湍流大气中激光上行和下行传输时相位奇点的演化
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摘要
利用激光大气传输四维程序数值模拟了激光在湍流大气中上行和下行传输时产生的相位奇点的变化过程。由模拟结果可知,当光束自地面向空中垂直上行传输时,相位奇点数密度随传输高度的变化有一个从无到有、从快速增加到缓慢增加、达到峰值后又减小的过程;湍流越强,畸变光场中产生的相位奇点数密度越大,达到的峰值越高,且达到峰值后减小的幅度也越大,但达到峰值时对应的传输高度越低;当激光自空中某一位置垂直下行传输时,相位奇点数密度随传输距离的增加有一个从无到有、从缓慢增加到快速增加且在接近地平面处急剧增加的过程。另外,通过对模拟结果的曲线拟合发现,激光在湍流大气中上行传输时产生的相位奇点数密度与传输高度的关系符合黑体辐射公式;当激光在湍流大气中下行传输时,相位奇点数密度随传输距离的增加呈指数增加。
Behavior of phase singularities in the distorted optical field is studied by numerical modeling using four-dimension code when a laser beam propagates through uplink and downlink atmospheric turbulence paths.The results reveal that,when the laser beam propagates along an uplink turbulent atmosphere path,the density of phase singularities(DPS)starts at zero and then grows rapidly with the increasing of the propagating height.When the beam propagates to a certain height,the DPS reaches its maximum and then begins to decrease.Such a height changes with the turbulence strength.The stronger the turbulence strength,the bigger the generated DPS,and the lager the maximum DPS with correspondingly lower height.When the laser beam propagates along a downlink turbulent atmosphere path,the stronger turbulence strength is taken,the phase singularities emerge at a higher altitude and the DPS in distorted optical field is bigger near the ground.The functional form of the DPS has a shape of monotone increase with the decrease of the propagation height and the DPS reaches its maximum near the ground.In addition,formulas describing the relationship between the DPS and propagation height/distance are found out.When the laser beam propagates through turbulent atmosphere along an uplink path,the formula is very similar to the formula used for describing the Blackbody radiation in physics.When the laser beam propagates along a downlink atmospheric turbulence path,the DPS seems to be growing exponentially with the propagating distance.
Behavior of phase singularities in the distorted optical field is studied by numerical modeling using four-dimension code when a laser beam propagates through uplink and downlink atmospheric turbulence paths.The results reveal that,when the laser beam propagates along an uplink turbulent atmosphere path,the density of phase singularities(DPS)starts at zero and then grows rapidly with the increasing of the propagating height.When the beam propagates to a certain height,the DPS reaches its maximum and then begins to decrease.Such a height changes with the turbulence strength.The stronger the turbulence strength,the bigger the generated DPS,and the lager the maximum DPS with correspondingly lower height.When the laser beam propagates along a downlink turbulent atmosphere path,the stronger turbulence strength is taken,the phase singularities emerge at a higher altitude and the DPS in distorted optical field is bigger near the ground.The functional form of the DPS has a shape of monotone increase with the decrease of the propagation height and the DPS reaches its maximum near the ground.In addition,formulas describing the relationship between the DPS and propagation height/distance are found out.When the laser beam propagates through turbulent atmosphere along an uplink path,the formula is very similar to the formula used for describing the Blackbody radiation in physics.When the laser beam propagates along a downlink atmospheric turbulence path,the DPS seems to be growing exponentially with the propagating distance.
引文
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[14] Li Youkuan.Branch point effect on adaptive correction[C]//Proc of SPIE.2004,5490:1064-1070.
[15] Zhang Y,Tao C.Wavefront dislocations of Gaussian beams nesting optical vortices in a turbulent atmosphere[J].Chin Opt Lett,2004,2(10):559-561.
[16]葛筱璐,范承玉,王英俭.相位不连续点数目随湍流强度的变化[J].光学学报,2008,28(1):1-6.(Ge Xiaolu,Fan Chengyu,Wang Yingjian.Variation of phase branch point number with turbulence strength in laser propagation through atmosphere.Acta Optica Sinica,2008,28(1):1-6)
[17] Rao Ruizhong.Statistics of the fractal structure and phase singularity of a plane light wave propagation in atmospheric turbulence[J].Appl Opt,2008,47(2):269-276.
[18]饶瑞中.大气中的光学涡旋及其传播[J].红外与激光工程,2009,38(4):609-615.(Rao Ruizhong.Optical vortices and its propagation in the atmosphere.Infrared and Laser Engineering,2009,38(4):609-615)
[19]苑克娥,朱文越,饶瑞中.湍流大气中光束的相位不连续点数密度[J].光子学报,2009,38(2):410-413.(Yuan Ke’e,Zhu Wenyue,Rao Ruizhong.Density of phase branch points for a light wave propagation in atmospheric turbulence.Acta Photonica Sinica,2009,38(2):410-413)
[20] Oesch D W,Sanchez D J,Matson C L.The aggregate behavior of branch points—measuring the number and velocity of atmospheric turbulence layers[J].Opt Express,2010,18(21):22377-22392.
[21] Oesch D W,Sanchez D J,Tewksbury-Christle C M.Aggregate behavior of branch points—persistent pairs[J].Opt Express,2012,20(2):1046-1059.
[22]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.(Wang Yingjian.Some problems’discuss about the laser propagation in the atmosphere and its phase compensation.Hefei:Anhui Institute of Optics and Fine Mechanics,Chinese Academy of Sciences,1996).
[23] Smith F G.Atmospheric propagation of radiation[M].Bellingham:SPIE Press,1993.
[24]宋正方.应用大气光学基础[M].北京:气象出版社,1990.(Song Zhengfang.Elements of applied atmospheric optics.Beijing:China Meterorological Press,1990)
[25]孙刚,翁宁泉,肖黎明,等.不同地区大气折射率结构常数分布特性及分析[J].强激光与粒子束,2005,17(4):485-490.(Sun Gang,Weng Ningquan,Xiao Liming,et al.Profile and character of atmospheric structure constants of refractive index.High Power Laser and Particle Beams,2005,17(4):485-490)
[2] Nye J F,Berry M V.Dislocation in wave trains[J].Proc R Soc Lond A,1974,336(1605):165-190.
[3] Berry M V.Disruption of wavefronts:statistics of dislocations in incoherent Gaussian random waves[J].J Phys A,1978,11(1):27-37.
[4] Berry M V.Singularities in waves and rays[M]//Les Houches Session XXV—Physics of Defects(Balian R,kléman M,Poirier J P,ed.),Amsterdam:North-Holland,1981,35:453-543.
[5] Nye J F,Hajnal J V,Hannay J H.Phase saddles and dislocations in two-dimensional wave such as tides[J].Proc R Soc Lond A,1988,417(1852):7-20.
[6] Berry M V.Much ado about nothing:optical dislocation lines[C]//Proc of SPIE.1998,3487:1-15.
[7] Berry M V,Dennis M R.Phase singularities in isotropic random waves[J].Proc R Soc Lond A,2000,456(1605):2059-2079.
[8] Fried D L,Vaughn J L.Branch cuts in the phase function[J].Appl Opt,1992,31(15):2865-2882.
[9] Fried D L.Branch point problem in adaptive optics[J].J Opt Soc Am A,1998,15(15):2759-2768.
[10] Voitsekhovich V V,Kouznetsov D,Morozov D K h.Density of turbulence-induced phase dislocations[J].Appl Opt,1998,37(21):4525-4535.
[11]范承玉,王英俭,龚知本.光波相位不连续点的探测[J].光学学报,2001,21(11):1388-1391.(Fan Chengyu,Wang Yingjian,Gong Zhiben.Detection of branch-point in light phase.Acta Optica Sinica,2001,21(11):1388-1391)
[12]饶瑞中.湍流大气中的准直激光束:分形结构与相位不连续点[J].强激光与粒子束,2002,14(4):501-504.(Rao Ruizhong.Collimated laser beam in a turbulent atmosphere:fractal structure and phase branch points.High Power Laser and Particle Beams,2002,14(4):501-504)
[13]范承玉,王英俭,龚知本.相位不连续点对自适应光学的影响[J].强激光与粒子束,2003,15(5):435-438.(Fan Chengyu,Wang Yingjian,Gong Zhiben.Effect of branch points on adaptive optics.High Power Laser and Particle Beams,2003,15(5):435-438)
[14] Li Youkuan.Branch point effect on adaptive correction[C]//Proc of SPIE.2004,5490:1064-1070.
[15] Zhang Y,Tao C.Wavefront dislocations of Gaussian beams nesting optical vortices in a turbulent atmosphere[J].Chin Opt Lett,2004,2(10):559-561.
[16]葛筱璐,范承玉,王英俭.相位不连续点数目随湍流强度的变化[J].光学学报,2008,28(1):1-6.(Ge Xiaolu,Fan Chengyu,Wang Yingjian.Variation of phase branch point number with turbulence strength in laser propagation through atmosphere.Acta Optica Sinica,2008,28(1):1-6)
[17] Rao Ruizhong.Statistics of the fractal structure and phase singularity of a plane light wave propagation in atmospheric turbulence[J].Appl Opt,2008,47(2):269-276.
[18]饶瑞中.大气中的光学涡旋及其传播[J].红外与激光工程,2009,38(4):609-615.(Rao Ruizhong.Optical vortices and its propagation in the atmosphere.Infrared and Laser Engineering,2009,38(4):609-615)
[19]苑克娥,朱文越,饶瑞中.湍流大气中光束的相位不连续点数密度[J].光子学报,2009,38(2):410-413.(Yuan Ke’e,Zhu Wenyue,Rao Ruizhong.Density of phase branch points for a light wave propagation in atmospheric turbulence.Acta Photonica Sinica,2009,38(2):410-413)
[20] Oesch D W,Sanchez D J,Matson C L.The aggregate behavior of branch points—measuring the number and velocity of atmospheric turbulence layers[J].Opt Express,2010,18(21):22377-22392.
[21] Oesch D W,Sanchez D J,Tewksbury-Christle C M.Aggregate behavior of branch points—persistent pairs[J].Opt Express,2012,20(2):1046-1059.
[22]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.(Wang Yingjian.Some problems’discuss about the laser propagation in the atmosphere and its phase compensation.Hefei:Anhui Institute of Optics and Fine Mechanics,Chinese Academy of Sciences,1996).
[23] Smith F G.Atmospheric propagation of radiation[M].Bellingham:SPIE Press,1993.
[24]宋正方.应用大气光学基础[M].北京:气象出版社,1990.(Song Zhengfang.Elements of applied atmospheric optics.Beijing:China Meterorological Press,1990)
[25]孙刚,翁宁泉,肖黎明,等.不同地区大气折射率结构常数分布特性及分析[J].强激光与粒子束,2005,17(4):485-490.(Sun Gang,Weng Ningquan,Xiao Liming,et al.Profile and character of atmospheric structure constants of refractive index.High Power Laser and Particle Beams,2005,17(4):485-490)