximations are removed, clarifying previous debates.

Contribution

It demonstrates that the total transverse OAM of STOVs is conserved without relying on narrowband or paraxial approximations, using the standard electromagnetic OAM definition.

Findings

Transverse OAM conservation holds beyond narrowband and paraxial limits.

Standard OAM definition suffices for conservation laws.

Previous non-conservation claims are due to approximations.

Abstract

The transverse orbital angular momentum (OAM) of spatiotemporal optical vortices (STOVs) has been a topic of active debate in recent years. Previous studies, relying on narrowband and paraxial approximations, resulted in unprecedented conclusions. Some researchers have proposed that electromagnetic waves require a modified definition of OAM to ensure conservation. In this work, we demonstrate that the transverse OAM of STOVs is highly sensitive to these commonly adopted approximations. Using the standard definition of OAM for electromagnetic waves, we demonstrate that the total transverse OAM is conserved during propagation once the narrowband and paraxial assumptions are removed.