## 3 Results and Discussion
With low thermal conductivity, the heat absorbed by the crystal from the pump pulse would accumulate because the pulse interval is shorter than the thermal-relaxation time. With the repetition rate increasing, the thermal effect would be more harmful [26]. The thermal diffusivity is 0.502 mm\({}^{2}\) s\({}^{-1}\) for BGSe crystal along the \(a\) crystallographic axis [18], while the thermal diffusion time constant \(\tau\) is about 376 ms, which is much longer than commonly used mid-infrared crystal, e.g., 5.7 ms for ZGP crystal. The prolonged accumulation of heat would lead to thermal lens effect and thermal dephasing which is unbeneficial to the parametric progress. Improving the cooling structure and a using narrow pump beam with high quality could rapidly reduce the thermal effects in BGSe crystal. The increase of the output energy of OPO at 250 Hz may be the joint result of the thermal focusing effect of Nd:YAG and the stabilization of the thermal effect in BGSe crystal. The influence of the OPO cavity length to the input-output characteristics were studied at 4.06 \(\upmu\)m with the fixed repetition rate at 100 Hz, as shown in Figure 4a. For different cavity lengths of 30 mm, 50 mm and 80 mm, the maximum output energies were 1.28 mJ/pulse, 1 mJ/pulse and 0.87 mJ/pulse, respectively. With the decrease of the cavity length, the transit period of the signal wave in the OPO cavity would decrease, which was beneficial to the interaction between the pump and the signal wave and led to the increase of the mid-infrared output energy. The OPO thresholds were measured to be 2.65 mJ/pulse, 3.38 mJ/pulse and 5.00 mJ/pulse for the cavity lengths of 30 mm, 50 mm and 80 mm, respectively. The experimental results verify the OPO theory established by [PERSON] and [PERSON] [22]. With the decrease of the cavity length, the instantaneous cavity net gain increased which leads to the decrease of threshold and the increase of conversion efficiency. The conversion efficiencies of the BGSe-OPO with different cavity lengths were shown in Figure 4b. The maximum conversion efficiency of 12.8% was obtained for the cavity length of 30 mm. For different cavity lengths of 30 mm, 50 mm and 80 mm, the slope efficiencies were measured to be 16.4%, 13.7% and 15.6%. The slope efficiency was measured to be almost constant for each cavity length, which means the back-conversion effect is negligible. With the increase of pump energy, the thermal effect caused by crystal absorption to the pump wave became more serious, causing the decrease of conversion efficiency. Figure 4: (**a**) The input-output characteristics of the BGSe-based DP-SRO with different cavity lengths; (**b**) The conversion efficiency of the BGSe-based DP-SRO with different cavity lengths. By rotating the BGSe crystal, the tuning range of 3.62-4.10 \(\upmu\)m was obtained in the BGSe-OPO. The theoretical wavelength-tuning curves versus the phase-matching angle of Type I BGSe-OPO is calculated based on the Sellmeier equations given in [27]:  
\[n_{x}^{2} =5.952953+\frac{0.250172}{\lambda^{2}-0.081614}-0.001709\cdot\lambda^{2} \tag{1}\] \[n_{y}^{2} =6.021794+\frac{0.256951}{\lambda^{2}-0.079191}-0.001925\cdot \lambda^{2}\] (2) \[n_{z}^{2} =6.293976+\frac{0.282648}{\lambda^{2}-0.094057}-0.002579\cdot \lambda^{2} \tag{3}\]  
The experimental results fit well with the theoretical calculation in Figure 5a. Figure 5b shows the tuning output characteristics of the BGSe-OPO. The tunable output decreased at both sides of the tuning curve due to the increasing pump loss from the Fresnel reflection. The abnormal valley of the tuning curve in Figure 5b around 4.34 \(\upmu\)m was deduced to be related to the crystal impurities and defects. Figure 6 shows the temporal pulse profiles of the pump wave and the mid-infrared wave, measured by Si photodiode (Thorlabs, DET025A/M, Newton, NJ, USA) and (HgCdZn) Te photodiode (Vigo, PCI-9, Ozarow, Mazowiecki, Poland), respectively.