## 4 Experimental Results and Discussion  
### Output Power of the SLM Nd:YVO\({}_{4}\) Laser  
Figure 2 provides the output-power results of the all-solid-state Nd:YVO\({}_{4}\) laser at free-running and SLM oscillation. One power meter (PM400, THORLABS) measured all power in this experiment. The conversion efficiency from pump light to free-running laser was 46.7%. The gray line in Figure 2a is the linear fitting of the free-running output power. The laser's slope efficiency at free-running oscillation was 51.5%, equivalent to the gradient of the fitting line. Figure 2b gives the SLM output power of the Nd:YVO\({}_{4}\) laser after a 4%-reflectivity FP etalon was inserted into the oscillator. Circles and triangles in Figure 2b signify the SLM laser output with FP etalons made of K9 glass and LT crystal, respectively. The threshold  
Figure 2: The output-power results of the all-solid-state Nd:YVO\({}_{4}\) laser at (**a**) free-running and (**b**,**c**) SLM oscillation. pump power for SLM oscillation was 0.93 W (K9 etalon) and 0.81 W (LT etalon). The threshold value of the pump power with a 4%-reflectivity LT etalon was lower than that at free-running operation. This decline was because the frequency of the first-oscillating longitudinal mode changed after the LT etalon was put into the oscillator, and subsequently, the mode's gain increased. The highest SLM output power from two FP etalons was at close levels, 0.18 W (K9 etalon) and 0.19 W (LT etalon). The gray dash-dot and dotted lines in Figure 2b were the linear fittings of the SLM output power, respectively, from K9 glass and LT crystal etalons. Both slope efficiencies (35.2% with K9 etalon and 24.8% with LT etalon) were smaller than that in the free-running condition due to the insertion loss of two FP etalons [17; 18; 19]. The slope efficiency with LT etalon was not as high as that with K9 etalon because the LT crystal absorbed a 1064 nm laser [20]. In Figure 2c, the blue diamonds denote the SLM laser power when the K9-glass etalon of 80% reflectivity was placed in the laser's oscillator. In this case, the laser's threshold pump power rose to 1.93 W, more than twice that with the 4%-reflectivity K9 etalon. This increase also resulted from the insertion loss of the 80%-reflectivity FP etalon. When the tilted angle of the 80%-reflectivity etalon was lower than \(1^{\circ}\), the etalon, together with the first cavity mirror, constituted a second oscillator in the laser. The formation of the second oscillator made it difficult for us to achieve SLM operation in the laser. Different series of longitudinal modes from two oscillators oscillated simultaneously, and we could not inhibit the oscillation of the modes from the second oscillator. To avoid the occurrence of the second oscillator, we adjusted the angle of the 80%-reflectivity FP etalon to larger than \(2^{\circ}\). Thus, the insertion loss induced by this FP etalon climbed. Another consequence of the increasing insertion loss from the 80%-reflectivity etalon was a low slope efficiency (4.7%) for SLM laser power. This slope efficiency is from the linear fitting, displayed as a gray dotted line in Figure 2c. The highest SLM laser output with the 80%-reflectivity K9-glass FP etalon was 0.11 W. This power value was lower than that with the 4%-reflectivity FP etalons, as the second longitudinal mode oscillated earlier at a high pump power owing to the spatial hole burning. We acknowledged the significant difference in power output between the free-running laser and the SLM laser with FP etalons shown in Figure 2. On the one hand, this difference was due to the insertion loss introduced by the FP etalons, which reduced the overall power of the laser. On the other hand, the single mode-selecting element had a limited capacity for longitudinal mode suppression. To simplify the laser structure, we employed only one mode-selecting component--an etalon. With the pumping power increasing, the laser transitioned to the multi-longitudinal mode operation.