Fig. 1. schematic diagram of laser propagation in slant atmospheric turbulence.激光在大气湍流中斜程传输时的示意图

Fig. 2. Two-dimensional intensity distribution of Gaussian vortex beam with coma in slant atmospheric turbulence at different propagation distance:　(a1)−(a3) ; (b1)−(b3) 含彗差涡旋光束在大气湍流中不同传输距离时的光强分布.　(a1)−(a3) ; (b1)−(b3)

Fig. 3. Normalized intensity distribution of Gaussian vortex beam with coma when the propagation distance is different. Topological charge (a) , (b) . 拓扑荷数　(a) 和(b) 时带有彗差的涡旋光束在大气湍流中不同传输距离的归一化光强分布

Fig. 4. The phase change of the vortex beam with no aberration, with coma and with spherical aberration propagated in atmospheric turbulence when the topological charges are different. Distance z = 3639 m: (a1)−(a3) with no aberration; (b1)−(b3) with comakC₃ = 0.5; (c1)−(c3) with spherical aberrationkC₄ = 0.5. Phase responding to black (–π)-white (π). 拓扑荷数不同时, 无像差、带有彗差和带有球差的涡旋光束在大气湍流中传输时相位变化. 传输距离z = 3639 m (a1)−(a3)无像差; (b1)−(b3)带有彗差kC₃ = 0.5; (c1)−(c3)带有球差kC₄ = 0.5. 相位对应黑色(–π)-白色( )

Fig. 5. The effects of coma aberration coefficients on the intensity distribution of Gaussian vortex beam. Topological charge (a) , (b) . 拓扑荷数　(a) 和(b) 时不同彗差系数对涡旋光束光强分布的影响

Fig. 6. The effects of spherical aberration coefficients on the intensity distribution of Gaussian vortex beam. Topological charge (a) , (b) 拓扑荷数　(a) 和(b) 时球差系数对涡旋光束光强分布的影响

Fig. 7. Phase change of vortex beams with different coma and spherical aberration propagated through atmospheric turbulence. Distance z = 3639 m, topological charge n = 1: (a1)−(a3) with coma; (b1)−(b3) with spherical aberration. Phase responding to black (–π)-white (π). 分别带有不同彗差和球差系数的涡旋光束在湍流中传输时相位分布. 传输距离z = 3639 m, 拓扑核数n = 1　(a1)−(a3)带有彗差; (b1)−(b3)带有球差. 相位对应黑色(–π)-白色π)

Fig. 8. The effects of coma coefficients (a) and topological charges (b) on the beam drift.彗差系数(a)以及拓扑荷数(b)对涡旋光束的光束漂移影响

Fig. 9. Curves of beam drift with different transmission distance, zenith angles and topological charges. The solid line: , the dash line: . 光束漂移量随着传输距离、天顶角和拓扑荷数的变化曲线. 实线: 拓扑荷数 , 虚线: 拓扑荷数

Fig. 10. The effects of zenith angles, topological charges (a) and spherical aberration coefficients (b) on beam drift of vortex beam.天顶角、拓扑荷数(a)以及球差系数(b)对光束漂移的影响

Fig. 11. Comparison of beam drift of Gaussian vortex beams with coma and spherical aberration at different zenith angles and different transmission distances.分别带有彗差和球差的涡旋光束在不同传输距离不同天顶角时的光束漂移量对比