高斯-谢尔模型阵列光束在湍流大气中的空间相干性

基于广义Huygens-Fresnel 原理和Rytov 相位结构函数二次近似的方法,推导出了径向分布高斯-谢尔模(GSM)阵列光束在湍流大气中传输时的交叉谱密度函数解析表达式,并利用表征光束相干性的空间复相干度系数,详细分析了GSM 阵列光束在大气湍流中传输时的空间相干性变化规律。研究结果表明:径向分布GSM 阵列光束的空间相干性由子光束空间相干长度、传输距离、大气折射率结构常数及相对径向填充因子等因素共同确定;径向分布GSM 阵列光束通过湍流大气时,其空间相干度在传输过程中会出现多峰值现象,但是随着传输距离增大,多峰值现象逐渐消失并趋向于高斯分布,并且随着距离增大空间相干度宽度逐渐减小,光束空间相干性变差。

Spatial coherence properties of GSM array beams in turbulent atmosphere

Based on the extended Huygens-Fresnel principle and the quadratic approximation of Rytov's phase structure function, the analytical expression for the cross-spectral density function of the Gaussian Schell-Model (GSM) array beams propagating in atmospheric turbulence was derived. The degree of spatial coherence of GSM array beams in atmospheric turbulence was investigated numerically. The result shows that the spatial coherence properties of the GSM array beams are determined by the coherent length of beamlets, the transmission distance, the refractive index structure constant of atmospheric turbulence and the relative radial fill factor of the source in common. It also shows that the spatial coherence of the GSM array beams ends as Gaussian distribution, but multiple peaks are existed during the transmission, the width of the degree of coherence becomes smaller with the transmission distance continues increase which means that the degree of spatial coherence turns worse.