## 3 Results and Discussion
The optimal values of the fitness parameters for the 8\({}^{th}\) iteration are in this case \(\alpha=10^{12}\) and \(\theta=365^{\circ}\). In (**d**) the temporal evolution of the intensity of the XUV pulse resulting from the second interaction region after the 8\({}^{th}\) iteration is shown, which is an isolated single cycle pulse centered at 36 eV. The inset in (**d**) shows the value of the normalized \(\chi^{2}\) parameter as a function of the iteration number. From approximately the 8\({}^{th}\) iteration, the duration of the intensity profile of the resulting central XUV pulse does not change substantially. Note that the labels in the vertical axis of (**a**) and (**c**) indicate a logarithmic scale. weak perturbations of the IR pulse seem to be generally more effective. This supports the fact that the short trajectories contribute most on the optimal configuration, since they are more robust against changes in the intensity compared with the long trajectories [2]. In order to compare the effect of a weaker XUV field on the iterative procedure, the previous simulations have been repeated by scanning the attenuation parameter from \(\alpha=10^{11}\) to \(\alpha=10^{12}\) in steps of \(\Delta\alpha=5\times 10^{11}\). The corresponding results are shown in Figure 6c,d. Clearly, the iterative procedure is more effective by _gently_ perturbing the IR field, achieving in this case an isolated single cycle pulse of 120 as at a central photon energy of 36 eV. Weaker XUV intensities have been computed with no further improvements of the optimization in this case. **Figure 2.0** (Color online) Optimization of the HHG spectral region 50-70 eV obtained by considering a single feedback loop. The scan in \(\theta\) is from \(\theta=-720^{\circ}\) to \(\theta=720^{\circ}\), and \(\alpha\) is scanned from \(\alpha=10^{7}\) to \(\alpha=10^{8}\). The value of the normalized \(\chi^{2}\) function is 0.8771 for the original spectrum and 0.2309 for the optimized one. In (**a**) the spectral intensity of the original and optimized spectra are shown, as indicated. The IR driving pulse together with the optimal XUV pulse are shown in (**b**). The amplitude of the IR pulse is normalized, and the one corresponding to the XUV pulse has been rescaled to allow its visualization. In this case the optimal values of the fitness parameters are \(\alpha=10^{8}\) and \(\theta=550^{\circ}\). (**c**,**d**) show the temporal evolution of the intensities of the XUV pulses resulting from the second interaction region, before and after optimization, respectively, which are centered at a photon energy of 60 eV. The inset in (**d**) shows the spectral phase for the original and optimized spectra. Note that the labels in the vertical axis of (**a**) indicate a logarithmic scale. Finally, the optimization of the spectral amplitude has also been considered in a spectral region near the cutoff, as a second significative example, which shows the generality of the control technique. The filtered spectral region in this case is centered at 60 eV with a bandwidth of 20 eV, and the results are shown in Figure 2.1 The numerical algorithm considers only a single feedback loop and scans from \(\alpha=10^{7}\) to \(\alpha=10^{8}\), in steps of \(\Delta\alpha=10^{7}\), and from \(\theta=-720^{\circ}\) to \(\theta=720^{\circ}\), in steps of \(\Delta\theta=10^{\circ}\). The optimal values obtained in this case are \(\alpha=10^{8}\) and \(\theta=550^{\circ}\). Figure 7a shows how the spectral intensity is modified basically near the cutoff, _i.e._, in the spectral region that is to be optimized. As in the case analyzed in Figure 2, where the optimization was considered for a region well in the plateau, the optimal position of the XUV\({}_{1}\) pulse with respect to the IR driving pulse lies near the late temporal wing, as shown in Figure 7b.