Analytical expressions of second-order intensity moments and $M^2$ factors for a conically refracted (CR) Gaussian beam and its components are derived. $M^2$ for a CR beam is shown to depend on a single parameter, the ratio of the CR ray cylinder radius and the input Gaussian beam waist radius. In typical CR conditions when this ratio is much greater than one, $M^2$ is also much greater than one even though the divergence angle for a CR beam is the same as for the input Gaussian beam. The increased $M^2$ value results from the much larger size of CR beam in the focal plane compared with the waist size of input Gaussian beam. $M^2$ values derived from focal- and Fourier-plane intensity profiles agree with theoretically predicted ones. Second-order moments and $M^2$ factors of a CR beam and its components are compared with those of Gaussian, Laguerre–Gauss, and modified Bessel–Gauss beams.

二阶强度矩的解析表达式和 ${米}^2$ 推导出锥形折射 (CR) 高斯光束及其分量的因子。 ${米}^2$显示 CR 光束取决于单个参数，即 CR 射线圆柱半径与输入高斯束腰半径之比。在此比率远大于 1 的典型 CR 条件下，${米}^2$即使 CR 光束的发散角与输入高斯光束的发散角相同，也远大于 1。增加的${米}^2$ 值是由于焦平面中 CR 光束的尺寸比输入高斯光束的腰围尺寸大得多。 ${米}^2$来自焦平面和傅立叶平面强度分布的值与理论预测值一致。二阶矩和${米}^2$ 将 CR 光束及其组件的因子与高斯光束、拉盖尔-高斯光束和修正贝塞尔-高斯光束的因子进行比较。