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为了研究高斯光束在湍流等离子体鞘套中的传输特性, 根据广义惠更斯-菲涅耳原理, 采用基于快速傅里叶变换的功率谱反演法, 用多随机相位屏来模拟湍流带来的影响. 根据超声速飞行器绕流等离子体流场厚度在厘米级别的特点, 光束在两个相位屏之间的传输过程中采用菲涅耳衍射积分的两次快速傅里叶变换算法(double fast Fourier transform algorithm), 利用多随机相位屏模拟等离子体鞘套湍流对光束传输产生的影响, 解决了多随机相位屏模拟湍流研究中的超短距离传输问题. 当飞行高度为45 km, 飞行速度为18马赫时, 通过对超声速飞行器绕流等离子体流场的统计分析, 发现在此飞行条件下折射率起伏方差的强度范围10–11—10–14. 对高斯光束在湍流等离子体流场中的传输特性进行了数值仿真. 结果表明: 在等离子体鞘套湍流中折射率起伏强度、波长、传输距离等都是影响高斯光束质量的重要因素. 折射率方差越大, 传输距离越长, 光斑弥散越严重, 光强起伏越大, 光强减弱也越明显. 光束的波长越长, 高斯光束抑制湍流的能力越强, 光斑弥散程度越小, 光强起伏也越小.In this paper, the characteristics of Gaussian beam propagation through turbulent plasma sheath are studied. According to the generalized Huygens-Fresnel principle, the random phase screen is generated by power spectrum inversion method based on the fast Fourier transform. The random phase screen is used to simulate turbulence effect. The thickness of the plasma sheath is of about centimeter order of magnitude. Compared with the single fast Fourier transform algorithm, the double fast Fourier transform algorithm is not prone to under-sampling and can obtain good image results, even if the diffraction distance is 1 mm. Therefore, double fast Fourier transform algorithm is used for investigating the beam propagation between two phase screens. The turbulence effect of the plasma sheath surrounding a hypersonic vehicle is simulated by the multi-random phase screens. When the flight altitude is 45 km and the flight speed is 18 Mach, the intensity of refractive index fluctuation variance ranges from
${10}^{ - 11} $ to$ {10}^{ - 14} $ indicated by analyzing the plasma flow field around the hypersonic vehicle. The characteristics of the Gaussian beam propagation through the turbulent plasma are numerically simulated. The results show that the refractive index fluctuation, wavelength and transmission distance are important factors affecting the Gaussian beam quality. The larger the refractive index variance, the more severe the spot dispersion and the more obvious the light intensity fluctuation. As wavelength is longer, the ability of the Gaussian beam to resist turbulence becomes stronger and the dispersion of the light spot and the intensity fluctuation are smaller. The beam distortion and the spot dispersion become more severe as the transmission distance is longer.-
Keywords:
- light propagation /
- random media /
- random phase screen
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图 1 (a)五个区域; (b)五个区域的折射率方差
$\left\langle { n_1^2 } \right\rangle $ Fig. 1. (a) Five regions; (b) refractive index variance
$\left\langle {n_1^2 } \right\rangle $ in five regions.
图 2 折射率方差
$\left\langle {n_1^2 } \right\rangle $ (a)头部区域1; (b)侧部区域2Fig. 2. Refractive index variance
$\left\langle {n_1^2 } \right\rangle $ in different regions: (a) Head area 1; (b) side area 2.
图 3 在不同衍射距离下S-FFT和D-FFT两种算法的光强分布 (a) S-FFT,
$d$ = 100 mm; (b) D-FFT,$d$ = 100 mm; (c) S-FFT,$d$ = 10 mm; (d) D-FFT,$d$ = 10 mmFig. 3. Intensity distribution of S-FFT and D-FFT algorithm at different diffraction distances: (a) S-FFT,
$d$ = 100 mm; (b) D-FFT,$d$ = 100 mm; (c) S-FFT,$d$ = 10 mm; (d) D-FFT,$d$ = 10 mm.
图 5 不同传输条件时的高斯光束光强数值仿真 (a) λ = 1.55 × 10–6 m, ω0 = 40 mm, d = 13 mm; (b) ω0 = 40 mm, d = 13 mm,
$\langle n_1^2\rangle$ = 10–12; (c) λ = 1.55 × 10–6 m, ω0 = 40 mm,$\langle n_1^2\rangle$ = 10–12Fig. 5. Numerical simulation of intensity of Gaussian beam in different propagation conditions: (a) λ = 1.55 × 10–6 m, ω0 = 40 mm, d = 13 mm; (b) ω0 = 40 mm, d = 13 mm,
$\langle n_1^2\rangle$ = 10–12; (c) λ = 1.55 × 10–6 m, ω0 = 40 mm,$\langle n_1^2\rangle$ = 10–12.表 1 化学反应模型中的方程
Table 1. Reactions considered in chemistry model
No. Reaction 1 ${\rm {N_2} + M \rightleftharpoons N + N + M}$ 2 ${\rm {O_2} + M \rightleftharpoons O + O + M}$ 3 ${\rm NO + M \rightleftharpoons N + O + M}$ 4 ${\rm O + {N_2} \rightleftharpoons NO + N}$ 5 ${\rm NO + O \rightleftharpoons {O_2} + N}$ 6 ${\rm N + O \rightleftharpoons N{O^ + } + e}$ 
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[1] James P R, Churchill R J 1971 IEEE Trans. Aerosp. Electron. Syst. 7 879
[2] Shao C, Tian D Y, Chen W F 2016 Proceedings of the 34th AIAA Applied Aerodynamics Conference Washington D C, June, 2016 p3428
[3] Shao C, Nie L, Chen W F 2016 Aerosp. Sci. Technol. 51 151
Google Scholar
[4] Savino R, D’Ella M E, Carandente V 2015 J. Spacecr. Rockets 52 417
[5] Starkey R P 2015 J. Spacecr. Rockets 52 426
Google Scholar
[6] Li J T, Guo L X 2012 J. Electromagn. Waves Appl. 26 1767
[7] Belov I F, Borovoy V Y, Gorelov V A, Kireev A Y, Korolev A S, Stepanov E A 2001 J. Spacec. Rockets 38 249
Google Scholar
[8] Lyle C S, Norman D A 1973 J. Spacer. 10 170
Google Scholar
[9] Xie K, Yang M, Bai B W, Li X P, Zhou H, Guo L X 2016 J. Appl. Phys. 119 023301
Google Scholar
[10] Thoma C, Rose D V, Miller C L, Clark R E, Hughes T P 2009 J. Appl. Phys. 106 043301
Google Scholar
[11] Hartunian R A, Stewart G E, Fergason S D, Curtiss T J, Seibold R W 2007 Causes and Mitigation of Radio Frequency (RF) Blackout During Reentry of Reusable Launch Vehicles (Cambridge: U.S. Department of Transportation) Aerospace Report No. ATR-2007(5309)-1
[12] Yao B, Li X P, Shi L, Liu Y M, Zhu C Y 2017 IEEE Trans. Plasma Sci. 45 2227
Google Scholar
[13] Song Z G, Liu J F, Du Y X, Xi X L 2015 J. Appl. Phys. 121 1067
Google Scholar
[14] Shi L, Liu Y M, Fang S X, Li X P, Yao B, Zhao L, Yang M 2016 IEEE Trans. Plasma Sci. 44 1083
Google Scholar
[15] He G L, Zhan Y F, Zhang J Z, Ge N 2016 IEEE Trans. Plasma Sci. 44 232
Google Scholar
[16] Yao B, Li X P, Shi L 2016 Proc. SPIE 10141 101410J
[17] Lin T C, Sproul L K 2006 Comput. Fluids 35 703
Google Scholar
[18] Li J T, Yang S F, Guo L X 2017 IET Microw. Antennas Propag. 11 280
Google Scholar
[19] 李婉, 曾曙光, 刘雁 2015 激光与光电子学进展 52 080104
Li W, Zeng S G, Liu Y 2015 Laser Optoelectron. Prog. 52 080104
[20] 王龙, 沈学举, 张维安, 董红军, 何永强 2012 激光与红外 42 852
Google Scholar
Wang L, Shen X J, Wang W A, Dong H J, He Y Q 2012 Laser Infrar. 42 852
Google Scholar
[21] Schmidt J D 2010 Numerical Simulation of Optical Wave Propagation (Washington: Bellingham SPIE) pp166−172
[22] Yildiz F, Kurt H 2017 Proc. SPIE 10425 104250O
[23] Zhang Y L, Ma D L, Yuan X H, Zhou Z Y 2018 Proc. SPIE 10256 1025609
[24] Rebecca J E, Matthew E G 2006 Proc. SPIE 6303 630301
Google Scholar
[25] Farwell N H, Korotkova O 2014 Proc. SPIE 9224 922416
Google Scholar
[26] Korotkova O, Farwell N, Shchepakina E 2012 Wave Random Complex 22 260
Google Scholar
[27] Liu Z L, Chen J L, Zhao D M 2017 Appl. Opt. 56 3577
[28] [29] Keidar M, Kim M, Boyd I 2008 J. Spacecr. Rockets 45 445
Google Scholar
[30] Park C 1989 J. Thermophyss. 3 233
Google Scholar
[31] Schlichting H, Gersten K 2017 Boundary-layer Theory (Berlin Heidelberg: Springer Nature) pp68−73
[32] David C W 2006 Modeling for CFD (3rd Ed.) (USA: Birmingham) pp122−128
[33] Bamakrishnan R, Anandhanarayanan K, Krishnamurthy R, Chakraborty D 2017 J. Ins. Eng. India Ser. C 98 285
[34] Li L Q, Huang W, Yan L, Zhao Z T, Liao L 2017 Int. J. Hydrogen Energy 42 19318
Google Scholar
[35] Kim K H, Kim C,Rho O H 2001 J. Comp. Phys. 174 38
Google Scholar
[36] Yoon S, Jameson A 1988 AIAA J. 26 1025
Google Scholar
[37] Tromeur E, Garnier E, Sagaut P 2006 J. Fluids. Eng. 128 239
Google Scholar
[38] Richardson M B, Clark R L 1987 Proc. SPIE 0788 6
[39] 牛化恒, 韩一平 2017 激光技术 41 452
Niu H H, Han Y P 2017 Las. Technol. 41 452
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