电磁-高斯谢尔模型阵列光束在大气湍流中的传输特性
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摘要
根据广义惠更斯菲涅尔原理与维格纳分布函数相结合的方法,导出了电磁高斯谢尔模型阵列光束(EGSMA Beams)在大气湍流中传输的均方根空间扩展、角扩展以及M~2因子的解析式。(分析了其传输特性与光束宽度、初始相干长度、阵列光束数量、初始偏振度、湍流内尺度以及折射率结构常数的关系。)研究结果表明相对M~2因子随初始偏振度、初始相干长度和折射率结构常数的减小,以及阵列光束数量、光束宽度、和湍流内尺度的增大而减小,此时相对M~2因子受大气湍流影响更小。当经过大约5km的传输距离后,初始相干长度对相对M~2因子的影响开始明显加大,且随传输距离增大而增大。同时研究结果表明当阵列光束数量增加越多时,相对M~2因子越接近1。并且分析得出初始偏振度以及折射率结构常数对相对M~2因子的影响大于相对均方根空间扩展和角扩展。
Based on the generalized Huygens-Fresnel integral and the second-order moments of the Wigner distribution function,the analytical formulas for the root-mean-square(rms)spatial width,rms angular width and M~2-factor of electromagnetic Gaussian-Shell model array beams(EGSMA beams)propagating through the atmospheric turbulence are derived.The relationships of the propagation properties of EGSMA beams in turbulence with the initial beam width,initial coherence length,the beam array number,initial degree of polarization,inner scale of the turbulence and the structure parameter of the refractive index fluctuations of the turbulence are analyzed.The results show that compared with the relative M~2-factor decreases with the decreases of initial degree of polarization,coherence lengths and the refractive index fluctuations of the turbulence,and with the increases of beam array number,larger beam width and larger inner scale,the relative M~2-factor of EGSMA beams in turbulence is less affected by turbulence.And it is known that when the propagation distance is about 5 km or more,the influence of coherence lengths on the relative M~2-factor is increased obviously as the increase of propagation distance.Fur-thermore,it is also found that the value of the relative M~2-factor is close to 1 with the beam array number increasing.Meanwhile,the relative M~2-factor is influenced by the structure parameter of the refractive index fluctuations of the turbulence more seriously compared with those influenced by the relative rms spatial width and angular width.
Based on the generalized Huygens-Fresnel integral and the second-order moments of the Wigner distribution function,the analytical formulas for the root-mean-square(rms)spatial width,rms angular width and M~2-factor of electromagnetic Gaussian-Shell model array beams(EGSMA beams)propagating through the atmospheric turbulence are derived.The relationships of the propagation properties of EGSMA beams in turbulence with the initial beam width,initial coherence length,the beam array number,initial degree of polarization,inner scale of the turbulence and the structure parameter of the refractive index fluctuations of the turbulence are analyzed.The results show that compared with the relative M~2-factor decreases with the decreases of initial degree of polarization,coherence lengths and the refractive index fluctuations of the turbulence,and with the increases of beam array number,larger beam width and larger inner scale,the relative M~2-factor of EGSMA beams in turbulence is less affected by turbulence.And it is known that when the propagation distance is about 5 km or more,the influence of coherence lengths on the relative M~2-factor is increased obviously as the increase of propagation distance.Fur-thermore,it is also found that the value of the relative M~2-factor is close to 1 with the beam array number increasing.Meanwhile,the relative M~2-factor is influenced by the structure parameter of the refractive index fluctuations of the turbulence more seriously compared with those influenced by the relative rms spatial width and angular width.
引文
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[20]ZHOU Pu,MA Yan-xing,WANG Xiao-lin,et al.Average spreading of a Gaussian beam array in non-Kolmogorov turbulence[J].Optics Letters,2012,35(7):1043-1045.
[21]ZHOU Pu,LIU Ze-jin,XU Xiao-lin,et al.Propagation of coherently combined flattened laser beam array in turbulent atmosphere[J].Optics&Laser Technology,2009,41(4):403-407.
[22]ZHOU Pu,LIU Ze-jin,XU Xiao-lin,et al.Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere[J].Optics and Lasers in Engineering,2009,47(1):1254-1258.
[23]JI Xiao-ling,SHAO Xiao-li.Influence of turbulence on the beam propagation factor of Gaussian Schell-model array beams[J].Optics Communications,2010,283(6):869-873.
[24]LU Fang,ZHAO Dan,HAN Xiang-e.Propagation of beam array with random phase through atmospheric turbulence in a slat path[J].Acta Optica sinica,2015,35(8):0801005-1-0801005-6.卢芳,赵丹,韩香娥.湍流大气中随机相位光束阵列的斜程传输特性[J].光学学报,2015,35(8):0801005-1-0801005-6.
[2]Shirai T,Dogariu A,Wolf E.Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence[J].J.Opt.Soc.Am.A.,2003,20(6):1094-1102.
[3]ZHONG Yan-hi,CUI Zhi-feng,SHI Jian-ping,et al.Propagation properties of partially coherent Laguerre-Gaussian,beams in turbulent atmosphere[J].Opt.Laser Technol,2011,43(4):741-747.
[4]DAN You-quan,ZHANG Bin.Beam propagation factor of partially coherent flat-topped beams in a turbulent[J].Opt.Express,2008,16(20):15563-15575.
[5]XU Yong-gen,YANG Ting,Dan You-quan,et al.Average intensity and spreading of partially coherent dark hollow beam through the atmospheric turbulence along a slant path[J].Optik,2016,127(19):7794-7802.
[6]TIAN Huan-huan,XU Yong-gen,YANG Ting,et al.Propagation characteristics of partially coherent anomalous elliptical hollow Gaussian beam propagating through atmospheric turbulence along a slant path[J].J.Mod.Opt.,2017,64(4):422-429.
[7]XU Yong-gen,TIAN Huan-huan,YANG Ting,et al.Propagation characteristics of partially coherent flat-topped beams propagating through inhomogeneous atmospheric turbulence[J].Appl.Opt.,2017,56(10):2691-2696.
[8]XU Yong-gen,DAN You-quan,YU Jia-yi,et al.Propagation properties of partially coherent dark hollow beam in inhomogeneous atmospheric turbulence[J].J.Mod.Opt.,2016,21(63):2186-2197.
[9]Gbur G,Wolf E Spreading of partially coherent beams in random media[J].J.Opt.Soc.Am.A.,2002,19(8):1592-1598.
[10]LIU Xian-Long,WANG Fei,LIN Liu,et al.Generation and propagation of an electromagnetic Gaussian Schell-model vortex beam[J].J.Opt.Soc.Am.A.,2015,32(11):2058-2065.
[11]YAO Min,CAI Yang-jian,EYYUBOGLU H T,et al.Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity[J].Opt.Lett.,2008,33(19):2266-2268.
[12]ZHU Shi-jun,CAI Yang-jian,KOROTKOVA Olga.Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam[J].Opt.Express,2010,18(12):12587-12598.
[13]ZHANG Bi-ling,XU Yong-gen,Dan You-quan,et al.Beam spreading and M2-factor of electromagnetic Gaussian Schell-model beam propagating in inhomogeneous atmospheric turbulence[J].Optik.2017,149:398-408.
[14]KOROTKOVA Olga.Scintillation index of a stochastic electromagnetic beam propagating in random media[J].Opt.Commun,2008,281(9):2342-2348.
[15]AVRAMOV-ZAMUROVIC S,NELSON C,MALEK-MADANI R,et al.Polarization-induced reduction in scintillation of optical beams propagating in simulated turbulent atmospheric channels[J].Waves Random Complex Media,2014,24(4):452-462.
[16]YUAN Yang-sheng,CAI Yang-jian,ZHAO Cheng-liang,et al.Propagation factors of laser array beams in turbulent atmosphere[J].J.Mod.Opt.,2010,57(8):621-631.
[17]HUANG Yong-ping,GAO Zeng-hui,ZHANG Bin.Propagation properties based on second-order moments for correlated combination partially coherent Hermite-Gaussian linear array beams in non-Kolmogorov turbulence[J].J.Mod.Opt.,2013,60(10):841-850.
[18]AI Yang-li,DAN You-quan.Range of turbulence-negligible propagation of Gaussian Schell-model array beams[J].Opt.Commun,2011,284(13):3216-3220.
[19]WANG Fei,CAI Yang-jian.Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere[J].Opt.Express,2010,18(24):24661-24672.
[20]ZHOU Pu,MA Yan-xing,WANG Xiao-lin,et al.Average spreading of a Gaussian beam array in non-Kolmogorov turbulence[J].Optics Letters,2012,35(7):1043-1045.
[21]ZHOU Pu,LIU Ze-jin,XU Xiao-lin,et al.Propagation of coherently combined flattened laser beam array in turbulent atmosphere[J].Optics&Laser Technology,2009,41(4):403-407.
[22]ZHOU Pu,LIU Ze-jin,XU Xiao-lin,et al.Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere[J].Optics and Lasers in Engineering,2009,47(1):1254-1258.
[23]JI Xiao-ling,SHAO Xiao-li.Influence of turbulence on the beam propagation factor of Gaussian Schell-model array beams[J].Optics Communications,2010,283(6):869-873.
[24]LU Fang,ZHAO Dan,HAN Xiang-e.Propagation of beam array with random phase through atmospheric turbulence in a slat path[J].Acta Optica sinica,2015,35(8):0801005-1-0801005-6.卢芳,赵丹,韩香娥.湍流大气中随机相位光束阵列的斜程传输特性[J].光学学报,2015,35(8):0801005-1-0801005-6.