涡旋光束在湍流大气中传输时，其振幅和相位会发生随机起伏，导致在接收平面处的光强起伏及光束扩展等。以低阶拉盖尔-高斯涡旋光束为例，利用激光大气传输四维程序数值模拟了不同条件下的涡旋光束在湍流大气中传输时引起的光束扩展。由模拟结果可知，传输距离越长或湍流越强，涡旋光束在大气中传输时的束宽扩展受湍流的影响越大；涡旋光束的拓扑荷数越高、光束的束腰越小或光波的波长越长，其束宽扩展受大气湍流的影响越小。湍流的内尺度和外尺度也会影响涡旋光束的光束扩展，但影响程度相对较小。另外，通过计算仿真还比较了涡旋光束和普通高斯光束在湍流大气中传输时引起的光束扩展的差异。

When the vortex beam propagates through the turbulent atmosphere, the random variations will be produced in the amplitude and phase of the beam. And the intensity fluctuations and spread of the radiation pattern will be induced at the observation plane. some results about the vortex beams broadening are obtained by numerical modeling using four-dimension code when the vortex beams propagate through the turbulent atmosphere under different conditions. The vortex beams are the lower order Laguerre-Gaussian modes. The results indicate that if the propagation distance is longer or the turbulence is stronger, the beam broadened by the turbulence will be more severe. And if the topological charge is higher, or the beam′s waist width is narrower, or the wavelength is longer, the beam broadened by the turbulence will be smaller. Though the inner scale and the outer scale of turbulence have an effect on the beam broadening, the influence of them is relatively weak. In addition, the broadening of vortex beam and fundamental Gauss beam through the turbulent atmosphere are compared numerically.