Theoretical models and analytic expressions for buildup time of pulsed confocal unstable optical parametric oscillators with uniform or Gaussian reflectivity mirrors

A theoretical model and a simplified analytic expression are developed to describe the buildup time of a pulsed confocal unstable optical parametric oscillator (OPO) with a uniform-reflectivity mirror (URM) or a Gaussian-reflectivity mirror (GRM). Two analytic expressions have been demonstrated to correspond to theoretical models with a sufficient degree of accuracy. The effects of a variety of cavity and pump parameters on the buildup time of an OPO were investigated and analyzed. It was found that a GRM unstable OPO generally exhibits a shorter buildup time than the corresponding URM unstable OPO with equally effective output coupling.