## 1 Introduction  
Although continuous light can transport vortices with an arbitrarily high magnitude of the topological charge \(l\), and therefore an arbitrarily high orbital angular momentum (OAM) (see, for example, [1, 2]), pulsed light cannot [3, 4]. This is a consequence of the coupling between the OAM and the temporal degrees of freedom in the pulsed vortices, as described also in [5, 6]. Theoretically, this coupling affects pulsed vortices of any duration and topological charge, but it is only with the advances of the current technology in the generation of increasingly shorter vortices [7, 8, 9, 10, 11, 12, 13, 14, 15] of high quality (without angular and topological charge dispersions), at high powers, and approaching the single-cycle regime, and with the use of these ultrafast vortices in strong-field light-matter interactions for the generation of high harmonics and attosecond pulses with increasingly high OAM [16, 17, 18, 19, 20], that the effects of this coupling will be observable. They will then have an impact on ultrafast vortex applications such as classical and quantum information and entanglement [21, 22, 23, 24], transfer of OAM to matter [25], materials processing [26], or nanosurgery [27]. Understanding the effects of OAM-temporal coupling is also fundamental when using the chirality of these vortices to probe the chiral properties of matter on ultrashort time scales [28, 29]  
Spatiotemporal couplings in ultrashort, pulsed light beams have been known for a long time (see, e.g., [30]), particularly in ultrashort, fundamental Gaussian beams in their various forms [31, 32, 33, 34, 35]. The OAM-temporal coupling is a particular spatiotemporal coupling, namely an azimuthal-temporal coupling, which seems to be rather more pronounced than the radial-temporal coupling in ultrashort Gaussian beams. In [3; 4; 5; 6], the effects of OAM-temporal coupling aew described for the first time in ultrafast vortices shaped as the pulsed Laguerre-Gauss (LG) beams commonly used in the experiments, as well as shaped as pulsed Bessel beams or diffraction-free X-waves. These effects are reviewed in [36], where it turns out that the OAM-temporal coupling manifests itself with different effects in different parts of the vortex. With a given broadband laser source, the carrier frequency experiences an important blue shift with respect to the laser mean frequency, \(\bar{\omega}\) (defined in the standard way [37] as the centroid of the spectral density), in the immediate vicinity of the vortex center, which is accompanied by an increment the number of oscillations, and these two effects are more pronounced as the magnitude of the topological charge is larger [4; 36]. On the contrary, in the ring surrounding the vortex where the pulse energy is maximum, or \"bright\" ring for a time-integrating detector, the mean or carrier frequency is approximately the same as that of the laser source regardless of the topological charge, and the number of oscillations and duration of the pulse, \(\Delta t\) (defined by means of the central second-order moment of the pulse intensity), are larger than those obtainable with the available spectral bandwidth of the laser source, increasing with the magnitude of the topological charge in such a way that the duration is always above the minimum possible duration, \(\sqrt{|l|}/\bar{\omega}\), of an ultrafast vortex of charge \(l\)[3; 5; 36]. In this paper, we point out that the ring of the ultrafast vortex where the pulse energy is maximum is not always of primary interest. High pulse energy may result from long duration with relatively low peak intensity, while as short and as intense as possible pulses (resulting probably in lower energy) are typical demands in ultrafast nonlinear optics experiments, particularly in strong-field laser-matter interactions [16; 17; 18; 19; 20]. In these situations, minimum duration with a given laser source spectrum is obtained with uniform spectral phases, i.e., with transform-limited or unchirped pulses.