## 3 Results and Discussion  
### Energy Characteristics  
We found that the efficiency of 589 nm generation, \(\eta_{589}\) = (E\({}_{589}\)/E\({}_{532}\)) \(\times\) 100%, was almost equal for pump spots of \(\sim\)2 and \(\sim\)4 mm. The difference did not exceed \(\pm\)5% and can be attributed to the errors during the attenuation of E\({}_{532}\) when setting the given I\({}_{532}\) for minor (2 mm) spots. Table 1 represents the \(\eta_{589}\) data obtained for a 4 mm spot. The maximum conversion efficiency was obtained in lasers with a flat cavity. Note that larger efficiencies (>62% with a flat cavity) could be obtained at I\({}_{532}\) > 350 MW/cm\({}^{2}\). In lasers with an unstable cavity, the efficiency was a little lower. However, in lasers with stable spherical cavities, the efficiency was considerably reduced in comparison with flat-cavity lasers. The lowest values of \(\eta_{589}\) were obtained with spherical cavities with mirrors with the lowest radius of curvature. As the 589 nm radiation here is actually created by 559 nm radiation, we also measured the conversion efficiencies of 559 nm generation, \(\eta_{559}\) = E\({}_{559}\)/E\({}_{532}\)\(\times\) 100%, in different laser cavities with an output mirror optimized for 559 nm generation (a high reflection at 532 nm and 98% transmission at 559 nm). The results for the 4 mm spot are shown in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline
**Pump Mirror Curvature** & **I\({}_{532}\) = 120 MW/cm\({}^{2}\)** & **I\({}_{532}\) = 220 MW/cm\({}^{2}\)** & **I\({}_{532}\) = 350 MW/cm\({}^{2}\)** \\ \hline Flat & 43 & 54 & 57 \\ \hline Convex, R = 2000 mm & 36 & 49 & 53 \\ \hline Convex, R = 750 mm & 32 & 44 & 47 \\ \hline Concave, R = 1000 mm & 25 & 30 & 31 \\ \hline Concave, R = 500 mm & 11 & 16 & 19 \\ \hline \end{tabular}
\end{table} 
Table 1: Conversion efficiency of the Raman laser at 589 nm. \begin{table}
\begin{tabular}{c c c c} \hline
**Pump Mirror** & **I\({}_{532}\) = 120 MW/cm\({}^{2}\)** & **I\({}_{532}\) = 220 MW/cm\({}^{2}\)** & **I\({}_{532}\) = 350 MW/cm\({}^{2}\)** \\ \hline Flat & 41 & 61 & 67 \\ \hline Convex, R = 2000 mm & 40 & 60 & 64 \\ \hline Convex, R = 750 mm & 37 & 58 & 62 \\ \hline Concave, R = 2000 mm & 14 & 31 & 39 \\ \hline \end{tabular}
\end{table} 
Table 2: Conversion efficiency of the Raman laser at 559 nm. A comparison of the results in Tables 1 and 2 reveals very similar relations between the laser efficiency and the cavity configuration for 589 nm and 559 nm generation. Thus, we believe that the reduction in \(\eta_{\text{589}}\), in general, is caused by the worsening of the 532\(\rightarrow\)559 nm conversion at the first stage of the cascade process (532\(\rightarrow\)559\(\rightarrow\)589 nm). The worsening of the 532\(\rightarrow\)559 nm conversion in the Raman laser with a spherical cavity can be explained, similar to [10], by the worse spatial overlap between the 532 nm pump radiation and 559 nm Stokes radiation. In our case, for a large spot size and a homogeneous pump, we can neglect the variation in the pump and Stokes field distribution along the resonator axis and only take into account the dependence of the Stokes field transversal distribution on the cavity configuration. The overlap is characterized by a normalized overlap integral of the Stokes and pump transverse intensity profiles [11]:  
\[1/\text{A}_{\text{eff}}=(\int\text{I}_{532}\text{I}_{559}\text{dA})/(\int\text {I}_{532}\text{dA})^{2}\]  
where integration is performed over the entire area A of the pumping beam.