Effects of the Coupling between the Orbital Angular Momentum and the Temporal Degrees of Freedom in the Most Intense Ring of Ultrafast Vortices

Abstract

It has been recently shown that the orbital angular momentum (OAM) and temporal degrees of freedom in ultrafast (few-cycle) vortices are coupled. This coupling manifests itself with different effects in different parts of the vortex, as has been shown for the ring surrounding the vortex where the pulse energy is maximum, and also in the immediate vicinity of the vortex center. In may applications, however, the ring of maximum energy is not of primary interest, but that where the pulse peak intensity is maximum, which is particularly true in nonlinear optics applications such as the experiments with ultrafast vortices exciting high harmonics and attosecond pulses carrying also OAM. This article describes the effects of the OAM-temporal coupling at the ring of maximum pulse peak intensity, which does not always coincide with the ring of maximum pulse energy. We find that there exists an upper bound to the magnitude of the topological charge that an ultrafast vortex with prescribed pulse shape at its most intense ring can carry, and vice versa, a lower bound to the duration of the pulse at the most intense ring for a given magnitude of the topological charge. These bounds imply that with a given laser source spectrum, the duration of the synthesized ultrafast vortex increases with the magnitude of the topological charge. Explicit analytical expressions of ultrafast vortices containing these OAM-temporal couplings are given that can be of interest in a variety of applications, particularly in the study of their propagation and interaction with matter.

General laws of the propagation of ultrafast vortices in free space

“…Indeed the propagation dynamics of UFVs differs in substantial aspects from that of fundamental pulses without OAM because of a strong coupling between the temporal and OAM degrees of freedom in the UFV, as reported in [30][31][32][33][34] for Laguerre-Gauss-type UFVs and in [34][35][36] for nondiffracting X-type vortices. The effects of this coupling remain small, but are observable, at low topological charges and/or many-cycle durations, but become large and dominate the propagation dynamics when the single-cycle and high topological charge regimes are approached.…”

“…Given these huge experimental efforts, it is somewhat surprising the little amount of theoretical work on the propagation characteritics of UFVs [25][26][27][28][29][30][31][32][33][34][35][36], even in the a priori simplest situation of free-space propagation. A comprehensive theory of the propagation dynamics of UFVs, similar to that developed a few decades ago for fundamental, few-cycle pulses without OAM [37][38][39][40][41][42][43][44] when the single-cycle regime was reached [45], is still pending.…”