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根据广义惠更斯-菲涅耳原理和交叉谱密度函数的表达式,推导出部分相干高斯-谢尔涡旋光束在大气湍流中传输时光强分布的积分形式,通过一些特殊积分处理得到完整的解析表达式,分析讨论了传输距离、湍流强度和光束自身参数等对光束光强分布的影响。结果表明:部分相干涡旋光束在大气湍流中传输时,随着传输距离的增加,光强分布逐渐由空心分布转化为高斯分布;当拓扑荷数为0时,随着传输距离的增加,光强分布一直保持高斯分布;在湍流强度不变的情况下,拓扑荷数越小,相干长度越短,束腰宽度越长,光强分布由空心分布转化为高斯分布所需要的传输距离越短。
According to the generalized Huygens-Fresnel principle and the cross-spectral density function expression, the integral form of light intensity distribution of partially coherent Gaussian-Shear vortex beams propagating in atmospheric turbulence is deduced. Through some special integral processing, the integral Analytical expressions, analysis of the transmission distance, turbulence intensity and the beam itself parameters on the light intensity distribution. The results show that the light intensity distribution gradually changes from hollow distribution to Gaussian distribution as the coherent vortex beam propagates in atmospheric turbulence. When the topological charge is zero, with the increase of transmission distance, Strong distribution always keeps Gaussian distribution. Under the condition of constant turbulence intensity, the smaller the topological charge, the shorter the coherence length and the longer the waist width, the shorter the transmission distance needed to convert the light intensity distribution from the hollow distribution to the Gaussian distribution .