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基于分层传输模型和Mie散射理论, 在粒子散射模型中充分考虑了谱分布特征, 数值模拟了800 nm飞秒激光在冰云、水云、雾、气溶胶和降雨环境中的传输特性. 结果表明, 谱分布和粒子相态对光丝传输特性有较大的影响. 雨滴的粒径较大, 光丝在降雨环境中传输时, 由于散射导致的能量衰减最强, 产生的光丝峰值光强和能量最低. 同时, 光丝能量在空间的分布不均, 产生了明显的多丝结构, 并导致光丝长度缩短. 水云和雾具有类似的谱分布特征, 光丝在水云和雾中的传输特性十分相似. 但由于雾中的粒子尺度更小, 光丝的能量较高, 光丝分布更集中. 气溶胶对光丝的散射最弱, 因此在传输前期没有对光丝的结构产生影响, 并以稳定的单丝结构传输, 光丝的峰值光强和能量最高, 但在距离成丝位置一段距离后光丝结构才逐渐出现扰动. 相同谱分布下, 由于冰粒子的散射能力强于水粒子, 造成光丝在冰云中的能量更低, 光丝分布不集中, 光丝的数量明显增多.During recent years, the filamentation of femtosecond laser in the atmosphere has contributed considerable interest to researchers. However, the actual atmosphere can result in different scattering medium, which are adverse to the application of filamentation in the atmosphere. In order to study the propagation of femtosecond laser in real scattering medium, the propagation of 800 nm femtosecond laser in ice cloud, water cloud, fog, aerosol and rainfall is simulated numerically. Combined with the theory of stratified medium model and Mie scattering theory, we constructed a scattering model with a changeable size distribution function in the nonlinear laser model. The results indicated that the different size distribution and phase state of particles have different influence on the propagation properties of the filaments. As the rainfall was dominated by large raindrops, the scattering on filament was the strongest, resulting in the lowest peak intensity and energy. In the case, the distribution of filament energy was extremely inhomogeneous, causing the shortest length of filament and generation of multi-filament. In the image of fluence distribution, a diffraction ring can be observed clearly in the rainfall but was blurred in other medium. The propagation properties of filaments in water cloud and fog were similar because of the same size distribution. However, due to the size of particle in fog was smaller than that in water cloud, the filaments had more higher energy and more concentrated distribution in fog. In addition, the scattering of ice particles was stronger than that of liquid droplets, so the energy of filament in ice cloud was lower than that in water cloud, resulting a reducing of the length and number of filaments in ice cloud. The size of aerosols was the smallest, which had the weakest influence on the filament. Accordingly, in the early of propagation, there had little perturbance on the filament and the beam was transmitting with a stable single filament, and results in the highest peak intensity and energy. With the propagation increasing, the accumulation of scattering attenuation produced the perturbation on filament at a position after the onset of filamentation.
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Keywords:
- femtosecond laser /
- filamentation /
- size distribution /
- scattering medium
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图 1 分层传输模式概念图 Δz为屏间距, L为散射屏的宽度
Fig. 1. Stratified-medium model. Δz is distance between screens, L is the width of the screen.
图 2 (a)粒子对激光光场的散射扰动图; (b)利用散射相函数获得不同粒径粒子(100, 15, 10, 5 μm)的前向散射角
Fig. 2. (a) Scattering on light field by particles; (b) Use the scattering phase function to obtain forward scattering angle of particles with different sizes.
图 3 不同散射介质的粒子谱分布图 (a)云; (b)雾; (c)雨; (d)气溶胶
Fig. 3. Size distributions of different scattering medium: (a) Cloud; (b) Fog; (c) Rain; (d) Aerosol.
图 4 (a)不同散射介质内飞秒激光轴上峰值光强随传播距离的变化, I0 = 5.2 × 1012 W/cm2; (b)不同散射介质内激光能量随传输距离的变化
Fig. 4. (a) The peak intensity on axis as a function of the propagation distance in different scattering medium, I0 = 5.2 × 1012 W/cm2; (b) The laser energy as a function of the propagation distance in different scattering medium.
图 5 不同散射场中光丝的截面能流随传播距离的变化 (a)降雨; (b)冰云; (c)水云; (d)雾; (e)气溶胶; (f)干净空气; F0 = 0.592 J/cm2
Fig. 5. Fluence distribution F/F0 as a function of the propagation distance in different scattering medium: (a) Rain; (b) Ice-cloud; (c) Water-cloud; (d) Fog; (e) Aerosol; (f) Clear air. F0 = 0.592 J/cm2.
表 1 粒子谱函数参数
Table 1. Size distributions parameters.
Cloud Fog Rain Aerosol a 1.8078 2.3730 5.3333 × 105 4.000 × 105 b 0.3610 3/2 8.9443 20 μ 2 6 1 2 ν 1 1 1/2 1 
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[1] Reintjes J, Carman R L, Shimizu F 1973 Phys. Rev. A 8 1486
Google Scholar
[2] Koulouklidis A D, Fedorov V Y, Tzortzakis S 2016 Phys. Rev. A 93 033844
Google Scholar
[3] Wei S S, Li S Y, Guo F M, Yang Y J, Wang B B 2013 Phys. Rev. A 87 063418
Google Scholar
[4] Rodriguez M, Sauerbrey R, Wille H, Fujii T, André Y B, Mysyrowicz A, Klingbeil L, Rethmeier K, Kalkner W, Kasparian J, Salmon E, Yu J, Wolf J P 2002 Opt. Lett. 27 772
Google Scholar
[5] Wang T J, Yuan S, Chen Y P, Chin S L 2013 Chin. Opt. Lett. 11 25
[6] Chin S L, Brodeur A, Petit S, Kosareva O G 1999 J. Nonlinear Opt. Phys. 8 121
Google Scholar
[7] Rohwetter P, Kasparian J, Stelmaszczyk K, Hao Z Q, Henin S, Lascoux N, Nakaema W M, Petit Y, Queisser M, Salamé R, Salmon E, Wöste L, Wolf J P 2010 Nat. Photonics 4 451
Google Scholar
[8] Courvoisier F, Boutou V, Kasparian J, Salmon E, Méjean G, Yu J, Wolf J P 2003 Appl. Phys. Lett. 83 213
Google Scholar
[9] Méchain G, Méjean G, Ackermann R, Rohwetter P, André Y B, Kasparian J, Prade B, Stelmaszczyk K, Yu J, Salmon E, Winn W, Schlie L A, Mysyrowicz A, Sauerbrey R, Wöste L, Wolf J P 2005 Appl. Phys. B 80 785
Google Scholar
[10] Zemlyanov A A, Geints Y E 2006 Opt. Commun. 259 799
Google Scholar
[11] Militsin V O, Kouzminskii L S, Kandidov V P 2005 Proc. SPIE 5708 277
Google Scholar
[12] Jeon C, Harper D, Lim K, Durand M, Chini M, Baudelet M, Richardson M 2015 J. Opt. 17 055502
Google Scholar
[13] Matthews M, Pomel F, Wender C, Kiselev A, Duft D, Kasparian J, Wolf J P, Leisner T 2016 Sci. Adv. 2 e1501912
Google Scholar
[14] Zemlyanov A A, Geints Y E 2007 Opt. Commun. 270 47
Google Scholar
[15] Kandidov V P, Militsin V O 2006 Appl. Phys. B 83 171
Google Scholar
[16] 付光宇 2013 硕士学位论文(成都: 西南交通大学)
Fu G Y 2013 M. S. Thesis (Chengdu: Southwest Jiaotong University) (in Chinese)
[17] Silaeva E P, Kandidov V P 2009 Atmos. Ocean. Opt. 22 26
Google Scholar
[18] Couairon A, Mysyrowicz A 2007 Phys. Rep. 441 47
Google Scholar
[19] Kandidov V P, Shlenov S A, Kosareva O G 2009 Quantum Electron 39 205
Google Scholar
[20] Militsin V O, Kachan E P, Kandidov V P 2006 Quantum Electron. 36 1032
Google Scholar
[21] Kandidov V P, Militsin V O, Bykov A V, Priezzhev A V 2006 Quantum Electron. 36 1003
Google Scholar
[22] 廖国男 著(郭彩丽, 周诗健 译) 2004 大气辐射导论: 第2版(北京: 气象出版社)第174−263页
Lion K N (translated by Guo C L, Zhou S J) 2004 An Introduction to Atmospheric Radiation: Second Edition (Beijing: China Meteorological Press) pp174−263 (in Chinese)
[23] 胡帅 2018 博士学位论文(长沙: 国防科技大学)
Hu S 2018 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[24] 盛裴轩, 毛节泰, 李建国, 葛正谟, 张霭琛, 桑建国, 潘乃先, 张宏升 2013 大气物理学: 第二版(北京: 北京大学出版社) 第478页
Sheng P X, Mao J T, Li J G, Ge Z M, Zhang A C, Sang J G, Pan N X, Zhang H S 2013 Atmospheric Physics: Second Edition (Beijing: Peking University Press) p478 (in Chinese)
[25] Zahedpour S, Wahlstrand J K, Milchberg H M 2015 Opt. Lett. 40 5794
Google Scholar
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