## 2 Experiments and Results  
### Front-End and Regenerative Amplifier  
The schematic of the laser system is shown in Figure 1. The master oscillator is a home-built Nd:YVO\({}_{4}\) mode-locked laser, providing up to 280 mW, 8.4 ps laser pulses at a wavelength of 1064 nm and a frequency of 80 MHz. The OPCPA system we serve is seeded by a commercial ultrafast laser (Vitara, Coherent Corporation, Santa Clara, CA, United States) centered at 800 nm. The laser is then converted to 4 \(\upmu\)m via a three-stage OPA based on KTiOAsO\({}_{4}\) (KTA) nonlinear crystals [8]. The 4 \(\upmu\)m laser will serve as the signal pulses in the following OPCPA process. OPA is an interactive process between pump pulses and signal pulses, thus the temporal and spatial overlap between two pulses determines actual gain performance. To achieve perfect temporal synchronization, the Nd:YVO\({}_{4}\) mode-locked oscillator is designed to operate at 80 MHz, which is the same with the commercial 800 nm laser. The commercial 800 nm oscillator is equipped with a synchronization accessory, which can synchronize its oscillator to an external Radio Frequency (RF) source. Part of the Nd:YVO\({}_{4}\) mode-locked laser pulses are utilized and converted into a master signal by a photo-diode. The synchronization accessory will accept the trigger and automatically adjust the length of the cavity to achieve precise frequency synchronization with the master Nd:YVO\({}_{4}\) oscillator. At the same time, the trigger signal from the Nd:YVO\({}_{4}\) mode-locked oscillator is transmitted to a synchronizer, which provides all delay signals for latter electrical devices. Pulses from the Nd:YVO\({}_{4}\) mode-locked oscillator first pass through a half-wave plate (HWP), which works with a polarization beam splitter (PBS), to control the pulse energy injected into the amplification system by rotating the HWP. A Pockels cell (PC) is operated at half-wave voltage with a repetition of 100 Hz, working together with two PBSs and an HWP to achieve pulse picking and isolation from the damage of returning pulses. When the half-wave voltage is applied to the Pockels cell, pulses will maintain p-polarization after passing through the Pockels cell and the HWP. When the  
Figure 1: Schematic of the laser system. HR: high reflector; HWP: half-wave plate; PBS: polarization beam splitter; PD: photo diode; PC: Pockels cell; FR: Faraday rotator; TFP: thin-film plate; QWP: quarter-wave plate; LD: laser diode; VBG: volume Bragg grating. voltage is off, laser pulses will change their polarization after passing through the HWP and exit from either PBS. Before they are injected into the regenerative amplifier, laser pulses of 100 Hz are aligned and expanded to 1.8 mm with a pair of plano-convex lenses, which suit the cavity mode of the regenerative amplifier. Before seeding the regenerative amplifier, laser pulses pass through an optical isolator composed of a PBS, an HWP, and a Faraday rotator (FR) to ensure extra protection for the oscillator. The regenerative amplifier has a linear cavity with a stable cavity mode. The diode-pumped amplification module (Cutting Edge Optronics, RBAT30-1P, St. Charles, MO, USA) has a rod-shaped Nd:YAG crystal with a diameter of 3 mm and a length of 60 mm. When operated at 180 A and 300 Hz with a pulse width of 250 us, this module has a stored energy of 197.7 mJ. In this system, the operating parameters are set at 75 A and 100 Hz with a duration of 250 us, which matches the upper state lifetime of the Nd:YAG gain material. A Pockels cell is operated at quarter-wave voltage with an operation frequency of 100 Hz, whose time delay is precisely controlled by the synchronizer to achieve correct build-up of the pulse energy in the cavity before exiting. To achieve better temporal overlap between pump pulses and signal pulses in the OPA process, pump pulses should also be stretched to tens of picoseconds to suit the temporal width of signal pulses.