为了研究激光在高斯镜平凸非稳腔中的模式和相位特征，在SIEGMAN分析多元件非稳腔的理论基础上，采用有限元数值方法计算耦合输出镜镜面反射率为高斯分布的圆镜平凸非稳腔本征模场分布。将光场在腔内一次往返的ABCD系数代入惠更斯－基尔霍夫衍射积分方程，可以写出光场往返一次的衍射积分方程。将镜面分割成若干个等宽圆环，把衍射积分方程转化成矩阵相乘形式，经过数值计算，得到理想空腔和非共轴空腔优先起振的光场本征模式分布结果与相位特性。计算结果表明，当合适选择输出镜半径与高斯反射率分布，可以得到光斑半径为0．3cm的基模高斯光束输出，此计算结果与实验结果相符。同时也讨论了耦合输出镜对光束质量的影响。

In order to study the mode and the phase characteristic of laser in an unstable resonator with Gaussian reflectivity mirrors,a finite element method is presented to numerically calculate mode-fields of the spherical plano-convex unstable resonator with Gaussian reflectivity mirrors,which is based on the canonical formulation of SIEGMAN's theory for analyzing multi-element unstable resonators. The round-trip cylindrical Huygen's integral is expressed for the resonator in terms of spherical resonator analysis and ABCD matrix. The Huygen's integral is transformed to a finite sum format by dividing the output mirror into several width-equal circles. The eigenmode and phase result of self-reproduce field of perfect empty resonator and misalignment empty resonator are obtained via numerical calculation. The calculation result indicates that when the radius and Gaussian reflectivity of output mirror are appropriately selected,the fundamental mode distribution of Gaussian beam which has a spot radius of 0.3cm can be obtained. The calculation result accords with the experiment result. Simultaneously the influence of the output mirror on the beam quality is also discussed.