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The effects of thermal blooming on orbital angular momentum (OAM) and phase singularity of dual-mode vortex beams under different wind directions and wind speeds are studied in this paper. Owing to the different symmetries of dual-mode vortex beams superimposed by different modes, the effects of thermal blooming on them depend on not only wind speed, but also wind direction. Based on the scalar wave equation and the hydrodynamic equation, a four-dimensional (4D) computer code to simulate the time-dependent propagation of dual-mode vortex beams in the atmosphere is devised by using the multiphase screen method and finite difference method. It is found that for a certain wind direction, the value of OAM increases with the wind speed decreasing because the thermal blooming becomes more serious, i.e. the thermal blooming effect promotes the OAM of dual-mode vortex beam to grow. For example, when the angle between the wind direction and the beam is 0 < θ < 50°, the OAM of the dual-mode vortex beams with a topological charge difference of 2 increases with wind speed decreasing, and there is an optimal angle (
$ \theta \approx {20^ \circ } $ ) to maximize OAM. Therefore, for a certain wind direction and wind speed, the OAM of dual-mode vortex beam propagating in the atmosphere can be larger than that in free space, and can be larger than the OAM of single-mode vortex beam. The dual-mode vortex beam with higher modes requires smaller wind speed to make its OAM larger than the OAM in free space. In addition, the larger the difference in topological charge between the two element beams of a dual-mode vortex beam, the more stable the OAM of the dual-mode vortex beam is. On the other hand, the evolution of linear edge dislocation singularity under atmospheric thermal blooming is also investigated in this paper. When the wind direction is perpendicular to the dislocation line, the linear edge dislocation singularity disappears. If the wind direction is parallel to the dislocation line, the linear edge dislocation singularity always exists. At other angles, the linear edge dislocation singularity will evolve into optical vortex pairs. The results obtained in this paper have a certain reference value for the propagation of lasers in the atmosphere and optical communication.-
Keywords:
- dual-mode vortex beam /
- wind-dominated thermal blooming /
- orbital angular momentum /
- linear edge dislocation singularity
[1] Andrews L C, Phillips R L 2005 Laser Beam Propagation Through Random Media (2nd. Ed.) (Bellingham: SPIE Press) pp478–479
[2] Sprangle P, Hafizi B, Ting A, Fischer R 2015 Appl. Opt. 54 F201
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 单模子光束及双模涡旋光束的光强(a1—a3)和相位(b1—b3)分布
Figure 1. Intensity (a1–a3) and phase (b1–b3) of single-mode subbeams and a dual-mode vortex beams.
图 2 l1 = 1, l2 = 3时, 横截面的光强和能流分布 (a) 源平面; (b) 自由空间; (c) 在大气中
Figure 2. Beam intensity and energy flow distributions at cross section at l1 = 1 and l2 = 3: (a) Source plane; (b) free space; (c) in the atmosphere.
图 3 双模涡旋光束的OAM随θ变化 (a) l1 = 1, l2 = 3时, 不同风速; (b) v = 3 m/s时, 不同模式
Figure 3. OAM of dual-mode vortex beams versus θ: (a) Different wind speeds at l1 = 1 and l2 = 3; (b) different modes at v = 3 m/s.
图 4 l1 = 1, l2 = 3, v = 3 m/s 时, OAM密度(a)—(d)和能流分布(e)—(h)
Figure 4. OAM density (a)–(d) and energy flow distribution (e)–(h) at l1 = 1, l2 = 3 and v = 3 m/s.
图 5 拓扑荷相差为2的双模涡旋光束的OAM随θ变化. 实线为大气(v = 3 m/s), 虚线为自由空间
Figure 5. OAM of the dual-mode vortex beams with a topological charge difference of 2 versus θ. Solid line is in the atmosphere (v = 3 m/s), dotted line is in free space.
图 6 双模涡旋光束的OAM随风速的变化. 实线为大气, 虚线为自由空间 (a) θ = 20°; (b) θ = 150°
Figure 6. OAM of dual-mode vortex beams as a function of wind speed. Solid line is in the atmosphere, dotted line is in free space: (a) θ = 20°; (b) θ = 150° .
图 7 v = 3 m/s时, 不同双模涡旋光束的OAM随θ变化
Figure 7. OAM of different dual-mode vortex beams versus θ at v = 3 m/s.
图 8 l1 = 1, l2 = –1时, 线刃型位错奇点在自由空间和大气中的演化
Figure 8. Evolution of linear edge dislocation singularity in free space and in the atmosphere at l1 = 1 and l2 = –1.
图 9 l1 = 1, l2 = –1时, 风向不同的双模涡旋光束横向能流图
Figure 9. Transverse energy flow of dual-mode vortex beams under different wind direction, l1 = 1 and l2 = –1.
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[1] Andrews L C, Phillips R L 2005 Laser Beam Propagation Through Random Media (2nd. Ed.) (Bellingham: SPIE Press) pp478–479
[2] Sprangle P, Hafizi B, Ting A, Fischer R 2015 Appl. Opt. 54 F201
Google Scholar
[3] Jabczyński J K, Gontar P 2021 Def. Technol. 17 1160
Google Scholar
[4] Rubenchik A M, Fedoruk M P, Turitsyn S K 2009 Phys. Rev. Lett. 102 233902
Google Scholar
[5] Liu X Y, Qian X M, He R, Liu D D, Cui C L, Fan C Y, Yuan H 2021 Star. Atmosphere 12 1315
Google Scholar
[6] Allen L, Beijersbergen M W, Spreeuw R, Woerdman J P 1992 Phys. Rev. A 45 8185
Google Scholar
[7] Simpson N B, Dholakia K, Allen L, Padgett M J 1997 Opt. Lett. 22 52
Google Scholar
[8] Wang J, Yang J Y, Fazal I M, Ahmed N, Yan Y, Huang H, Ren Y X, Yue Y, Dolinar S, Tur M, Alan E 2012 Nat. Photon. 6 488
Google Scholar
[9] Liu Y D, Gao C Q, Gao M W, Qi X Q, Weber H 2008 Opt. Commun. 281 3636
Google Scholar
[10] Gao C Q, Qi X Q, Liu Y D, Weber H 2010 Opt. Express 18 72
Google Scholar
[11] Lin J, Yuan X C, Tao S H, Burge R E 2005 Opt. Lett. 30 3266
Google Scholar
[12] Soskin M S, Gorshkov V N, Vasnetsov M V, Malos J T, Heckenberg N R 1997 Phys. Rev. A 56 4064
Google Scholar
[13] 黄素娟, 谷婷婷, 缪庄, 贺超, 王廷云 2014 物理学报 63 244103
Google Scholar
Huang S J, Gu T T, Miao Z, He C, Wang T Y 2014 Acta Phys. Sin. 63 244103
Google Scholar
[14] Ke X Z, Zhao J 2019 Optik 183 302
Google Scholar
[15] Liu Y X, Zhang K N, Chen Z Y, Pu J X 2019 Optik 181 571
Google Scholar
[16] Nong L Y, Ren J J, Guan Z W, Wang C F, Ye H P, Liu J M, Li Y, Fan D Y, Chen S Q 2022 Opt. Express 30 27482
Google Scholar
[17] Smith D C 1977 P. IEEE 65 1679
Google Scholar
[18] Ji X L, Eyyuboğlu H T, Ji G M, Jia X H 2013 Opt. Express 21 2154
Google Scholar
[19] Zhao L, Wang J, Guo M J, Xu X, Qian X M, Zhu W Y, Li J 2021 Opt. Laser Technol. 139 106982
Google Scholar
[20] Maxim A M, Evgeny V D, Rafael A V 2010 Opt. Lett. 35 670
Google Scholar
[21] Qiu D, Tian B Y, Ting H, Zhong Z Q, Zhang B 2021 Appl. Opt. 60 8458
Google Scholar
[22] 钟哲强, 张翔, 张彬, 袁孝 2023 物理学报 72 064204
Google Scholar
Zhong Z Q, Zhang X, Zhang B, Yuan X 2023 Acta Phys. Sin. 72 064204
Google Scholar
[23] Vaity P, Singh R P 2011 Opt. Lett. 36 2994
Google Scholar
[24] Gebhardt F G 1990 Proc. SPIE 122 2
Google Scholar
[25] Li Y K, Chen D Q, Xu X S, Zhang X W 1993 Atmospheric Propagation and Remote Sensing II 1968 424
Google Scholar
[26] Strohbehn J W 1978 Laser Beam Propagation in the Atmosphere (Springer) p224
[27] Fleck J A, Morris J R 1976 Appl. Phys. 10 2
[28] Litvin I A 2012 J. Opt. Soc. Am. A 29 901
Google Scholar
[29] Liang G, Wang Y Q, Guo Q, Zhang H C 2018 Opt. Express 26 8084
Google Scholar
[30] Indebetouw G 1993 J. Mod. Optic. 40 73
[31] Soskin M S, Vasnetsov M V 2001 Singular Optics (Netherlands: Progress in Optics) 42 219
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