Mode Competition During the Pulse Formation in Passively $Q$-switched Nd:YAG Lasers

We present a detailed theoretical and experimental study of the development of the EM field in pulsed, passively Q-switched solid-state lasers. We solve the rate equations separately for the gain medium and a passive Q-switch, thus accounting for the beam propagation and profile variations between them. Our model enables us to follow the pulse formation from a randomly generated seed EM field, thus monitoring the instantaneous beam pattern. The rate equations used include excited-state absorption in saturable absorber as well as the pumping term. The latter proves to be important when analyzing the beam profiles when passive Q-switching is used. In the case of stronger pumping, the formation of the second laser pulse is observed and shows mode structure characteristic of higher order Laguerre-Gaussian beams. Theoretical results are compared with experiment for three different types of laser resonators. Positive-branch unstable resonators with an ordinary and a super-Gaussian output mirror were studied in order to obtain top-hat beam profile. A plano-concave stable resonator was used as a reference. The calculated beam profiles and temporal developments are in good agreement with the experimental results which proves that the presented computational method can be used to predict the performance of other resonator designs.