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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.
The M2 factor matrix of Hermite - Gaussian optical field is proposed. By introducing the cross terms of the half width of beam and the crossing term of M2 factor, the M2 factor matrix after the optical field is rotated by a certain angle in the same coordinate system is deduced. The numerical simulation The change of each factor related to the M2 factor matrix with the rotation angle of the light field gives the trajectory curve of the M2 vector of the light field with the rotation angle of the light field.The calculated results are consistent with the theoretical deduction, The factor matrix can be used to unify the two-dimensional Hermite-Gaussian optical field before and after rotation by the rotation matrix.The method can be generalized to the theoretical analysis of the beam quality of a general two-dimensional high-order Gaussian beam, which is universal, The actual measurement of quality has important theoretical significance.