By considering the single-photon absorption (SPA) and two-photon absorption (TPA) processes in the GaAs saturable absorber, the coupled rate equations for a diode-pumped passively Q-switched and mode-locked (QML) laser with GaAs coupler under Gaussian approximation are given. The key parameters of an optimally coupled passively QML laser can be obtained by numerically solving these equations. 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. Sample calculations for a diode-pumped passively Q-switched mode-locked c-cut Nd:GdVO 4 laser with a GaAs saturable absorber are presented to demonstrate the optimal method applicable.