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, which is relevant at low photon numbers in quantum optics, and also in the highly nonlinear process as the high-harmonics generated with twisted beams. These results have also applications as multi-level classical and quantum free-space or satellite, communications, spectroscopy, and high-harmonic generation.
Miguel A. Porras and C. Conti in arXiv:1911.1222