Transverse orbital angular momentum of spatiotemporal optical vortices

Abstract

Spatiotemporal optical vortices (STOVs) are electromagnetic wave packets that transport a phase line singularity perpendicular to their propagation direction. We address the problem of the transverse orbital angular momentum (OAM) ``per photon" actually transported by STOVs propagating in free space or non-dispersive media, the most frequent experimental situation. Unlike longitudinal vortices in monochromatic light beams, STOVs do not carry any net transverse OAM about a fixed transverse axis crossing its center. However, STOVs transport an intrinsic transverse OAM per photon about a moving, transverse axis through its center, and an opposite extrinsic transverse OAM. Their applications would thus preclude setting particles at rest into rotation, but STOVs could transmit their intrinsic transverse OAM to photons of other waves. The intrinsic transverse OAM per photon of an elliptically symmetric STOV of frequency ${\omega }_0$ and topological charge $l$ is $\gamma l/2{\omega }_0$, where $\gamma$ is the STOV ellipticity. Thus circularly symmetric STOVs ($\gamma =1$) carry half the intrinsic longitudinal OAM of circularly symmetric monochromatic light beams with a vortex of the same $l$ and ${\omega }_0$. We show that the formula $(\gamma +1/\gamma )l/2{\omega }_0$ for the intrinsic transverse OAM in Phys. Rev. A 107, L031501 (2023) yields infinite values and is not conserved on propagation for a particular STOV. When STOVs lose their elliptical symmetry upon propagation, they preserve the intrinsic transverse OAM $\gamma l/2{\omega }_0$ despite the phase singularity may split, the split singularities may disappear, or even change the sign of their topological charges.

8 pages, 3 figures

References in corpus (7)

• Spatio-temporal vortex beams and angular momentum
• Roadmap on spatiotemporal light fields
• Spatiotemporal Vortex Pulses: Angular Momenta and Spin-Orbit Interaction
• Orbital angular momentum of optical, acoustic, and quantum-mechanical spatiotemporal vortex pulses
• Spatiotemporal optical vortex solitons: Dark solitons with transverse and tilted phase line singularities
• Second harmonic generation of spatiotemporal optical vortices and conservation of orbital angular momentum
• Transverse Shifts and Time Delays of Spatiotemporal Vortex Pulses Reflected and Refracted at a Planar Interface

Cited by in corpus (6)

• Observation of acoustic spatiotemporal vortices
• Generation of Spatiotemporal Vortex Pulses by Simple Diffractive Grating
• Spatio-temporal optical vortices: principles of description and basic properties
• On the Ehrenfest theorem and centroids of relativistic particles
• Spatiotemporal optical vortex (STOV) polariton
• Orbital angular momentum of spatiotemporal vortices: a ray-mechanical analogy