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Research progress of partially coherent beams propagation in turbulent atmosphere

Wang Fei Yu Jia-Yi Liu Xian-Long Cai Yang-Jian

Research progress of partially coherent beams propagation in turbulent atmosphere

Wang Fei, Yu Jia-Yi, Liu Xian-Long, Cai Yang-Jian
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  • Compared with coherent laser beams, partially coherent beams have advantages of effectively reducing turbulence-induced extra beam spreading, beam wander and intensity scintillation on propagation through turbulent atmosphere, and have promising applications in free-space optical communications, laser radar and remote sensing. Recently, more and more attention was paid to the propagation of partially coherent beams through turbulent atmosphere. In this article, we first review historically the research progress of the propagation of partially coherent beams in atmospheric turbulence. And we describe in detail the basic theory for the calculation of average intensity, second-order moment and scintillation index of partially coherent beams in turbulence based on the extended Huygens-Fresnel principle and Rytov method. We also present a phase screen method of numerically simulating the propagation of coherent beams through turbulent atmosphere, and then extend such a method to treating the propagation of partially coherent beams.
      Corresponding author: Cai Yang-Jian, yangjiancai@suda.edu.cn
    • Funds: Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91750201), the National Natural Science Fund for Distinguished Young Scholar, China (Grant No. 11525418), the National Natural Science Foundation of China (Grant No. 11474213), and the Qing Lan Project of Jiangsu Province, China.
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    [2]

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    [3]

    Tatarskii V I 1961 Wave Propagation in a Turbulent Medium (New York: McGraw-Hill) pp8-237

    [4]

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    [5]

    Fante R L 1974 J. Opt. Soc. Am. 64 592

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    [7]

    Lutomirski R F, Yura H T 1971 Appl. Opt. 10 1652

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    [10]

    Kon A I, Tatarskii V I 1972 Radiophys. Quantum Electron. 15 1187

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    Leader J C 1978 J. Opt. Soc. Am. 68 175

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    Leader J C 1981 J. Opt. Soc. Am. 71 542

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    Dogariu A, Amarande S 2003 Opt. Lett. 28 10

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    Wang D D, Wang F, Cai Y J, Chen J 2012 J. Mod. Opt. 59 372

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    Wang F, Cai Y J, Eyyuboğlu H T, Baykal Y 2010 Prog. Electromagn. Res. 103 33

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    Yang A L, Zhang E T, Ji X L, Lu B D 2008 Opt. Express 16 8366

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    Li J H, Yang A L, Lu B D 2008 J. Opt. Soc. Am. A 25 2670

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    Wang F, Cai Y J, Eyyuboğlu H T, Baykal Y 2011 Appl. Phys. B 103 461

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    Alavinejad M, Khatiri M, Ghafary B 2009 Opt. Commun. 282 3541

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    Yuan Y S, Cai Y, Qu J, Eyyuboğlu H T, Baykal Y, Korotkova O 2009 Opt. Express 17 17344

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    Cai Y J, Korotkova O, Eyyuboǧlu H T, Baykal Y 2008 Opt. Express 16 15834

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    Baykal Y, Eyyuboǧlu H T 2007 Appl. Opt. 46 5044

    [69]

    Korotkova O 2008 Opt. Commun. 281 2342

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    Gu Y L, Gbur G 2010 J. Opt. Soc. Am. A 27 2621

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    Wang F, Cai Y J, Eyyuboǧlu H T, Baykal Y 2012 Opt. Lett. 37 184

    [73]

    Cai Y J, Chen Y H, Wang F 2016 Opt. Lett. 41 4182

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    Chen R, Liu L, Zhu S J, Wu G F, Wang F, Cai Y J 2014 Opt. Express 22 1871

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    Wang F, Li J, Martinez-Piedra G, Korotkova O 2017 Opt. Express 25 26055

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    Wang M H, Yuan X H, Ma D L 2017 Appl. Opt. 56 2851

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    Xu H F, Zhang Z, Qu J, Huang W 2014 Opt. Express 22 22479

    [85]

    Korotkova O, Shchepakina E 2014 J. Opt. 16 045704

    [86]

    Mei Z R, Schchepakina E, Korotkova O 2013 Opt. Express 21 17512

    [87]

    Tong Z S, Korotkova O 2012 Opt. Lett. 37 3240

    [88]

    Lajunen H, Saastamoinen T 2011 Opt. Lett. 36 4104

    [89]

    Gu Y L, Gbur G 2013 Opt. Lett. 38 1395

    [90]

    Yuan Y S, Liu X L, Wang F, Chen Y H, Cai Y J, Qu J, Eyyuboğlu H T 2013 Opt. Commun. 305 57

    [91]

    Avramov-Zamurovic S, Nelson C, Guth S, Korotkova O 2016 Appl. Opt. 55 3442

    [92]

    Korotkova O, Avramov-Zamurovic S, Nelson C, MalekMadani R, Gu Y L, Gbur G 2014 Proc. SPIE 9224 92240M

    [93]

    Banakh V A, Krekov G M, Mironov V L, Khmelevtsov S S, Tsvik R S 1974 J. Opt. Soc. Am. 64 516

    [94]

    Banakh V A, Mironov V L 1977 Opt. Lett. 1 172

    [95]

    Yura H T, Hanson S G 1989 J. Opt. Soc. Am. A 6 564

    [96]

    Andrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media (Bellingham, WA: SPIE) pp73, 74

    [97]

    Dan Y Q, Zhang B 2009 Opt. Lett. 34 563

    [98]

    Dan Y Q, Zhang B 2008 Opt. Express 16 15563

    [99]

    Wang F, Cai Y J 2010 Opt. Express 18 24661

    [100]

    Liu X L, Yu J Y, Cai Y J, Ponomarenko S 2016 Opt. Lett. 41 4182

    [101]

    Berman G P, Chumak A A 2006 Phys. Rev. A 71 013805

    [102]

    Liu X L, Shen Y, Liu L, Wang F, Cai Y J 2013 Opt. Lett. 38 5323

    [103]

    Wang F, Liu X L, Liu L, Yuan Y S, Cai Y J 2013 Appl. Phys. Lett. 103 091102

    [104]

    Recolons J, Dios F 2005 Proc. SPIE 5891 589107

    [105]

    Xiang J S 2012 Opt. Express 20 681

    [106]

    Wolf E Wolf E 1982 J. Opt. Soc. Am. 72 343

    [107]

    Wolf E 1982 J. Opt. Soc. Am. 72 343

    [108]

    Gori F, Santarsiero M 2015 Opt. Lett. 40 1587

    [109]

    Xiao X F, Voelz D 2006 Opt. Express 14 6986

    [110]

    Qian X M, Zhu W Y, Rao R Z 2009 Opt. Express 17 3782

    [111]

    Zhang Y L, Ma D L, Zhou Z Y, Yuan X H 2017 Appl. Opt. 56 2922

    [112]

    Basu S, Hyde M W, Xiao X F, Voelz D G, Korotkova O 2014 Opt. Express 22 31691

    [113]

    Hyde M W, Bose-Pillai S R, Wood R A 2017 Appl. Phys. Lett. 111 101106

    [114]

    Hyde M W, Bose-Pillai S, Xiao X, Voelz D G 2017 J. Opt. 19 025601

  • [1]

    Kolmogorov A N 1941 Dokl. Akad. Nauk SSSR 30 299

    [2]

    Chernov L A 1960 Wave Propagation in a Random Medium (New York: McGraw-Hill) pp15-180

    [3]

    Tatarskii V I 1961 Wave Propagation in a Turbulent Medium (New York: McGraw-Hill) pp8-237

    [4]

    Beran M 1970 J. Opt. Soc. Am. 60 518

    [5]

    Fante R L 1974 J. Opt. Soc. Am. 64 592

    [6]

    Brown W P 1971 J. Opt. Soc. Am. 61 1051

    [7]

    Lutomirski R F, Yura H T 1971 Appl. Opt. 10 1652

    [8]

    Yura H T 1972 Appl. Opt. 11 1399

    [9]

    Feizulin Z I, Kravtsov Y A 1967 Radiophys. Quantum Electron. 10 33

    [10]

    Kon A I, Tatarskii V I 1972 Radiophys. Quantum Electron. 15 1187

    [11]

    Leader J C 1978 J. Opt. Soc. Am. 68 175

    [12]

    Wang S C H, Plonus M A 1979 J. Opt. Soc. Am. 69 1297

    [13]

    Leader J C 1981 J. Opt. Soc. Am. 71 542

    [14]

    Wang S J, Baykal Y, Plonus M A 1983 J. Opt. Soc. Am. 73 831

    [15]

    Banach V A, Buldakov V M, Mironov V L 1983 Opt. Spectrosc. 54 1054

    [16]

    Banakh V A, Buldakov V M 1983 Opt. Spectrosc. 55 707

    [17]

    Wu J 1990 J. Mod. Opt. 37 671

    [18]

    Wu J, Boardman A D 1991 J. Mod. Opt. 38 1355

    [19]

    Gbur G, Wolf E 2002 J. Opt. Soc. Am. A 19 1592

    [20]

    Dogariu A, Amarande S 2003 Opt. Lett. 28 10

    [21]

    Shirai T, Dogariu A, Wolf E 2003 J. Opt. Soc. Am. A 20 1094

    [22]

    Ricklin J C, Davidson F M 2002 J. Opt. Soc. Am. A 19 1794

    [23]

    Ricklin J C, Davidson F M 2003 J. Opt. Soc. Am. A 20 856

    [24]

    Korotkova O, Andrews L C, Phillips R L 2004 Opt. Eng. 43 330

    [25]

    Young C Y, Gilchrest Y V, Macon B R 2002 Opt. Eng. 41 1097

    [26]

    Eyyuboǧlu H T, Baykal Y 2005 Appl. Opt. 44 976

    [27]

    Eyyuboǧlu H T 2005 Opt. Commun. 245 37

    [28]

    Cai Y J, He S L 2006 Opt. Lett. 31 568

    [29]

    Cai Y J, Lin Q, Eyyuboǧlu H T, Baykal Y 2008 Opt. Express 16 7665

    [30]

    Cil C Z, Eyyuboǧlu H T, Baykal Y, Korotkova O, Cai Y J 2010 Appl. Phys. B 98 195

    [31]

    Chu X X 2011 Opt. Lett. 36 2701

    [32]

    Wang T, Pu J X, Chen Z Y 2009 Opt. Commun. 282 1255

    [33]

    Cai Y J, Chen Y, Eyyuboǧlu H T, Baykal Y 2007 Appl. Phys. B 88 467

    [34]

    Zhou P, Wang X L, Ma Y X, Ma H T, Xu X J, Liu Z J 2011 Appl. Opt. 50 1234

    [35]

    Chen C Y, Yang H M, Kavehrad M, Zhou Z 2014 Opt. Lasers Eng. 52 106

    [36]

    Ji X L, Pu Z C 2010 Opt. Commun. 283 3884

    [37]

    Wang K L, Zhao C L 2014 Opt. Laser Technol. 57 44

    [38]

    Baykal Y 2014 Appl. Opt. 53 1284

    [39]

    Cheng K, Jiao L Y, Zhong X Q 2016 Opt. Commun. 367 112

    [40]

    Ma D T, Wei J B, Zhuang Z W 2004 Acta Opt. Sin. 24 1020 (in Chinese) [马东堂, 魏急波, 庄钊文 2004 光学学报 24 1020]

    [41]

    Yuan Y S, Cai Y J 2007 Opt. Commun. 27 1

    [42]

    Cai Y J, He S L 2006 Appl. Phys. Lett. 89 041117

    [43]

    Wang H Y, Li X Y 2008 Opt. Commun. 281 2337

    [44]

    Eyyuboğlu H T, Baykal Y, Cai Y J 2007 J. Opt. Soc. Am. A 24 2891

    [45]

    Wang D D, Wang F, Cai Y J, Chen J 2012 J. Mod. Opt. 59 372

    [46]

    Ji X L, Li X Q 2010 J. Opt. 12 035403

    [47]

    Wang F, Cai Y J, Eyyuboğlu H T, Baykal Y 2010 Prog. Electromagn. Res. 103 33

    [48]

    Aksenov V P, Kanev F Y, Pogutsa C E 2009 Proc. SPIE 7388 738807

    [49]

    Yang A L, Zhang E T, Ji X L, Lu B D 2008 Opt. Express 16 8366

    [50]

    Li J H, Yang A L, Lu B D 2008 J. Opt. Soc. Am. A 25 2670

    [51]

    Wang F, Cai Y J, Eyyuboğlu H T, Baykal Y 2011 Appl. Phys. B 103 461

    [52]

    Alavinejad M, Khatiri M, Ghafary B 2009 Opt. Commun. 282 3541

    [53]

    Alavinejad M, Ghafary B 2008 Opt. Lasers Eng. 46 357

    [54]

    Wang H Y, Li X Y 2010 Opt. Lasers Eng. 48 48

    [55]

    Yuan Y S, Cai Y, Qu J, Eyyuboğlu H T, Baykal Y, Korotkova O 2009 Opt. Express 17 17344

    [56]

    Salem M, Korotkova O, Dogariu A Wolf E 2004 Waves Random Media 14 513

    [57]

    Korotkova O, Salem M, Dogariu A, Wolf E 2005 Waves Random Complex Media 15 353

    [58]

    Korotkova O, Salem M, Wolf E 2004 Opt. Commun. 233 225

    [59]

    Du X Y, Zhao D M, Korotkova O 2007 Opt. Express 15 16909

    [60]

    Wu G H, Luo B, Yu S, Dang A H, Guo H 2011 J. Opt. 13 035706

    [61]

    Lu W, Liu L R, Sun J F, Yang Q G, Zhu Y J 2007 Opt. Commun. 27 1

    [62]

    Zhu Y, Zhao D M 2009 Appl. Phys. B 96 155

    [63]

    Cai Y J, Korotkova O, Eyyuboǧlu H T, Baykal Y 2008 Opt. Express 16 15834

    [64]

    Roychowdhury H, Ponomarenko S A, Wolf E 2005 J. Mod. Opt. 52 1611

    [65]

    Chen Z Y, Pu J X 2007 J. Opt. A 9 1123

    [66]

    Wang H, Liu D, Zhou Z 2010 Appl. Phys. B 101 361

    [67]

    Chen R, Dong Y M, Wang F, Cai Y J 2013 Appl. Phys. B 112 247

    [68]

    Baykal Y, Eyyuboǧlu H T 2007 Appl. Opt. 46 5044

    [69]

    Korotkova O 2008 Opt. Commun. 281 2342

    [70]

    Baykal Y, Eyyuboǧlu H T, Cai Y J 2009 Appl. Opt. 48 1943

    [71]

    Gu Y L, Gbur G 2010 J. Opt. Soc. Am. A 27 2621

    [72]

    Wang F, Cai Y J, Eyyuboǧlu H T, Baykal Y 2012 Opt. Lett. 37 184

    [73]

    Cai Y J, Chen Y H, Wang F 2016 Opt. Lett. 41 4182

    [74]

    Chen R, Liu L, Zhu S J, Wu G F, Wang F, Cai Y J 2014 Opt. Express 22 1871

    [75]

    Cui Y, Wei C, Zhang Y T, Wang F, Cai Y J 2015 Opt. Commun. 354 353

    [76]

    Wang X Y, Yao M W, Qiu Z L, Yi X, Liu Z J 2015 Opt. Express 23 12508

    [77]

    Wang F, Li J, Martinez-Piedra G, Korotkova O 2017 Opt. Express 25 26055

    [78]

    Wang F, Korotkova O 2017 Opt. Express 25 5057

    [79]

    Tang M M, Zhao D M 2015 Opt. Express 23 32766

    [80]

    Wang M H, Yuan X H, Ma D L 2017 Appl. Opt. 56 2851

    [81]

    Song Z Z, Liu Z J, Zhou K Y, Sun Q G, Liu S T 2017 Chin. Phys. B 26 024201

    [82]

    Song Z Z, Liu Z J, Zhou K Y, Sun Q G, Liu S T 2016 Opt. Express 24 1804

    [83]

    Yu J Y, Chen Y H, Liu L, Liu X L, Cai Y J 2015 Opt. Express 23 13467

    [84]

    Xu H F, Zhang Z, Qu J, Huang W 2014 Opt. Express 22 22479

    [85]

    Korotkova O, Shchepakina E 2014 J. Opt. 16 045704

    [86]

    Mei Z R, Schchepakina E, Korotkova O 2013 Opt. Express 21 17512

    [87]

    Tong Z S, Korotkova O 2012 Opt. Lett. 37 3240

    [88]

    Lajunen H, Saastamoinen T 2011 Opt. Lett. 36 4104

    [89]

    Gu Y L, Gbur G 2013 Opt. Lett. 38 1395

    [90]

    Yuan Y S, Liu X L, Wang F, Chen Y H, Cai Y J, Qu J, Eyyuboğlu H T 2013 Opt. Commun. 305 57

    [91]

    Avramov-Zamurovic S, Nelson C, Guth S, Korotkova O 2016 Appl. Opt. 55 3442

    [92]

    Korotkova O, Avramov-Zamurovic S, Nelson C, MalekMadani R, Gu Y L, Gbur G 2014 Proc. SPIE 9224 92240M

    [93]

    Banakh V A, Krekov G M, Mironov V L, Khmelevtsov S S, Tsvik R S 1974 J. Opt. Soc. Am. 64 516

    [94]

    Banakh V A, Mironov V L 1977 Opt. Lett. 1 172

    [95]

    Yura H T, Hanson S G 1989 J. Opt. Soc. Am. A 6 564

    [96]

    Andrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media (Bellingham, WA: SPIE) pp73, 74

    [97]

    Dan Y Q, Zhang B 2009 Opt. Lett. 34 563

    [98]

    Dan Y Q, Zhang B 2008 Opt. Express 16 15563

    [99]

    Wang F, Cai Y J 2010 Opt. Express 18 24661

    [100]

    Liu X L, Yu J Y, Cai Y J, Ponomarenko S 2016 Opt. Lett. 41 4182

    [101]

    Berman G P, Chumak A A 2006 Phys. Rev. A 71 013805

    [102]

    Liu X L, Shen Y, Liu L, Wang F, Cai Y J 2013 Opt. Lett. 38 5323

    [103]

    Wang F, Liu X L, Liu L, Yuan Y S, Cai Y J 2013 Appl. Phys. Lett. 103 091102

    [104]

    Recolons J, Dios F 2005 Proc. SPIE 5891 589107

    [105]

    Xiang J S 2012 Opt. Express 20 681

    [106]

    Wolf E Wolf E 1982 J. Opt. Soc. Am. 72 343

    [107]

    Wolf E 1982 J. Opt. Soc. Am. 72 343

    [108]

    Gori F, Santarsiero M 2015 Opt. Lett. 40 1587

    [109]

    Xiao X F, Voelz D 2006 Opt. Express 14 6986

    [110]

    Qian X M, Zhu W Y, Rao R Z 2009 Opt. Express 17 3782

    [111]

    Zhang Y L, Ma D L, Zhou Z Y, Yuan X H 2017 Appl. Opt. 56 2922

    [112]

    Basu S, Hyde M W, Xiao X F, Voelz D G, Korotkova O 2014 Opt. Express 22 31691

    [113]

    Hyde M W, Bose-Pillai S R, Wood R A 2017 Appl. Phys. Lett. 111 101106

    [114]

    Hyde M W, Bose-Pillai S, Xiao X, Voelz D G 2017 J. Opt. 19 025601

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  • Received Date:  04 May 2018
  • Accepted Date:  24 May 2018
  • Published Online:  20 September 2018

Research progress of partially coherent beams propagation in turbulent atmosphere

    Corresponding author: Cai Yang-Jian, yangjiancai@suda.edu.cn
  • 1. School of Physical Science and Technology, Soochow University, Suzhou 215006, China;
  • 2. Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China;
  • 3. Center of Light Manipulations and Applications, College of Physics and Electronics, Shandong Normal University, Jinan 250358, China
Fund Project:  Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91750201), the National Natural Science Fund for Distinguished Young Scholar, China (Grant No. 11525418), the National Natural Science Foundation of China (Grant No. 11474213), and the Qing Lan Project of Jiangsu Province, China.

Abstract: Compared with coherent laser beams, partially coherent beams have advantages of effectively reducing turbulence-induced extra beam spreading, beam wander and intensity scintillation on propagation through turbulent atmosphere, and have promising applications in free-space optical communications, laser radar and remote sensing. Recently, more and more attention was paid to the propagation of partially coherent beams through turbulent atmosphere. In this article, we first review historically the research progress of the propagation of partially coherent beams in atmospheric turbulence. And we describe in detail the basic theory for the calculation of average intensity, second-order moment and scintillation index of partially coherent beams in turbulence based on the extended Huygens-Fresnel principle and Rytov method. We also present a phase screen method of numerically simulating the propagation of coherent beams through turbulent atmosphere, and then extend such a method to treating the propagation of partially coherent beams.

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