 Solution

The Q-switched energy extraction efficiency in the ideal loss convention of ii isThe first factor reflects the definition of inversion: one stimulated transition reduces the upper population and increases the lower population, changing $N^{\ast }=N_2-(g_2/g_1)N_1$ by $1+g_2/g_1=\beta$. Thus one emitted photon consumes $\beta$ units of inversion. The second factor accounts for the inversion left after the pulse; finite pumping above threshold does not generally extract all the initially stored inversion. This $\eta$ is not the wall-plug efficiency and does not include the energy cost of pumping or the factor $\zeta$ for imperfect output extraction.