## 4 Discussion
### Comparison between the Experiment and the Theory
These optical-to-optical conversion efficiencies, slope efficiencies and pump thresholds are compared in Table 2. From the theory, with the output coupler transmittance of 10%, the pump threshold was 0.42 W and the maximum output power was 1.89 W at the maximum pump power of 5.0 W. The highest optical-to-optical conversion and slope efficiencies were 37.8% and 41.3%,  
Figure 3: Optical-to-optical conversion efficiency versus laser spot radii with the output coupler transmittance \(T=10\%\) at the maximum pump power of 5.0 W. The red dashed line is the contour line that afforded the optical-to-optical conversion efficiency of 32.4%, which is the highest experimentally obtained efficiency with the output coupler transmittance of 10%. respectively. The highest optical-to-optical conversion efficiency in the experiment is 5.4% lower than that in the theory, the highest slope efficiency in the experiment is 1.2% higher than that in the theory, and the pump threshold in the experiment is approximately 3 times higher than that in the theory. Figure 4: \(Cont\). In general, the slope efficiency is proportional to the coupling efficiency inside and outside the laser cavity, and the mode-matching efficiency between the laser and the pump beam and the pump threshold is proportional to the total cavity loss and the effective mode volume of the laser and pump beam. Therefore, there was a high probability that the mode-matching efficiency is almost appropriate for the highest efficiencies, however, the effective mode volume in the experiment was approximately 3 times larger than the optimum volume. The reason for the difference between the experimental effective mode volume and the theoretical optimum effective mode volume may be due to the deviation of the laser spot radius from the optimum value for high efficiency, as shown in Figure 3. These results mean that it is possible that the efficiencies can be further improved by lowering the pump threshold by a factor of 3 through optimization of the laser spot radii. Figure 5 shows the laser output powers as functions of the incident pump power using the contour line region laser spot radii in Figure 3 with the output coupler transmittance of 10%. As shown in Figure 5, the pump threshold and slope efficiency vary depending on the laser spot radii. The reason for the variation, even though the highest optical-to-optical \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\boldsymbol{y_{\infty}}\) (\%)} & \multicolumn{2}{c}{\(\boldsymbol{y_{\infty}}\) (\%)} & \multicolumn{2}{c}{\(\boldsymbol{P_{\text{th}}}\) (\(\boldsymbol{W}\))} \\ \cline{2-7}  & **Experiment** & **Theory** & **Experiment** & **Theory** & **Experiment** & **Theory** \\ \hline \(T=2\%\) & 18.0 & 18.9 & 20.4 & 19.6 & 0.58 & 0.23 \\ \(T=5\%\) & 29.2 & 30.7 & 34.2 & 32.4 & 0.75 & 0.29 \\ \(T=10\%\) & 32.4 & 37.8 & 42.5 & 41.3 & 1.19 & 0.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the experiment and the theory of the highest optical-to-optical conversion efficiencies (\(\boldsymbol{y_{\infty}}\)) and the corresponding slope efficiencies (\(\boldsymbol{y_{\text{s}}}\)) and pump thresholds (\(\boldsymbol{P_{\text{th}}}\)). Figure 4: Experimental and theoretical laser output powers as functions of the incident pump power. (**a**) The output coupler transmittance \(T=10\%\). The red squares show the experimental results and the red solid line shows the theoretical results. (**b**) The output coupler transmittance \(T=5\%\). The blue squares show experimental results and the blue dotted line shows theoretical results. (**c**) The output coupler transmittance \(T=2\%\). The green circles show the experimental results and the green dashed line shows the theoretical results. conversion efficiencies at the maximum pump power of 5.0 W were the same, is that the effective mode volume and mode-matching efficiency vary with the laser spot radii.