厄米-高斯光束的M2因子矩阵

提出了厄米-高斯光场的M²因子矩阵.引入束半宽平方的交叉项、M²因子的交叉项，理论推导出了在同一坐标系下光场旋转一定角度后的M²因子矩阵，数值模拟了与M²因子矩阵有关的各参数随光场旋转角度变化的规律，给出了光场的M²因子矢量点随光场旋转角度变化的轨迹曲线.计算结果与理论推导结果相符，证实了利用M²因子矩阵可以将旋转前后的二维厄米-高斯光场用旋转矩阵统一起来.该方法可推广到对一般的二维高阶高斯光束的光束质量的理论分析上，具有普适性，对光束质量的实际测量有重要的理论指导意义.关键词：M²因子矩阵')" href="#">M²因子矩阵厄米-高斯光束非对称激光束矩阵光学

M2 factor matrix for two-dimensional Hermite-Gaussian beam

The M² factor matrix for two dimensional Hermite Gaussian field is proposed. By introducing coupled beams half width and coupled M² factor, the M² factor matrix of the mode after being rotated around the propagation axis by some angle has been derived theoretically in the same coordinate. The rules of change of parameters related to M² factor matrix varying with the modes' rotation angle have been simulated numerically; and the track of M² factor vectors versus the modes' rotation angle has been given. Calculation results are in good agreement with theoretically derived ones, which proves that by using M² factor matrix, M² factors of a Hermite Gaussian mode after rotation by a certain angle can be related with those of the same mode before rotation. This method is universally applicable to the beam quality analysis for asymmetric higher Gaussian beams, and is very important in guiding the mesurement of beam quality in practice.