## 4 Results and Discussion  
Firstly, a theoretical simulation model was established based on three-wave mixing equations to adjust the parameters of OPO. By supposing a pump beam with good Gaussian distribution in space and time and considering the effect of absorption and spatial birefringent walk-off in BGSe crystal, the relationship between the idler energy at 6.45 \(\upmu\)m and input pump energy was simulated by the SNLO software, as well as plotted in Figure 3 with a black dashed curve. In the model, with the increase of the pump energy, there was no saturation phenomenon for the idler wave output energy. Figure 2: Schematic of the experimental setup. ISO: optical isolator; TS: telescope system; HWP: half-wave-plate at 1.064 \(\upmu\)m; PBS: 45\({}^{\circ}\) polarized beam splitter at 1.064 \(\upmu\)m; M1: input coupler (plane mirror); M2: output coupler (plane mirror); Ge: germanium filter mirror. Inset: transmission spectrum of uncoated BGSe sample in 0.2–20 \(\upmu\)m range. With the above parameters, the experimental input-output characteristic is shown, as plotted in Figure 3 red solid circles (measured by an energy meter of OPHIR, PE10-C, metallic probe, with the maximum range of 10 mJ covering the wavelength range from 0.15 to 12 \(\upmu\)m). The oscillator exhibits pump threshold energy as low as 10 mJ, which corresponds to the energy fluence of 0.318 J/cm\({}^{2}\). Then, the output pulse energy increases monotonically when the injected pump energy is below \(\sim\)58 mJ; then, a rollover can be noticed, while the input pump energy exceeds \(\sim\)58 mJ. A maximum pulse energy was up to 1.23 mJ at 6.45 \(\upmu\)m under the pump energy of 58 mJ, corresponding to a peak power density of 60.7 MW/cm\({}^{2}\). The optical-optical conversion efficiency is 2.1%, from 1.064 to 6.45 \(\upmu\)m. The pump pulse energy could not be improved further, as it was limited by the damage threshold of AR coating at BGSe crystal end facts (\(\sim\)80 MW/cm\({}^{2}\)). It is observed in Figure 3 that the simulated results are in close agreement with the experimental data when the injected pump energy is below \(\sim\)30 mJ. At higher pump energy, the experimental data are a little less than the numerical results, which may be attributed to ignoring the effect of the thermally-induced diffraction caused by BGSe crystal absorption in the simulation. Similarly, the OPO optical-optical conversion efficiency, from 1.064 to 6.45 \(\upmu\)m, versus BGSe crystal length at the fixed pump pulse energy of 58 mJ was calculated, as presented in Figure 4 (red curve). It can be seen in Figure 4 that the conversion efficiency increases with increasing BGSe crystal length to be \(\sim\)9% around with a 22 mm long crystal. Then, the conversion efficiency falls off after a crystal longer than 22 mm, due to back conversion. The BGSe crystal we used was the only available crystal with a length of 18 mm. The experimental datum is also shown in the Figure 4. It is in close agreement with the simulated OPO conversion efficiency of 2.6%, which is similar to the conversion efficiency of \(\sim\)3.3% in Ref. [20]. To confirm further the correctness of the simulation of optical-optical conversion efficiency, as a function of crystal length, the other experimental datum at the BGSe crystal length of 16.5 mm was added to Figure 4. The experimental optical-optical conversion efficiency is about 1%, close to the simulated value of 1.15%. Therefore, we think the simulation of optical-optical conversion efficiency, as a function of the crystal length, is credible. Although spatial birefringent walk-off in BGSe crystal was considered in simulation, the walk-off length was about 69 mm, assuming three waves with the same spot radii of 1 mm, which was much longer than the length of the crystal (18 mm) in our experiment. Therefore, the walk-off effect weakly influenced the conversion efficiency.