在腔内倍频的连续激光器速率方程中考虑抽运光束、反转粒子数密度以及腔内基频和倍频光子数密度的空间分布,通过归一化相关参量显示出该速率方程的解依赖于3个无量纲综合参量,这3个参量为:抽运光束与激光光束截面比、归一化的抽运水平及一个与倍频晶体倍频能力有关的参量ηSHG.通过数值求解该速率方程,得到了一组关于方程的通解与3个综合参量之间关系的普适曲线.同时确定了最佳抽运光束与激光光束截面比以及最佳ηSHG,还与平面波近似下获得的结果进行了比较. Considering the spatial distribution of the pump beam, the inverted particle number density and the fundamental frequency and multiplicative photon number density in the continuous multiplier-rate laser equation, the solution dependence of the rate equation is shown by normalizing the relevant parameters The three non-dimensional integrated parameters are the pump beam-to-laser beam cross-section ratio, the normalized pump level, and a parameter, ηSHG, that is related to the frequency multiplying power of the frequency doubling crystal. The rate equation , We get a set of universal curves about the relationship between the general solution of the equation and the three comprehensive parameters.At the same time, the optimal pumping beam to laser beam section ratio and the best ηSHG are determined, and the results obtained with the plane wave approximation Compare