## 3 Results
### Wavelength Tunability and Temperature Tolerance of the DFG Laser  
To evaluate the temperature tolerance and tunability of the DFG laser, we examined the temperature tuning curve of the DFG power across three different PPLN lengths. This study involved both experimental measurements and simulations using the Sellmeier equation for MgO-doped lithium niobate [26]. Figure 5 shows the normalized DFG power as a function of the PPLN temperature, with the experimental data indicated by squares for the 40 mm PPLN, triangles for the 29 mm PPLN, and circles for the 50 mm PPLN, while the simulation results are depicted by a solid line. The close alignment between the experimental and simulated peak power locations, as well as the Full Width at Half Maximum (FWHM), validates the accuracy of our model and confirms DFG output generation. The actual values of the FWHM in degrees Celsius are as follows: 7 degrees (50 mm), 8.25 degrees (40 mm), and 10.7 degrees (29 mm). In nonlinear optics phenomena, this change in the FWHM can be derived from phase-matching considerations and is often expressed using a _sinc\({}^{2}\)_ function. For a nonlinear process to achieve efficient phase matching, the interaction must maintain coherence over the entire length of the PPLN crystal. However, the phase-matching bandwidth becomes narrower as the crystal length increases. This effect arises because longer crystals impose stricter requirements for phase matching due to the _sinc\({}^{2}\)_ function, and the temperature tuning the FWHM is inversely related to the crystal length [8; 29]. Our results demonstrate that as the PPLN length increases, the tunability decreases; specifically, the 50 mm crystal exhibited slightly lower tunability compared to the shorter crystals, yet it achieved higher output power. This is the expected behavior from theory, so confirming this experimentally serves as a useful check that we are observing DFG governed by focused Gaussian beam theory. Figure 5: The temperature tuning curve of DFG power as a function of the PPLN temperature for three lengths—29 mm, 40 mm, and 50 mm—with corresponding constant signal wavelengths of approximately 1541 nm. The close matching between the experimental data (triangles for 29 mm, squares for 40 mm, and circles for 50 mm) and the simulated results (solid line) validates the accuracy of the model. The Full Width at Half Maximum (FWHM) values are approximately 10.7 \({}^{\circ}\)C (29 mm), 8.25 \({}^{\circ}\)C (40 mm), and 7 \({}^{\circ}\)C (50 mm), confirming stable DFG output. The stability of the measurements was achieved using a standard thermoelectric cooler paired with an in-house machined copper heat sink, which also served as the crystal housing. Overall, the experimental data matches well with the simulation results, confirming the reliability of our modeling approach and the effectiveness of the DFG system. For wavelength tunability, the DFG laser output was further characterized by fixing the PPLN temperature at two-degree intervals from 16 \({}^{\circ}\)C to 56 \({}^{\circ}\)C, where the thermoelectric cooler (TEC) functions optimally, and adjusting the multiwavelength C-band fiber laser. The C-band fiber laser provides signal light from 1530 nm to 1555 nm with 1 nm spacing steps, a total power of nearly 380 mW, and a bandwidth of approximately 0.085 nm (FWHM) at 1540 nm. The pump bandwidth at 1064 nm is around 0.5 nm. Figure 6 presents the simulated DFG output power for the 40 mm PPLN, yielding a peak power of around 42 mW, as previously reported, with a signal bandwidth of 1539-1552 nm (approximately 13 nm). This corresponds to an idler tunability of \(\sim\)3390-3440 nm or 50 nm, which is illustrated on the secondary x-axis at the top of Figure 6.  
In the experiment, a temperature change of 40 \({}^{\circ}\)C resulted in a tuning bandwidth of 12 nm, while the simulation indicated a bandwidth of about 13 nm for a temperature change of 48 \({}^{\circ}\)C, showing good agreement with the experimental data.