Couplings between the temporal and orbital angular momentum degrees of freedom in ultrafast vortices with propagation-invariant temporal shape

TL;DR

This paper investigates the intrinsic coupling between temporal and orbital angular momentum degrees of freedom in ultrafast vortices, revealing universal space-time correlations and bounds related to vortex topological charge, with implications for various optical applications.

Contribution

It generalizes and unifies previous results to show universal space-time correlations in propagation-invariant ultrafast vortices with OAM, highlighting a structural space-time coupling.

Findings

Pulse duration bound by topological charge in high-intensity regions

Blue-shift and increased carrier oscillations near vortex in low-intensity regions

Universal space-time correlations in propagation-invariant ultrafast vortices

Abstract

In any form of wave propagation, strong spatiotemporal coupling appears when non-elementary, three-dimensional wave-packets are composed by superimposing pure plane waves, or spontaneously generated by light-matter interaction and nonlinear processes. Ultrashort pulses with orbital angular momentum (OAM), or ultrashort vortices, furnish a critical paradigm in which the analysis of the spatiotemporal coupling in the form of temporal-OAM coupling can be carried out accurately by analytical tools. By generalizing and unifying previously reported results, we show that universal and spatially heterogeneous space-time correlations occur in propagation-invariant temporal pulses carrying OAM. In regions with high intensity, the pulse duration has a lower bound fixed by the topological charge of the vortex and such that the duration must increase with the topological charge. In regions with low intensity in the vicinity of the vortex, a large blue-shift of the carrier oscillations and an increase of the number of them is predicted for strongly twisted beams. We think that these very general findings highlight the existence of a structural coupling between space and time. These results have also applications in free-space communications, spectroscopy, and high-harmonic generation.