激光腔稳定性的衍射解法

由高斯振幅分布的光场之菲涅耳衍射，求得高斯光束的空间传播形式．在此基础上求解激光腔ＴＥＭ０，０模之腰斑Ｗ０２及其相对于腔镜的位置，由此自然地得到，激光腔稳定条件即是激光器产生的高斯光束腰斑大于零的条件。在此过程中，完全摒弃了矩阵光学方法，而强调光波衍射对谐振腔稳定性的基本重要性．引入约化半径ｒ１，ｒ２作参数绘制稳区图．稳区图共有四个明显的稳定区，每一区正好与激光腔一种稳定结构对应．此稳区图比广为采用的ｇ１，ｇ２参数双曲线图直观、方便、实用．提出了求解激光束参数的图解法，此方法有利于激光腔设计者全面地掌握激光器工作状态．

SOLUTION TO THE LASER CAVITY STABILITY BY DIFFRACTION

The explicit expression of the Gaussian beam is obtained as a result of the Fresnel diffraction of a Gaussian-distributed plane field. Thereby the waist w of the TEM0.0mode and its position relative to the reflecting mirrors for a given laser cavity are calculated by matching the mirrors with the possibly existing Gaussian beam. The stability conditions for the laser cavity are naturally brought about, which are nothing but conditions underwhich Gaussian beams with positively-valued waist are excited. In the work, the customarily established matrix treatment to the subject is completely discarded while the importance of the Fresnel diffraction is emphasized. We then re-shape the stability diagram with the reduced radii r1,r2 of the reflecting mirrors as variables instead of the widely employed g1, g2variables. It turns out that there are four distinct stable zones in the diagram, each of which corresponds to a clearly defined stable laser cavity structure. The diagram appears informative, directly perceived and easy to be referred to. Finally, we demonstrate the way of seeking for the Gaussian beam parameters by working on a family of characteristics of Gaussian beams. This graphic method enables one to visualize the laser operation clearly and fully.