## 3 Results  
### Laser Spectra  
Initially, we investigated the temperature dependence of the laser spectra for the Tm,Ho:YAP crystal in order to gain a comprehensive understanding of the dual-wavelength output and the switching and balancing processes. The laser spectra were recorded using an optical spectrum analyzer (Horiba i550, Kyoto, Japan) with a 0.1 nm resolution. Figure 1: Experimental setup. (**a**) Schematic diagram of the Tm,Ho:YAP SDWL, with the temperature-controlled crystal mounted in an oxygen-free copper holder. (**b**) Photograph of the cryostat with a pair of plane-parallel optical windows. As shown in Figure 2, when the pump power is maintained at approximately 5.0 W, precise temperature adjustment will alter the output wavelength of the laser. The laser wavelengths can switch between 2000 nm and 2119 nm, or simultaneously emit both wavelengths with varying intensity levels. At cryogenic temperatures, the Tm,Ho:YAP laser operates as a three-level system, where Tm\({}^{3+}\) serves as a sensitizing ion. Tm\({}^{3+}\) in \({}^{3}\)H\({}_{6}\) (ground state) absorb pump light at 794.1 nm and transition to the excited-state \({}^{3}\)H\({}_{4}\) level. Subsequently, they return to the \({}^{3}\)F\({}_{4}\) level through a rapid cross-relaxation process. The energy of Tm\({}^{3+}\) in \({}^{3}\)F\({}_{4}\) level is similar in magnitude to that of Ho\({}^{3+}\) in \({}^{5}\)I\({}_{7}\). When the population of the \({}^{3}\)F\({}_{4}\) level increases sharply, an energy-transfer process (ET: Tm\({}^{3+}\)\({}^{3}\)F\({}_{4}\)\(\leftrightarrow\) Ho\({}^{3+}\)\({}^{5}\)I\({}_{7}\)) occurs between Tm\({}^{3+}\) and Ho\({}^{3+}\), leading to a continuous increase in the population of Ho\({}^{3+}\) at the \({}^{5}\)I\({}_{7}\) level. Once a population inversion is established between the excited state and the ground state of Ho\({}^{3+}\), a 2 \(\upmu\)m laser can be achieved with \({}^{5}\)I\({}_{7}\)-\({}^{5}\)I\({}_{8}\) transition. Finally, it should be noted that the generation of dual wavelengths is a result of the energy-level splitting that occurs in both \({}^{5}\)I\({}_{7}\) and \({}^{5}\)I\({}_{8}\), as indicated in Figure 3. Additionally, the population at the splitting energy level follows a Boltzmann distribution, with the Boltzmann occupancy factor changing with temperature. Therefore, the rate of spontaneous emission at 2119 nm increases with temperature, while the value at 2000 nm is reduced. It is worth noting that although the laser crystal was cooled as a whole, the two laser wavelengths actually originated from different areas of the gain medium excited by the pump beam. As is well known, when longitudinal diode pumping is used, the temperature  
Figure 3: Schematic diagram of energy-level transitions and splitting in Tm,Ho:YAP crystals. Figure 2: The switchable and intensity-controllable laser spectra. distribution inside the gain medium is typically non-uniform and Lorentzian-shaped. This suggests that the amount of fluorescence at the 2000 nm and 2119 nm wavelengths in Tm,Ho:YAP is not homogeneous, but rather depends on local temperature. Therefore, the rate of spontaneous emission at the 2119 nm wavelength is likely to be higher in the central part of the pump beam where the temperature is higher, whereas the rate of spontaneous emission at 2000 nm is superior in the surrounding area, where the temperature is lower. According to the change process of the spectrum in Figure 2, prior to the temperature exceeding 49 K, there is only a single wavelength output of 2000 nm. However, as the temperature increases from 49 K to 53 K, the intensity of the 2000 nm wavelength component gradually diminishes, while the intensity of the 2119 nm wavelength component progressively augments. Once the temperature surpasses 53 K, only a single wavelength output of 2119 nm is present. We believed that the optimal temperature for balanced output powers at two emission wavelengths was approximately 51 K, which was to be precisely determined in the following power measurement experiment.