## 2 Design and Performance of Ultra-Intense \"J-KAREN\" Laser System
### Cryogenic-Cooled Ti:sapphire Power Amplifier  
A conventional four-pass Ti:sapphire preamplifier further amplifies the broadband pulse energy. The preamplifier uses a 20 mm diameter Ti:sapphire crystal pumped by the second harmonic of a commercial Q-switched Nd:YAG laser (Continuum, Powerlite 9010) that delivers \(\sim\)700 mJ (532 nm) pulse energy at 10 Hz. The pump beam is split into two beams that are relay imaged to opposite faces of the Ti:sapphire crystal. Image relaying is used throughout the optical train to minimize the diffractive effects, maintain beam uniformity, and to optimize coupling efficiency between the pump and the signal beams. Preamplification to a maximum energy \(\sim\)220 mJ is obtained.  
The pump laser also heats the Ti:sapphire crystal. Originating mainly from the difference between the pump and the amplified beam photon energies (quantum defect), heating generates a spatial refractive index gradient in the crystal, which is a source of unwanted thermal lensing of the amplified beam. Thermal lensing in Ti:sapphire gain media can be major problem if unaddressed in preamplifier design. So, in this Ti:sapphire preamplifier, the appropriate beam divergence is introduced (by adjusting the lenses separation in the upstream Galilean beam expander at the OPCPA exit), which matches the thermal focusing power of the Ti:sapphire preamplifier to counteract the thermal lens effect in the crystal. The input seed laser beam diameter is larger than the pump beam diameter. However, thermal focusing reduces the seed beam diameter to a collimated \(\sim\)6 mm after four-pass amplification. At the Ti:sapphire preamplifier exit, the beam is subsequently up-collimated to an \(\sim\)18 mm diameter and introduced into the four-pass cryogenically cooled Ti:sapphire power amplifier, which uses a 40 mm diameter AR-coated Ti:sapphire crystal. The power amplifier is pumped at 10 Hz by \(\sim\)6.5 J of second harmonic energy delivered by six commercial frequency-doubled, Q-switched Nd:YAG lasers (Spectra-Physics, Quanta-Ray Pro-350). All pump lasers are also image relayed to maintain a uniform spatial profile and to prevent damage to optics that can be caused by diffractive effects. As with the preamplifier, high average pump power can induce strong thermal lensing. We  
Figure 3: **(a)** Amplified output spectra after OPCPA preamplifier stage with (solid red curve) and without (dashed gray curve) OPCPA amplification; **(b)** Amplified output spectra after second saturable absorber with (solid red curve) and without (dashed gray curve) OPCPA adjustment.  
implemented cryogenic cooling to increase thermal conductivity, while reducing both refractive index gradient and the thermomechanical stress. Cryogenic cooling results internal focal lengths near 4000 m under the maximum pumping condition, rendering thermal lensing insignificant [62; 63; 64; 12].  
The output energies from power amplifier are obtained by increasing the pump energy while maintaining the Ti:sapphire crystal temperature at 100 K in the cryogenic chamber. A maximum output energy of over 3.2 J is achieved with an incident pump energy of \(\sim\)6.5 J as shown in Figure 4. The excellent power stability of less than \(\pm\)2% is observed over a 1 h interval, which is well in excess of the amplifier thermalization time at the highest pump level. The whole system is highly stable for several hours. The amplified pulse spectrum from the Ti:sapphire amplifier is redshifted due to saturation. As a mitigating measure, the amplifier input spectrum is, therefore, blueshifted by tuning the phase-match setting of the BBO crystals in the OPCPA preamplifier. We obtain the spectral bandwidth of \(\sim\)50 nm from the power amplifier.