## 2 Experiments and Results
### High Average Power Picosecond Amplifier System at 100 kHz  
As mentioned above, while the high energy picosecond laser operating at the repetition rate of 1 kHz is an excellent pump source for OPCPA, OPO, OPG, and UV light generation, a high power picosecond laser running at a higher repetition rate, such as 100 kHz, is preferred in the field of processing. Based on the experience introduced in Section 2.1, we demonstrated a 100 kHz, 37.5 W picosecond DPSS laser system, which was an excellent source for high efficiency laser processing.  
At a higher repetition rate, the energy density is lower, but more heat is produced in the crystal. Reducing the diameter of the laser beam in the crystal is a good choice because of the smaller heat generation area and comparatively higher efficiency. Another reason for a smaller beam diameter was that a 3 mm diameter BBO Pockels cell was used as an electro-optic switch and worked at the repetition rate of 100 kHz, and the laser beam in the Pockels cell had to be smaller than that mentioned in Section 2.1.2. Thus, a thermal compensation cavity with a laser beam size smaller than that in Figure 4 was designed and constructed as a regenerative amplifier shown in Figure 10. The convex mirrors were replaced with concave mirrors (\(R\) = 600 mm). The laser beam was about 550 \(\upmu\)m in the crystal and 730 \(\upmu\)m in the Pockels cell as the focal length of the thermal lens changed from 300 mm to infinity. This cavity was more suitable for high-repetition-rate amplifier performance. A 0.3 at. %, a-cut, 3 \(\times\) 3 \(\times\) 10 mm\({}^{3}\) Nd:YVO\({}_{4}\) crystal antireflection-coated at 808 nm and around 1 \(\upmu\)m (\(t>99\%\)) was used for this cavity.  
Figure 9: Power curve and beam quality of the side-pumped amplifier. **(a)** Power curve; **(b)** Beam quality.  
The crystal was wrapped with indium foil and mounted tightly on a water-cooled copper heat sink at 14 \({}^{\circ}\)C. The pumping source was a fiber-coupled CW laser diode with a 200 \(\upmu\)m core diameter centered at 808 nm (Focuslight, China). Figure 11a shows the power curve of the regenerative amplifier. At the CW pump power of 15.5 W, 2.6 W average output power was obtained at the repetition rate of 100 kHz by injecting a 15 ps seed pulse from a 1064.4 nm, 80 MHz picosecond oscillator. Figure 11b shows the beam quality of the output pulses as good as \(M^{2}<1.2\).  
To further improve the average power, a hybrid power amplifier was also used. The hybrid power amplifier consisted of three stages of end-pumped single-pass amplifiers with CW laser diodes and a side-pumped module introduced in Section 2.1. The 2.6 W output pulses from the regenerative amplifier were then amplified by the single-pass amplifiers. The 0.3 at. %, a-cut, \(3\times 3\times 10\) mm\({}^{3}\) Nd:YVO\({}_{4}\) crystals were employed as gain media. At the total pump power of 88.5 W, an output average power of 21 W was obtained at 1064.4 nm, corresponding to a pulse energy of 210 \(\upmu\)J and an optical efficiency of 20.8%. At last, the picosecond pulses were amplified to 37.5 W by the side-pumped module at a pump power of 900 W. The pulse energy was as high as 375 \(\upmu\)J at a repetition rate of 100 kHz. Figure 12 shows the power curves and beam images of the power amplifiers.  
Figure 11: **(a)** Power curve of regenerative amplification; **(b)** Beam quality of the output pulses from the regenerative amplifier.  
Figure 10: Diagram of the regenerative amplifier running at the repetition rate of 100 kHz. M1, M6: Concave mirrors, \(R\) = 900 mm; M2, M5: Concave mirrors, \(R\) = 600 mm; M3, M4, M7–M10: Plane high-reflection mirrors; PC: Pockels cell; TFP: Thin-film polarizer; FR: Faraday rotator; GL: Glan prism.