# Numerical Investigation of the Temporal Contrast in ps-OPCPA with Compact Double BBO Arrangement
## 3 Results and Discussion  
### Temporal Contrast in the Traditional OPCPA Arrangement  
The parametric amplification of signal pulses and PSF in a BBO crystal (type I, \(\alpha=2.274^{\circ}\), phase matching angle \(\theta=23.664^{\circ}\), pump wavelength \(\lambda_{p}=532\) nm) is simulated here. The case in which PSF has a perfect phase-matching condition and the case in which PSF has the same phase mismatch with the signal are also compared. In our simulation, the pump pulse has a Gaussian temporal profile with a duration of 100 ps and pulse energy of 20 mJ, focused to a pump intensity of about 10 GW/cm\({}^{2}\). The seed pulse has a super-Gaussian spectral profile with the energy of 1 uJ and it is stretched to 60 ps with the second-order negative chirp.  
Figure 2a describes the signal energy and PSF energy versus the crystal length. Figure 2b describes the signal to noise energy ratio (SNR) versus the crystal length and the initial SNR is \(5\times 10^{7}\) (50 times on average). For both cases, the signal to noise ratio (SNR) decreases in the beginning of the amplification process because the idler grows from a zero electric field, which slows the efficient amplification of the signal. After propagating a short distance, the idler energy approaches the signal energy, and a slow increase of SNR is seen due to the much higher signal energy than the PSF energy. At the crystal length of 3.5 mm corresponding to the signal energy of 3.3 mJ, the saturation effect shows up and the SNR starts decreasing dramatically. When operated at this position, SNR is reduced to 3.3 \(\times\) 10\({}^{7}\) and 4.1 \(\times\) 10\({}^{7}\) for the cases in which PSF has the perfect phase-matching condition and the same phase-matching condition with the signal, respectively. The highest achievable signal energy is 5 mJ at the crystal length of 4 mm. At the crystal length of 5 mm, OPCPA moves into the oversaturated region, and the signal energy converts back to 2 mJ. The corresponding SNR is 2.1 \(\times\) 10\({}^{6}\) and 2.9 \(\times\) 10\({}^{6}\) for the two phase-matching conditions of PSF. The result shows that, although phase-matching properties have impacts on the parametric amplification, the difference of the PSF energy between two phase-matching cases is not significant in our simulation. The difference could be bigger for a longer crystal length. In the following simulation, only PSF with perfect phase matching is considered. The temporal profile of the signal and PSF is depicted in Figure 3a and the background level is observed to be 3 \(\times\) 10\({}^{-11}\), 4 \(\times\) 10\({}^{-11}\) and 5 \(\times\) 10\({}^{-10}\) relative to the main pulse at the crystal length of 3.5 mm, 4 mm and 5 mm, respectively. As expected, the temporal contrast becomes worse as the crystal length increases. To ensure a better temporal contrast, the crystal length of 3.5 mm is recommended and the corresponding output spectrum expanding from 700 nm to 1100 nm is illustrated in Figure 3b for the comparison with the spectrum in a double BBO arrangement as will be discussed in Section 3.2.