Transverse Orbital Angular Momentum of Spatiotemporal Optical Vortices

|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) actually transported by STOVs propagating in free space or non-dispersive media, the most frequent experimental situation. An elliptically symmetric STOV of topological charge l and carrier frequency omega(0) carries an intrinsic transverse OAM per unit energy gamma/=2 omega(0), where gamma is the STOV ellipticity. Intrinsic stands for the OAM about a moving transverse axis passing permanently through the STOV center. For circular STOVs (gamma= 1) this value is half the intrinsic longitudinal OAM of monochromatic light beams of the same charge and frequency. This result agrees with that in Phys. Rev. Lett., Vol. 127, 193901, 2021. The formula (gamma | 1/gamma)2 omega(0) for the intrinsic transverse OAM in Phys. Rev. A, Vol. 107, L031501, 2023 yields infinite values and is not conserved on propagation for particular STOVs. When STOVs propagate losing their elliptical symmetry, they preserve the intrinsic transverse OAM gamma=2 omega(0) despite the phase singularity may split, the split singularities may disappear, or even change the sign of their topological charges. The total transverse OAM of a STOV about a fixed transverse axis crossing its center vanishes because the extrinsic transverse OAM is opposite to the intrinsic OAM, which may preclude applications such as setting particles into rotation, but STOVs could transmit their intrinsic OAM to the photons of other waves, as in nonlinear frequency conversion processes.