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In this work, a comprehensive investigation of dynamic evolution for pulsed solid state laser using topological insulator as saturable absorber (SA) is reported. Without material damage, dynamic transition from Q-switched (QS) state to continuous wave (CW) state in the laser cavity is observed when the pumping rate to the Nd 3+ :YAG laser crystal increases. With a sufficiently large pumping rate, the initiated laser spiking damps and relaxes to CW state similar to a laser system without intracavity SA. Formulated by well-known laser rate equations, analysis of the perturbations around fixed points reveals the instability spectrum that is able to explain the observed transition in experiments. Theoretically, the parameters space to support QS operation are given in terms of the ratio of saturation intensity of laser gain media over the saturation intensity of SA, pumping speed, the ratio of relaxation time of laser gain media over cavity lifetime and the modulation depth of the SA. The result of this work suggests a simple approach to understand passive Q-switched (PQS) laser with SAs of low saturation intensity and guidelines to the design of laser system employing low-saturation materials as SA, such as two-dimensional TI material.

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