We present a new formalism for the analysis of passively Q-switched laser s
ystems that facilitates the performance of sensitivity studies and system o
ptimizations. The developed formalism is general enough to include the impa
ct of an ESA process in the saturable absorber Q-switch and, therefore, is
applicable to Cr4+:YAG passively Q-switched systems. To illustrate the use
of the developed formalism, we have applied it to a comparative analysis of
two laser systems based on Nd:YAG and Yb:YAG.