# Numerical Investigation of the Temporal Contrast in ps-OPCPA with Compact Double BBO Arrangement
## 3 Results and Discussion
### Temporal Contrast in the Compact Double BBO Arrangement
In Config 1.1 the central temporal region of pump has been consumed in the first BBO, while in Config 1.2 this part of the pump has not been consumed in the first BBO but in the second BBO. As a result, PSF in Config 1.2 will be amplified efficiently in both crystals, and thus PSF in Config 1.2 would have a larger gain. The spectrum ranging from 700 nm to 1200 nm is also achieved in Config 2.1 and Config 2.2, as illustrated in Figure 5c,d. As shown in Figure 6a, Config 2.1 has a better temporal contrast of \(2\times 10^{-10}\) at 45 ps before the main pulse than Config 2.2 with the temporal \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Config 1.1** & **Config 1.1** & **Config 2.1** & **Config 2.2** \\ \hline Noncollinear angle (\({}^{\circ}\)) & 2.304 & 2.304 & 2.079 & 2.079 \\ Phase-matching angle of the 1 st & & & & \\ BBO (\({}^{\circ}\)) & 23.73 & 23.46 & 23.53 & 23.31 \\ Length of the 1 st BBO (mm) & 3.5 & 3.7 & 3.5 & 3.7 \\ Phase-matching angle of the & & & & \\
2 nd BBO (\({}^{\circ}\)) & & & & \\ Length of the 2 nd BBO (mm) & 4.1 & 3.6 & 3.6 & 3.6 \\ Output energy (m)) & 4.4 & 4.2 & 4.3 & 3.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of cascaded configurations. Figure 4: Compact double BBO arrangement. contrast of \(1\times 10^{-9}\) at 30 ps before the main pulse. Similar to the comparison between Config 1.1 and Config 1.2, the difference of the temporal contrast between Config 2.1 and Config 2.2 is because the former alignment consumes the central part of the pump in the first crystal, while the latter alignment consumes the outer part of the pump in the first crystal. However, although Config 2.1 is more preferred than Config 2.2, its level of the pedestal is still one order of magnitude higher than the level in Config 1.1. It is possibly due to the difference of two configurations. There are two spectral interacting regions between the cascade crystals in Config.2.1 and only one spectral interacting region in Config 1.1. As a result, the respective phase-matching spectrum of cascaded crystals in Config 2.1 needs to be closer to maintain the similar output energy compared with Config 1.1. It enables PSF around 800 nm and 1100 nm has more potential to be amplified efficiently after the two crystals in Config 2.1, which leads to the deterioration of the temporal contrast. Among the above four discussed schemes, Config 1.1 performs best with the spectrum ranging from 700 nm to 1200 nm and the background level of \(2\times 10^{-11}\) to the main pulse. The advantage of Config 1.1 is to consume the pump region with higher intensity in the first BBO and avoid too much spectral overlap in two cascaded crystals. As shown in Figure 6b, there is a negligible difference between the traditional single BBO arrangement and the double BBO arrangement in terms of the incoherent background. However, the inset of Figure 6b shows that Config 1.1 has a worse temporal contrast in the time window of \(-1.7\) ps to \(1.7\) ps, which may be caused by the spectral modulation in the double BBO configuration. Figure 5: (**a**) Cascaded spectrum in Config 1.1, (**b**) in Config 1.2, (**c**) in Config 2.1 and (**d**) in Config 2.2. The blue and red line represent the spectrum at the exit of the first and the second BBO crystal respectively. A more realistic spectrum that is similar to the frontend output in [15] is also simulated for the single crystal configuration and Config 1.1 while keeping other parameters unchanged, as depicted in Figure 7. The result shows that the output temporal contrast seeded by a more realistic spectrum does not have obvious change compared with seeding an ideal spectrum discussed above.