中文摘要：

建立了激光谐振腔往返传输矩阵．通过求解往返传输矩阵的特征值与特征向量．获得了激光谐振腔模式特征。该方法可以用于快速计算同阶贝塞耳函数的所有谐振腔模式和衍射损耗，其结果与Fox—Li数值迭代方式计算结果完全一致。分别就对称谐振腔往返传输矩阵的A^2与单程传输矩阵A的特征值及特征向蔚之间的关系和物理意义．以及非对称谐振腔往返传输矩阵AB与BA的特征值及特征向量之间关系和物理意义进行了分析和讨论，建立了数学表达式，并可以通过改变传输矩阵来提高计算效率。分析了对称共焦腔离散单元数量对光腔模式计算结果的影响．建立了最佳离散单元数量与谐振腔镜片半径的关系表达式，并实现了大菲涅耳系数共焦腔模式的计算。

英文摘要：

Round-way transmission matrix of laser resonator was founded, whose eigenvalue and eigenvector are used for calculating diffraction loss and corresponding mode distribution. The calculated results fit well with the Fox I.i method. The relation of eigenvalue and eigenvector of round-way transmission matrix A^2 and one-way transmission matrix A of symmetrical laser resonator, and that of round way transmission matrix AB and BA of asymmetrical laser resonator, were analyzed. The mathematics expression of transmission matrix relation was founded, which is used for improving calculation efficiency. The calculation discussed the effect of confoeal cavity discrete unit amount on the resonator mode. And mathematics expression between optimizing discrete unit amount and radius of resonator mirror was built, and confocal cavity mode with big Fresnel coefficient was calculated.