## 3 Design for a TW-Scale MIR Waveform Synthesizer for Generating Water Window IAP
### TW-Class MIR Laser Source Based on DC-OPA  
In our recent work, we successfully generated an IR laser with 100-mJ-class energy, a TW-class peak power IR laser, and a 10 Hz repetition rate [52] using a DC-OPA [53; 54; 55; 56; 57]. The nonlinear crystals employed in the DC-OPA system were \(\beta\)-BaB\({}_{2}\)O\({}_{4}\) (BBO) crystals. Using this laser source, laser pulses with three colors, as shown in Figure 9, can be provided to construct a waveform synthesizer. The two colors of the IR pulses labelled main pulse and control pulse 1 in the synthesizer are flexibly tunable in the ranges of 1.6-2.4 \(\upmu\)m and 1.2-1.6 \(\upmu\)m (these two colors are generated in pairs, one is the same as the seed used for DC-OPA, the other is obtained from difference frequency generation (DFG)), respectively, which is very helpful for manipulating the waveform in the synthesizer by tuning the wavelength [33]. The third color, control pulse 2 is provided by a Ti:sapphire chirped pulse amplifier (CPA), which is  
Figure 8: (a,b) show IAPs calculated from spectra in Figure 7b,c, respectively, generated by the three color synthesizer. Red curves indicate obtained IAP durations while black curves indicate TL durations. Figure 7: (a) intensity (\(E^{2}\)) of electric fields of three-color synthesizer (orange shaded) and a 0.99-cycle laser pulse at 1.73 \(\upmu\)m (green). HH spectra after 60-mm-long (b) and 70-mm-long (c) gas cells. Transmission of Sn filters are plotted in (b,c). also a pump source for the DC-OPA system. The duration of the compressed pulse with a stabilized CEP is \(\sim\)28 fs (FWHM) [58]. However, the durations of the main pulse and control pulse 1 are 40-50 fs (FWHM), which are longer than those in our simulation in Section 2, which required a pulse duration of 30 fs (FWHM). We find that BiB\({}_{3}\)O\({}_{6}\) (BiBO) [59; 60] and LiB\({}_{3}\)O\({}_{5}\) (LBO) crystals are suitable for generating TW-class IR pulses by a DC-OPA system with shorter durations (shorter than five optical cycles) near 1.95 \(\upmu\)m and 1.35 \(\upmu\)m. We calculate phase-matching results over a broad bandwidth which are shown in Figure 10a,b as two-dimensional plots for BiBO and LBO crystals with cutting angles of \(\theta=11^{\circ}\) (XZ plane) and \(\phi=15^{\circ}\) (XY plane), respectively. A smaller phase mismatch indicates better phase matching. For the BiBO crystal, the two designed phase-matching conditions (the designed signal chirp is the same as that of the seed) in experiment are plotted as blue and red curves. For the LBO crystal, the designed phase-matching condition (red) in the experiment follows the optimal phase-matching. Thus, we can use both BiBO and LBO crystals for the DC-OPA system to create IR pulses for the synthesizer. Because LBO has a much higher damage threshold as well as a very large aperture, it is the preferred crystal for our DC-OPA system. When we employ a LBO crystal with a 30 mm aperture, the durations of the pump and seed pulses are \(\sim\)2 ps. Moreover, in Figure 10, the chirp signs of the pump and seed are opposite under an optimized phase-matching condition. Hence, we can employ negative and positive chirps for the pump and seed pulses in the DC-OPA system, which are precisely controlled by changing the grating separation and using an acousto-optic programmable dispersive filter (AOPDF), respectively. Then, the DFG pulse is negatively chirped. With these chirp signs, we can compress the pulses using bulk materials after the DC-OPA (e.g., fused silica for the main pulse and SF10 for control pulses), which do not deteriorate the stability of CEPs. Figure 9: Hundred millijoule and multi-TW-class MIR fs pulses generated by a BBO-crystal-based DC-OPA system with flexible tunability in the range of 1.2–2.4 \(\upmu\)m. Main pulse and control pulse 1 are generated in pairs in the DC-OPA system through parametric amplification. The pulse energy and spectrum at each central wavelength are shown by red dots and shaded curves, respectively.