非旋转对称光束的像散系数a_(ZF)

Astigmatic coefficient of laser beam without rotational symmetry

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M^4参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a_(ZF)表示光束的像散特性,最终给出了用像散系数a_(ZF)表达的M^4参数(M_(xx)~4、M_(yy)~4、M_(xy)~4和M_r^4)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a_(ZF)及光束在主方向上的M^4参数等。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a_(ZF)、J_(ZF1)和J_(ZF2)。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。

Based on the second-order moment method,considering astigmatic beam without rotational symmetry,the M^4 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 a（ZF）was adopted to describe the astigmatic characteristics of laser beam. The M^4-parameters（M（xx）^4,M（yy）^4,M（xy）^4 and Mr^4） can be expressed by the astigmatic coefficient a（ZF）. In addition,the astigmatic coefficient a（ZF）and the principal M4 parameters can be calculated by measuring M^4 parameters of the laser beam. When laser beam passes through aberration-free optical system,the propagation constants a（ZF）,J（ZF1） and J（ZF2） remain unchanged. The obtained results have an important practical reference value for the design,manufacture and application of laser.