# Multistage Smoothing Compressor for Multistep Pulse Compressors
## 4 Sample Design for a 100 PW Laser
The approximate size (1365 \(\times\) 650 mm\({}^{2}\)) of the beam on the last grating is still smaller than that of the largest grating with an approximate size of 1450 \(\times\) 700 mm\({}^{2}\). With this 25 mm spatial chirp width, the possible LSIM or hotspots, coming from both near-field and far-field effects of the optics after PS_II, can be effectively smoothed according to the previous simulation. When considering that the pre-compressor has already induced approximately 5 mm \(\times\) 5 mm in the X and Y directions, which equals a 25 mm spatial chirp width in one direction, the LSIM with a period of less than 3 mm in the middling spatial frequency can also be smoothed well. As a result, a highly smoothing laser beam is achieved at the output of the asymmetric four-grating compressor. Note that the length difference between the two grating pairs can be conveniently varied according to different requirements; thus, different spatial chirp widths can be induced using the asymmetric four-grating compressor. Since the total induced spatial chirp width on G2 is approximately 440 mm, it should be noted that the second grating G2 can cut light by a width of about 160 mm on both edges. The light cutting by the grating sharp edges induce diffraction and then LSIM to the laser beam after G2. According to the diffraction theory at a straight edge [29], the diffracted light intensity varies with the distance between the diffracted light source and the receiving screen. The maximum diffraction intensity can reach approximately 1.5 times that of the initial intensity. Based on the above input parameters, the red dotted line in Figure 6 shows the one-dimensional beam profile after G2 without light cutting. In the asymmetric four-grating compressor, the distance between G2 and G3 is variable. In our case, the shortest distance of the upper edge is set to 3 m, whereas the longest distance of the bottom edge is set to 5.5 m. The one-dimensional beam intensity profile on the G3 grating can be obtained by summing all the diffraction profiles at different wavelengths, as shown by the blue solid line in Figure 6. This shows that the intensity of the light cutting on both edges is about one-fifth of the maximum intensity of the laser beam. According to the calculation, the LSIM induced by the edge diffraction does not exceed or affect the top-hat region; therefore, it does not cause damage risks to G3. The energy loss induced by light cutting is calculated to be approximately 1.9%. Note that the diffraction-induced LSIM by G2 is absolutely smoothed after G4 owing to the large spatial chirp width induced by the grating pair of G3 and G4. The spectral cutting of G2 has been used in many grating-based compressors. A kHz Ti:sapphire laser system with a beam diameter of 15 mm is used to prove the light cutting induced diffraction effect, as shown in Figure 6c,e, where the light cutting occurs at the peak intensities of approximately 0.2 and 0.5. The simulation results of the edge diffraction are shown in Figure 6b,d. The red lines and blue lines are one-dimensional beam intensity profiles without and with light cutting, respectively. The insets of Figure 6c,e are the corresponding 2D beam profiles. The good agreement between the experimental and simulated results confirms the accuracy of the simulation program. It means the light-cutting-induced influence by G2 in the 100 PW sample laser can be neglected. Since the full-spectral-bandwidth regions on each grating will experience the strongest laser fluence, only the laser fluence of this region is considered. In the first grating, the effective beam size on the grating is approximately 1320 mm in the X-direction and 640 mm in the Y-direction. For an amplified laser pulse with 2500 J input, the laser fluence is 2500/(132 \(\times\) 64) \(\approx\) 296 mJ/cm\({}^{2}\), which is twofold lower than the grating damage threshold of approximately 600 mJ/cm\({}^{2}\) with a nanosecond pulse duration [22,30].