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Vortex beam has potential applications in free space optical communication because of its capacity of data transmission. Therefore, it is necessary to study the propagation characteristics of vortex beams in atmospheric turbulence. When the vortex beam propagates in the atmospheric turbulence the beam drift will occur, which has a great influence on the free space optical communication. In this paper, the beam drift of vortex beams with coma and spherical aberration transmitted in atmospheric turbulence is studied by using multi-phase screen and Fourier transform method. The numerical results show that as the transmission distance increases, the effects of both coma and spherical aberration on the beam drift are enhanced. The larger the transmission zenith angle and the coma coefficients, the greater the beam drift of the vortex beam is. However, the beam drift decreases with spherical aberration coefficient increasing. When the zenith angle and the transmission distance are both unchanged, the beam drift of the both vortex beams decrease with topological charges increasing. The influence of coma aberration on beam drift is bigger than that of spherical aberration.
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Keywords:
- coma /
- spherical aberration /
- beam drift /
- vortex
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Google Scholar
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Google Scholar
Zheng X T, Guo L X, Cheng M J, Li J T 2018 Acta Phys. Sin. 67 214206
Google Scholar
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Google Scholar
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Google Scholar
[5] Juhasz T, Loesel F H, Kurtz R M, Horvath C, Bille J F, Mourou G 1999 IEEE J. Sel. Top. Quantum Electron. 5 902
Google Scholar
[6] Qian Y X, Shi Y L, Jin W M, Hu F R, Ren Z J 2019 Opt. Express 27 18085
Google Scholar
[7] Allen L, Beijersbergen M W, Spreeuw J C, Woerdman J P 1992 Phys. Rev. A 45 8185
Google Scholar
[8] He H, Friese M E, Heckenberg N R, Rubinsztein-Dunlop H 1995 Phys. Rev. Lett. 75 826
Google Scholar
[9] Auguita J A, Neifeld M A, Vasic B V 2008 Appl. Opt. 47 2414
Google Scholar
[10] Wu J Z, Li H, Li Y J 2007 Opt. Eng. 46 019701
Google Scholar
[11] 葛筱璐, 王本义, 国承山 2016 光学学报 36 0301002
Ge X L, Wang B Y, Guo C S 2016 Acta Opt. Sin. 36 0301002
[12] Ge X L, Wang B Y, Guo C S 2015 J. Opt. Soc. Am. A 32 837
[13] Li J, Chen X, Duffie S M, Najjar M A, Rafsanjani H, Korotkova O 2019 Opt. Commun. 446 178
Google Scholar
[14] Sandalidis H G 2011 Appl. Opt. 50 952
Google Scholar
[15] 柯熙政, 邓莉君 2016 无线光通信中的部分相干光传输理论 (北京:科学出版社) 第14页
Ke X Z, Deng L J 2016 The Theory of Partially Coherent Optical Transmission in Wireless Optical Communication (Beijing: Science Press) p14 (in Chinese)
[16] Aksenov V P, Pogutsa C E 2012 Appl. Opt 51 7262
Google Scholar
[17] Huang Y, Yuan Y S, Liu X L, Zeng J, Wang F, Yu J Y, et al 2018 Appl. Sci 8 2476
Google Scholar
[18] Wu G H, Dai W, Tang H, Guo H 2015 Opt. Commun. 336 55
Google Scholar
[19] Xu Y G, Tian H H, Dan Y Q, Feng H, Wang S J 2017 J. Mod. Opt. 64 844
Google Scholar
[20] 狄颢萍, 张淇博, 周木春, 辛煜, 赵琦 2018 中国激光 45 0305001
Di H P, Zhang Q B, Zhou M C, Xin Y, Zhao Q 2018 Chin. J. Laser 45 0305001
[21] 程振, 楚兴春, 赵尚弘, 邓博于, 张曦文 2015 中国激光 42 1213002
Cheng Z, Chu X C, Zhao S H, Deng B Y, Zhang X W 2015 Chin. J. Laser 42 1213002
[22] Dabby F W, Whinnery J R 1968 Appl. Phys. Lett. 13 284
Google Scholar
[23] Born M, Wolf E 1997 Principles of Optics (6th ed.) (Cambridge: Cambridge University Press)
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Google Scholar
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Google Scholar
Qian X M, Zhu W Y, Rao R Z 2009 Acta. Phys. Sin. 58 6633
Google Scholar
[27] Fleck J A, Morris J R, Feit M D 1976 Appl. Phys. 10 129
[28] Ke X Z, Lei S C 2016 Appl. Opt. 55 3897
Google Scholar
[29] 李大海, 曹益平, 张启灿, 王琼华 2013 现代工程光学 (北京: 科学出版社) 第217页
Li D H, Cao Y P, Zhang Q C, Wang Q H 2013 XianDai GongCheng GuangXue (Beijing: Science Press) p217 (in Chinese)
[30] 陈鸣, 高太长, 刘磊, 胡帅, 曾庆伟, 李刚, 等 2017 强激光与粒子束 29 091008
Chen M, Gao T C, Liu L, Hu S, Zeng Q W, Li G, et al 2017 High Power Laser and Particle Beams 29 091008
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图 1 激光在大气湍流中斜程传输时的示意图
Figure 1. schematic diagram of laser propagation in slant atmospheric turbulence.
图 2 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)
$n = 1$ ; (b1)−(b3)$n = 2$ Figure 2. Two-dimensional intensity distribution of Gaussian vortex beam with coma in slant atmospheric turbulence at different propagation distance: (a1)−(a3)
$n = 1$ ; (b1)−(b3)$n = 2$ 
图 3 拓扑荷数 (a)
$n = 1$ 和(b)$n = 2$ 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Figure 3. Normalized intensity distribution of Gaussian vortex beam with coma when the propagation distance is different. Topological charge (a)
$n = 1$ , (b)$n = 2$ .
图 4 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(
${\text{π}}$ )Figure 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 coma kC3 = 0.5; (c1)−(c3) with spherical aberration kC4 = 0.5. Phase responding to black (–π)-white (π).
图 5 拓扑荷数 (a)
$n = 1$ 和(b)$n = 2$ 时不同彗差系数对涡旋光束光强分布的影响Figure 5. The effects of coma aberration coefficients on the intensity distribution of Gaussian vortex beam. Topological charge (a)
$n = 1$ , (b)$n = 2$ .
图 6 拓扑荷数 (a)
$n = 1$ 和(b)$n = 2$ 时球差系数对涡旋光束光强分布的影响Figure 6. The effects of spherical aberration coefficients on the intensity distribution of Gaussian vortex beam. Topological charge (a)
$n = 1$ , (b)$n = 2$ 
图 7 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)
Figure 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).
图 8 彗差系数(a)以及拓扑荷数(b)对涡旋光束的光束漂移影响
Figure 8. The effects of coma coefficients (a) and topological charges (b) on the beam drift.
图 9 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
$n = 1$ , 虚线: 拓扑荷数$n = 2$ Figure 9. Curves of beam drift with different transmission distance, zenith angles and topological charges. The solid line:
$n = 1$ , the dash line:$n = 2$ .
图 10 天顶角、拓扑荷数(a)以及球差系数(b)对光束漂移的影响
Figure 10. The effects of zenith angles, topological charges (a) and spherical aberration coefficients (b) on beam drift of vortex beam.
图 11 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
Figure 11. Comparison of beam drift of Gaussian vortex beams with coma and spherical aberration at different zenith angles and different transmission distances.
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[1] Qiu S, Liu T, Li Z M, Wang C, Ren Y, Shao Q L, et al 2019 Appl. Opt 58 2650
Google Scholar
[2] 郑晓桐, 郭立新, 程明建, 李江挺 2018 物理学报 67 214206
Google Scholar
Zheng X T, Guo L X, Cheng M J, Li J T 2018 Acta Phys. Sin. 67 214206
Google Scholar
[3] Paterson C 2005 Phys. Rev. Lett. 94 153901
Google Scholar
[4] Wang J, Yang J Y, Fazal I M, Ahmed N, Yan Y, Ren Y X, et al 2012 Nat. Photonics 6 488
Google Scholar
[5] Juhasz T, Loesel F H, Kurtz R M, Horvath C, Bille J F, Mourou G 1999 IEEE J. Sel. Top. Quantum Electron. 5 902
Google Scholar
[6] Qian Y X, Shi Y L, Jin W M, Hu F R, Ren Z J 2019 Opt. Express 27 18085
Google Scholar
[7] Allen L, Beijersbergen M W, Spreeuw J C, Woerdman J P 1992 Phys. Rev. A 45 8185
Google Scholar
[8] He H, Friese M E, Heckenberg N R, Rubinsztein-Dunlop H 1995 Phys. Rev. Lett. 75 826
Google Scholar
[9] Auguita J A, Neifeld M A, Vasic B V 2008 Appl. Opt. 47 2414
Google Scholar
[10] Wu J Z, Li H, Li Y J 2007 Opt. Eng. 46 019701
Google Scholar
[11] 葛筱璐, 王本义, 国承山 2016 光学学报 36 0301002
Ge X L, Wang B Y, Guo C S 2016 Acta Opt. Sin. 36 0301002
[12] Ge X L, Wang B Y, Guo C S 2015 J. Opt. Soc. Am. A 32 837
[13] Li J, Chen X, Duffie S M, Najjar M A, Rafsanjani H, Korotkova O 2019 Opt. Commun. 446 178
Google Scholar
[14] Sandalidis H G 2011 Appl. Opt. 50 952
Google Scholar
[15] 柯熙政, 邓莉君 2016 无线光通信中的部分相干光传输理论 (北京:科学出版社) 第14页
Ke X Z, Deng L J 2016 The Theory of Partially Coherent Optical Transmission in Wireless Optical Communication (Beijing: Science Press) p14 (in Chinese)
[16] Aksenov V P, Pogutsa C E 2012 Appl. Opt 51 7262
Google Scholar
[17] Huang Y, Yuan Y S, Liu X L, Zeng J, Wang F, Yu J Y, et al 2018 Appl. Sci 8 2476
Google Scholar
[18] Wu G H, Dai W, Tang H, Guo H 2015 Opt. Commun. 336 55
Google Scholar
[19] Xu Y G, Tian H H, Dan Y Q, Feng H, Wang S J 2017 J. Mod. Opt. 64 844
Google Scholar
[20] 狄颢萍, 张淇博, 周木春, 辛煜, 赵琦 2018 中国激光 45 0305001
Di H P, Zhang Q B, Zhou M C, Xin Y, Zhao Q 2018 Chin. J. Laser 45 0305001
[21] 程振, 楚兴春, 赵尚弘, 邓博于, 张曦文 2015 中国激光 42 1213002
Cheng Z, Chu X C, Zhao S H, Deng B Y, Zhang X W 2015 Chin. J. Laser 42 1213002
[22] Dabby F W, Whinnery J R 1968 Appl. Phys. Lett. 13 284
Google Scholar
[23] Born M, Wolf E 1997 Principles of Optics (6th ed.) (Cambridge: Cambridge University Press)
[24] Pu J X, Zhang H H 1998 Opt. Commun. 151 331
Google Scholar
[25] Chu X X, Zhou G Q 2007 Opt. Express 15 7697
Google Scholar
[26] 钱仙妹, 朱文越, 饶瑞中 2009 物理学报 58 6633
Google Scholar
Qian X M, Zhu W Y, Rao R Z 2009 Acta. Phys. Sin. 58 6633
Google Scholar
[27] Fleck J A, Morris J R, Feit M D 1976 Appl. Phys. 10 129
[28] Ke X Z, Lei S C 2016 Appl. Opt. 55 3897
Google Scholar
[29] 李大海, 曹益平, 张启灿, 王琼华 2013 现代工程光学 (北京: 科学出版社) 第217页
Li D H, Cao Y P, Zhang Q C, Wang Q H 2013 XianDai GongCheng GuangXue (Beijing: Science Press) p217 (in Chinese)
[30] 陈鸣, 高太长, 刘磊, 胡帅, 曾庆伟, 李刚, 等 2017 强激光与粒子束 29 091008
Chen M, Gao T C, Liu L, Hu S, Zeng Q W, Li G, et al 2017 High Power Laser and Particle Beams 29 091008
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