Based on a four-level rate equation model, we numerically simulated the nonlinear dynamics of a diode-pumped solidstate passively Q-switched laser. A Nd:YAG and a Cr4+:YAG is used as the gain medium and the saturable absorber in this system, respectively. Through setting the pumping rate or the round-trip optical loss at different values, the diodepumped solid-state passively Q-switched Nd:YAG/Cr4+:YAG laser may operate at the period-one, period-two, multiperiod or chaotic states. For a certain specific state, the time series, the power spectra and the Poincaré maps are represented. Moreover, the route for the diode-pumped solid-state passively Q-switched Nd:YAG/Cr4+:YAG laser entering into chaos is revealed by mapping the bifurcation.
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