Spatiotemporal Vortex Pulses: Angular Momenta and Spin-Orbit Interaction

Recently, spatiotemporal optical vortex pulses carrying a purely transverse intrinsic orbital angular momentum were generated experimentally [Optica 6, 1547 (2019)OPTIC82334-253610.1364/OPTICA.6.001547; Nat. Photonics 14, 350 (2020)NPAHBY1749-488510.1038/s41566-020-0587-z]. However, an accurate theoretical analysis of such states and their angular-momentum properties remains elusive. Here, we provide such analysis, including scalar and vector spatiotemporal Bessel-type solutions as well as description of their propagational, polarization, and angular-momentum properties. Most importantly, we calculate both local densities and integral values of the spin and orbital angular momenta, and predict observable spin-orbit interaction phenomena related to the coupling between the transverse spin and orbital angular momentum. Our analysis is readily extended to spatiotemporal vortex pulses of other natures (e.g., acoustic).