## 3 Characterization of Front-End Light Source Performance  
### Spectro-Temporal Characterization  
The pulse contrast improvement cannot be measured precisely with enough dynamic range at this energy level. However, as previously demonstrated [26], the extinction ratio of the polarization management is the only limit to the overall contrast enhancement. In the current system, we measured an extinction ratio of 4 orders of magnitude, which, starting from a contrast ratio of the order of 10\({}^{8}\)[24], leads us to infer the temporal contrast of front-end system to be of the order of 10\({}^{12}\). Figure 2: **(a)** Initial fundamental spectral amplitude (shaded area) and phase (dashed black line), measured after the TGC. XPW spectrum (red line) with a Gaussian fit (dashed blue line, 105 nm FWHM); **(b)** Density plot of XPW spectra (averaged over 50 shots) recorded every 5 nm over 90 nm. Lower spread corresponds to higher stability; **(c)** Temporal intensity profile and residual spectral phase of the compressed XPW pulse measured by SRSI. The initial fundamental and XPW spectra are compared in Figure 2(a). The initial laser spectrum is shaped into a perfectly Gaussian spectrum during the nonlinear process. This feature is a direct consequence of the XPW temporal cleaning properties [27, 28, 29]. This is an essential point for the final spatio-temporal quality of the output pulses. Moreover, extensive spectral broadening is measured. The calculated FWHM spectral bandwidth is increased by a factor of 2.4. The expected temporal shortening (the ratio of input laser pulse duration over output XPW pulse duration using Fourier-transform limited values) is around 3. The discrepancy comes from the differing spectral intensity profiles. The output spectrum supports sub-10 fs duration (8.6 fs Fourier transform limited). At lower efficiencies, for an unchirped pulse, spectral broadening following XPW is a direct consequence of the shortening of the pulse duration by a factor of 1.7 [23]. Here, the higher XPW efficiency is associated with important self-phase modulation (SPM) on the fundamental beam, and thus significant spectral broadening, a feature that is transferred onto the XPW wave. Simultaneous pulse shortening during the process prevents the XPW pulse from spectral and temporal distortions [30]. The higher the XPW efficiency, the more pronounced the broadening. This is illustrated in Figure 3, displaying the spectral evolution of the fundamental and XPW waves with respect to input pulse energy. While the fundamental spectrum exhibits features typical of SPM, the process provides smooth and homogeneous broadening of the XPW spectrum. These clean spectral features indicate that SPM on the XPW beam is negligible. Although significant spectral broadening and reshaping during XPW have already been observed before [27], they are particularly emphasized here. This results from the combination of high efficiency and perfect spectral phase correction thanks to the spectral phase-loop optimization of the [PERSON] device (Figure 2(a)). In order to characterize pulse fidelity of the front-end, we then verified the spectral repeatability. The short-term stability is measured by the acquisition of 500 consecutive spectra of the amplified and XPW pulses. Despite the fact that broadening is due to nonlinear effects, spectral stability is not degraded after XPW and remains below 2% RMS across the entire spectrum. The long-term stability was monitored by recording the spectrum at regular intervals over 90 nm, showing only minor variations (Figure 2(b)). The available spectral bandwidth for further amplification will therefore not be significantly affected by the weak energy fluctuations of the input amplifier beam. Figure 3: Fundamental (measured after the nonlinear interaction) and XPW normalized spectra as a function of laser input energy. Each spectrum is averaged over 500 shots.