## 4 Results and Discussion
In the following work, we enabled scale-up for the single pulse energy or conversion efficiency at 6.45 \(\upmu\)m by choosing an optimum crystal length of about 22 mm, based on improving our crystal growth technique or optimizing the OC transmittance and thermal distribution in a shorter length BGSe crystal. Figure 3: Output idler energy at 6.45 \(\upmu\)m versus input energy in simulation and experiment. The pulse temporal profiles of pump and idler beams were measured via InGaAs (DET10A/M, THORLABS, rise time \(<\) 1 ns, 200-1100 nm) and HgCdTe (PDAVJ10, THORLABS, 2.0-10.6 \(\upmu\)m, bandwidth 100 MHz) photo-detectors, respectively, which were simultaneously connected with 2 GHz bandwidth digital oscilloscopes (Tektronix, MSO 5204B, Beaverton, OR, USA). The measured typical oscilloscope traces are displayed in the Figure 5, under the input pulse energy of 58 mJ, suggesting the pump and idler pulse durations of 30.4 and 24.3 ns, respectively. The idler FWHM pulse duration was shorter than the incident pump pulse duration because of the temporal gain narrowing effect [22]. The typical spectrum characterization of the pump wave was measured by optical spectrum analyzer (Ocean Optics, Dunedin, FL, USA, HR4000, resolution 0.02 nm, 200 nm\(\sim\)1100 nm). The measurement result is shown in the upper inset of Figure 6. The pump central wavelength is located at 1064.1 nm, with a spectral width of \(\sim\)0.8 nm. Moreover, according to the OPO momentum conservation condition (1/\(\lambda_{\mathrm{p}}\) = 1/\(\lambda_{\mathrm{s}}\) + 1/\(\lambda_{\mathrm{i}}\)) and phase-matching angle (\(\theta\) = 47.1\({}^{\circ}\) and \(\varphi\) = 0) of BGSe, in this case, the signal wavelength \(\lambda_{\mathrm{s}}\) and idler wavelength \(\lambda_{\mathrm{i}}\) were calculated to be 1.274 and 6.45 \(\upmu\)m, respectively. The linewidth of signal and idler light may be generated with a wide band of pump light and divergence angle of pump beam. In our experiment, the pump beam is collimated in BGSe crystal, so we focus on the effect of the pump beam linewidth on idler beam linewidth. When three waves are collinear in BGSe crystal, according to the conservation of momentum and  
Figure 4: Simulated optical-optical conversion efficiency from 1.064 to 6.45 \(\upmu\)m versus crystal length at mixed pump pulse energy of 58 mJ. The black dots represent the experimental data at the BGSe crystal lengths of 16.5 and 18 mm, respectively. Figure 5: Measured temporal profiles of the incident pump and idler lasers. energy at type-I phase-matching, the coupling equations of the signal, idler, and pump lights can be written by:  
\[\omega_{p}n_{p}^{o}=\omega_{s}n_{s}^{e}+\omega_{i}n_{i}^{e} \tag{8}\]  
\[\Delta\omega_{p}=\Delta\omega_{s}+\Delta\omega_{i} \tag{9}\]  
where \(n_{j}\) is the refractive index of the nonlinear crystal at angular frequency, \(\omega_{j}\) for the pump, signal, or idler waves (\(j=p,s,i\)), and \(\Delta\omega_{j}\) (\(j=p,s,i\)) represents the spectral FWHM of the pump, signal, and idler beams, respectively. The above two equations are combined, and the higher-order terms are ignored, so the idler linewidth is generated by the pump linewidth, as follows [23]:  
\[\Delta\lambda_{i}=\left(\frac{n_{eff,p}-n_{eff,s}}{n_{eff,i}-n_{eff,s}}\right) \times\frac{\lambda_{i}^{2}}{\lambda_{p}^{2}}\times\Delta\lambda_{p} \tag{10}\]  
where \(n_{eff,j}\) (\(j=p,s,i\)) can be written as follows:  
Figure 4.0  
Further, assuming the pump, idler, and signal beams with a Gaussian spectral profile, the corresponding linewidths at 1.274 and 6.45 \(\upmu\)m were estimated according to Equations (10) and (11) and shown in Figure 6a. It can be seen that the linewidth at 6.45 \(\upmu\)m is about 4.7 nm. In addition, the exact emitted idler wavelength was monitored by a spectrometer (Arcoptix FT-IR 2-12, 0.4/cm, 2-12 \(\upmu\)m, Arcoptix, Neuchatel, Switzerland). The typical result of an idler beam at 6451.6 nm is plotted in Figure 6b, with a corresponding spectral FWHM of \(\sim\)6.8 nm, which is less than that in Ref. [20].