## 3 Results  
### DFG Power and Black-Box Efficiency  
Figures 2 and 3 display the DFG mid-infrared (mid-IR) output power and black-box efficiency relative to 808 nm pump power across different lengths of periodically poled lithium niobate (PPLN). Insets in these figures identify each PPLN length, enabling a direct comparison of length-dependent DFG performances. Specifically, the red circle represents the 50 mm PPLN, the green square corresponds to the 40 mm PPLN, and the purple triangle denotes the 29 mm PPLN. The x-axis indicates the 808 nm pump power, while the y-axis shows the DFG power output measured post-Ge filter.  
Upon coupling the EDFA signal into the 50 mm PPLN, we obtained DFG power levels up to 63 mW at 3437 nm, with an 808 nm pump power of 4.7 W and a signal power of 400 mW (measured at the output of the focusing lens). This setup yielded a black-box efficiency of 3.4% W\({}^{-1}\). Experimental data points are represented by shapes, while the solid line shows simulated DFG power based on the assumption that both input beams are focused at the PPLN center. The cavity loss was treated as a fitting variable, with all other input variables experimentally measured.  
The results reveal that an increase in the crystal length leads to higher DFG output power and black-box efficiency, which is expected due to the extended nonlinear interaction length. Data collection was conducted at a fixed temperature and signal power while varying the pump power. The close alignment between the simulation results and experimental data underscores the robust performance of the system, with these measurements representing the highest recorded black-box efficiency. There is a dip in the experimental efficiency versus the simulated efficiency for the longer crystal, which could be explained by small differences in the simulation assumptions versus the experimental conditions. The efficiency for focused Gaussian beams is highly dependent on both the beam sizes as well as beam positions in the crystal, and the phase-matching condition is more difficult to maintain over larger crystals. As a result, this small discrepancy could be explained by differences in the beam positions, small changes in the beam radii, and difficulty in maintaining a constant temperature of the longer PPLN for focused Gaussian beams, all of which could add up to a noticeable difference between the simulation and experiment. It would be possible to spend more time fitting variables to the experimental data to achieve a tighter fit, but the overall agreement in the trend was good enough that this was deemed unnecessary.  
Figure 2: Measured and simulated DFG mid-infrared output power as a function of 808 nm pump power for three different periodically poled lithium niobate (PPLN) lengths: 29 mm (purple triangles), 40 mm (green squares), and 50 mm (red circles). The x-axis represents the pump power, while the y-axis shows the DFG output power after the germanium (Ge) filter. The solid lines represent simulated DFG power, assuming both input beams are focused at the PPLN center. The inset shows the three PPLN lengths tested, highlighting their significant impact on DFG performance characteristics. The DFG threshold remains nearly constant for different PPLN lengths because it is primarily determined by the intracavity 1064 nm laser, which is influenced by cavity losses. These losses have negligible dependence on PPLN length, since the propagation loss within the PPLN is insignificant.  
This dataset highlights the efficiency of our system, demonstrating the ability to achieve substantial output power while ensuring effective phase matching. Overall, the findings are promising, not only showing strong agreement with theoretical predictions but also suggesting that overlap efficiency optimization can further enhance the output power, which is relevant for applications like greenhouse gas detection and optical communication [6].