最佳耦合调Q激光器理论

Theory of the Optimally Coupled Q-switched Laser

描述调Q激光器运转的通用方程是自然超越方程，需要数值解，这大大增加了实际设备的优化难度。在本文中，我们论证了使用拉格朗日乘法的数值方法，可以得到最佳耦合激光器的所有关键参数的简单解析表达式。例如对一个给定的泵浦功率，使用一个最佳反射率获得最大激光效率。这些参数（包括最佳反射率、输出能量、抽运效率、脉宽、峰值功率、等）都能被表示成一个简单无量纲变量Z-的函数，z被定义为非饱和小信号增益与耗散（无用）光功率的比值，然后与几个简单常量相乘。通过几个曲线图和一个简单的手算结果的帮助，能快速完成激光器的设计优化和性能设计规划。最后介绍了一个高增益Nd：YAG和一个低增益紫翠玉激光器的计算案例，作为该方法的具体说明。

The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions. This greatly complicates the optimization of real devices. In this paper, we demonstrate that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i. e. , one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters （ which include the optimum reflectivity, output energy, extraction efficiency,pulse width,peak power, etc. ） can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative （nonuseful） optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can he accom- plished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd：YAG and a low-gain alexandrite laser are presented as illustrations of the technique.