Optimization of passively Q-switched and mode-locked laser with Cr:YAG saturable absorber

By considering the Gaussian spatial distributions of the intracavity photon density and the initial population-inversion density, the coupled rate equations for a diode-pumped passively Q-switched and mode-locked (QML) laser with Cr⁴⁺:YAG saturable absorber are given. These coupled rate equations are solved numerically and the key parameters of an optimally coupled passively QML laser are determined for the first time. These key parameters include the parameters of the gain medium, the saturable absorber and the resonator, which can maximize the pulse energy of singly Q-switched envelope. The optimal calculations for a diode-pumped passively QML Nd:GdVO₄ laser with Cr⁴⁺:YAG saturable absorber are presented to demonstrate the numerical simulation applicable.