基于广义惠更斯-菲涅耳原理和维格纳分布函数方法, 推导出了部分相干双曲正弦高斯(ShG)光束在湍流大气中M2因子的解析表达式。在此基础上研究了部分相干ShG光束的湍流距离, 即湍流引起的光束扩展可忽略的范围。采用Von Karman谱分别对M2因子和湍流距离进行了数值计算, 并分析了内外尺度的影响。研究表明: M2因子随束腰宽度和离心参数的增加存在极小值; 湍流距离随束腰宽度的增加存在极大值, 随离心参数的增加而增加, 大气湍流对离心参数较大的光束影响较小。另外, M2因子和湍流距离与折射率结构参数、内尺度、外尺度、波长和相干参数等密切相关。

Based on the extended Huygens-Fresnel principle and the method of the Wigner distribution function, the analytical formula for the M2-factor of the partially coherent sinh-Gaussian (ShG) beam in turbulent atmosphere is derived. Furthermore, the turbulence distance of ShG beam is investigated in which the effect of the atmospheric turbulence on the beam can be negligible. Numerical calculation is done for the M2-factor and turbulence distance using Von Karman turbulence spectrum, and the effect of the inner and outer scale on ShG beam is analyzed. The results show that the M2 factor exists a minimum with increasing beam width and decentered parameter; the turbulence distance exists a maximum with increasing beam width, and increases with increasing decentered parameter, the influence of the turbulence is less on the ShG beams with a larger decentered parameter. In addition, the M2 factor and the turbulence distance are closely related to the structure constant of the refractive index fluctuations, the inner scale, outer scale, wavelength and coherent parameter.