根据非Kolmogorov湍流谱和二阶矩理论得到非Kolmogorov湍流中光束漂移模型的一般表达式, 结果表明光束漂移与湍流参数(广义指数参数α、折射率结构参数C2n、湍流外尺度L0和湍流内尺度l0)以及输入平面上的初始二阶矩有关。以部分相干反常椭圆空心高斯光束(PCAEHGB)为例, 对光束漂移的均方根值Bw和相对光束漂移Br进行数值模拟。结果表明, 广义指数参数、折射率结构参数、湍流内尺度、湍流外尺度、相干长度和束腰半径越大, Bw和Br越大。当C2n=10-14 m3-α、传输总路径L=10 km时, Bw≈0.22 m; 当L≈5 km时, Br达到最大。在相同参数条件下,PCAEHGB受湍流的影响比高斯-谢尔模型光束小。

Based on the non-Kolmogorov turbulence spectrum and the theory of second moments, a general analytical expression of beam wander model in non-Kolmogorov turbulence is derived. The results indicate that the beam wander depends on turbulence parameters including the generalized exponent parameter α, refractive index structure parameter C2n, turbulence outer scale L0, turbulence inner scale l0 and initial second moments of laser beam at the input plane. Taking the partially coherent anomalous elliptical hollow Gaussion beam (PCAEHGB) as an example, we simulate the root-mean-square (RMS) beam wander Bw and the relative beam wander Br numerically. It shows that Bw and Br increase with the increasing generalized exponent parameter, refractive index structure parameter, turbulence inner scale, turbulence outer scale, coherence length and beam waist radius. The results also indicate that Bw≈0.22 m when C2n=10-14 m3-α and the total propagation path length L=10 km, and Br reaches the maximum value when L≈5 km. Furthermore, PCAEHGB is less affected by turbulence than Gaussian-Schell model beam under the condition of the same parameters.