非旋转对称光束的像散系数aZF

摘要

Based on the second-order moment method,considering astigmatic beam without rotational symmetry,the M4 parameters were adopted to describe the beam quality.The analytical expressions of beam-waist and divergence angle for astigmatic Gaussian beam without rotational symmetry were derived.And the astigmatic coefficient azF was adopted to describe the astigmatic characteristics of laser beam.The M4-parameters (M4xx,M4yy,M4y and Mr4) can be expressed by the astigmatic coefficient aZF.In addition,the astigmatic coefficient aZF and the principal M4 parameters can be calculated by measuring M4 parameters of the laser beam.When laser beam passes through aberration-free optical system,the propagation constants aZF,JZF1 and JZF2 remain unchanged.The obtained results have an important practical reference value for the design,manufacture and application of laser.%基于二阶矩定义,综合考虑像散光束的非旋转对称性,提出采用M4参数来描述光束的像散特性.推导出了在指定方位角上像散基模高斯光束、像散厄米高斯光束传输和像散光束的束腰、发散角的解析表达式,提出采用像散系数aZF表示光束的像散特性,最终给出了用像散系数aZF表达的M4参数(Mxx4、Myy4、Mxy4和Mr4)的解析表达式.另外,根据实测光束的M4参数反过来也可以求出光束的像散系数aZF及光束在主方向上的M4参数等.光束经过无像差旋转对称光学系统传输时,其传输不变量为aZF、JzF1和JZF2.本文所得结果对实际工作中激光器的设计、制造和应用有重要的参考价值.