## 3 Results and Discussion  
The spectrum of the generated SC obtained by the combination of the spectrum analyzers and the FTIR system is presented in Figure 3. The SC covered 380 nm-4 \(\upmu\)m. Due to the ultra-broad bandwidth of the SC, the main difficulty of its characterization using XFROG arose from the necessary phase-matching angle. Since the MIR portion of the spectrum and their application in MIR-OPA were the main interest of our research, we selected the region above 2.5 \(\upmu\)m using a long pass filter. This indeed lifted the strict requirements on the phase-matching. The properties of this region of the SC were characterized with the SFG-XFROG. The obtained results are presented in Figure 5. As can be seen from Figure 5b,d, the retrieved trace and spectrum exhibited fine features. The discrepancy between the measured trace and the retrieved trace indicated the pulse-to-pulse spectral instability of the generated SC pulses. The fine features could not be detected in the measured trace because each spectrum was accumulated over many shots, and it smeared out such features, making the recorded trace look smooth [53; 54]. The information redundancy of the XFROG made it possible for it to recover these features. Indeed, it was shown by [PERSON] et al. that single-shot measurements would reveal similar features in the measured spectrum as well [53]. The spectral phase and stability of the SC from bulk YAG in mid-IR has not been studied so far to the best of our knowledge. Even though the observed instabilities in our results were the intrinsic property of the self-phase modulation process (SPM) in media, the existence of such features may limit the applicability of such SC in fields such as biological applications (e.g., coherent anti-Stokes Raman scattering microscopy) and MIR-OPA systems. Since in the optical parametric amplification process, the amplified signal would inherit seed properties, it is of great importance to minimize the presence of such instabilities in the SC. It has been previously shown that the SCG process is extremely sensitive to the pump pulse spectral properties [55; 56; 57]. Initial instabilities in the pump pulses would result in pulse-to-pulse variation of the SC properties. Due to the fact that the center wavelength of the driving pump in our system fell into the water-absorption region, its spectral profile was highly modulated owing to the water absorption lines, as can be seen in Figure 2. The severity of the spectral modulation was  
Figure 5: (**a**) Measured trace, (**b**) retrieved trace, (**c**) retrieved temporal profile, and (**d**) retrieved spectrum from the SFG-XFROG for SC pulses generated by the output of the regenerative amplifier after 45 round trips. Best error value of 0.011.  
determined by the propagation distance in air. Since we used a regenerative amplifier to generate the pump pulse, we could control the distance that the pulses traveled in the air by changing the number of round trips that the pulses traveled inside the amplifier cavity. It was previously shown in [48] that reducing the number of the round trips would result in an improved spectral profile and bandwidth of the amplified signal obtained from the regenerative amplifier. We reduced the number of round trips of the initial pump pulses in the regenerative amplifier to two-thirds of the initial value (30 rounds) and re-recorded the spectrum of the output pulses. Figure 6 depicts the comparison between the output spectrum for 45 and 30 round trips (RT). Similar to the previously-reported results in [48], an increase in the bandwidth and improvement on the features inside the spectrum can be observed. Using the same pulse energy (15 \(\upmu\)), we focused the initial pump pulses from the regenerative amplifier after 30 round trips into the YAG and similarly characterized the generated SC. The visible part of the SC spectrum did not exhibit significant changes. Once again, the mid-IR region of the SC, which was of particular interest to us, was recorded using the FTIR system.