湍流对部分相干双曲余弦高斯列阵光束扩展和光束传输因子的影响
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摘要
激光束在大气湍流中的传输理论及实验研究,对于激光通讯、激光测距、激光雷达以及激光武器等领域的应用有着重要的意义。近年来,激光列阵合成技术由于在高功率系统、惯性约束聚变和高能武器等方面的应用也越来越受到人们的关注。而实际激光束存在部分相干情况。因此,研究部分相干列阵光束在大气湍流中的传输特性是十分有意义的。本文研究了湍流对部分和完全相干双曲余弦高斯(ChG)列阵光束扩展和光束传输因子的影响。主要内容总结如下:
1.研究了ChG列阵激光束通过大气湍流传输的角扩展及方向性。利用积分变换技巧推导出了ChG列阵光束通过大气湍流传输的二阶矩束宽和角扩展的解析公式,给出了ChG列阵光束与一束高斯光束具有相同角扩展的条件。研究表明:相干合成的ChG列阵光束的角扩展比非相干合成的小,但是,非相干合成的ChG列阵光束的角扩展受湍流影响比相干合成的小。此外,相干合成的ChG列阵光束的角扩展随离心参数,束腰宽度和相对子光束间距的变化均出现振荡,但湍流中的振荡减弱。非相干合成的ChG列阵光束的角扩展与相对子光束间距和光束数目无关。
2.采用湍流距离(湍流距离是指大气湍流导致的光束横截面积扩展达10%时光束的传输距离)定量地研究了湍流对部分相干ChG列阵光束扩展的影响。基于广义惠更斯—菲涅耳原理,采用Rytov相位结构函数二次近似和积分变换技巧,推导出了部分相干ChG列阵光束通过大气湍流传输时湍流距离的表达式。详细研究了部分相干ChG列阵光束的湍流距离随着大气湍流强度、光束参数(即子光束数,光束相干参数,离心参数,相对子光束间距)以及光束叠加方式(即交叉谱密度函数叠加和光强叠加)的变化情况。研究表明:部分相干ChG列阵光束的光束扩展会随着大气湍流强度的增大而增大,但是当选择合适的光束参数以及光束叠加方式时,可以减小湍流对部分相干ChG列阵光束扩展的影响。
3.采用光束传输因子(M~2因子)作为光束质量的评价参数,研究了ChG列阵光束通过大气湍流传输的M~2因子。利用Rytov相位结构函数二次近似和积分变换技巧推导出了ChG列阵光束在大气湍流中传输的M~2因子的解析公式,并采用相对M~2因子研究了湍流对M~2因子的影响。研究表明:在大气湍流中M~2因子不再是一个传输不变量,湍流使得M~2因子增大。非相干合成情况下,M~2因子随着传输距离、离心参数、相对子光束间距和子光束数目的增大而增大。相干合成情况下,M~2因子随离心参数和相对子光束间距的增大呈现振荡上升。相干合成情况下的M~2因子比非相干合成的要小。然而,非相干合成情况下的M~2因子受湍流影响比相干合成的要小。特别地,相干合成情况下,选取适当的相对子光束间距可以减小湍流对M~2因子的影响。此外,随着子光束数目的增大,相干合成的M~2因子受湍流影响增大,而非相干合成的M~2因子受湍流影响减小。
The theoretical and experimental study on the laser beams propagating through atmospheric turbulence is of great significance for the applications of laser communications, laser ranging, laser radar, laser weapons, and so on. In recent years, the laser array combining technique has been paid more and more attention for its applications in high-power system, inertial confinement fusion, high-energy weapons, and so on. In practice, partially coherent beams are often encountered. Therefore, it is very meaningful to study the propagation properties of partially coherent array beams in atmospheric turbulence. The influence of turbulence on the spreading and beam propagation factor of the partially coherent and fully coherent cosh-Gaussian(ChG) array beams has been studied in this thesis. The main works are summarized as follows:
1. The angular spread and directionality of ChG array beams propagating through atmospheric turbulence are studied. The closed-form expressions for the mean-squared beam width and the angular spread of ChG array beams propagating through atmospheric turbulence are derived by has the same directionality as one single Gaussian beam is given. It is shown that the angular spread of ChG array beams for the coherent combination is smaller than that for the incoherent combination. However, the angular spread of ChG array beams for the incoherent combination is less sensitive to turbulence than that for the coherent combination. In addition, The angular spread of ChG array beams for the coherent combination exists oscillatory behavior with the changes of the decentered parameter, the waist width and the relative separation distance of beams. However, the oscillatory behavior becomes weaker in turbulence. The angular spread of ChG array beams for the incoherent combination is independent of the relative separation distance of beams and the beam number.
2. The influence of turbulence on the beam spreading of partially coherent ChG array beams is studied quantitatively by the turbulence distance which represents the distance at which the spreading due to the turbulence accounts for 10% of the cross-sectional area of the beam. Based on the extended Huygens-Fresnel principle, the expression for the turbulence distance of partially coherent ChG array beams propagating through atmospheric turbulence is derived by using the quadratic approximation of Rytov’s phase structure fuction and integral transform technique. The changes of the turbulence distance versus the spatial power spectrum of the refractive index fluctuations, the beam parameters (i.e., the beam number, the beam coherence parameter, the decentered parameter, the relative separation distance of beams) and the type of the beam superposition (i.e., the superposition of the cross-spectral density function and the superposition of the intensity) are studied in detail. It is showed the turbulence distance of the partially coherent ChG array beams will increase with the the spatial power spectrum of the refractive index fluctuations, but the effect of turbulence on the spreading of partially coherent ChG array beams can be reduced by choosing the suitable beam parameters and the suitable type of the beam superposition.
3. The beam propagation factor(M~2-factor)is taken as the characteristic parameter of beam quality, and the M~2-factor of ChG array beams propagating through atmospheric turbulence is studied. The analytical formula for the beam propagation factor (M~2-factor) of ChG array beams propagating through atmospheric turbulence is derived by using the quadratic approximation of Rytov’s phase structure fuction and integral transform technique, and the influence of turbulence on the M~2-factor is studied by using the relative M~2-factor. It is shown that the M~2-factor is not a propagation invariant in turbulence, and the turbulence results in an increase of the M~2-factor. For the incoherent combination, the M~2-factor of ChG array beams increases with increasing the propagation distance, the beam parameter, the relative beam separation distance and the beam number. For the coherent combination, the M~2-factor of ChG array beams increases with the oscillatory behavior as the beam parameter or the relative beam separation distance increases. For the coherent combination the M~2-factor is always smaller than that for the incoherent combination. However, for the incoherent combination the M~2-factor is always less sensitive to turbulence than that for the coherent combination. In particular, the influence of turbulence on the M~2-factor can be reduced by a suitable choice of the relative beam separation distance. In addition, with increasing the beam number, the M~2-factor is more sensitive to turbulence for the coherent combination, while for the incoherent combination the M~2-factor is less sensitive to turbulence.
1.研究了ChG列阵激光束通过大气湍流传输的角扩展及方向性。利用积分变换技巧推导出了ChG列阵光束通过大气湍流传输的二阶矩束宽和角扩展的解析公式,给出了ChG列阵光束与一束高斯光束具有相同角扩展的条件。研究表明:相干合成的ChG列阵光束的角扩展比非相干合成的小,但是,非相干合成的ChG列阵光束的角扩展受湍流影响比相干合成的小。此外,相干合成的ChG列阵光束的角扩展随离心参数,束腰宽度和相对子光束间距的变化均出现振荡,但湍流中的振荡减弱。非相干合成的ChG列阵光束的角扩展与相对子光束间距和光束数目无关。
2.采用湍流距离(湍流距离是指大气湍流导致的光束横截面积扩展达10%时光束的传输距离)定量地研究了湍流对部分相干ChG列阵光束扩展的影响。基于广义惠更斯—菲涅耳原理,采用Rytov相位结构函数二次近似和积分变换技巧,推导出了部分相干ChG列阵光束通过大气湍流传输时湍流距离的表达式。详细研究了部分相干ChG列阵光束的湍流距离随着大气湍流强度、光束参数(即子光束数,光束相干参数,离心参数,相对子光束间距)以及光束叠加方式(即交叉谱密度函数叠加和光强叠加)的变化情况。研究表明:部分相干ChG列阵光束的光束扩展会随着大气湍流强度的增大而增大,但是当选择合适的光束参数以及光束叠加方式时,可以减小湍流对部分相干ChG列阵光束扩展的影响。
3.采用光束传输因子(M~2因子)作为光束质量的评价参数,研究了ChG列阵光束通过大气湍流传输的M~2因子。利用Rytov相位结构函数二次近似和积分变换技巧推导出了ChG列阵光束在大气湍流中传输的M~2因子的解析公式,并采用相对M~2因子研究了湍流对M~2因子的影响。研究表明:在大气湍流中M~2因子不再是一个传输不变量,湍流使得M~2因子增大。非相干合成情况下,M~2因子随着传输距离、离心参数、相对子光束间距和子光束数目的增大而增大。相干合成情况下,M~2因子随离心参数和相对子光束间距的增大呈现振荡上升。相干合成情况下的M~2因子比非相干合成的要小。然而,非相干合成情况下的M~2因子受湍流影响比相干合成的要小。特别地,相干合成情况下,选取适当的相对子光束间距可以减小湍流对M~2因子的影响。此外,随着子光束数目的增大,相干合成的M~2因子受湍流影响增大,而非相干合成的M~2因子受湍流影响减小。
The theoretical and experimental study on the laser beams propagating through atmospheric turbulence is of great significance for the applications of laser communications, laser ranging, laser radar, laser weapons, and so on. In recent years, the laser array combining technique has been paid more and more attention for its applications in high-power system, inertial confinement fusion, high-energy weapons, and so on. In practice, partially coherent beams are often encountered. Therefore, it is very meaningful to study the propagation properties of partially coherent array beams in atmospheric turbulence. The influence of turbulence on the spreading and beam propagation factor of the partially coherent and fully coherent cosh-Gaussian(ChG) array beams has been studied in this thesis. The main works are summarized as follows:
1. The angular spread and directionality of ChG array beams propagating through atmospheric turbulence are studied. The closed-form expressions for the mean-squared beam width and the angular spread of ChG array beams propagating through atmospheric turbulence are derived by has the same directionality as one single Gaussian beam is given. It is shown that the angular spread of ChG array beams for the coherent combination is smaller than that for the incoherent combination. However, the angular spread of ChG array beams for the incoherent combination is less sensitive to turbulence than that for the coherent combination. In addition, The angular spread of ChG array beams for the coherent combination exists oscillatory behavior with the changes of the decentered parameter, the waist width and the relative separation distance of beams. However, the oscillatory behavior becomes weaker in turbulence. The angular spread of ChG array beams for the incoherent combination is independent of the relative separation distance of beams and the beam number.
2. The influence of turbulence on the beam spreading of partially coherent ChG array beams is studied quantitatively by the turbulence distance which represents the distance at which the spreading due to the turbulence accounts for 10% of the cross-sectional area of the beam. Based on the extended Huygens-Fresnel principle, the expression for the turbulence distance of partially coherent ChG array beams propagating through atmospheric turbulence is derived by using the quadratic approximation of Rytov’s phase structure fuction and integral transform technique. The changes of the turbulence distance versus the spatial power spectrum of the refractive index fluctuations, the beam parameters (i.e., the beam number, the beam coherence parameter, the decentered parameter, the relative separation distance of beams) and the type of the beam superposition (i.e., the superposition of the cross-spectral density function and the superposition of the intensity) are studied in detail. It is showed the turbulence distance of the partially coherent ChG array beams will increase with the the spatial power spectrum of the refractive index fluctuations, but the effect of turbulence on the spreading of partially coherent ChG array beams can be reduced by choosing the suitable beam parameters and the suitable type of the beam superposition.
3. The beam propagation factor(M~2-factor)is taken as the characteristic parameter of beam quality, and the M~2-factor of ChG array beams propagating through atmospheric turbulence is studied. The analytical formula for the beam propagation factor (M~2-factor) of ChG array beams propagating through atmospheric turbulence is derived by using the quadratic approximation of Rytov’s phase structure fuction and integral transform technique, and the influence of turbulence on the M~2-factor is studied by using the relative M~2-factor. It is shown that the M~2-factor is not a propagation invariant in turbulence, and the turbulence results in an increase of the M~2-factor. For the incoherent combination, the M~2-factor of ChG array beams increases with increasing the propagation distance, the beam parameter, the relative beam separation distance and the beam number. For the coherent combination, the M~2-factor of ChG array beams increases with the oscillatory behavior as the beam parameter or the relative beam separation distance increases. For the coherent combination the M~2-factor is always smaller than that for the incoherent combination. However, for the incoherent combination the M~2-factor is always less sensitive to turbulence than that for the coherent combination. In particular, the influence of turbulence on the M~2-factor can be reduced by a suitable choice of the relative beam separation distance. In addition, with increasing the beam number, the M~2-factor is more sensitive to turbulence for the coherent combination, while for the incoherent combination the M~2-factor is less sensitive to turbulence.
引文
[1]谢晓芬,宋晓羽.激光发展概况[J].长春师院学报,1994,1:40-42.
[2]安毓英.第四章激光传输技术[J].激光与红外,2002,32(6):437-438.
[3]纪雯.激光相干合成效果的研究[D].成都:电子科技大学,2009.
[4] Li Bingzhong, LüBaida. Irradiance-moments characterization of off-axis Gaussian beam combinations by means of the Wigner distribution function[J]. Optik, 2002, 113(11):469-475.
[5]程勇,刘洋,许立新.激光相干合成技术研究新动向[J].红外与激光工程,2007,36(2):163-166.
[6]孙玲,赵鸿,杨文是等.多光束激光相干合成技术研究[J].激光与红外,2007,37(2):111-113.
[7]刘泽金,周朴,王小林等.激光相干合成的历史、现状与发展趋势[J].中国激光,2010,37(9):2221-2231.
[8]吕百达,张彬.激光束的相干合成技术[J].激光杂志,1998,19(1):6-14.
[9]肖瑞,周朴,侯静等.激光器的部分相干性对光纤激光器列阵相干合成远场图样的影响[J].物理学报,2007,56(2):819-822.
[10]徐立国,方存忠,蒋万铎等.高功率激光器MOPA相干合成系统分析[J].量子光学学报,2010,16(1):74-78.
[11]Fan T Y. Laser beam combining for high-power, high-radiance sources[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2005, 11(3):567-577.
[12]Casperson L W, Hall D G, Tovar A A. Hermite-sinusoidal-Gaussian beams in complex optical systems[J]. J. Opt. Soc. Am. A, 1998, 15(4):954-961.
[13]Casperson L W, Hall D G, Tovar A A. Sinusoidal-Gaussian beams in complex optical systems[J]. J. Opt. Soc. Am. A, 1997, 14(12):3341-3348.
[14]Tovar A A , Casperson L W. Production and propagation of Hermite- sinusoidal-Gaussian laser beams[J].J . Opt . Soc. Am. A, 1998,15(9):2425-2432.
[15]王喜庆,吕百达.厄米-双曲正弦-高斯光束的M~2因子[J].物理学报,2002,52(2):247-251.
[16]唐慧琴,朱开成,朱正和等.一类新平顶光束的束传播因子[J].强激光与粒子束,2007,19(10):357-359.
[17]汤明玥.湍流对厄米高斯及列阵双曲余弦高斯光束的传输和远场光束质量的影响[D].成都:四川师范大学,2008.
[18]LüB D, Zhang B. M H.Beam propagation factor and mode coherence coefficients of hyperbolic-cosine-Gaussian beams[J].Opt Lett., 1999,24:640—643.
[19] LüB D, Ma H, Zhang B. Propagation properties of cosh-Gaussian beams[J]. Opt Commun., 1999, 164: 165-170.
[20]张彬,楚晓亮,吕百达.双曲余弦高斯光束的模相关和模结构分析[J].激光技术,2001,25(5):372-375.
[21]徐延亮,王喜庆.双曲余弦-高斯光束的相干模分解[J].激光杂志,2008,29(6):47-48.
[22]Wu J. Propagation of a Gaussian Shell beam through turbulent media[J]. J. Mod. Opt., 1990, 37(3): 671～678.
[23]Gbur G, Wolf E. Spreading of partially coherent beams in random media[J]. J. Opt. Soc. Am. A 2002, 19(8): 1592～1598 .
[24]Dogariu A, Amarande S. Propagation of partially coherent beams: turbulence-induced degradation[J]. Opt. Lett., 2003,28(1):10-12.
[25]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.
[26]季小玲,黄太星,吕百达.部分相干双曲余弦高斯光束通过湍流大气的光束扩展[J].物理学报,2006,55(2):978-982
[27]李长伟,吕百达.部分相干双曲余弦-高斯光束的传输特性及空间整形[J].强激光与粒子束,2007,19(10):1589-1593.
[28]Shirai T, Dogariu A, Wolf E. Directionality of Gaussian Schell-model beams propagating in atmospheric turbulence[J]. Optics Letters , 2003, 28(8):610-612.
[29]陈晓文,季小玲.湍流对环状光束扩展的影响[J].物理学报,2009,58(4):2435-2442.
[30]Eyyuboglu H T , Baykal Y. Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulence atmosphere[J]. J. Opt. Soc. Am. A, 2005, 22(12):2709-2718.
[31]Xiao X , Ji X L, LüB D. The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field[J]. Optics & Laser Technology,2008,40:129-136.
[32]Yang A L, Zhang E T, Ji X L et al. Angular spread of partially coherent Hermite-cosh-Gaussian beams propagatingthrough atmospheric turbulence[J]. Optic Express, 2008,16(12):8367-8380.
[33]Liu Y S, Chen C H, Chuo Y C. Propagation of Hermite-Gaussian Beam Array in the Far Field[J].Lasers and Electro-Optics-Pacific Rim,2007.
[34]Wu G H, Lou Q H, Zhou J et al. Beam combination of a radial laser array: Flat-topped beam[J]. Optics & Laser Technology,2008, 40:890-894.
[35]Baida Lü, Hong Ma.Coherent and incoherent combinations of off-axis Gaussian beams with rectangular symmetry[J]. Optics Communications, 1999, 171(4-6):185-194.
[36]Cai Yangjian, Lin Qiang, Baykal Y. et al.. Off-axis Gaussian Schell-model beam and partially coherent laser array beam in a turbulent atmosphere [J]. Opt. Commun.,2007, 278(1):157-167.
[37]X. Ji ,Z. Pu .Angular spread of Gaussian Schell-model array beamspropagating through atmospheric turbulence[J]. Appl Phys B,2008,93:915-923.
[38]Cai Y, Chen Y, Eyyuboglu H T , Baykal Y .Propagation of laser array beams in a turbulent atmosphere[J]. Appl. Phys. B, 2007,88:467-474
[39]Pu Zhou , ZejinLiu , XiaojunXu, XiuxiangChu. Propagation of coherently combined flattened laser beam array in turbulent atmosphere[J]. Optics & Laser Technology, 2009, 41:403-407.
[40]Entao Zhang, Xiaoling Ji, Dangxiao Yang, and Baida Lu.Propagation and far-field beam quality of M×N Hermite–Gaussian beams propagating through atmospheric turbulence. [J]. Journal of Modern Optics,2008,55(3):387-400.
[41]Yingbin Zhu, Daomu Zhao, and Xinyue Du. Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere[J]. Optic Express,2008,16(22):18437-18442.
[42]Pu Zhou, Xiaolin Wang, Yanxing Ma et al. Propagation of partially coherent partially phase-locked laser array in turbulent atmosphere[J].Optics Communications,2010,283:1071-1074.
[43]汤眀玥,陈晓文,季小玲.湍流对M×N列阵双曲余弦高斯光束传输和远场光束质量的影响[J].光子学报,2009,38(3):713-718.
[44]Siegman A E. New developments in laser resonators[J]. Proc. SPIE 1990; 1224: 2-14.
[45]Song Yu, Hong Guo, Xiquan Fu,et all. Propagation properties of elegant Hermite–cosh-Gaussian laser beams[J]. Optics Communications, 2002, 204:59-66.
[46]Deng Dongmei. Propagation properties of off-axis cosh Gaussian beam combinations through a first-order optical system[J]. Physics Letters A,2004,333.
[47]Zhou G. Generalized beam propagation factors of truncated partially coherent cosine-Gaussian and cosh-Gaussian beams[J]. Opt. & Laser Technology,2010, 42(3) : 489-496.
[48]Wu Guohua, Guo Hong, Deng Dongmei. Paraxial propagation of partially coherent flat-topped beam[J].Optics Communications,2006,260(2):687-690.
[49]赵娜,唐淳,谢刚等.多束超高斯激光的相干合成的数值模拟[J].强激光与粒子束,2007,19(11):1780-1782.
[50] Liping Liu, Yi Zhou, Fanting Kong. Phase locking in a fiber laser array with varying path lengths [ J ]. Applied Physics Letters, 2004, 85 (21) : 4837 - 4839.
[51]李晓庆.部分相干列阵激光束通过大气湍流的传输特性研究[D].成都:四川师范大学,2009.
[52]吕百达,激光光学[M],四川大学出版社,1992.
[53]步青华.部分相干平顶光束在大气湍流中的传输特性研究[D].南京:南京理工大学,2009.
[54]尹纪欣.波束在湍流大气中的传播特性研究[D].西安:电子科技大学,2010.
[55]苗二龙.自由空间量子密钥分配[D].合肥:中国科学技术大学,2006.
[56]闫传忠.基于分形的大气湍流随机相位屏数值模拟[D].青岛:中国海洋大学,2009.
[57]杨帆.湍流对多色部分相干电磁光束传输特性影响[D].成都:四川师范大学,2009.
[58]王海燕.基于张量方法研究部分相干光和部分偏振光在大气湍流中的传输特性[D].南京:南京理工大学,2010.
[59]张洪江.大气湍流中激光波束和脉冲传输特性[D].西安:电子科技大学,2009.
[60]张建柱.大气湍流对部分相干平顶高斯光束影响的研究[D].北京:中国工程物理研究院,2004.
[61]饶瑞中,光在大气湍流中的传播[M].合肥:安徽科学技术出版, 2005
[62] R J Hill, C. J. Howard, Quantitative phase analysis from neutron powder diffraction datausing the Rietveld method [J]. J. Appl. Cryst., 1987, 20(6): 467-474.
[63] M. Roggemann , Imaging through turbulence [M]. Boca Raton: CRC Press, 1996
[64]R.J.Hill, S.F.Clifford , Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation [J]. J. Soc.Am.A, 1978, 68(7): 293-294.
[65]李宏升,湍流对大气中传输光束的影响[D].长春:长春理工大学,2002.
[66]陈昆.光无线通信伺服跟踪技术研究[D].武汉:华中科技大学,2007.
[67]袁仁民,曾宗泳。大尺度相干结构的光学特性研究[J].光学学报,2001,21(1):19-23.
[68]Andrems L. C.Analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere [J].J.Mod.Opt.,1992,39:1849-1853.
[69]陈晓文.部分相干光通过湍流大气传输的空间相干性及方向性研究[D].成都:四川师范大学,2009.
[70]刘琦.大气湍流对无线光通信误码率影响的研究[D].西安:电子科技大学,2009.
[71]Andrews L C, Phillips R. L. Laser Beam Propagation through Random Media[M]. Bellingham, Washington:SPIE Press, 1998.
[72]Wang.S. C. H., Plonus M. A., Yang C. F., Irradiance scintillations of a partially coherent source in extremely strong turbulence [J]. Applied Optics, 1979, 18(8): 1133-1135.
[73]Leader. J. C., Atmospheric propagation of partially coherent radiation [J]. J. Opt. Soc. Am, 1978, 68(1): 175-185.
[74]姚宇鹯.半导体激光器光束质量评估[D].西安:电子科技大学,2007.
[75]康小平.非傍轴标量和矢量光束的光束质量研究[D].成都:四川大学,2006.
[76]陈尚武.高能激光系统光束质量评价相关问题研究[D].杭州:浙江大学,2007.
[77]Siegman A. E., How to (Maybe) Measure Laser Beam Quality [J]. OSA. TOPS,1998, 17:184-201.
[78]Gbur G and Wolf E. Spreading of partially coherent beams in random media[J]. J. Opt .Soc. Am.A, 2002, 19(8):1592-1598.
[79]Garay A. Continuous wave deuterium fluoride laser beam diagnostic system[J], SPIE, 1998, 888:17-22.
[80]Cai Yangjian, He Sailing. Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulence atmosphere[J]. Appl. Phys .Lett., 2006, 89(4): 041117.
[81]Ji Xiaoling, Chen Xiaowen , LüBaida. Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence[J]. J. Opt. Soc. Am. A, 2008, 25(1):21-28.
[82]陈晓文,汤明玥,季小玲.大气湍流对部分相干厄米-高斯光束空间相干性的影响[J].物理学报,2008,57(4):2607-2612.
[83]Li Jinhong , Yang Ailin , LüBaida . Comparative study of the beam-width spreading of partially coherent Hermite-sinh-Gaussian beams in atmospheric turbulence[J]. J. Opt. Soc. Am. A, 2008, 25(11):2670-2679.
[84]Eyyubolu H T, Baykal Y. Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere[J].Appl Opt.,2005,44(6):976-83.
[85]张涛;陈晓文;季小玲.部分相干双曲余弦高斯光束在湍流大气中传输的光谱变化[J].四川师范大学学报,2010,33(1):73-77.
[86]黄太星.光束的聚焦特性和部分相干光通过湍流大气传输光束扩展的研究[D].成都:四川师范大学,2006.
[87]李晓庆,季小玲.部分相干厄米-高斯列阵光束通过湍流大气传输的方向性[J].光学学报,2009,29(12):3241-3247.
[88]季小玲.大气湍流对径向分布高斯列阵光束扩展和方向性的影响[J].物理学报,2010,59(1):692.
[89]Ji Xiaoling , Zhang Entao , LüBaida . Supermposed partially coherent beams propagating through atmospheric turbulence[J]. J. Opt .Soc. Am. B, 2008, 25(5):825-833.
[90]Wang S C H, Plonus M A .Optical beam propagation for a partially coherent source in the turbulent atmosphere [J]. J. Opt. Soc. Am, 1979, 69(9):1297 -1304.
[91]LüB D, Zhang B, Luo S R. Far-field intensity distribution, M2 factor, and propagation of flattened Gaussian beams[J]. Appl. Opt., 1999, 38(21): 4581-4.
[92]Zhou G. Beam propagation factors of a Lorentz–Gauss beam[J]. Appl. Phys. B, 2009,96(1): 149-153.
[93]Mahdieh M H. Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor[J]. Opt.Commun., 2007,281(13):3395-3402.
[94]Dan Y, Zhang B. Beam propagation factor of partially coherent flat-topped beams in aturbulent atmosphere[J]. Opt. Expr., 2008, 16(20):15563-15575.
[95]艾扬利,但有全,明德烈.湍流大气中部分相干双曲余弦高斯光束的M2因子[J].中国激光,2010,37(11):2849-2853.
[96]Mandel L, Wolf E. Optical Coherence and Quantum Optics[M].Cambridge: Cambridge Uinversity Press,1995.
[2]安毓英.第四章激光传输技术[J].激光与红外,2002,32(6):437-438.
[3]纪雯.激光相干合成效果的研究[D].成都:电子科技大学,2009.
[4] Li Bingzhong, LüBaida. Irradiance-moments characterization of off-axis Gaussian beam combinations by means of the Wigner distribution function[J]. Optik, 2002, 113(11):469-475.
[5]程勇,刘洋,许立新.激光相干合成技术研究新动向[J].红外与激光工程,2007,36(2):163-166.
[6]孙玲,赵鸿,杨文是等.多光束激光相干合成技术研究[J].激光与红外,2007,37(2):111-113.
[7]刘泽金,周朴,王小林等.激光相干合成的历史、现状与发展趋势[J].中国激光,2010,37(9):2221-2231.
[8]吕百达,张彬.激光束的相干合成技术[J].激光杂志,1998,19(1):6-14.
[9]肖瑞,周朴,侯静等.激光器的部分相干性对光纤激光器列阵相干合成远场图样的影响[J].物理学报,2007,56(2):819-822.
[10]徐立国,方存忠,蒋万铎等.高功率激光器MOPA相干合成系统分析[J].量子光学学报,2010,16(1):74-78.
[11]Fan T Y. Laser beam combining for high-power, high-radiance sources[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2005, 11(3):567-577.
[12]Casperson L W, Hall D G, Tovar A A. Hermite-sinusoidal-Gaussian beams in complex optical systems[J]. J. Opt. Soc. Am. A, 1998, 15(4):954-961.
[13]Casperson L W, Hall D G, Tovar A A. Sinusoidal-Gaussian beams in complex optical systems[J]. J. Opt. Soc. Am. A, 1997, 14(12):3341-3348.
[14]Tovar A A , Casperson L W. Production and propagation of Hermite- sinusoidal-Gaussian laser beams[J].J . Opt . Soc. Am. A, 1998,15(9):2425-2432.
[15]王喜庆,吕百达.厄米-双曲正弦-高斯光束的M~2因子[J].物理学报,2002,52(2):247-251.
[16]唐慧琴,朱开成,朱正和等.一类新平顶光束的束传播因子[J].强激光与粒子束,2007,19(10):357-359.
[17]汤明玥.湍流对厄米高斯及列阵双曲余弦高斯光束的传输和远场光束质量的影响[D].成都:四川师范大学,2008.
[18]LüB D, Zhang B. M H.Beam propagation factor and mode coherence coefficients of hyperbolic-cosine-Gaussian beams[J].Opt Lett., 1999,24:640—643.
[19] LüB D, Ma H, Zhang B. Propagation properties of cosh-Gaussian beams[J]. Opt Commun., 1999, 164: 165-170.
[20]张彬,楚晓亮,吕百达.双曲余弦高斯光束的模相关和模结构分析[J].激光技术,2001,25(5):372-375.
[21]徐延亮,王喜庆.双曲余弦-高斯光束的相干模分解[J].激光杂志,2008,29(6):47-48.
[22]Wu J. Propagation of a Gaussian Shell beam through turbulent media[J]. J. Mod. Opt., 1990, 37(3): 671～678.
[23]Gbur G, Wolf E. Spreading of partially coherent beams in random media[J]. J. Opt. Soc. Am. A 2002, 19(8): 1592～1598 .
[24]Dogariu A, Amarande S. Propagation of partially coherent beams: turbulence-induced degradation[J]. Opt. Lett., 2003,28(1):10-12.
[25]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.
[26]季小玲,黄太星,吕百达.部分相干双曲余弦高斯光束通过湍流大气的光束扩展[J].物理学报,2006,55(2):978-982
[27]李长伟,吕百达.部分相干双曲余弦-高斯光束的传输特性及空间整形[J].强激光与粒子束,2007,19(10):1589-1593.
[28]Shirai T, Dogariu A, Wolf E. Directionality of Gaussian Schell-model beams propagating in atmospheric turbulence[J]. Optics Letters , 2003, 28(8):610-612.
[29]陈晓文,季小玲.湍流对环状光束扩展的影响[J].物理学报,2009,58(4):2435-2442.
[30]Eyyuboglu H T , Baykal Y. Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulence atmosphere[J]. J. Opt. Soc. Am. A, 2005, 22(12):2709-2718.
[31]Xiao X , Ji X L, LüB D. The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field[J]. Optics & Laser Technology,2008,40:129-136.
[32]Yang A L, Zhang E T, Ji X L et al. Angular spread of partially coherent Hermite-cosh-Gaussian beams propagatingthrough atmospheric turbulence[J]. Optic Express, 2008,16(12):8367-8380.
[33]Liu Y S, Chen C H, Chuo Y C. Propagation of Hermite-Gaussian Beam Array in the Far Field[J].Lasers and Electro-Optics-Pacific Rim,2007.
[34]Wu G H, Lou Q H, Zhou J et al. Beam combination of a radial laser array: Flat-topped beam[J]. Optics & Laser Technology,2008, 40:890-894.
[35]Baida Lü, Hong Ma.Coherent and incoherent combinations of off-axis Gaussian beams with rectangular symmetry[J]. Optics Communications, 1999, 171(4-6):185-194.
[36]Cai Yangjian, Lin Qiang, Baykal Y. et al.. Off-axis Gaussian Schell-model beam and partially coherent laser array beam in a turbulent atmosphere [J]. Opt. Commun.,2007, 278(1):157-167.
[37]X. Ji ,Z. Pu .Angular spread of Gaussian Schell-model array beamspropagating through atmospheric turbulence[J]. Appl Phys B,2008,93:915-923.
[38]Cai Y, Chen Y, Eyyuboglu H T , Baykal Y .Propagation of laser array beams in a turbulent atmosphere[J]. Appl. Phys. B, 2007,88:467-474
[39]Pu Zhou , ZejinLiu , XiaojunXu, XiuxiangChu. Propagation of coherently combined flattened laser beam array in turbulent atmosphere[J]. Optics & Laser Technology, 2009, 41:403-407.
[40]Entao Zhang, Xiaoling Ji, Dangxiao Yang, and Baida Lu.Propagation and far-field beam quality of M×N Hermite–Gaussian beams propagating through atmospheric turbulence. [J]. Journal of Modern Optics,2008,55(3):387-400.
[41]Yingbin Zhu, Daomu Zhao, and Xinyue Du. Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere[J]. Optic Express,2008,16(22):18437-18442.
[42]Pu Zhou, Xiaolin Wang, Yanxing Ma et al. Propagation of partially coherent partially phase-locked laser array in turbulent atmosphere[J].Optics Communications,2010,283:1071-1074.
[43]汤眀玥,陈晓文,季小玲.湍流对M×N列阵双曲余弦高斯光束传输和远场光束质量的影响[J].光子学报,2009,38(3):713-718.
[44]Siegman A E. New developments in laser resonators[J]. Proc. SPIE 1990; 1224: 2-14.
[45]Song Yu, Hong Guo, Xiquan Fu,et all. Propagation properties of elegant Hermite–cosh-Gaussian laser beams[J]. Optics Communications, 2002, 204:59-66.
[46]Deng Dongmei. Propagation properties of off-axis cosh Gaussian beam combinations through a first-order optical system[J]. Physics Letters A,2004,333.
[47]Zhou G. Generalized beam propagation factors of truncated partially coherent cosine-Gaussian and cosh-Gaussian beams[J]. Opt. & Laser Technology,2010, 42(3) : 489-496.
[48]Wu Guohua, Guo Hong, Deng Dongmei. Paraxial propagation of partially coherent flat-topped beam[J].Optics Communications,2006,260(2):687-690.
[49]赵娜,唐淳,谢刚等.多束超高斯激光的相干合成的数值模拟[J].强激光与粒子束,2007,19(11):1780-1782.
[50] Liping Liu, Yi Zhou, Fanting Kong. Phase locking in a fiber laser array with varying path lengths [ J ]. Applied Physics Letters, 2004, 85 (21) : 4837 - 4839.
[51]李晓庆.部分相干列阵激光束通过大气湍流的传输特性研究[D].成都:四川师范大学,2009.
[52]吕百达,激光光学[M],四川大学出版社,1992.
[53]步青华.部分相干平顶光束在大气湍流中的传输特性研究[D].南京:南京理工大学,2009.
[54]尹纪欣.波束在湍流大气中的传播特性研究[D].西安:电子科技大学,2010.
[55]苗二龙.自由空间量子密钥分配[D].合肥:中国科学技术大学,2006.
[56]闫传忠.基于分形的大气湍流随机相位屏数值模拟[D].青岛:中国海洋大学,2009.
[57]杨帆.湍流对多色部分相干电磁光束传输特性影响[D].成都:四川师范大学,2009.
[58]王海燕.基于张量方法研究部分相干光和部分偏振光在大气湍流中的传输特性[D].南京:南京理工大学,2010.
[59]张洪江.大气湍流中激光波束和脉冲传输特性[D].西安:电子科技大学,2009.
[60]张建柱.大气湍流对部分相干平顶高斯光束影响的研究[D].北京:中国工程物理研究院,2004.
[61]饶瑞中,光在大气湍流中的传播[M].合肥:安徽科学技术出版, 2005
[62] R J Hill, C. J. Howard, Quantitative phase analysis from neutron powder diffraction datausing the Rietveld method [J]. J. Appl. Cryst., 1987, 20(6): 467-474.
[63] M. Roggemann , Imaging through turbulence [M]. Boca Raton: CRC Press, 1996
[64]R.J.Hill, S.F.Clifford , Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation [J]. J. Soc.Am.A, 1978, 68(7): 293-294.
[65]李宏升,湍流对大气中传输光束的影响[D].长春:长春理工大学,2002.
[66]陈昆.光无线通信伺服跟踪技术研究[D].武汉:华中科技大学,2007.
[67]袁仁民,曾宗泳。大尺度相干结构的光学特性研究[J].光学学报,2001,21(1):19-23.
[68]Andrems L. C.Analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere [J].J.Mod.Opt.,1992,39:1849-1853.
[69]陈晓文.部分相干光通过湍流大气传输的空间相干性及方向性研究[D].成都:四川师范大学,2009.
[70]刘琦.大气湍流对无线光通信误码率影响的研究[D].西安:电子科技大学,2009.
[71]Andrews L C, Phillips R. L. Laser Beam Propagation through Random Media[M]. Bellingham, Washington:SPIE Press, 1998.
[72]Wang.S. C. H., Plonus M. A., Yang C. F., Irradiance scintillations of a partially coherent source in extremely strong turbulence [J]. Applied Optics, 1979, 18(8): 1133-1135.
[73]Leader. J. C., Atmospheric propagation of partially coherent radiation [J]. J. Opt. Soc. Am, 1978, 68(1): 175-185.
[74]姚宇鹯.半导体激光器光束质量评估[D].西安:电子科技大学,2007.
[75]康小平.非傍轴标量和矢量光束的光束质量研究[D].成都:四川大学,2006.
[76]陈尚武.高能激光系统光束质量评价相关问题研究[D].杭州:浙江大学,2007.
[77]Siegman A. E., How to (Maybe) Measure Laser Beam Quality [J]. OSA. TOPS,1998, 17:184-201.
[78]Gbur G and Wolf E. Spreading of partially coherent beams in random media[J]. J. Opt .Soc. Am.A, 2002, 19(8):1592-1598.
[79]Garay A. Continuous wave deuterium fluoride laser beam diagnostic system[J], SPIE, 1998, 888:17-22.
[80]Cai Yangjian, He Sailing. Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulence atmosphere[J]. Appl. Phys .Lett., 2006, 89(4): 041117.
[81]Ji Xiaoling, Chen Xiaowen , LüBaida. Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence[J]. J. Opt. Soc. Am. A, 2008, 25(1):21-28.
[82]陈晓文,汤明玥,季小玲.大气湍流对部分相干厄米-高斯光束空间相干性的影响[J].物理学报,2008,57(4):2607-2612.
[83]Li Jinhong , Yang Ailin , LüBaida . Comparative study of the beam-width spreading of partially coherent Hermite-sinh-Gaussian beams in atmospheric turbulence[J]. J. Opt. Soc. Am. A, 2008, 25(11):2670-2679.
[84]Eyyubolu H T, Baykal Y. Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere[J].Appl Opt.,2005,44(6):976-83.
[85]张涛;陈晓文;季小玲.部分相干双曲余弦高斯光束在湍流大气中传输的光谱变化[J].四川师范大学学报,2010,33(1):73-77.
[86]黄太星.光束的聚焦特性和部分相干光通过湍流大气传输光束扩展的研究[D].成都:四川师范大学,2006.
[87]李晓庆,季小玲.部分相干厄米-高斯列阵光束通过湍流大气传输的方向性[J].光学学报,2009,29(12):3241-3247.
[88]季小玲.大气湍流对径向分布高斯列阵光束扩展和方向性的影响[J].物理学报,2010,59(1):692.
[89]Ji Xiaoling , Zhang Entao , LüBaida . Supermposed partially coherent beams propagating through atmospheric turbulence[J]. J. Opt .Soc. Am. B, 2008, 25(5):825-833.
[90]Wang S C H, Plonus M A .Optical beam propagation for a partially coherent source in the turbulent atmosphere [J]. J. Opt. Soc. Am, 1979, 69(9):1297 -1304.
[91]LüB D, Zhang B, Luo S R. Far-field intensity distribution, M2 factor, and propagation of flattened Gaussian beams[J]. Appl. Opt., 1999, 38(21): 4581-4.
[92]Zhou G. Beam propagation factors of a Lorentz–Gauss beam[J]. Appl. Phys. B, 2009,96(1): 149-153.
[93]Mahdieh M H. Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor[J]. Opt.Commun., 2007,281(13):3395-3402.
[94]Dan Y, Zhang B. Beam propagation factor of partially coherent flat-topped beams in aturbulent atmosphere[J]. Opt. Expr., 2008, 16(20):15563-15575.
[95]艾扬利,但有全,明德烈.湍流大气中部分相干双曲余弦高斯光束的M2因子[J].中国激光,2010,37(11):2849-2853.
[96]Mandel L, Wolf E. Optical Coherence and Quantum Optics[M].Cambridge: Cambridge Uinversity Press,1995.