In this paper, by considering Gaussian distribution of the intracavity photon density, the coupled rate equations for the diode-pumped doubly Q-switched and mode-locked (QML) laser with EO modulator and GaAs saturable absorber are presented. These equations are numerically solved, and the key parameters of an optimally coupled doubly QML laser have been determined. These key parameters include parameters of the gain medium, the small-signal transmission of saturable absorber as well as the modulation frequency of EO modulator, which can maximize the pulse energy of singly Q-switched envelope. A diode-pumped doubly QML Nd:Lu0.15Y0.85VO4 laser with EO modulator and GaAs saturable absorber is constructed, the experimental results have verified numerical simulation applicable.
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