## 2 Experiments and Results
### Power Amplifiers and Compensation of Thermal Effects  
The power amplification stage consists of two successive laser gain configurations. The first setup contains a diode-pumped gain module (Cutting Edge Optronics, REA6306-1P), which has a rod-shaped Nd:YAG crystal with a diameter of 6 mm and a length of 120 mm. This module has a maximum operating parameter of 180 A and 300 Hz, a condition under which it has a stored energy of 513.3 mJ. In this system, the module is operated at 100 A and 100 Hz with a small signal gain of 3.49 in consideration of controllable thermal effects and sufficient amplification performance. After exiting from the serrated aperture, laser pulses pass through the gain module and a Faraday rotator, and are reflected back. The laser pulses change their polarization after the double-pass of the Faraday rotator and exit from thin film polarizer (TFP). In the diode-pumped gain module, unabsorbed pumping light will bring about heat accumulation. A water-cooling circulatory system is used to take away the redundant heat to prevent the fracture of the gain crystal. The pumping system together with a water-cooling system will result in a nonuniform radial temperature distribution in the rod-shaped crystal. The thermal strains in the rod-shaped crystal brought by the nonuniform radial temperature distribution will result in a change in the refractive index via the photoelastic effect, which will lead to a thermally induced birefringence and thermal lensing. The thermally induced birefringence will bring about depolarization and lead to a loss of laser energy when pulses pass through polarization-related devices. According to Reference [9], thermally induced depolarization will be compensated when laser pulses pass through the same gain module with a 90-degree polarization rotation. Thus, a Faraday rotator is placed between the gain module and HR1 to achieve the polarization rotation and depolarization compensation. With our measurements, the loss of depolarization is below 3%. After the double-pass of Gain Module 2, laser pulses are relay-imaged from HR1 to Surface 1 and expanded from 6 to 10 mm with an imaging system composed of a pair of plano-convex lenses. Laser pulses will show little convergence due to a thermal lensing effect in Gain Module 2. When operated at 100 Hz and 100 A, the gain module has a measured focal length of 30 m, as shown in Figure 3. Thus, in the imaging setup, the distance between two lenses is precisely adjusted to achieve the compensation of the thermal lensing effect and alignment for the laser beam. In order to avoid air breakdown, a vacuum tube is placed in the imaging setup. An HWP and Faraday rotator are placed inside the imaging setup together with two TFPs to achieve another optical isolation. After the double-pass of Gain Module 2, laser pulses are amplified to 38.5 mJ. The second part of the power amplification setup consists of two identical gain modules (Cutting Edge Optronics, REA12006-3P), which has a rod-shaped Nd:YAG crystal with a diameter of 10 mm and a length of 120 mm. Each has a stored energy of 1.05 J when operated at 125 A and 300 Hz. Both gain modules are operated at 100 A and at 100 Hz with a small signal gain of 2.88 in this system. An equivalent focal length of 3.2 m is measured in such an operating situation. To obtain the best beam distribution in the exit, the laser beam should be relay-imaged from Surface 1 to HR2 and then to the exit. We take advantage of the thermal lensing of the gain module. A plano-convex lens with a focal length of 500 mm is placed behind with a distance of 400 mm to the center of the gain module. After passing through the gain module and the plano-convex lens, laser pulses converge at the focus point. Another identical gain module and a plano-convex lens are placed symmetrically with the focus point. Thermal lenses in two gain modules together with two plano-convex lenses consist of an equivalent imaging system.