The effects of the jet engine turbulence on a Gaussian Schell-Model (GSM) beam array propagating in a jet engine plume are studied theoretically. The analytical expressions of the cross-spectral density (CSD) function, the spectral degree of coherence (DOC) and the mean-squared beam width for a GSM beam array propagating through a jet engine plume region are derived based on the extended Huyens-Fresnel integral. It is found that the profile of spectral density and the DOC of a GSM beam array gradually transfer to an elliptical shape as the propagation distance increases, and the elliptical degree becomes greater with increasing source coherence length. Besides, as the source coherence length decreases, the effect of the jet engine turbulence on the beam broadening is smaller and the profile of the DOC appears sidelobes at short distance. It is also found that the values of effective coherence width nearly remain the same for different values of source coherence length after propagating a certain distance. Furthermore, the effects of the number of beamlets on the beam width and effective coherence width are investigated in detail.

中文翻译：

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喷气发动机排气诱导湍流中高斯谢尔模型光束阵列的传播特性

从理论上研究了喷气发动机湍流对在喷气发动机羽流中传播的高斯谢尔模型 (GSM) 光束阵列的影响。基于扩展的 Huyens-Fresnel 推导出 GSM 波束阵列通过喷气发动机羽流区域的交叉谱密度 (CSD) 函数、谱相干度 (DOC) 和均方波束宽度的解析表达式不可缺少的。发现随着传播距离的增加，GSM波束阵列的谱密度和DOC曲线逐渐向椭圆形转变，并且随着源相干长度的增加，椭圆度变大。此外，随着源相干长度的减小，喷气发动机湍流对波束展宽的影响更小，DOC的轮廓在近距离出现旁瓣。还发现传播一定距离后，对于不同的源相干长度值，有效相干宽度的值几乎保持相同。此外，详细研究了子束数量对光束宽度和有效相干宽度的影响。