# 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  
The compact double BBO arrangement is depicted in Figure 4. In this arrangement, two same-cut crystals are placed closely and the idler will not be depleted in the process of amplification. The pump and signal facilitate the same non-collinear angle in two crystals but the phase matching angles are different by adjusting the orientation of crystals. Consequently, different spectral components are amplified in series thereby supporting a broader overall bandwidth. It would be particularly useful if it also maintains the high temporal contrast of OPCPA as shown in Section 3.1. In this section, we will calculate the temporal contrast in four types of double BBO arrangements. Our goal is to achieve ultrabroad spectrum and high temporal contrast simultaneously and look for the optimal design. For demonstration, the typical parameters of the crystals in four schemes are listed in the Table 1. As we will see, Config 1.1 and Config 1.2 amplify the short and long wavelength part of the signal spectrum separately in the cascaded crystals. The difference of these two configurations is that the short wavelength part is firstly amplified in Config 1.1, while the long wavelength part is firstly amplified in Config 1.2. In Config 2.1 and Config 2.2, the central and outer part of the spectrum is amplified respectively in two crystals. These two schemes also differ only with  
Figure 3: **(a)** Temporal contrast by compressing the signal to the Fourier transform limited duration at the crystal length of 3.5 mm, 4 mm and 5 mm; (**b**) Seed spectrum and the amplified signal spectrum at the crystal length of 3.5 mm. Figure 2: **(a)** The signal energy and PSF energy versus the crystal length. The black line represents the signal energy. The blue line represents the PSF energy assuming that it has the perfect phase-matching condition. The red line represents the PSF energy assuming that it has the same phase mismatch with signal. **(b)** The signal-to-noise energy ratio (SNR) versus the crystal length. The blue line represents the case that PSF has perfect phase-matching condition. The red line represents the case that PSF has the same phase mismatch with signal. respect to the amplification order of the spectrum. The parameters of the pump and seed are the same as those used in Section 3.1. Figure 5a,b illustrates the amplified spectrum in Config 1.1 and Config 1.2. In both schemes, the bandwidth is successfully increased by 100 nm in the long wavelength region than the bandwidth under the traditional configuration as shown in Figure 3. The spectral oscillations in Figure 5 are caused by the recombination of the signal and idler [15]. The idler generated in the first BBO would interact with the signal in the second BBO and produce pump photons. In addition, this interaction is related to the huge phase mismatch, so the spectral oscillations are produced. These oscillations can be reduced by lowering the gain over the whole spectrum. What matters is that, even with a large gain, the temporal contrast better than \(2\times 10^{-11}\) before the main pulse is preserved in Config 1.1, as shown in Figure 6a. It indicates that the ultrabroad spectrum ranging from 700 nm to 1200 nm and high temporal contrast can be simultaneously realized in Config 1.1. In addition, the temporal contrast of \(9\times 10^{-11}\) at approximately 20 ps before the main pulse is achieved in Config 1.2. The deterioration of the temporal contrast in Config 1.2 could be understood as below. In order to avoid the deep dip of the overall spectrum, the little overlap of the two phase-matching spectrum in two crystals is inevitable. It follows that the PSF in the overlapped spectral region (i.e., the region around 1060 nm in Config 1.1 and Config 1.2) could gain much more energy after being amplified in the two crystals. This phenomenon is more evident for the central temporal part of PSF because in this temporal part the corresponding pump pulses have the highest pump intensity.