## 2 Design and Performance of Ultra-Intense \"J-KAREN\" Laser System
### Spatiotemporal Quality  
The near-field spatial intensity distributions of the green pump beams from each DKDP crystal and the intensity distributions along the vertical and horizontal cross sections of these beams are also shown in Figure 6. The near-field spatial intensity distributions are imaged by a CCD camera through a set of image-relay optics with high-energy (\(\sim\)100 J) green beams. As seen, the beams exhibit poor spatial qualities that are not suitable for directly pumping the Ti:sapphire amplifier. Most of the energy is concentrated in the outer edge area and, therefore, optical damage or parasitic oscillation could likely occur. Figure 7 shows the homogenized intensity distributions that are generated in the plane of the Ti:sapphire crystal for both pumping sides after passing through the DOEs. From these figures, it is seen that near-perfect flat-topped intensity distributions are successfully generated and the DOE capability for beam homogenization is demonstrated. Because the use of beam homogenizers can prevent crystal damage and parasitic oscillation due to the spatial irregularities of pump beams, this should allow greater amplification by allowing pumping at higher fluence. Figure 8 shows the near-field spatial profiles of 28 J amplified broadband beam from the final amplifier. The intensity distribution along the vertical and horizontal cross section of the beam is also shown. As seen, the beam profiles had near homogeneous flat-topped spatial intensity distributions. We have also evaluated the filling factor, which is defined as the ratio of peak intensity to average intensity of a spatial profile. A filling factor of 70% is obtained for 28 J broadband output beam. Amplified pulses are finally recompressed in a grating based compressor consisting of 1480 groove/mm gratings. The output pulse spectrum without pumping the final amplifier has a bandwidth of 50 nm (FWHM), and the recompressed pulse duration is 29.5 fs (FWHM) as shown in Figure 9. The pulse duration and spectral phase after the compressor are measured using high-dynamic range instruments, namely a single-shot commercial system (Wizzler, FASTLITE) or a home-build scanning transient grating FROG (frequency-resolved optical gating). The measured phase is used as feedback to the AOPDF to minimize the phase distortion. Figure 5: Measured output energy from Ti:sapphire final amplifier _versus_ pump energy. Figure 8: Near-field spatial intensity distribution of the final amplifier output. Figure 6: Near-field spatial intensity distributions of the green beams from each DKDP crystal; **(a)** first crystal, **(b)** second crystal. Figure 7: Near-field spatial intensity distributions of the green beams from each crystal side. The contrast is measured using the third-order cross correlator (modified Sequoia unit by Amplitude Technologies, Chaland, France) in the several hundred picoseconds range without pumping final amplifier, as shown in Figure 10. The incident fluence for the cross correlator is 8 mJ/cm\({}^{2}\). The peaks around the main pulse are attributed to multiple reflections of the main pulse at the optical components in the beam line and the third-order cross correlator. The post-pulses act as prepulses for the third-order cross-correlation signal. The contrast is improved by two orders of magnitude with the second saturable absorber in our system. At about 500 ps prior to the main pulse, the measured contrast is 1.4 \(\times\) 10\({}^{12}\) (detection limited). It is very difficult to measure and evaluate the contrast while pumping the final amplifier due to the single-shot mode limitation. We have used the numerical model based on the Frantz-Nodvik simulation [69], and we have calculated the gains of the final amplifier for the main pulse and ASE. The calculation predicts that the contrast should be better than 5 \(\times\) 10\({}^{11}\), even though we use the final amplifier in a maximum pumping condition.