柱坐标系中截断光束的广义M2因子

推导出截断圆对称光束二阶矩的传输方程，它们与无截断光束的二阶矩满足相似的传输定律.因此，基于广义截断二阶矩方法，将直角坐标系中截断二维光束的二阶矩特征参数推广到柱坐标系中的截断圆对称光束，类似方法定义的广义M²因子（M²_G因子）是一个传输不变量.对理论的自洽性作了物理解释.推导出柱坐标系中截断超高斯光束的二阶矩参数和M²_G因子.对一些有意义的特殊情况作了讨论，并以数值计算例作了说明. 关键词： 光束描述 截断光束 圆对称性 广义截断二阶矩(GTSM) 2因子（M²_G因子）')" href="#">广义M²因子（M²_G因子）

Generalized M2 factor of truncated beams in the cylindrical coordinate system

The propagation equations of second-order moments of truncated circularly symmetric beams are derived, which obey the propagation laws similar to those for the non-truncated case. Based on the method of generalized truncated second-order moments, the second-order characteristic parameters of two-dimensional truncated beams in the rectangular coordinate system are extended to the truncated circularly symmetric beams in the cylindrical coordinate system, and the generalized M² factor (M²_G factor) can be defined in a similar way and remains invariant upon propagation. The consistency of the theory is interpreted physically. The second-order moments parameters and M²_G factor of truncated super-Gaussian beams in the cylindrical coordinate system are derived and some interesting special cases are discussed and illustrated with numerical examples.