Dynamics and stability of a laser system with second-order nonlinearity

We use a multimode rate-equation model to investigate the stability of a laser system with second-order nonlinearity and compare the results with the literature on intracavity frequency-doubled lasers. The emphasis is on the Hopf bifurcation between the asymptotically stable state and the stable oscillation that occurs with variation of the conversion efficiency from the fundamental frequencies to their sum. This bifurcation results in two simple expressions that describe the stability curve, depending on material and cavity parameters. We also report on an experimental confirmation of the predicted temporal behavior of sum-frequency generation.