Modeling the pulse shape of Q-switched lasers to account for terminal-level relaxation

To account for the effect of lower-level relaxation, we have derived a characteristic equation for describing the laser pulse from the modified rate equations for Q-switched lasers. The pulse temporal profile is related to the ratio of the lower-level lifetime to the cavity lifetime and the number of times the population inversion density is above the threshold. By solving the coupled rate equations numerically, the effect of terminal-level lifetime on pulse temporal behaviour is analysed. The mode is applied to the case of a diode-pumped Nd:YAG laser that is passively Q-switched by a Cr⁴⁺:YAG absorber. Theoretical results show good agreement with the experiments.