Comparison of passive Q-switching and Q-switched mode-locking transition in Nd:MgO:LiNbO3 laser based on cavity length modulation

The transition from passive Q-switching (PQS) to Q-switched mode-locking (QML) in the Nd:MgO:LiNbO 3 laser is systematically investigated. A coupled rate equation model is established by introducing a hyperbolic secant function into the PQS photon density equations. The cavity length is identified as a key parameter for the transition. Both simulations and experiments reveal a critical cavity-length range, within which the output evolves from a Q-switched envelope to a stable QML pulse train. Experimentally, PQS operation is achieved at a cavity length of 60 mm and a pump power of 20 W, yielding a pulse width of 18.6 ns and a repetition frequency of 13.1 kHz. At an extended cavity length of 190 mm and a pump power of 24 W, the system shifts into a critical transitional state, generating 4.8 ns mode-locked spikes at a repetition frequency of 789 MHz. Further increasing the cavity to 400 mm yields stable 1084 nm QML output, delivering a significantly compressed pulse width of 495 ps, a 370 MHz repetition frequency, and a maximum output power of 0.844 W. This study elucidates the critical role of cavity length in modulating the pulse evolution from Q-switched envelopes to QML pulse trains.