基于广义Huygens-Fresnel原理和非Kolmogorov大气湍流折射率起伏谱密度函数，采用Wigner分布函数的二阶矩方法，推导出了在大气湍流中传输的部分相干双曲余弦厄米高斯光束束宽和M2因子的解析表达式。研究表明：相对束宽和归一化M2因子随传输距离的增大而增大；光束阶数越大、相干长度越小、双曲余弦参数越小，相对束宽和归一化M2因子受大气湍流影响越小；相对束宽随束腰宽度的增大存在极大值，在一定的相干长度范围内，归一化M2因子随束腰宽度的增大存在极小值；相对束宽和归一化M2因子随广义指数的变化均存在极大值，随内尺度的增大而逐渐减小，随外尺度的增大几乎没有变化。%Based on the extended Huygens-Fresnel principle and non-Kolmogorov spectrum, the analytical expressions for beam width and M 2-factor of partially coherent Hermite-cosh-Gaussian beams going through a non-Kolmogorov turbulence are derived by means of second moments for the Wigner distribution function. Results show that the relative beam width and normalized M 2-factor of partially coherent Hermite-cosh-Gaussian beams going through a non-Kolmogorov turbulence will increase when propagating in the turbulent atmosphere, and will be less affected by turbulent atmosphere with a larger beam, smaller coherent length, smaller Ch-part parameter. The relative beam width has a maximum value for increasing waist width, and normalized M 2-factor has a minimum value for increasing waist width in a specific extent of coherent length. The relative beam width and normalized M 2-factor both have maximum values according to the generalized power law, but decrease with increasing inner scale, and have nearly no change with increasing outer scale.
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