Simultaneous Q-switching and mode locking (QML) in a diode-pumped Nd:LuVO4 laser using a GaAs wafer as saturable absorber is experimentally demonstrated in a Z-type folded cavity. The repetition rate of the Q-switched pulse envelop increases from 48 to 116 kHz and the average output power increases from 88 to 498 mW as the pump power increases from 1.7 to 8.2 W. It is found that QML is easily realized in a Z-type cavity. The mode-locked pulse inside the Q-switched pulse has a repetition rate of 111 MHz, and its average pulse width is estimated to be about 345 ps. Using a hyperbolic secant square function and considering the Gaussian distribution of the intra-cavity photon density to model the mode-locked pulse, we propose a developed rate equation model for the Q-switched and mode-locked lasers. The numerical solutions of the equations are in good agreement with the experimental results.
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