## 2 Design and Performance of Ultra-Intense \"J-KAREN\" Laser System
### OPCPA Preamplifier  
In the second CPA stage, the OPCPA preamplifier replaces the more conventional regenerative amplifier in order to maintain the high contrast and broad spectral bandwidth. The cleaned pulses of higher energy are temporally stretched (chirped) in a grating-based all-reflective Offner stretcher [52] is composed of gratings with a groove density of 1480 grooves/mm, a 1000 mm radius of curvature concave mirror (320 mm diameter), a \(-\)500 mm radius of curvature convex mirror (160 mm long, 15 mm high), and a roof mirror. Immediately downstream of the stretcher, the AOPDF controls spectral phase prior to further amplification. A Faraday isolator and the Pockels cell with a pair of polarizers provide needed optical isolation between the oscillator and the amplifiers. The stretched pulses with duration \(\sim\)1 ns and energy \(\sim\)1.5 \(\upmu\)J are introduced into the three-stage OPCPA preamplifier, consisting of three type I \(\beta\)-barium borate (BBO) crystals. Parametric fluorescence is known to degrade contrast in the high-gain regime where seed energies are low (of the order of nanojoules) and pump intensities are high. Therefore, contrast improvement can be achieved with higher seed energy levels (\(\sim\)1.5 \(\upmu\)J) and a lower OPCPA gain requirement [53; 54; 55]. Our OPCPA preamplifier consists of three (BBO) crystals. A BBO crystal is chosen as the nonlinear crystal because of its high effective nonlinear coefficient. The size of the first two crystals is \(7\times 7\times 19.5\) mm, and that of the third crystal is \(7\times 7\times 16\) mm. Both antireflection-coated (AR-coated) crystals are cut at 23.8\({}^{\circ}\) to maximize the gain bandwidth and to facilitate type I noncollinear angular phase matching with an external angle between the seed and the pump of 3.9\({}^{\circ}\). Each crystal is mounted on a precision rotation stage to optimize the angle between the input beams and the crystal. A common pump pulse is used for the OPCPA to reduce the system size and complexity. Each crystal has a 2\({}^{\circ}\) wedged output face to suppress intracavity oscillation [11; 35; 56]. The pump pulses for the OPCPA are generated by the second harmonic of a commercial Q-switched single-longitudinal mode seeded Nd:YAG laser (Spectra-Physics, GCR-150), producing 220 mJ (532 nm) of energy with 5.5 ns (FWHM) )pulse duration at 10 Hz. The output temporal profile is smooth and near-Gaussian and the spatial profile almost a flattop. Pump pulses are relayed to a plane between the three BBO crystals with a vacuum image telescope that precisely matches the pump beam diameter to that of the seed (\(\sim\)4.1 mm at the 1/e\({}^{2}\) intensity points). Figure 2 shows the amplification gain _versus_ pump energy in our OPCPA system. OPCPA gain is measured with a photodiode and a calibrated neutral density filter set. With an energy of 1.5 \(\upmu\)J, the input seed intensity is near 12 kW/cm\({}^{2}\). Most OPCPA systems operate with very high gain, of the order of 10\({}^{7}\)-10\({}^{11}\)[56; 57; 58; 59; 60]. However, our OPCPA provides a maximum gain of only \(\sim\)6 \(\times\) 10\({}^{3}\) with an incident pump fluence of 0.8 J/cm\({}^{2}\) (corresponding to a pump energy of 107 mJ) and amplifies the seed pulses to \(\sim\)10 mJ. Parametric fluorescence can deteriorate the temporal pulse contrast when using the low seed energy in combination with the high pump intensities that are typical. Temporal pulse contrast can, therefore, be improved by operating the OPCPA in a higher seed energy, low-gain mode. Pump and seed pulses are synchronized in time by a Thales Laser ISEO unit, with a characteristic timing jitter of less than \(\pm\)0.5 ns in our system. Automatic beam alignment system for seed beam is  
used to implement beam adjustment to improve long-term stability. We obtain a measured shot-to-shot energy stability over 10 min of \(\pm\)5% in our OPCPA system.