中文摘要：

高功率激光通常具有振幅调制和相位畸变．采用统计光学方法推导了截断的有振幅调制和位相畸变光束在大气湍流中传输的等效曲率半径R的解析公式．研究表明：随着位相畸变参量、振幅调制参量和光束截断参量的增大，光束在自由空间中的R增大，但R受湍流的影响也会增大；并且高斯光束在自由空间中的R最大，但其受湍流影响也最大．因此，在大气湍流中传输到足够远时，截断的有振幅调制和位相畸变光束的R就要比高斯光束的大．特别地，相对等效曲率半径尼随传输距离为非单调变化，存在一个最小值，即在该位置处R受湍流的影响最大．此外，达到风最小值所需传输距离随光束位相畸变和振幅调制的加剧而增大．

英文摘要：

Usually, high-power laser beams are amplitude modulated and have phase fluctuations （PFs）. The analytic formula of the effective radius R of curvature of truncated laser beams with amplitude modulations （AMs） and PFs propagating through atmospheric turbulence is derived by using the statistical optics method. It is shown that the R in free space increases with the increases of the phase fluctuation parameter, the intensity modulation parameter and the truncated parameter. And the influence of turbulence on the R also increases with the increases of the three parameters. Furthermore, the R of Gaussian beams is largest in free space, but it is most affected by turbulence. Therefore, in turbulence the R of truncated laser beams with AMs and PFs is even larger than that of Gaussian beams when the propagation distance is large enough. In particular, the relative effective radius Rr of curvature varies non-monotonically with propagation distance, and there exists a minimum at a propagation distance where the influence of turbulence on the R is largest. In addition, the position where the Rr reaches its minimum increases with the increasees of intensity modulation and phase fluctuation.