## 3 Results and Discussion  
The crystal was prealigned in air for most efficient frequency conversion using the frontend A2-amplified pulses with a repetition rate of 1 Hz. With the far-field diagnostic and the adaptive optics system the collimation of the A2-pulses could be adapted to the fully amplified pulses. After this prealignment the target chamber was evacuated and the fully amplified pulses were used to adjust the crystal rotation with the aim of maximum output energy. It was found that the crystal rotation needed to be aligned with better than 1 mrad accuracy. In Figure 3a) the dependence of the output energy on the input energy is shown. In this measurement we achieved a maximum pulse energy of 3.05 J for an input pulse energy of 11.8 J. For this pulse, we measured a maximum fluence of 200 mJ/cm\({}^{2}\) in the fundamental pulse, which results in a conversion efficiency of \(\eta\) = 26%. Corresponding to the tuning curve in Figure 3a the efficiency was calculated and depicted in Figure 3b. The maximum conversion efficiency slightly above 30% was achieved for pulse energies betweeen 6 J and 8 J. Compared to work of other groups (e.g., Hillier _et al._[21], \(\eta\) = 75%) the efficiency we have measured is barely the half of such an optimal value. With an otherwise identical but small size (5 mm aperture) KDP crystal we measured the efficiency for the conversion of \(\mathrm{TEM}_{00}\)-spatial pulses resulting in a maximum efficiency of 38% at comparable intensities. To the best of our knowledge, the comparatively low conversion efficiency may be caused by effects of the cubic nonlinearity, which are explained in detail in [24], and the limited phase matching due to the crystal thickness of 2 mm. Furthermore, imperfections in the crystal, deviations of the wavefront from ideal flatness, back conversion and the non-ideal spatial and temporal beam profile of the fully amplified laser pulses (ideal temporal and spatial profile for SHG would be a flat-top profile) are contributing. However, the moderate efficiency in our experiment is part of ongoing research and will likely be improved in the future. Measures for improvement will comprise a homogenization of the near-field profile of the IR-beam and a flattening of the IR-wave front. Currently the latter is optimized to generate a minimal focal spot in the IR, which is not necessarily equivalent to a flat IR-wavefront at the position of the frequency doubling crystal. Furthermore, tests with crystals of different thickness will be carried out. In Figure 3c a typical spectral intensity distribution is shown for a full energy shot. The spectrum was measured with an integrating sphere and shows a FWHM spectral width of 4.5 nm around the center wavelength of 515 nm. To verify the pulse duration we built a single-shot \(2^{\mathrm{nd}}\)-order autocorrelator for 515 nm pulses. Since it was not possible to install the correlator in the experimental area we measured the pulse duration with the aforementioned identical small size KDP-sample. In these measurements we have observed that the frequency doubled pulse duration is a factor of \(\sqrt{2}\) shortened with respect to the initial pulse duration. This fits well to theory and we assume a pulse duration below 120 fs for the high-energy frequency doubled pulses. Furthermore, during the high-energy laser shots we have measured the focal spot of the frequency doubled pulses with a high-quality f/2-imaging system (Figure 2 ). In Figure 3d the spatial distribution in the focal plane of the green laser pulses is shown. The calibration represents the size of the focal spot behind the main focussing parabola. The adaptive optics system was used to flatten the wavefront of the 1030 nm pulses. The area within which the intensity is larger than \(I_{\mathrm{max}}/2\) (\(A_{\mathrm{FWHM}}\)) is 7.1 \(\mu\mathrm{m}^{2}\) and  
Figure 3: Measurements of the second harmonic generation (SHG) pulses.