The root-mean-square (rms) spatial and angular widths of partially coherent Sinh-Gaussian (PCShG) beams propagating through inhomogeneous atmospheric turbulence are investigated based on the generalized extended Huygens-Fresnel principle. Analytical formulae of the rms spatial and angular widths are derived, and the effect of the outer scale on the beam spreading for PCShG beams in inhomogeneous atmospheric turbulence is also studied by using the modified von Kármán spectrum and Hufnagel-Valley atmospheric turbulence profile model. The impacts of the turbulent parameters (inner scale and outer scale), coherent parameter and decentered parameter on PCShG beams are discussed by numerical calculations. It is shown that the rms spatial width increases with increasing the outer scale, and the effect is obvious especially for the PCShG beam with the smaller decentered parameters and larger zenith angles. Typically, the saturation value of rms angular width becomes larger for a larger outer scale.

中文翻译：

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外尺度对非均匀大气湍流中部分相干正弦高斯光束的影响

基于广义扩展惠更斯-菲涅耳原理研究了通过非均匀大气湍流传播的部分相干正弦高斯 (PCShG) 光束的均方根 (rms) 空间和角宽度。推导了rms空间宽度和角宽度的解析公式，并利用修正的von Kármán谱和Hufnagel-Valley大气湍流剖面模型研究了外尺度对PCShG光束在非均匀大气湍流中波束扩展的影响。通过数值计算讨论了湍流参数（内尺度和外尺度）、相干参数和偏心参数对PCShG梁的影响。结果表明，rms空间宽度随着外部尺度的增加而增加，尤其对于偏心参数较小、天顶角较大的PCShG光束效果明显。通常，对于更大的外部尺度，rms 角宽度的饱和值变得更大。