Mode evolution mechanism of Pr³⁺:YLF single longitudinal mode laser

We develop a theoretical model of multimode rate equation that accurately describes mode evolution mechanism of prelase Q-switched Pr³⁺:YLF single longitudinal mode (SLM). We find that it is important to consider the effect of gain difference when calculating the mode competition time accurately. We identify that there is an optimal parameter for the two step signal of acoustic-optic modulator which determines the stability of SLM output. Then, a visible light direct oscillation Q-switched SLM Pr³⁺:YLF laser at 639.5 nm is obtained, and the experimental results is agree with the simulation very well.