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

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.