基于广义惠更斯菲涅耳原理和维格纳分布函数的二阶矩方法, 推导出部分相干双曲余弦高斯(ChG)光束在湍流大气中的束宽、远场发散角和M2因子的解析表达式。研究结果表明, 部分相干ChG光束在湍流大气中传输时, 均方根角宽度、M2因子和相对M2因子随着传输距离的增大而增大, 且与束腰宽度、波长、离心参数、相干参数及湍流强度等有关; 均方根角宽度随着光束离心参数的增大存在极小值。当传输距离较远时, 随着离心参数的增大, M2因子存在极小值; 离心参数较大的光束受湍流的影响较小。

Based on the extended Huygens-Fresnel principle and the method of second moments of the Wigner distribution function, the analytical formulas for the root-mean-square (RMS) spatial width, the RMS angular width, and the M2-factor of the partially coherent cosh-Gaussian (ChG) beam in turbulent atmosphere have been derived, which can be applied to cases of different spatial power spectra of the refractive index fluctuations of the turbulent atmosphere. It can be shown that the RMS angular width, M2 factor and relative M2 factor of a partially coherent ChG beam in turbulence increase with the propagation distance and depend on the waist width, wavelength, coherent parameter, decentered parameter, and spatial power spectrum of the refractive index fluctuations. The RMS angular width as a function of the decentered parameter has a minimum at any given propagation distance. For long propagation distance, the M2-factor as a function of the decentered parameter also has a minimum, and the beams with a larger decentered parameter are less affected by the turbulence.