Wolf效应,即部分相干光除满足定标律之外,即使在自由空间中传输时其光谱一般也会发生变化,是一类著名的相关诱导光谱变化现象。以高斯谢尔模型(GSM)光束作为部分相干光的典型例子,研究湍流对高斯谢尔模型光束光谱移动的影响。基于部分相干光的传输定理,并考虑湍流的存在,推导出了高斯谢尔模型光束通过湍流介质的光谱公式,并作了数值计算。研究表明,无论定标律是否满足,湍流都会影响高斯谢尔模型光束的光谱。湍流越强,与无湍流情况比较光谱移动越大。特别是,若不满足定标律时轴外光谱还会出现分裂。高斯谢尔模型光束在湍流介质中的光谱移动由光束的空间相干性、折射率结构常数C2n和位置等参量决定。

The Wolf effect, i.e., the spectrum of partially coherent light generally changes on propagation even in free space unless the light obeys the scaling law, is a well-known phenomenon of the correlation-induced spectral changes. This paper deals with the influence of turbulence on the spectral shift of the Gaussian Schell-model (GSM) beam, which is taken as a typical example of partially coherent light. Based on the propagation law of partially coherent light and consideration of the presence of turbulence, an expression for the spectrum of GSM beams propagating through turbulence media is derived and numerical calculations are performed. It is shown that the turbulence affects the spectrum of GSM beams, whenever the scaling law holds or does not hold true. The stronger the turbulence is, the larger spectral shift appears in comparison to the case without turbulence. In particular, there is off-axis spectral splitting if the scaling law fails. The spectral shift of GSM beams in turbulence media depends on the beam spatial coherence, refraction index structure constant c2n and position parameter in general.