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Effects of orbital angular momentum on the pulse shape at the most intense ring of ultrafast vortices

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.