Q-switched energy extraction efficiency ($\eta ={\beta }^{-1}(1-N_f^{\ast }/N_i^{\ast })$)

For an ideal pulse with negligible stored seed photons and useful output accounting for all cavity photon loss, the extracted energy is $(N_i^{\ast }-N_f^{\ast })V_g\hslash {\omega }_L/\beta$. The factor $\beta =1+g_2/g_1$ converts inversion depletion into stimulated transitions. With over-pumping $r=N_i^{\ast }/N_{\mathrm{th}}^{\ast }$, the nonzero extraction branch satisfies $r\beta \eta =-\ln (1-\beta \eta )$. A fraction $0.95$ of the maximum energy requires $r=-\ln (0.05)/0.95$.