## 3 Experimental Results and Discussions
### Main Amplifier and Suppression of SRS effect  
In the Nd:YVO\({}_{4}\) crystal of the main amplifier, the maximum peak power of the amplified pulse can reach about 100 MW, which can easily bring about stimulated Raman scattering (SRS). In the progress of SRS, the Stokes wave of Raman light has power gain \(exp(G)\). The exponent \(G\) is given by  
\[G=g_{R}IL \tag{1}\]  
where \(g_{R}\) is the Raman gain, \(I\) is the amplified fundamental pulse intensity, and \(L\) is the length of the nonlinear Raman medium. The first Stokes wavelength beams will appear when \(G\) is 25-30 [31]. The Raman gain of \(g_{R}\) of YVO\({}_{4}\) crystal is 16.13 cm/GW [32]. So when  
\[IL\leq 1.55\;\mathrm{GW/cm} \tag{2}\]  
the Raman gain in YVO\({}_{4}\) crystal will be below the threshold of SRS progress, and YVO\({}_{4}\) crystal cannot produce the Stokes wave. In our experiment, a 1064 nm laser with intensity of 2.65 GW/cm\({}^{2}\) was once injected into a Nd:YVO\({}_{4}\) crystal with a length of 1.5 cm, which brought about the first Stokes wave (\(\lambda=1175.84\) nm), as shown in Figure 4. The Raman shift of Nd:YVO\({}_{4}\) was 890 cm\({}^{-1}\), which was almost the same as that of YVO\({}_{4}\) crystal. After passing through Nd:YVO\({}_{4}\) crystal, the energy loss of fundamental 1064 nm laser reached to 20%. Therefore, the generation and accumulation of Raman  
Figure 3: Time signal to noise ratio of maximum output energy: (**a**) Pre-pulse amplitude when the photodetector was overexposed; (**b**) main pulse amplitude when the photodetector was operated in the linear range. Figure 2: Signal to noise ratio and pre-pulse energy at different amplifiers when a regenerative amplifier was used as the pre-amplifier. light must be prevented in pulse amplification. However, this will affect the working parameters of the Nd:YVO\({}_{4}\) amplifier. The laser intensity continues to increase as the amplification based on the Nd:YVO\({}_{4}\) amplifier increases. To avoid the SRS process, Equation (2) must be satisfied in a high peak power amplifier. \[\int_{0}^{L}I(l)dl\leq 1.55\;\mathrm{GW/cm} \tag{3}\]  
What is more, if  
\[I_{max}L\leq 1.55\;\mathrm{GW/cm} \tag{4}\]  
There will be no significant Raman light. \(I_{max}\) is the maximum intensity in the amplification process. So the crystal length \(L\) in an amplifier based on Nd:YVO\({}_{4}\) is limited to the maximum amplified intensity for averting the SRS process. At the same time, crystal length \(L\) also affects the absorption efficiency of pump light of end-pumped Nd:YVO\({}_{4}\) crystal. To obtain enough absorption efficiency, absorption coefficient \(\alpha\) and crystal length \(L\) in an end-pumped configuration should satisfy Equation (5) [33]. \[\alpha L=4\sim 5 \tag{5}\]  
However, absorption coefficient \(\alpha\) is an important factor of crystal thermal fracture. According to Reference [33; 34], thermal fracture limits pump power for end-pumped Nd:YVO\({}_{4}\) crystal. During the QCW pump operation, the generally accepted way to avoid thermal fracture is pumping the crystal with an average power less than thermal fracture pump power \(P_{av}\), which is less than the fracture pump power \(P_{cav}\) of CW pump operation. The maximum pump power at QCW operation is given by  
\[P_{av}=\eta P_{cav}=\eta\frac{1}{\alpha}\frac{4\pi R}{\xi} \tag{6}\]  
\(\eta\) is the correction factor, which depends on QCW pump duty cycle and repetition, considering a QCW pump duty cycle of 10% in Nd:YVO\({}_{4}\) crystal, \(\eta\approx 0.6\)[34]. \(R\) is thermal shock parameter depending on the mechanical and thermal properties of the host material. \(\xi\) is the fractional thermal loading. When Nd:YVO\({}_{4}\) crystal is pumped with 808 nm, \(\frac{4\pi R}{\xi}\) is about 250 \(W/\)cm [33]. Based on Equation (6), we can see that thermal fracture pump power \(P_{av}\) strongly depends on \(\alpha\). Lowering the dopant concentration can decrease the absorption coefficient and increase the fracture-limited pump power.