圆形平顶高斯光束阵列在湍流大气传输中的M2因子

应用Wigner分布函数的二阶矩定义和拓展Huygens–Fresnel原理研究了圆形平顶高斯光束阵列在湍流大气传输中的光束性质，得到其传输质量因子（ 因子）的解析表达式，进行了相应的数值计算和模拟。结果表明：在湍流大气中传输时，圆形平顶高斯光束阵列的传输质量因子随传播距离、湍流大气结构常数的增大和束腰宽度的减小而增大；当光束阵列阶数一定，阵列个数不断增加时，其传输质量因子先保持不变，然后开始减小，最后不再减小，而保持这个定值不变；当光束阵列的个数一定，阶数不断增加时，其传输质量因子减小，最后不再减小而保持不变。在自由空间中传输时，圆形平顶高斯光束阵列的传输质量因子保持不变。

M2 factor of flattened radial Gaussian laser beam array in turbulent atmosphere

The beam nature of the flattened radial Gaussian laser beam array in a turbulent atmosphere is investigated based on the extended Huygens-Fresnel integral and the Wigner distribution function for turbulence conditions. Analytical propagation formula for the propagation factor ( factor) are derived and numerical examples are illustrated. The results show that  the propagation factor of the flattened radial laser beam array beams in turbulent atmosphere increases when propagation distance and turbulent constant increase and beams width decreases. The propagation factor of the flattened radial laser beam array does not change at first, then it decreases, and it is invariant in the end when the flattened radial laser beam array’s orders are fixed and its numbers increase. The propagation factor of the flattened radial laser beam array  does not change, then it decreases, maintains a fixed value finally when the flattened radial laser beam array  numbers are fixed and its orders increase. The propagation factor is unchanged as the flattened radial laser beam array are propagating in free space.