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针对离轴正支共焦非稳腔中最低的三阶横模特征值随着腔参数的变化规律问题,基于适用于非稳腔结构的特征向量法,计算了有效菲涅耳数在63附近的不同腔参数下各阶横模的特征值。数值模拟结果表明,在几何放大率大于1.08的条件下,若有效菲涅尔数取在整数附近,1、2阶横模会周期性的发生模式交叉,所有基于Fox-Li迭代的算法很难得到自在现模。随着M的增加而增加,特征值的模值大小会随着几何放大率的增加而近似线性的减小,各阶模式的衍射损耗会线性增加,在非模式交叉的情况下,1、2阶横模特征值模值的差值会增加。
Aiming at the problem that the lowest third-order transverse mode eigenvalue of off-axis positive-branch confocal unstable chamber changes with the cavity parameters, the effective Fresnel number is calculated based on the eigenvector method applied to the unstable resonator structure The eigenvalues of transverse modes under different cavity parameters. The results of numerical simulation show that at the geometric magnification greater than 1.08, if the effective Fresnel numbers are around the integers, the first and second order transverse modes will periodically cross each other. All the algorithms based on Fox-Li iteration are difficult Get comfortable with the current model. With the increase of M, the modal value of the eigenvalue decreases linearly with the increase of geometric magnification, and the diffraction loss of each mode increases linearly. In the case of non-mode crossover, 1,2 The difference between the modulo-mode eigenvalues increases.