## 3 Results
### Output Power of the Tm,Ho:YAP SDWL  
The spectral measurement results indicate that the power of each wavelength will change with temperature variation, and there should exist an optimal temperature point at which the output power of two wavelengths is equal. The signal transmission fiber and PbS detector of the spectrometer cannot guarantee a completely consistent intensity response for the two wavelengths. Consequently, the peak intensities of the laser spectrum cannot be used to accurately determine the power ratio of the dual wavelengths. Therefore, at this stage, a power meter was employed to conduct a detailed analysis of the balancing process for the SDWL.  
The power meter used in the experiment was Coherent PM2, and, subsequently, the laser oscillation threshold with respect to incident pump power was found to be around 0.8 W. To explore the dynamics of the Tm,Ho:YAP SDWL, we utilized IR bandpass filters (T \(\approx\) 0.04% at 2000 nm and T \(\approx\) 61% at 2119 nm) to separate and record the output performance for each wavelength.  
Figure 4 depicts the temperature dependence of the output powers at 2000 and 2119 nm for three different pump powers of 2.95 W, 4.98 W and 7.03 W. We determined optimal temperature values of approximately 52.7, 50.2 and 47.7 K, and obtained an SDWL with 0.03, 0.15 and 0.25 W output powers at both 2000 nm and 2119 nm.  
Furthermore, we also observed that the optimal temperature point is almost located at the central position of the dual-wavelength temperature-change process. Taking the  
Figure 4: Output powers of the Tm,Ho:YAP SDWL at 2000 nm and 2119 nm with respect to the temperature at incident powers of (**a**) 2.95 W, (**b**) 4.98 W and (**c**) 7.03 W.  
dual-wavelength change process at a pump power of 4.98 W as an example, the critical temperature point for transitioning from a single 2000 nm wavelength output to a dual-wavelength output state is 48.2 K, and the critical temperature point for transitioning from a dual-wavelength output state to a single 2119 nm wavelength output is 52.1 K. The optimal temperature value required to achieve a balanced output is 50.2 K, which is approximately equal to the average of the two critical temperature values.  
Based on the local heating generated by the pump absorption, it can be observed that the optimal temperature for achieving a balance in output powers at two distinct wavelengths depends on the pump power. Further investigations have reported optimal temperature values for various pump intensities, which provide confirmation of the influence of the local heating phenomenon, which is clearly demonstrated in Figure 5.  
It was observed that the optimal temperature for balancing the dual-wavelength output powers shifts toward lower values with increasing pump power due to the local heating. Empirical evidence suggests that the optimal temperature to achieve a balance in output powers at two distinct wavelengths exhibits an approximately linear relationship with the level of pump power. Furthermore, the rate of change of the optimal temperature with respect to the pump power can be estimated as 1.19 K/W.  
Figure 6a shows the total SDWL output power in relation to temperature for different incident pump powers of 2.95, 4.98 and 7.03 W. It was observed that there was a slight improvement in overall performance as the temperature increased, and thus the overall output efficiency of the laser varies with temperature. Here, our primary focus is on the balanced output phenomenon at the optimal temperature; therefore, we calculated the output efficiency of the laser at the optimal temperature. According to Figure 6b, it can be calculated that at our maximal pump power of 11.8 W, the optical-to-optical conversion efficiency of the laser is 12.7%, and the slope efficiency was linearly fitted to be 15.8%.