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

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