Energy and photon centroids of spatiotemporal light pulses and consequences for their intrinsic orbital angular momentum

TL;DR

This paper derives a unified formalism for energy and photon centroid positions in spatiotemporal light pulses, clarifying their dynamics and implications for intrinsic orbital angular momentum (OAM) in complex optical fields.

Contribution

It introduces a comprehensive framework for analyzing energy and photon centroids in spatiotemporal pulses, revealing limitations in defining intrinsic OAM per photon.

Findings

Centroids follow distinct propagation dynamics influenced by pulse structure.

Intrinsic OAM cannot be assigned to individual STOV photons as expectation values.

Implications for quantum optics and light-matter interaction experiments.

Abstract

An ongoing debate surrounding the intrinsic transverse orbital angular momentum (OAM) attributed to spatiotemporal optical vortex (STOV) light pulses has raised the energy and photon-density centroids as two alternative frameworks to define the center of a free electromagnetic wavepacket. We herein derive, within a single formalism, lowest-order expressions for the positions and velocities of both centroids, directly applicable to an arbitrary scalar, near-paraxial and quasi-monochromatic pulse envelope formulated in space-time. Examining pulses with structures including temporal chirp, wavefront rotation, Gaussian-type STOVs and tilted lobulated profiles, we illustrate general principles underlying the shifts and propagation dynamics of the two centroids, and discuss how these properties underpin the value and conservation of intrinsic OAM referenced to either centroid. Finally, despite widespread use of the notion of intrinsic OAM "per photon", we argue that in neither framework could individual STOV photons be said to carry a well-defined quantum of intrinsic transverse OAM, as such quantities do not write as expectation values of a single operator for which STOV states could form a basis of orthogonal eigenmodes. This contrasts with the well-established quantization scheme for the total longitudinal OAM of light in spatial vortex beams, bearing implications for the interpretation of future experiments involving STOV pulses in quantum optics, nonlinear wave-mixing or light-matter interactions.