## 3 Design for a TW-Scale MIR Waveform Synthesizer for Generating Water Window IAP
### Stabilizing the Delay Jitter and Phase Jitter in the Synthesizer  
Temporal synchronization between each color inside a synthesizer strongly affects the waveform; thus, the temporal synchronization must be stabilized in order to maintain a stable waveform from  
Figure 11: Schematic drawing of a TW-scale MIR waveform synthesizer for generating water window IAPs. CPA, chirped pulse amplifier; SCG, supercontinuum generation; DM, dichroic mirror; DL, delay line; BS, beam splitter; FS, fused silica; CM, chirp mirror; CC, concave mirror; BOC, balanced optical cross-correlator; HWP, half-wave plate. Figure 10: Calculated phase mismatch of a BiBO crystal **(a)** and an LBO crystal **(b)**. The white region indicates almost perfect phase matching. The solid curves show designed chirps for IR pulses to achieve high conversion efficiency as well as a broad spectral bandwidth. For the BiBO crystal, the two cases of chirp designs for the seed pulse are shown by blue and red curves. The horizontal axis indicates the spectral range of the pump laser for the DC-OPA system. shot to shot [36]. As shown in Figure 11, the synchronization can be achieved in two steps [40]. First, by introducing a continuous wave (CW) laser (He-Ne) which passes through each beam path to form an interferometer, the timing jitter between each beam path can be monitored and minimized by introducing active feedback [36] to delay stages DL2 and DL3. Second, the timing jitter between the main pulse and control pulse 2 can be monitored by a balanced optical cross-correlator (BOC) [61,62], and thus can be minimized by introducing further active stabilization (feedback to DL1). Then, the temporal synchronization between each color of the synthesizer is stabilized. Moreover, another parameter that must be considered is the CEP stability. This is because the CEP shift results in shot-to-shot changes in the intensity of IAPs, and multiple busts of IAPs appear at some CEP values [33]. Thus, to obtain a stable IAP for each laser shot, the CEP of each color must be stabilized. First, the seed pulse for the DC-OPA system at \(\sim\)1.9 \(\upmu\)m is generated through difference frequency generation in a standard OPA system (see Figure 11). Thus, the CEP of seed as well as its amplification after the DC-OPA system is passively stabilized. However, owing to timing jitter between the pump and the white-light-generated seed in the standard OPA), the CEP of the seed slightly fluctuates. Thus, feedback utilizing copropagating pump pulses is introduced to minimize the timing jitter (not shown in Figure 11). After the CEP of the seed pulse is stabilized, it is necessary to stabilize the CEP of the 10 Hz pump pulse for the DC-OPA system. In our previous experiment, we demonstrated the stabilization of the CEP of each shot of a TW laser with a 10 Hz repetition rate [58,63] using an indirect CEP stabilization method. In this setup, we employed the same method. Details are shown in Figure 11. A reference pulse (\(\sim\)1 mJ) with a repetition rate of 990 shots/s copropagates with a high-energy (\(\sim\)700 mJ) 10 Hz pulse to from a hybrid pulse train. Thus, these pulses experience exactly the same CEP noises, which are induced by grating vibration in the compressor, temperature changes, air turbulence, and beam-pointing fluctuation. Because the reference pulse energy is more than two orders lower than the high-energy 10 Hz pulse, it does not contribute to amplification in DC-OPA. After the two-stage DC-OPA, the hybrid pulse train is separated from the IR pulses. A small portion (\(\sim\)2 mJ) of the 10 Hz pulse is compressed by an approximately 10-cm-long SF10 bulk (when the LBO crystal is employed in DC-OPA), and is utilized as control pulse 2 in the synthesizer. The main portion of the reference pulse is split into two beams, one beam is used for monitoring the CEP of high-energy 10 Hz pulses after compression by the SF10 bulk.