A highly inclusive theory of Q-switched lasers is presented which applies to both actively and passively Q-switched lasers. The theory expands on the author’s previous publications on energy optimization to include: (1) saturable absorbers exhibiting excited state absorption and therefore a finite Figure of Merit (FOM); (2) unequal beam areas in the gain and absorbing media; and (3) both pulsed and CW pumping. Design curves for optimizing the output energy for pulse pumped lasers and CW pumped lasers at a desired pulse rate are provided. As in the author’s previous work, the optimization equation is obtained utilizing Lagrange Multipliers and yields the value of the parameter $\rho = ln(n_{i}/n_{f})$ which maximizes the single pulse energy, where $n_{i}$ and $n_{f}$ are the laser inversion population densities before and after Q-switching. Using this initial result, the associated optimum absorber transmission and mirror reflectivity, pulse energy, peak power, and pulse width can be computed sequentially via simple formulas. The aforementioned parameters can all be expressed as functions of two variables, $\alpha $ and $z_{eff}$ , which are slight modifications of the variables $\alpha $ and z previously introduced by the author for passively Q-switched lasers having infinite FOM and equal beam areas The term “plane wave theory” has sometimes been used by this and other authors in prior publications to describe a uniform pump profile in the laser medium, but we will refer to this special case more accurately as the “uniform pump theory”. The theory is extended here in the final section to include non-uniform pumping. The common case of a Q-switched laser end-pumped by a quasi-Gaussian CW laser is considered in detail and the theoretical results are found to agree well with experimental data.

中文翻译：

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调Q激光器的高度包容性理论

提出了一种高度包容的 Q 开关激光器理论，该理论适用于主动和被动 Q 开关激光器。该理论扩展了作者之前关于能量优化的出版物，包括： (1) 饱和吸收体表现出激发态吸收，因此具有有限的品质因数 (FOM)；(2) 增益介质和吸收介质中光束面积不等；(3) 脉冲和连续波泵浦。提供了用于在所需脉冲速率下优化脉冲泵浦激光器和 CW 泵浦激光器的输出能量的设计曲线。在作者之前的工作中，优化方程是利用拉格朗日乘子获得的，并产生参数的值 $\rho = ln(n_{i}/n_{f})$ 最大化单脉冲能量，其中 $n_{i}$ 和 $n_{f}$ 是 Q 开关前后的激光反转布居密度。使用这个初始结果，相关的最佳吸收器透射率和镜面反射率、脉冲能量、峰值功率和脉冲宽度可以通过简单的公式依次计算。上述参数都可以表示为两个变量的函数， $\alpha $ 和 $z_{eff}$ ，这是对变量的轻微修改 $\alpha $ 和 z 之前作者为具有无限 FOM 和相等光束面积的被动调Q 激光器引入的术语“平面波理论”有时被作者和其他作者在先前的出版物中用于描述激光介质中的均匀泵浦轮廓，但我们将这种特殊情况更准确地称为“均匀泵理论”。该理论在最后一节中进行了扩展，以包括非均匀泵送。详细考虑了由准高斯连续激光器端部泵浦的调Q激光器的常见情况，发现理论结果与实验数据非常吻合。