and

An improved model for passively Q-switched lasers has been developed which explicitly includes the effects of level lifetimes and excited state absorption in the saturable absorber as well as unequal beam diameters in the gain and absorbing media. The optimization equation yields the value of the parameter ρ =ln(ni/nf), where ni and nf are the inversion population densities before and after Q-switching, which maximizes the single-pulse energy. Using this result, the optimum absorber transmission, mirror reflectivity, and pulse energy (and the corresponding peak power and pulse width) can be computed sequentially via simple formulas. As in an earlier theory which did not include excited state absorption, the optimized parameters can be expressed as functions of two variables, αeff and zeff, which are slight modifications of the variables α and z previously introduced by one of the authors for passively Q-switched lasers having no excited state absorption and equal beam areas in the gain and absorbing media. In the new model, we define αeff = Esatamp /Esatabs=αA/As, equal to the ratio of the laser saturation energy to the absorber saturation energy, and β = 1/zeff = 1/FOM + (1-1/FOM)/z. In these parameter definitions, A and As are the beam areas in the gain and absorber media respectively, z = 2lnG0/L as before, G0 is the single-pass small-signal gain, L is the round-trip dissipative loss, and FOM = σgs/σes is the absorber figure of merit corresponding to the ratio of the ground state to excited state cross-sections