涡旋光束在湍流大气中的光束扩展
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摘要
涡旋光束在湍流大气中传输时,其振幅和相位会发生随机起伏,导致在接收平面处的光强起伏及光束扩展等。以低阶拉盖尔-高斯涡旋光束为例,利用激光大气传输四维程序数值模拟了不同条件下的涡旋光束在湍流大气中传输时引起的光束扩展。由模拟结果可知,传输距离越长或湍流越强,涡旋光束在大气中传输时的束宽扩展受湍流的影响越大;涡旋光束的拓扑荷数越高、光束的束腰越小或光波的波长越长,其束宽扩展受大气湍流的影响越小。湍流的内尺度和外尺度也会影响涡旋光束的光束扩展,但影响程度相对较小。另外,通过计算仿真还比较了涡旋光束和普通高斯光束在湍流大气中传输时引起的光束扩展的差异。
When the vortex beam propagates through the turbulent atmosphere, the random variations will be produced in the amplitude and phase of the beam. And the intensity fluctuations and spread of the radiation pattern will be induced at the observation plane. some results about the vortex beams broadening are obtained by numerical modeling using four-dimension code when the vortex beams propagate through the turbulent atmosphere under different conditions. The vortex beams are the lower order Laguerre-Gaussian modes. The results indicate that if the propagation distance is longer or the turbulence is stronger, the beam broadened by the turbulence will be more severe. And if the topological charge is higher, or the beam′s waist width is narrower, or the wavelength is longer,the beam broadened by the turbulence will be smaller. Though the inner scale and the outer scale of turbulence have an effect on the beam broadening, the influence of them is relatively weak. In addition, the broadening of vortex beam and fundamental Gauss beam through the turbulent atmosphere are compared numerically.
When the vortex beam propagates through the turbulent atmosphere, the random variations will be produced in the amplitude and phase of the beam. And the intensity fluctuations and spread of the radiation pattern will be induced at the observation plane. some results about the vortex beams broadening are obtained by numerical modeling using four-dimension code when the vortex beams propagate through the turbulent atmosphere under different conditions. The vortex beams are the lower order Laguerre-Gaussian modes. The results indicate that if the propagation distance is longer or the turbulence is stronger, the beam broadened by the turbulence will be more severe. And if the topological charge is higher, or the beam′s waist width is narrower, or the wavelength is longer,the beam broadened by the turbulence will be smaller. Though the inner scale and the outer scale of turbulence have an effect on the beam broadening, the influence of them is relatively weak. In addition, the broadening of vortex beam and fundamental Gauss beam through the turbulent atmosphere are compared numerically.
引文
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3 W M Lee,X C Yuan,W C Cheong.Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optica micromanipulation[J].Opt Lett,2004,29(15):1796-1798.
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9 T Wang,J Pu,Z Chen.Beam-spreading and topological charge of vortex beams propagating in a turbulent atmosphere[J].Opt Commun2009,282(7):1255-1259.
10 Wang Tao,Pu Jixiong,Chen Ziyang.Propagation of vortex beams in a turbulent atmosphere[J].Acta Optica Sinica,2008,28(s2):82-86王涛,蒲继雄,陈子阳.涡旋光束在湍流大气中的传输特性[J].光学学报,2008,28(s2):82-86.
11 G Gbur,R K Tyson.Vortex beam propagation through atmospheric turbulence and topological charge conservation[J].J Opt Soc Am A2008,25(1):225-230.
12 X L Ge,B Y Wang,C S Guo.Evolution of phase singularities of vortex beams propagating in atmospheric turbulence[J].J Opt Soc Am A,2015,32(5):837-842.
13 S Orlov,K Regelskis,V Smilgevic?ius,et al..Propagation of Bessel beams carrying optical vortices[J].Opt Commun,2002,209(1-3)155-165.
14 Y Zhang,C Tao.Wavefront dislocations of Gaussian beams nesting optical vortices in a turbulent atmosphere[J].Chin Opt Lett,20042(10):559-561.
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18 C Ding,L Pan,B Lu.Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel-Gauss pulsed beam[J].J Opt Soc Am A,2009,26(12):2654-2661.
19 V P Lukin,P A Konyaev,V A Sennikov.Beam spreading of vortex beams propagating in turbulent atmosphere[J].Appl Opt,2012,51(10):C84-C87.
20 I P Lukin.Formation of a ring dislocation of a coherence of a vortex optical beam in turbulent atmosphere[C].SPIE,2013,9066:90660Q
21 Y Gu.Statistics of optical vortex wander on propagation through atmospheric turbulence[J].J Opt Soc Am A,2013,30(4):708-716.
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23 I P Lukin.Mean intensity of vortex Bessel beams propagating in turbulent atmosphere[J].Appl Opt,2014,53(15):3287-3293.
24 Li Fang,Tang Hua,Jiang Yuesong,et al..Spiral spectrum of Laguerre-Gaussian beams propagating in turbulent atmosphere[J].Act Physica Sinica,2011,60(1):014204.黎芳,唐华,江月松,等.拉盖尔-高斯光束在湍流大气中的螺旋谱特性[J].物理学报,2011,60(1):014204.
25 Li Fang.Propagation characteristics of optical vortices beam in intermediate fluctuation turbulent atmosphere[J].Laser&Optoelectronic Progress,2013,50(7):070101.黎芳.涡旋光束在中强度湍流大气中的传输特性[J].激光与光电子学进展,2013,50(7):070101.
26 Wang Haiyan,Chen Chuanlin,Du Jialei,et al..Propagation of Bessel-Gaussian beams with optical vortices in turbulent atmosphere[J]Acta Photonica Sinica,2013,42(5):505-510.王海燕,陈川琳,杜家磊,等.贝塞尔高斯涡旋光束在大气湍流中的传输特性[J].光子学报,2013,42(5):505-510.
27 F Wang,Y Cai,H T Eyyubog?lu,et al..Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere[J].Progress in Electromagnetics Research,2010,103(1):33-56.
28 Y Xu,Y Li,X Zhao.Intensity and effective beam width of partially coherent Laguerre-Gaussian beams through a turbulent atmosphere[J].J Opt Soc Am A,2015,32(9):1623-1630.
29 Ke Xizheng,Han Meimiao,Wang Mingjun.Spreading and wander of partially coherent beam propagating along a horizontal-path in th atmospheric turbulence[J].Acta Optica Sinica,2014,34(11):1106003.柯熙政,韩美苗,王明军.部分相干光在大气湍流中水平传输路径上的展宽与漂移[J].光学学报,2014,34(11):1106003.
30 J Li,A Yang,B Lü.Comparative study of the beam-width spreading of paratially coherent Hermite-sinh-Gaussian beams in atmospheri turbulence[J].J Opt Soc Am A,2008,25(11):2670-2679.
31 Yang Ailin,Li Jinhong,LüBaida.A comparative study of the beam-width spreading and angular spread in atmospheric turbulence[J]Acta Physica Sinica,2009,58(4):2451-2460.杨爱林,李晋红,吕百达.大气湍流中光束束宽扩展和角扩展的比较研究[J].物理学报,2009,58(4):2451-2460.
32 Wang Yingjian.Study on the laser propagation in the atmosphere and its phase compensation[D].Hefei:Anhui Institute of Optics and Fine Mechanics,Chinese Academy of Sciences,1996.王英俭.激光大气传输及其位相补偿的若干问题探讨[D].合肥:中国科学院安徽光学精密机械研究所,1996.
33 R L Phillips,L C Andrews.Spot size and divergence for Laguerre Gaussian beams of any order[J].Appl Opt,1983,22(5):643-644.
34 D L Knepp.Multiple phase-screen calculation of the temporal behavior of stochastic waves[C].IEEE,1983,71(6):722-737.
35 W A Coles,J P Filice,R G Frehlich,et al..Simulation of wave propagation in three-dimensional random media[J].Appl Opt,1995,34(12):2089-2101.
36 R Frehlich.Simulation of laser propagation in a turbulent atmosphere[J].Appl Opt,2000,39(3):393-397.
2 C Paterson.Atmospheric turbulence and orbital angular momentum of single photons for optical communication[J].Phys Rev Lett,200594(15):153901.
3 W M Lee,X C Yuan,W C Cheong.Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optica micromanipulation[J].Opt Lett,2004,29(15):1796-1798.
4 N B Simpson,K Dholakia,L Allen,et al..Mechanical equivalence of spin and orbital angular momentum of light:an optical spanner[J]Opt Lett,1997,22(1):52-54.
5 L Allen,S M Barnett,M J Padgett.Optical angular momentum[M].London:Institute of Physics Publishing,2003.
6 Luo Wei,Cheng Shubo,Yuan Zhanzhong,et al..Power-exponent-phase vortices for manipulating particles[J].Acta Optica Sinica,201434(11):1109001.罗伟,程书博,袁战忠,等.幂指数相位涡旋光束用于微粒操控[J].光学学报,2014,34(11):1109001.
7 G Molina-Terriza,J P Torres,L Torner.Management of the angular momentum of light:preparation of photons in multidimensional vecto states of angular momentum[J].Phys Rev Lett,2001,88(1):013601.
8 A Vin?otte,L Bergé.Femtosecond optical vortices in air[J].Phys Rev Lett,2005,95(19):193901.
9 T Wang,J Pu,Z Chen.Beam-spreading and topological charge of vortex beams propagating in a turbulent atmosphere[J].Opt Commun2009,282(7):1255-1259.
10 Wang Tao,Pu Jixiong,Chen Ziyang.Propagation of vortex beams in a turbulent atmosphere[J].Acta Optica Sinica,2008,28(s2):82-86王涛,蒲继雄,陈子阳.涡旋光束在湍流大气中的传输特性[J].光学学报,2008,28(s2):82-86.
11 G Gbur,R K Tyson.Vortex beam propagation through atmospheric turbulence and topological charge conservation[J].J Opt Soc Am A2008,25(1):225-230.
12 X L Ge,B Y Wang,C S Guo.Evolution of phase singularities of vortex beams propagating in atmospheric turbulence[J].J Opt Soc Am A,2015,32(5):837-842.
13 S Orlov,K Regelskis,V Smilgevic?ius,et al..Propagation of Bessel beams carrying optical vortices[J].Opt Commun,2002,209(1-3)155-165.
14 Y Zhang,C Tao.Wavefront dislocations of Gaussian beams nesting optical vortices in a turbulent atmosphere[J].Chin Opt Lett,20042(10):559-561.
15 Y Zhang,M Tang,C Tao.Partially coherent vortex beams propagation in a turbulent atmosphere[J].Chin Opt Lett,2005,3(10):559-561
16 G Gibson,J Courtial,M Padgett,et al..Free-space information transfer using light beams carrying orbital angular momentum[J].Op Express,2004,12(22):5448-5456.
17 K Zhu,G Zhou,X Li,et al..Propagation of Bessel-Gaussian beams with optical vortices in turbulent atmosphere[J].Opt Express,200816(26):21315-21320.
18 C Ding,L Pan,B Lu.Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel-Gauss pulsed beam[J].J Opt Soc Am A,2009,26(12):2654-2661.
19 V P Lukin,P A Konyaev,V A Sennikov.Beam spreading of vortex beams propagating in turbulent atmosphere[J].Appl Opt,2012,51(10):C84-C87.
20 I P Lukin.Formation of a ring dislocation of a coherence of a vortex optical beam in turbulent atmosphere[C].SPIE,2013,9066:90660Q
21 Y Gu.Statistics of optical vortex wander on propagation through atmospheric turbulence[J].J Opt Soc Am A,2013,30(4):708-716.
22 Q Cui,M Li,Z Yu.Influence of topological charge on random wandering of optical vortex propagating through turbulent atmosphere[J]Opt Commun,2014,329(20):10-14.
23 I P Lukin.Mean intensity of vortex Bessel beams propagating in turbulent atmosphere[J].Appl Opt,2014,53(15):3287-3293.
24 Li Fang,Tang Hua,Jiang Yuesong,et al..Spiral spectrum of Laguerre-Gaussian beams propagating in turbulent atmosphere[J].Act Physica Sinica,2011,60(1):014204.黎芳,唐华,江月松,等.拉盖尔-高斯光束在湍流大气中的螺旋谱特性[J].物理学报,2011,60(1):014204.
25 Li Fang.Propagation characteristics of optical vortices beam in intermediate fluctuation turbulent atmosphere[J].Laser&Optoelectronic Progress,2013,50(7):070101.黎芳.涡旋光束在中强度湍流大气中的传输特性[J].激光与光电子学进展,2013,50(7):070101.
26 Wang Haiyan,Chen Chuanlin,Du Jialei,et al..Propagation of Bessel-Gaussian beams with optical vortices in turbulent atmosphere[J]Acta Photonica Sinica,2013,42(5):505-510.王海燕,陈川琳,杜家磊,等.贝塞尔高斯涡旋光束在大气湍流中的传输特性[J].光子学报,2013,42(5):505-510.
27 F Wang,Y Cai,H T Eyyubog?lu,et al..Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere[J].Progress in Electromagnetics Research,2010,103(1):33-56.
28 Y Xu,Y Li,X Zhao.Intensity and effective beam width of partially coherent Laguerre-Gaussian beams through a turbulent atmosphere[J].J Opt Soc Am A,2015,32(9):1623-1630.
29 Ke Xizheng,Han Meimiao,Wang Mingjun.Spreading and wander of partially coherent beam propagating along a horizontal-path in th atmospheric turbulence[J].Acta Optica Sinica,2014,34(11):1106003.柯熙政,韩美苗,王明军.部分相干光在大气湍流中水平传输路径上的展宽与漂移[J].光学学报,2014,34(11):1106003.
30 J Li,A Yang,B Lü.Comparative study of the beam-width spreading of paratially coherent Hermite-sinh-Gaussian beams in atmospheri turbulence[J].J Opt Soc Am A,2008,25(11):2670-2679.
31 Yang Ailin,Li Jinhong,LüBaida.A comparative study of the beam-width spreading and angular spread in atmospheric turbulence[J]Acta Physica Sinica,2009,58(4):2451-2460.杨爱林,李晋红,吕百达.大气湍流中光束束宽扩展和角扩展的比较研究[J].物理学报,2009,58(4):2451-2460.
32 Wang Yingjian.Study on the laser propagation in the atmosphere and its phase compensation[D].Hefei:Anhui Institute of Optics and Fine Mechanics,Chinese Academy of Sciences,1996.王英俭.激光大气传输及其位相补偿的若干问题探讨[D].合肥:中国科学院安徽光学精密机械研究所,1996.
33 R L Phillips,L C Andrews.Spot size and divergence for Laguerre Gaussian beams of any order[J].Appl Opt,1983,22(5):643-644.
34 D L Knepp.Multiple phase-screen calculation of the temporal behavior of stochastic waves[C].IEEE,1983,71(6):722-737.
35 W A Coles,J P Filice,R G Frehlich,et al..Simulation of wave propagation in three-dimensional random media[J].Appl Opt,1995,34(12):2089-2101.
36 R Frehlich.Simulation of laser propagation in a turbulent atmosphere[J].Appl Opt,2000,39(3):393-397.