## 3 Results
### Beam Quality and Power Stability  
We conducted a further investigation of the beam quality of each wavelength of the Tm,Ho:YAP SDWL with balanced output at different pump powers (the optimal temperature values can be determined based on Figure 5). After performing a Gaussian transformation on the laser beam using a lens with a focal length of 100 mm, the two-dimensional laser profile of the beam waist was obtained by an infrared camera (Spiricon Pyrocam IIIHR, North Logan, UT, USA), and the beam quality of the SDWL was measured by a slit-scanning beam profiler (Thorlabs M2 MS, Newto, NJ, USA). Figure 5: Experimental results of the optimal temperature for balanced output powers of two distinct wavelengths with respect to the pump power and the linear fitting curve of the experimental data. Transverse distributions of the beam waist for the SDWL at 2000 nm and 2119 nm with pump powers of 2.95, 4.98, 6.10 and 7.03 W are illustrated in Figure 7a. The beam-profiling camera featured a 12.8 mm \(\times\) 12.8 mm active area, and we specifically captured a central 1.5 mm \(\times\) 1.5 mm region centered on the beam spot in the figure to offer a more detailed view of the beam's shape and distribution characteristics, showcasing subtle features and intensity variations. An integrated chopper was included in the camera setup to ensure the accuracy and reliability of the measurement for the 2 \(\upmu\)m continuous-wave (CW) beams, effectively managing the beam's intensity and preventing potential sensor damage or saturation. The transverse beam cross-sections, which represent the spatial extent of the beam at specific wavelengths, were also measured. For wavelengths of 2000 nm and 2119 nm, we determined that the beam cross-sections were approximately 465 \(\upmu\)m and 420 \(\upmu\)m, respectively. As previously mentioned, the two wavelengths of laser actually originate from different areas of the gain medium excited by the pump beam. We found that the beam-waist radius of the 2000 nm wavelength component, which originates from the surrounding area of the gain medium, is overall slightly larger than that of the 2119 nm wavelength component, which comes from the central area of the gain medium. This results in the beam-quality M\({}^{2}\) factor of the 2119 nm wavelength component being slightly better than that of the 2000 nm wavelength component, as shown in Figure 7b. For any specific wavelength component, the beam-waist radius remains almost unchanged, while the beam-quality M\({}^{2}\) factor increases with the pump power. This indicates that the far-field divergence angle of the SDWL has expanded. With our maximal incident pump power of 11.8 W, the beam-quality factors of the two wavelengths were measured to be M\({}^{2}_{2000}=1.39\) and M\({}^{2}_{2119}=1.30\), respectively. For a verification of the output stability, the dual-wavelength laser power was measured over 15 min, and the results are shown in Figure 8. The overall power level remained relatively stable, maintaining approximately 0.61 W. Although there was a slight drift in the output power of the two wavelength components, they consistently exhibited a complementary changing trend, such that when the power of one wavelength component increased, the power of the other wavelength component correspondingly decreased. The root-mean-square-error (RMSE) power instabilities were slightly higher than those of the single-wavelength solid-state laser. The RMSEs of the total output power and the individual powers at 2000 nm and 2119 nm were 2.3%, 1.9% and 1.2%, respectively. These results indicate that the stability at 2000 nm is somewhat lower than that at 2119 nm, which is consistent with the relationship between beam quality and beam-waist radius. Compared with the previous results for a common dual-wavelength laser based on a single laser crystal [26; 27], the power stabilities have been slightly improved. Figure 6: Total SDWL output power.