## 4 Experimental Results and Discussion  
In our experiment, the pump module, collimation system, coupling-out mirror and Nd:YVO\({}_{4}\) crystal were adjusted to be coaxial. The LD current was adjusted to obtain output power with the wavelength 1064 nm, at the maximum pump power of 18.66 W, the output power of the four-pass amplifier was 3.84 W at 500 kHz. After passing through the double-pass amplifier, a maximum amplified power of 16.19 W was obtained corresponding to the pulse energy of 32.38 \(\upmu\)J at a pumped current of 4 A. As shown in Figure 2. At a pump current of 1 A, the output power was 1.73 W; at a pump current of 7.4 A, a max pump power of 60 W and a output power of 26.4 W were obtained. The pump power of the double-pass amplifier was set to be 31.7 W because higher power may result in the self-excited oscillation. It can be observed that the output power increases linearly with the increasing of the pumped power and there are two turning points in the image. This is because the crystal has a strong absorption of 808 nm pump light, the efficiency will be greater when the current is less than 2 A, but the thermal effect gradually increases with the pump current gradually increasing, and the efficiency will gradually decrease, and it will decrease further when it reaches 5 A, therefore there are two turning points in the curve.  
Figure 2: Output power of 808 nm LD and the 1064 nm output laser versus pump current.  
The amplified pulses were monitored using a photodiode (ALPHALAS GMBH, UPD-40-UVIR-D, rise time \(<\) 40 ps). At 500 kHz, oscilloscope trace of the output pulse train is illustrated in Figure 3. We can observe that the amplifier generates very clean output pulses.  
Figure 4a shows the autocorrelation trace of the amplified pulses with the measured width of 17.6 ps at a repetition rate of 500 kHz. The pulse width of the output was slightly broadened compared with that of the seed pulses 16.3 ps. At output energy of 32.38 \(\upmu\)J, we measured the laser beam profile of the focused output beam using the knife-edge method [17], as is shown in Figure 4b. The \(M^{2}\) measured were 1.28 and 1.17 for the horizontal and vertical axes of the output, respectively. The roundness of the near-field intensity distribution is higher than 99%.  
Figure 4: _Cont._  
Figure 3: Oscilloscope trace of the double-pass amplified pulse train.  
It could be observed that there were differences between beam quality in the x direction and y direction. The main cause was the asymmetry of crystal cooling structure. Nd:YVO\({}_{4}\) crystals are sensitive to changes of temperature, so by optimizing the cooling structure of crystals in different directions, the beam quality in the x direction can be optimized. Compared to the reported papers about picosecond laser amplifier, the optic-optic conversion efficiency 51.07% obtained by this paper was the highest, and the beam quality \(M^{2}\) was also better. Experiments show that the laser has good stability; firstly, we cut the crystal with an angle to prevent the generation of ASE; In addition, the focus mirrors and the end surface of Nd:YVO\({}_{4}\) are AR coated with transmittance greater than 99.5%, and the crystal has a large static distance from the focus mirror, so there will be no resonance in the amplifier, the effect of back reflection is minimal in the laser and the laser runs well.