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All-solid-state passively Q-switched lasers can exhibit nonlinear behaviors such as period-doubling, injection locking, and chaos under specific conditions, offering new applications in fields like secure communication and random number generation. As a result, the nonlinear dynamics of laser systems are becoming increasingly important. Pump modulation is a typical method of controlling the nonlinear dynamical states of solid-state lasers. In this work, the nonlinear dynamical characteristics of an all-solid-state passively Q-switched Nd:YAG/Cr:YAG laser under pump modulation are investigated by solving a four-level rate equation system using the Runge-Kutta method. The results demonstrate that by adjusting key parameters including modulation frequency, modulation amplitude, and unmodulated pump rate, the laser system can exhibit rich dynamical states, including period-one, period-two, multi-period, and chaotic pulsation. By analyzing the bifurcation diagram, the evolution pattern of output laser pulse characteristics with parameter changes is revealed. The system mainly enters chaos through period-doubling and quasi-periodic routes, while exhibiting a unique phenomenon where the pulse peak and pulse frequency follow synchronized evolutionary paths but with opposite trends in intensity variation, indicating dynamic coupling effects between frequency and intensity domains. By constructing the nonlinear dynamical distributions within a three-dimensional pump modulation parameter space, the combined effects of modulation frequency, modulation amplitude, and unmodulated pump rate on the evolution of the laser's nonlinear dynamics are systematically investigated in this work. The results show that at lower unmodulated pump rates, the system cannot be driven into nonlinear states even when the modulation amplitude and frequency are relatively large. In contrast, under higher unmodulated pump rates, the appropriate tuning of modulation amplitude and frequency enables the system to transition from periodic states to chaotic behavior. This work not only elucidates the modulation mechanisms of pump parameters on the nonlinear dynamics of lasers, but also provides theoretical guidance for optimizing laser output performance and designing high-performance chaotic lasers, which is of great significance in promoting the applications of Q-switched lasers in precision measurement and secure communication fields.
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Keywords:
- pump modulation /
- all-solid-state passively Q-switched laser /
- Nd:YAG/Cr:YAG /
- nonlinear dynamics
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图 1 装置示意图
Figure 1. Schematic diagram of the setup.
图 2 (a) 泵浦速率随时间的变化; (b) 光子数密度随时间的变化; (c) 增益介质反转粒子数密度随时间的变化; (d) 可饱和吸收体粒子数密度随时间的变化
Figure 2. (a) Temporal evolution of the pump rate; (b) temporal evolution of photon number density; (c) temporal evolution of gain medium inversion population density; (d) temporal evolution of saturable absorber population density.
图 3 当未调制泵浦速率和调制幅度分别为1000 s–1和50%时, 不同调制频率下调Q激光脉冲序列、三维相图、轨迹图和分岔图 (a1)—(c1), (a2)—(c2), (a3)—(c3)分别为在调制频率为200, 220, 270 kHz下调Q激光脉冲序列、三维相图和轨迹图; (d1)和(d2)分别为调Q激光脉冲峰值和脉冲频率随调制频率变化的分岔图
Figure 3. When the unmodulated pump rate and modulation amplitude are 1000 s–1 and 50%, respectively, Q-switched laser pulse trains, 3D phase portraits, trajectory diagrams and bifurcation diagrams at different modulation frequencies. Panel (a1)–(c1), (a2)–(c2) and (a3)–(c3) show Q-switched laser pulse trains, 3D phase portraits and trajectory diagrams at modulation frequencies of 200, 220 and 270 kHz, respectively. Panel (d1) and (d2) present bifurcation diagrams of Q-switched laser pulse peak and pulse frequency versus modulation frequency.
图 4 当未调制泵浦速率和调制频率分别为1000 s–1和500 kHz时, 不同调制幅度下调Q激光脉冲序列、三维相图、轨迹图和分岔图 (a1)—(c1), (a2)—(c2), (a3)—(c3), (a4)—(c4)分别为调制幅度为20%, 40%, 48%, 55%下调Q激光脉冲序列、相图和轨迹图; (d1)和(d2)分别为调Q激光脉冲峰值和脉冲频率随调制幅度变化的分岔图
Figure 4. When the unmodulated pump rate and modulation frequency are 1000 s–1 and 500 kHz, respectively, Q-switched laser pulse trains, 3D phase portraits, trajectory diagrams and bifurcation diagrams under different modulation amplitude. Panel (a1)–(c1), (a2)–(c2), (a3)–(c3) and (a4)–(c4) show Q-switched laser pulse trains, phase portraits and trajectory diagrams at modulation amplitude of 20%, 40%, 48% and 55%, respectively. Panel (d1) and (d2) present bifurcation diagrams of Q-switched laser pulse peak and pulse frequency versus modulation amplitude.
图 5 当调制幅度和调制频率分别为50%和500 kHz时, 不同未调制泵浦速率下调Q激光脉冲序列、三维相图、轨迹图和分岔图 (a1)—(c1), (a2)—(c2), (a3)—(c3)分别为未调制泵浦速率为1200, 1300, 1400 s–1下调Q激光脉冲序列、三维相图和轨迹图; (d1)和(d2)分别为调Q激光脉冲峰值和脉冲频率随未调制泵浦速率变化的分岔图
Figure 5. When the modulation amplitude and modulation frequency are 50% and 500 kHz, respectively, Q-switched laser pulse trains, 3D phase portraits, trajectory diagrams and bifurcation diagrams under different unmodulated pump rates. Panel (a1)–(c1), (a2)–(c2) and (a3)–(c3) show Q-switched laser pulse trains, 3D phase portraits and trajectory diagrams at unmodulated pump rates of 1200, 1300 and 1400 s–1, respectively. Panel (d1) and (d2) present bifurcation diagrams of Q-switched laser pulse peak and pulse frequency versus unmodulated pump rate.
图 6 在调制频率fm、调制幅度Am、未调制泵浦速率P0构成的参数空间内脉冲峰值的非线性动力学分布 (a) fm = 500 kHz时, P0与Am构成参数空间内的非线性动力学分布; (b) Am = 50%时, fm与P0构成参数空间内的非线性动力学分布; (c) P0 = 1000 s–1时, Am与fm构成参数空间内的非线性动力学分布
Figure 6. Dynamic distributions of pulse peak in the parameter space of the modulation frequency fm, modulation amplitude Am, and unmodulated pump rate P0: (a) P0 and Am under fm = 500 kHz; (b) fmand P0 under Am = 50%; (c) Am and fm under P0= 1000 s–1.
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