## 2 Design and Performance of Ultra-Intense \"J-KAREN\" Laser System
### Large-Aperture Ti:sapphire Final Amplifier  
The pulses then undergo further amplification in the final amplifier, which uses a large-aperture 80 mm diameter Ti:sapphire crystal that is pumped with a frequency-doubled large-aperture high-energy glass laser. Our pump laser has single-pass master oscillator power amplifier architecture, operated at a few shots per hour. In the pump system, a long cavity Q-switched Nd:YAG master oscillator generates \(\sim\)200 mJ pulses of \(\sim\)28 ns duration (FWHM) at a 1064 nm wavelength, which matches the emission band of the Nd:silicate-glass rod amplifiers. The duration of the oscillator pulse should be as long as possible to enable high-output fluence operation without optical damage. The oscillator output is shaped with a soft aperture to a near flat-top intensity distribution and then preamplified to \(\sim\)1 J by a 9 mm diameter Nd:YAG rod preamplifier. The pulse energy is further increased in a chain of 16, 25, 45, and 64 mm diameter Nd:glass rod amplifiers to \(\sim\)180 J. At appropriate locations, spatial filters and optical isolators (a pair of Faraday isolators) are used to suppress reflections that can cause damage upstream along the laser chain. Figure 4: Measured output energy from Ti:sapphire power amplifier _versus_ pump energy. The 1064 nm output pulses are down collimated to a \(\sim\)40 mm diameter and are subsequently frequency doubled to 532 nm with two 60 mm \(\times\) 60 mm Type II KD\({}_{2}\)PO\({}_{4}\) (DKDP) crystals (Cleveland Crystals, Inc., Ohaio, USA). To achieve high conversion efficiency, we have used a quadrature arrangement for second harmonic generation (SHG), in which two nonlinear crystals cut for type II interaction are placed in series but are oriented perpendicular to each other [65, 66]. DKDP crystals are chosen because of the easy availability in large sizes. The input and output faces of the crystals are SolGel AR coated for both 532 and 1064 nm laser radiation. In the pump system, the maximum green pulse energy of 96 J is generated with an incident fundamental energy of 177 J at 504 MW/cm\({}^{2}\), corresponding to SHG efficiency of 54%. Dichroic mirrors separate the green and unconverted fundamental laser beams. With a half-wave plate and a thin-film polarizer, we generate an energy-balanced pair of green pump pulses from the DKDP crystals to provide similar energies for pumping both sides of the Ti:sapphire crystal. The two pulses are delivered to the Ti:sapphire crystal using reflective optics, image relaying, and DOEs (SILIOS Technologies). The polarization plane for one side is suitably oriented with respect to the Ti:sapphire crystal using a half-wave plate. We have selected DOEs for beam homogenization because they could produce a circular top-hat profile with sharp edges and they were readily available in the required size [10, 49]. The clear aperture of our AR-coated DOEs is 80 mm. Each DOE is divided into about 200 subcells, which are all expanded onto the same area at the target plane that lies in the Ti:sapphire crystal. The eight-level striped pattern corresponding to the engravings in the subcells in 1 mm thick fused silica material are specially calculated for our requested shape [67]. The diffraction efficiency of DOE is measured to be 82%. Because of some optical components, such as half-wave plates, dichroic mirrors, thin-film polarizers, reflective optics, and relaying optics [68], the measured transmittance efficiency from the second DKDP to Ti:sapphire crystal, including the DOE efficiency, is 67% in our case. The undiffracted and on-axis focused beams are dumped. The pulses from power amplifier are up-collimated and enter the three-pass Ti:sapphire final amplifier. The Ti:sapphire crystal is a commercially available disk (Crystal Systems, Inc.) that is 80 mm in diameter and 33 mm thick. The crystal is AR coated on two main surfaces, but not polished on the cylindrical outer surface.