## 3 Results and Discussion
In order to investigate the influence of the position at which the attosecond XUV\({}_{1}\) pulse is added with respect to the IR driving field on the optimization procedure, the previous simulations have been repeated by allowing the scan of the position angle \(\theta\) to run only from \(\theta=-180^{\circ}\) to \(\theta=180^{\circ}\), and by keeping the attenuation parameter fixed to \(\alpha=10^{7}\). As shown in Figure 4, an optimal angular position is found in this case at \(\theta=-22^{\circ}\), which results in a perturbation of the IR driving pulse around the end of its first cycle (see Figure 4b). By comparing Figures 2a and 4a, it can be observed that the effect of the shift of the position of the XUV\({}_{1}\) pulse to the higher values of the IR electric field results in a higher enhancement of the optimal spectral amplitude with respect to the original spectrum. Also, since the value of the normalized fitness function \(\chi^{2}\) for the optimal spectrum is not as low in this case (\(\chi^{2}=0.9893\)) as it was in the previous simulations (\(\chi^{2}=08929\)), _i.e._, the achieved spectrum is not as optimal, since the results in Figure 2 have been obtained by using a scan in \(\theta\) that includes the region of the scan considered in Figure 4, the resulting compression in time of the output pulse is not as efficient as in the previous case, as it is clear by comparing Figure 2d with Figure 4d. The time-frequency analysis from this case is shown in Figure 5. We can observe again that the perturbation by the XUV\({}_{1}\) pulse in the optimal configuration induces a considerable suppression of the long trajectories in the enhanced region. Note that the suppression of the long trajectories is however not as complete in this case as it was in the  
Figure 3: (Color online) Time-frequency analysis of the original (**a**) and optimized (**b**) spectra, for the case shown in Figure 2.  
case of Figure 3, but it can still be observed in the photon energy region between 21 and 51 eV, in the 3 last mostly IR contributing cycles. **Figure 4.** (Color online) Optimization of the HHG spectral region 21-51 eV obtained by considering a single feedback loop. The scan in \(\theta\) is from \(\theta=-180^{\circ}\) to \(\theta=180^{\circ}\), and \(\alpha\) is fixed to \(10^{7}\). The value of the normalized \(\chi^{2}\) function is 0.9998 for the original spectrum and 0.9893 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. The optimal value for the angular position results in \(\theta=-22^{\circ}\). (**c**) and (**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 36 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. The results shown in Figures 2 and 4 consider one iteration of the optimization procedure (see Figure 1). For a scan of the attenuation parameter such as the one that has been used (\(10^{6}<\alpha<10^{7}\)), no further optimization is observed in this case by considering additional iteration loops. In order to investigate the capabilities of the multiple iteration procedure, simulations have been performed by considering weak perturbations of the IR driving pulse and by allowing the iteration procedure to run until a convergence of the fitness function is obtained.