## 4 Discussion  
### Comparison between the Experiment and the Theory  
We theoretically analyzed and reproduced the experimental results of the output coupler transmittance of 10%, in which the highest efficiency was obtained, to confirm the reliability of our theoretical analysis described in Section 2.2. In this analysis, we used the same pump parameters as in the experiment: the same pump spot radii, focus positions, beam qualities and pump absorption efficiency at the pump wavelength of 532 nm (obtained in the experiments). First, we calculated the laser spot radii dependence of the optical-to-optical conversion efficiency \(\eta_{\text{oo}}\). Figure 3 shows the optical-to-optical conversion efficiency as a function of the laser spot radii for the vertical and horizontal axes with the output coupler transmittance of 10% at the maximum pump power of 5.0 W. Figure 3 also shows the red dashed 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% at the maximum pump power. As shown in Figure 3, the optimum laser spot radii for the highest optical-to-optical conversion efficiency were 12 \(\upmu\)m and 21 \(\upmu\)m for the vertical and horizontal axes, respectively. The optimum spot radii were almost the same for other output coupler transmittances. The optimum spot radius in the vertical axis is approximately 20% larger than the pump beam radius in the same axis, and the optimum spot radius in the horizontal axis is approximately 15% larger than the pump beam radius in the same axis. These laser spot radii dependencies of the optical-to-opticalconversion efficiency were employed in the theoretical analysis, and the experimental and theoretical results were compared. As shown in Figure 3, the spot radii dependence of the optical-to-optical conversion efficiency is relatively low in the high-efficiency region. The comparison between the theory and the experiment in Figure 3 indicates that the laser spot radii in the experiment were considered to deviate extremely from the optimal radii for the highest efficiencies. Nevertheless, in these experiments, higher efficiencies than before have been obtained to the best of our knowledge. This should be another reason why the slope efficiency is almost constant in the experiments, as shown in Figure 2. This means that even if the laser spot radii could vary by variation of thermal lens effects, the variation of slope efficiency is also low in the range of high optical-to-optical conversion efficiencies because of the low variation of optical-to-optical conversion efficiencies in this range. This low laser spot radii dependence of the efficiency is obtained from the high-intensity pumping. In general, when the output coupler transmittance is optimized to obtain the highest efficiency, the internal cavity laser intensity is lower than that at lower output coupler transmittances. However, under conditions of high-intensity pumping, it is easy to keep the internal cavity laser intensity high even when the output coupler transmittance is set to conditions of optimum coupling efficiency in order to obtain the highest efficiency. As a result, as shown in Figure 3, the optical-to-optical conversion efficiency in the high laser efficiency region did not vary much as the laser spot radii in the gain medium varied, because the induced emission remained strong enough in the high laser efficiency region. Figure 4 compares the experimental and theoretical dependencies of laser output power on incident pump power. The laser spot radii in the theory in Figure 4 were optimized for the highest optical-to-optical conversion efficiency.