把圆形高斯镜平凹腔自再现模的衍射积分方程转化为有限阶的矩阵方程, 在平面输出镜呈高斯分布的镜面变形时, 数值计算了激光场模式的场强、相位分布和模式本征值。结果表明, 当变形量较小时, 随着变形量的增加, 镜面上光场的分布范围增大, 也就说明模体积增大, 但镜面光场仍保持拉盖尔-高斯光束基模特征, 相位由平面慢慢变得凸起, 远场分布变化不明显。当变形量较大时, 光场分布开始发生畸变。从模式本征值的变化看, 在一定的变形范围内, 本征值下降不多, 说明较小的变形量对激光损耗影响不大, 仍能使激光较稳定输出。在圆形高斯镜平凹腔输出镜发生不大的高斯状变形的情况下, 仍有维持输出高质量激光束的能力。

Using the boundary finite-element method, the diffraction integral equation of the circular plano-concave resonator with a Gaussian-reflectivity mirror is transformed to the finite-order matrix equation. The mode distributions are calculated numerically. The results of calculation show that when the thermal deformation of the output mirror is small, the radius of the laser mode is increased following the increasing of mirror’s deformation. On the same time, the mode distribution keeps the foundational Laguerre-Gaussian mode shape, the far field distribution keep well and the mode eigenvalues decrease only a little. Just when the thermal deformation of the mirror is big enough, for instance, under the conditions are set in calculation, when the peak of deformation more than 1.1λ, following the thermal deformation increase, the laser field distribution is distorted, mode eigenvalues decrease sharply and far field distribution is expanded.