Modeling the Time-Dynamics of Miniature Passively $Q$ -switched Lasers

The pulse-buildup in miniature passively Q-switched lasers occurs in a similar time-scale as the phonon-assisted thermalization of the laser manifolds. We study how the time-dynamics of the laser is affected by the thermalization and relaxation processes using a dimensionless geometrical rate equation model for a homogeneously broadened four-level gain medium. The pulse length is found to depend strongly on the thermalization rate when the ratio of the ground-state absorption cross section of the saturable absorber to the spectroscopic emission cross section of the laser transition is small (lsim 10). Numerically calculated design curves are shown for the 1064 nm transition in Nd:YAG, and guidelines are given for applying the model to other transitions. Experimental results are used for estimating the thermalization time constant of Nd:YAG for the 1 mum transition group and the ground-state absorption cross section of the Cr⁴⁺:YAG saturable absorber crystal.