Orbital angular momentum of spatiotemporal vortices: a ray-mechanical analogy

TL;DR

This paper introduces a mechanical model of spatiotemporal vortex pulses that accurately reproduces their orbital angular momentum characteristics, providing a simplified analogy to complex wave phenomena.

Contribution

A novel mechanical model of STVPs using point particles that replicates wave-based OAM results, clarifying the quantification of transverse orbital angular momentum.

Findings

Mechanical model reproduces wave-based OAM results

Model captures elliptic configurations in space and spacetime

Quantization condition aligns model with wave phenomena

Abstract

Spatiotemporal vortex pulses (STVPs) are wavepackets that carry transverse orbital angular momentum (OAM), whose proper quantification has been the subject of recent debate. In this work, we introduce a simplified mechanical model of STVPs, consisting of a loop of non-interacting point particles traveling at a uniform constant speed but at slightly di!erent angles. We examine di!erent initial conditions for the particle loop, including configurations that are elliptic in space at a given time and configurations that are elliptic in spacetime at a fixed propagation distance. Furthermore, employing a non-uniform mass distribution allows the particle loop to mimic the STVP not only in configuration space but also in momentum space. Remarkably, when supplemented by a semiclassical vorticity quantization condition, our mechanical model exactly reproduces di!erent wave-based OAM results previously reported for paraxial STVPs.