标量和矢量部分相干光束的理论及实验研究
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摘要
激光束的传输和变换是激光物理和激光应用研究的重要基础课题。近几十年的研究发现，在某些领域，如：自由空间光通讯、惯性约束核聚变以及材料处理等领域，高相干性激光会容易带来散斑和更强的衍射。适当降低激光束的相干性，不仅能保持激光束的一般特性，还能减低光学元件以及湍流介质对激光束的不利影响。
以往人们都是把光当做完全相干光或完全非相干光来研究。严格的理论表明，所有的光场都是部分相干场，利用部分相干理论处理激光束的传输是最理想的。相干和偏振是光场的两个基本的特性，而通常用的标量理论则忽略了光束的偏振特性。近些年的研究表明，标量部分相干光理论在表征一些实际光束的时候，会丢失偏振信息。2003年，Wolf总结了以往的研究成果，并提出了部分相干部分偏振统一理论，该理论明确指出，光场的相干和偏振这两个特性是紧密联系的，部分相干矢量光束可以用交叉谱密度矩阵来表征。随后的理论和实验研究也证明了光束的相干特性和偏振特性是相互影响，相互联系的。
越来越多的研究发现，具有特殊形状的部分相干光束，如空心光束、平顶光束等，在很多领域具有重要的实用价值。因此，部分相干光束的合理整形显得非常有意义。我们在实验上利用相位元件、多模光纤以及液晶空间光调制器产生了部分相干空心光束、平顶光束、涡旋光束并测量了这些光束的光参数。
携带涡旋相位的光子具有轨道角动量，其轨道角动量的大小由拓扑荷数所决定，在光镊、光捕获、冷原子以及自由光通讯方面有重要应用价值。除了涡旋相位，带有扭曲相位的部分相干光束同样也可以具有轨道角动量。利用张量方法，得到了部分相干扭曲光束经过象散光学元件调制后的轨道角动量流表达式，计算结果显示，携带扭曲相位的部分相干光束轨道角动量会受象散光学元件调制。实验产生了部分相干各项同性高斯-谢尔模(GSM)光束，并通过测量光束在两个不同传输距离处的束腰宽度和相干长度，确定了产生光束的波前曲率半径。另外，还实验产生了部分相干电磁高斯-谢尔模(EGSM)光束，并利用光场的四阶关联测量了光束的参数。
1986年，Wolf发现了部分相干光在不满足“定标率”时，即使在自由空间传输，光谱也会发生频移，这一现象也成为“关联诱导光谱频移”。光谱频移是部分相干光的一个很重要的特性，在很多领域，如光谱测量、医疗诊断等具有重要应用。我们利用多模光纤以及径向偏振转换器产生了部分相干空心光束、平顶光束、径向偏振光束并测量了这些光束的聚焦光谱频移特性。
基于部分相干偏振统一理论，研究了部分相干电磁光束经过复杂象散光学系统、高斯谐振腔、非线性介质、人体组织后的光参数特性。特别是课题组提出的张量方法，为研究了部分相干光束在谐振腔内的传输提供了更为简便的方法。这些理论研究可以帮助人们深入了解各种部分相干光束的传输整形特点，为寻找实际需要的部分相干光束提供了重要依据。
部分相干光束在自由空间光通讯中的研究受到了广泛关注。利用张量方法、Wigner分布函数法以及二阶矩研究了部分相干扭曲GSM光束和EGSM光束在大气湍流中传输演化特性，包括光束的光场分布、光谱频移以及M2因子等特性。研究发现，初始光参数对光束的传输有较大的影响，通过选取合适的初始光束，可以有效的降低大气湍流对光信号的影响。
径向偏振光束在信息加密、高密度存储、超分辨测量、超分辨成像、材料加工以及粒子捕获等领域有重要的应用。基于象散光学系统中的广义Collins公式，研究了部分相干径向偏振光束经过象散系统后的光场分布，偏振度以及相干度。研究发现可以利用象散元件来调制部分相干径向光束的统计特性。此外，还从实验上研究了部分相干径向偏振光的杨氏双缝干涉实验，研究发现初始光束的相干性对远场干涉图像、相干度以及偏振度会产生显著地影响。
The propagation and transformation of laser beams play an important role in laserphysics and laser applications. In the past decades, more and more studies have found thatlaser beams with lower coherence are more useful than general laser beams in free-spaceoptical communications, inertial confinement fusion and laser processing. Low coherentlaser beams not only reserve the general characteristics of laser beams, but also can reducedisadvantages caused by random turbulent medium and optical elements.
Usually, people treat the light as completely coherent light and completely incoherentlight to investigate them. Strictly theory indicates that all light beams are partially coherentlight beams and the best way to deal with the laser beams is the partially coherent theory.Coherence and polarization are two basic properties of light field. The scalar theory weoften used ignores the polarization characteristics of light beams. In the past decades,scalar theory of partially coherent beams can’t completely characterize any practical beams,because of the polarization properties is lost. In2003, Wolf summarized previous studiesand gave out the partially coherent and partially polarized unified theory. This theoryclearly pointed out that coherence and polarization were closely related to each other, andpartially coherent electromagnetic beams can be characterized with the cross-spectraldensity(CSD). After then, lots of theoretical and experimental studies have shown that thecoherence and polarization properties of light beams affect each other.
More and more studies have found that partially coherent beam of special shapes,such as hollow beams, flat-topped beams have important practical value in many areas. So,reasonable shaping of partially coherent beams are becoming very meaningful. With thehelp of phase elements, multi-mode fiber(MMF) and liquid crystal spatial light modulator, we experimentally generated partially coherent hollow beams, flat-topped beams, vortexbeams and measured the beam parameters.
It’s well known that a light beam carrying vortex phase has orbital angularmomentum(OAM) determined by its topological charge, and vortex beam has importantapplications in optical tweezers, optical trapping, atom optics and free-space opticalcommunications. Besides the vortex phase, a general partially coherent beam carrying atwist phase proposed by Simon et al., may have OAM, as well. We derive the generalexpression for the OAM flux of an astigmatic partially coherent beam carrying twist phase(i.e., twisted anisotropic Gaussian Schell-model (TAGSM) beam) propagating through anastigmatic ABCD optical system. The numerical results show that we can modulate theOAM of a partially coherent beam by varying the parameter of the cylindrical thin lens. Weexperimentally produced partially coherent isotropic Gaussian-Schell model beam(GSM)and determined the radius of curvature by measuring the transverse beam widths and thetransverse coherence widths at two different planes. Moreover, we report the experimentalgeneration of an electromagnetic Gaussian-Schell-model (EGSM) beam and measure thebeam parameters based on the technique for measuring the fourth-order correlationfunction.
In1986, it is revealed by Wolf that the spectrum of a partially coherent beamgenerally changes on propagation, even in free space, unless the degree of coherencesatisfies a certain scaling law. This phenomenon is also called “correlation-induced spectralshift”. Spectral shift is an important property of partially coherent beams and can be foundimportant applications in spectroscopy and medical diagnostic. We experimentallygenerated partially coherent hollow beams, flat-topped beams and radially polarized beamsby using MMF and radial polarization converter(RPC). Furthermore, we experimentallymeasured the spectral changes of such beam focused by a thin lens.
Based on the unified theory of coherence and polarization, we investigated the beamparameters of partially coherent electromagnetic beams propagation through complexastigmatic optical system, Gaussian cavities, nonlinear media and human tissue. Especially, with the help of the tensor method proposed by our group before, the investigation ofpartially coherent beams passing through cavities became very convenient. All of thesetheoretical studies will help us in-depth understanding the propagation properties ofvarious partially coherent beams and finding the right partially coherent beams we need.
Partially coherent beams have attracted much more attention in application offree-space optical communications. By using a tensor method, Wigner distribution functionand second-order moments, we studied the properties of spectral intensity, spectral shiftand the M2-factor of partially coherent TGSM beam and EGSM beam propagation throughturbulent atmosphere. Studies have shown that initial beam parameters have great impacton the properties of output beam. By choosing appropriate initial beam can effectivelyreduce the disadvantages of atmospheric turbulence bring to the optical signal.
Radially polarized beams have been found useful for information encryption,high-density storage, super-resolution measurement, super-resolution imaging, materialthermal processing and particle trapping. Based on the generalized Collins formula of theastigmatic optical system, we analyzed the focusing properties of spectral intensity, degreeof polarization and degree of coherence of partially coherent radially polarized beam. It isdemonstrated that the astigmatism of the optical system can be used for modulating thestatistical properties of a focused partially coherent radially polarized beam. In addition,we also carry out theoretical and experimental study of Young’s double-slit interference ofpartially coherent radially polarized beam. It is shown that the initial coherencesignificantly affect the far-field interference pattern, degree of coherence and degree ofpolarization.
以往人们都是把光当做完全相干光或完全非相干光来研究。严格的理论表明，所有的光场都是部分相干场，利用部分相干理论处理激光束的传输是最理想的。相干和偏振是光场的两个基本的特性，而通常用的标量理论则忽略了光束的偏振特性。近些年的研究表明，标量部分相干光理论在表征一些实际光束的时候，会丢失偏振信息。2003年，Wolf总结了以往的研究成果，并提出了部分相干部分偏振统一理论，该理论明确指出，光场的相干和偏振这两个特性是紧密联系的，部分相干矢量光束可以用交叉谱密度矩阵来表征。随后的理论和实验研究也证明了光束的相干特性和偏振特性是相互影响，相互联系的。
越来越多的研究发现，具有特殊形状的部分相干光束，如空心光束、平顶光束等，在很多领域具有重要的实用价值。因此，部分相干光束的合理整形显得非常有意义。我们在实验上利用相位元件、多模光纤以及液晶空间光调制器产生了部分相干空心光束、平顶光束、涡旋光束并测量了这些光束的光参数。
携带涡旋相位的光子具有轨道角动量，其轨道角动量的大小由拓扑荷数所决定，在光镊、光捕获、冷原子以及自由光通讯方面有重要应用价值。除了涡旋相位，带有扭曲相位的部分相干光束同样也可以具有轨道角动量。利用张量方法，得到了部分相干扭曲光束经过象散光学元件调制后的轨道角动量流表达式，计算结果显示，携带扭曲相位的部分相干光束轨道角动量会受象散光学元件调制。实验产生了部分相干各项同性高斯-谢尔模(GSM)光束，并通过测量光束在两个不同传输距离处的束腰宽度和相干长度，确定了产生光束的波前曲率半径。另外，还实验产生了部分相干电磁高斯-谢尔模(EGSM)光束，并利用光场的四阶关联测量了光束的参数。
1986年，Wolf发现了部分相干光在不满足“定标率”时，即使在自由空间传输，光谱也会发生频移，这一现象也成为“关联诱导光谱频移”。光谱频移是部分相干光的一个很重要的特性，在很多领域，如光谱测量、医疗诊断等具有重要应用。我们利用多模光纤以及径向偏振转换器产生了部分相干空心光束、平顶光束、径向偏振光束并测量了这些光束的聚焦光谱频移特性。
基于部分相干偏振统一理论，研究了部分相干电磁光束经过复杂象散光学系统、高斯谐振腔、非线性介质、人体组织后的光参数特性。特别是课题组提出的张量方法，为研究了部分相干光束在谐振腔内的传输提供了更为简便的方法。这些理论研究可以帮助人们深入了解各种部分相干光束的传输整形特点，为寻找实际需要的部分相干光束提供了重要依据。
部分相干光束在自由空间光通讯中的研究受到了广泛关注。利用张量方法、Wigner分布函数法以及二阶矩研究了部分相干扭曲GSM光束和EGSM光束在大气湍流中传输演化特性，包括光束的光场分布、光谱频移以及M2因子等特性。研究发现，初始光参数对光束的传输有较大的影响，通过选取合适的初始光束，可以有效的降低大气湍流对光信号的影响。
径向偏振光束在信息加密、高密度存储、超分辨测量、超分辨成像、材料加工以及粒子捕获等领域有重要的应用。基于象散光学系统中的广义Collins公式，研究了部分相干径向偏振光束经过象散系统后的光场分布，偏振度以及相干度。研究发现可以利用象散元件来调制部分相干径向光束的统计特性。此外，还从实验上研究了部分相干径向偏振光的杨氏双缝干涉实验，研究发现初始光束的相干性对远场干涉图像、相干度以及偏振度会产生显著地影响。
The propagation and transformation of laser beams play an important role in laserphysics and laser applications. In the past decades, more and more studies have found thatlaser beams with lower coherence are more useful than general laser beams in free-spaceoptical communications, inertial confinement fusion and laser processing. Low coherentlaser beams not only reserve the general characteristics of laser beams, but also can reducedisadvantages caused by random turbulent medium and optical elements.
Usually, people treat the light as completely coherent light and completely incoherentlight to investigate them. Strictly theory indicates that all light beams are partially coherentlight beams and the best way to deal with the laser beams is the partially coherent theory.Coherence and polarization are two basic properties of light field. The scalar theory weoften used ignores the polarization characteristics of light beams. In the past decades,scalar theory of partially coherent beams can’t completely characterize any practical beams,because of the polarization properties is lost. In2003, Wolf summarized previous studiesand gave out the partially coherent and partially polarized unified theory. This theoryclearly pointed out that coherence and polarization were closely related to each other, andpartially coherent electromagnetic beams can be characterized with the cross-spectraldensity(CSD). After then, lots of theoretical and experimental studies have shown that thecoherence and polarization properties of light beams affect each other.
More and more studies have found that partially coherent beam of special shapes,such as hollow beams, flat-topped beams have important practical value in many areas. So,reasonable shaping of partially coherent beams are becoming very meaningful. With thehelp of phase elements, multi-mode fiber(MMF) and liquid crystal spatial light modulator, we experimentally generated partially coherent hollow beams, flat-topped beams, vortexbeams and measured the beam parameters.
It’s well known that a light beam carrying vortex phase has orbital angularmomentum(OAM) determined by its topological charge, and vortex beam has importantapplications in optical tweezers, optical trapping, atom optics and free-space opticalcommunications. Besides the vortex phase, a general partially coherent beam carrying atwist phase proposed by Simon et al., may have OAM, as well. We derive the generalexpression for the OAM flux of an astigmatic partially coherent beam carrying twist phase(i.e., twisted anisotropic Gaussian Schell-model (TAGSM) beam) propagating through anastigmatic ABCD optical system. The numerical results show that we can modulate theOAM of a partially coherent beam by varying the parameter of the cylindrical thin lens. Weexperimentally produced partially coherent isotropic Gaussian-Schell model beam(GSM)and determined the radius of curvature by measuring the transverse beam widths and thetransverse coherence widths at two different planes. Moreover, we report the experimentalgeneration of an electromagnetic Gaussian-Schell-model (EGSM) beam and measure thebeam parameters based on the technique for measuring the fourth-order correlationfunction.
In1986, it is revealed by Wolf that the spectrum of a partially coherent beamgenerally changes on propagation, even in free space, unless the degree of coherencesatisfies a certain scaling law. This phenomenon is also called “correlation-induced spectralshift”. Spectral shift is an important property of partially coherent beams and can be foundimportant applications in spectroscopy and medical diagnostic. We experimentallygenerated partially coherent hollow beams, flat-topped beams and radially polarized beamsby using MMF and radial polarization converter(RPC). Furthermore, we experimentallymeasured the spectral changes of such beam focused by a thin lens.
Based on the unified theory of coherence and polarization, we investigated the beamparameters of partially coherent electromagnetic beams propagation through complexastigmatic optical system, Gaussian cavities, nonlinear media and human tissue. Especially, with the help of the tensor method proposed by our group before, the investigation ofpartially coherent beams passing through cavities became very convenient. All of thesetheoretical studies will help us in-depth understanding the propagation properties ofvarious partially coherent beams and finding the right partially coherent beams we need.
Partially coherent beams have attracted much more attention in application offree-space optical communications. By using a tensor method, Wigner distribution functionand second-order moments, we studied the properties of spectral intensity, spectral shiftand the M2-factor of partially coherent TGSM beam and EGSM beam propagation throughturbulent atmosphere. Studies have shown that initial beam parameters have great impacton the properties of output beam. By choosing appropriate initial beam can effectivelyreduce the disadvantages of atmospheric turbulence bring to the optical signal.
Radially polarized beams have been found useful for information encryption,high-density storage, super-resolution measurement, super-resolution imaging, materialthermal processing and particle trapping. Based on the generalized Collins formula of theastigmatic optical system, we analyzed the focusing properties of spectral intensity, degreeof polarization and degree of coherence of partially coherent radially polarized beam. It isdemonstrated that the astigmatism of the optical system can be used for modulating thestatistical properties of a focused partially coherent radially polarized beam. In addition,we also carry out theoretical and experimental study of Young’s double-slit interference ofpartially coherent radially polarized beam. It is shown that the initial coherencesignificantly affect the far-field interference pattern, degree of coherence and degree ofpolarization.
引文
1. A. Einstein. On the quantum theory of radiation. Phys. Z.18,121-128,1917.
2. A. L. Schawlow and C. H. Townes. Infrared and optical masers. Phys. Rev.112,1940-1949,1958.
3. T. H. Maiman. Stimulated optical radiation in ruby. Nature,187,493-494,1960.
4.邓锡铭,王之江.光学量子放大器.科学通报,11,25-29,1961.
5. G. Fox and T. Li. Resonant modes in a maser interferometer. Bell Sys. Tech. J.40,450-456,1961.
6. H. Kogelnik. Imaging of optical modes-resonators with internal lenses. Bell Sys. Tech. J.44,455-462,1965.
7. S. A. Collins. Lens-systems diffraction integral written in terms of matrix optics. J. Opt. Soc. Am.60,1168-1177,1970.
8. Q. Lin and Y. Cai. Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schellmodel beams. Opt. Lett.27,216-218,2002.
9. Y. Cai and S. He. Propagation of a partially coherent twisted anisotropic Gaussian Schell-modelbeam in a turbulent atmosphere. Appl. Phys. Lett.89,04,1117,2006.
10. M. Yao, Y. Cai and H T Eyyuboglu. Evolution of the degree of polarization of an electromagneticGaussian Schell-model beam in a Gaussian cavity. Opt. Lett.33,2266-2268,2008.
11. P. Belland and J. P. Crenn. Changes in the characteristics of a Gaussian beam weakly diffracted bya circular aperture. Appl. Opt.21,522-527,1982.
12. W. H. Carter and M. F. Aburdene. Focal shift in Laguerre-Gaussian beams. J. Opt. Soc. Am. A,4,1949-1952,1987.
13. A. E. Siegman. Hermite-gaussian functions of complex argument as optical-beam eigen functions.J. Opt. Soc. Am. A,63,1093-1094,1973.
14. F. Gori. Flattened gaussian beams. Opt. Commun.107,335-341,1994.
15. R. Borghi. Elegant Laguerre-Gauss beams as a new tool for describing axisymmetric flattenedGaussian beams. J. Opt. Soc. Am. A,18,1627-1633,2001.
16. Y. Li. Light beams with flat-topped profiles. Opt. Lett.27,1007-1009,2003.
17. F. Gori, G. Guattari and C. Padovani. Bessel-Gauss beams. Opt. Commun.64,491-495,1987.
18. S. Marksteiner, C. M. Savage, P. Zoller and S. Rolston. Coherent atomic waveguides from hollowoptical fibers. quantized atomic motion. Phys. Rev. A,50,2680-2690,1994.
19. M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman and E. A. Cornell.Laser-guided atoms in hollow-core optical fibers Phys. Rev. Lett.75,3253-3256,1995.
20. H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee and W. Jhe. Laser spectroscopy of atoms guidingby evanescent waves in micro-sized hollow optical fibers. Phys. Rev. Lett.76,4500-4503,1996.
21. J. Yin and Y. Zhu. LP01-mode output beam from a micro-sized hollow optical fiber. A simpletheoretical model and its applications in atom optics. J. Appl. Phys.85,2473-2481,1999.
22. X. Xu, V. G. Minogin, K. Lee, Y. Wang and W. Jhe. Guiding cold atoms in a hollow laser beam.Phys. Rev. A,60,4796-4804,1999.
23. M. Born and E. Wolf. Principles of Optics. Pergamon,1980.
24. L. Mandel and E.Wolf. Optical coherence and Quantum Optics. Cambridge University Press,1995.
25.王云山.激光转镜扫描光束的优化和光斑特性分析.光电子激光,8,287-290,1997.
26. E. Wolf. Coherent-mode representation of Gaussian Schell-model sources and of their radiationfields. J. Opt. Soc. Am.72,923-928,1982.
27. E. Wolf. New theory of partial coherence in the space-frequency domain. II. Steady-state fields andhigher-order correlations. J. Opt. Soc. Am. A,3,76-85,1986.
28. E. Wolf and G. S. Agarwal. Coherence theory of laser resonator modes. J. Opt. Soc. Am. A,1,541-546,1984.
29. J. W. Goodman. Statistical Optics. Wiley, New York,1985.
30. E. Collett and E. Wolf. Is complete spatial coherence necessary for the generation of highlydirectional light beams? Opt. Lett.2,27-29,1978.
31. J. T. Foley and M. S. Zubairy. The directionality of Gaussian Schell-model beams. Opt. Commun.26,297-300,1978.
32. R. Grella. Synhesis of generalized Collett-Wolf sources. J. Optics (Paris),13,127-131,1982.
33. C. Palma and G. Cincotti. Spatial behavior of the Wolf effect in free propagation for GaussianSchell-model beams. J. Opt. Soc. Am. A,14,1885-1889,1997.
34. M. Santarsiero, F. Gori and R. Borghi. Spreading properties of beams radiated by partially coherentSchell-model sources. J. Opt. Soc. Am. A,16,106-112,1999.
35. A. T. Friberg and J. Turunen. Imaging of Gaussian Schell-model sources. J. Opt. Soc. Am. A,5,713-720,1988.
36. R. Simon, E. C. G. Sudarshan and N. Mukunda. Anisotropic Gaussian Schell-model beams passagethrough optical systems and associated invariants. Phys. Rev. A,31,2419-2434,1985.
37. J. Wu. Propagation of a Gaussian-Schell beam through turbulent media. J. Mod. Opt.37,671-684,1990.
38. Y. Cai and Q. Lin. Propagation of partially coherent twisted anisotropic Gaussian-Schell modelbeams through misaligned optical systems. Opt. Commun.211,1-8,2002.
39. Y. Cai, Q. Lin and D. Ge. Propagation of partially coherent twisted anisotropic GaussianSchell-model beams in dispersive and absorbing media. J. Opt. Soc. Am. A,19,2036-2042,2002.
40. Y. Cai and L. Hu. Propagation of partially coherent twisted anisotropic Gaussian Schell-modelbeams through an apertured astigmatic optical system. Opt. Lett.31,685-687,2006.
41. Y. Cai and U. Peschel. Second-harmonic generation by an astigmatic partially coherent beam. Opt.Express,15,15480-15492,2007.
42. F. Wang and Y. Cai. Second-order statistics of a twisted Gaussian Schell-model beam in turbulentatmosphere. Opt. Express,18,24661-24672,2010.
43. W. H. Carter and M. Bertolotti. An analysis of the far-field coherence and radiant intensity of lightscattered from liquid crystals. J. Opt. Soc. Am. A,68,329-333,1978.
44. P. D. Santis, F. Gori, G. Guattari and C. Palma. An example of a collett-wolf source. Opt. Commun.29,256-260,1979.
45. J. D. Farina, L.M. Narducci and E. Collet. Generation of highly directional beams from a globallyincoherent source. Opt. Commun.32,203-207,1980.
46. E. Tervonen, A.T. Friberg and J. Turunen. Gaussian Schell-model beams generated with syntheticacousto-optic holograms. J. Opt. Soc. Am. A,9,796-803,1992.
47. S. N. Dixit, I. M. Thomas and B.W. Woods. Random phase plates for beam smoothing on the Novalaser. Appl. Opt.32,2543-2554,1993.
48. F. Gori and M. Santarsiero.Devising genuine spatial correlation functions. Opt. Lett.32,3531-3533,2007.
49. J. Deshamps, D. Courjon and J. Bulabois. Gaussian Schell-model sources, an example and someperspectives. J. Opt. Soc. Am.73,256-261,1983.
50. H. Lajunen and T. Saastamoinen. Propagation characteristics of partially coherent beams withspatially varying correlations. Opt. Lett.36,4104-4106,2011.
51. Z. Tong and O. Korotkova. Nonuniformly correlated light beams in uniformly correlated media.Opt. Lett.37,3240-3242,2012.
52. Z. Mei and O. Korotkova. Random sources generating ring-shaped beams. Opt. Lett.38,91-93,2013.
53. F. Wang, X. Liu, Y. Yuan and Y. Cai. Experimental generation of partially coherent beams withdifferent complex degrees of coherence. Opt. Lett.38,1814-1816,2013.
54. F. Wang, X. Liu, L. Liu, Y. Yuan and Y. Cai, Experimental study of the scintillation index of aradially polarized beam with controllable spatial coherence. Appl. Phys. Lett.103,091102,2013.
55. Y. Chen, F. Wang L. Liu, C. Zhao and Y. Cai. Generation and propagation of a partially coherentvector beam with special correlation functions. Phys. Rev. A,89,013801,2014.
56. E. Wolf. Invariance of the spectrum of light on propagation. Phys. Rev. Lett.56,1370-1372,1986.
57. D. Fkalis and G. M. Morris. Spectral shifts produced by source correlations. Opt. Lett.13,4-6,1988.
58. J. Pu, H. Zhang and S. Nemoto. Spectral shifts and spectral switches of partially coherent lightpassing through an aperture. Opt. Commun.162,57-63,1999.
59. L. Pan and B. Lü. Spectral switches of polychromatic Gaussian beams passing through anastigmatic aperture lens. Opt. Commun.234,13-22,2004.
60. C. Ding, L. Pan and B. Lü. Effect of turbulence on the spectral switches of diffracted spatially andspectrally partially coherent pulsed beams in atmospheric turbulence. J. Opt. A: Pure Appl. Opt.11,105404,2009.
61. L. Pan, Z. Zhao, C. Ding and B. Lü. Effect of polarization on spectral switches in the diffraction ofstochastic electromagnetic beams. Appl. Phys. Lett.95,181112,2009.
62. H. C. Kandpal, A. Wasan, J. S. Vaishya, E. S. R. Gopal, M. Singh, B. B. Sanwal and R. Sagar.Application of spatial coherence spectroscopy for determining the angular diameters of stars:feasibility experiment. Indian J. Pure Appl. Phys.36,665-674,1998.
63. H. C. Kandpal. Experimental observation of the phenomenon of spectral switch. J. Opt. A: Pureand Appl. Opt.3,296-299,2001.
64. B. K. Yadav and H. C. Kandpal. Spectral anomalies of polychromatic DHGB and its applicationsin FSO. J. Lightwave Technol.29,960-966,2011.
65. A. Gerrard and J. M. Burch. Introduction to matrix methods in optics. London. New York, JohnWilly&Sons,1975.
66. J. Turunen and A.T. Friberg. Matrix representation of Gaussian Schell-model beams in opticalsystem, Opt. Laser. Technol.18,259-267,1986.
67. S. Wang and D. Zhao. Matrix Optics, CHEP&Springer,2000.
68. J. W. Goodman. Introduction to Fourier optics. London. New York, John Willy&Sons,1974.
69. R. Martinez-Herrero, P. M. Mejias, M. Sanchez and J. L. H. Neira. Third-and fourth-orderparametric characterization of partially coherent beams propagation through ABCD optical systems.Opt. Quantum. Electron.24, S1021-S1026,1992.
70. M. J. Bastiaans. The Wigner distribution function applied to optical signals and systems. Opt.Commun.25,26-30,1978.
71. M. J. Bastiaans. Wigner distribution function and its application to first-order optics. J. Opt. Soc.Am.69,1710-1716,1979.
72. M. J. Bastiaans. The Wigner distributions function of partially coherent light. J. Mod. Opt.28,1215-1224,1981.
73. R. Simon and N. Mukunda. Twisted Gaussian Schell-model beams. J. Opt. Soc. Am. A,10,95-109,1993.
74. D. Ambrosini, V. Bagini, F. Gori and M. Santarsiero. Twisted Gaussian Schell-model beams, asuperposition model. J. Mod. Opt.41,1391-1399,1994.
75. R. Simon, A. T. Friberg and E. Wolf. Transfer of radiance by twisted Gaussian Schell-model beamsin paraxial systems. Pure Appl. Opt.5,331,1996.
76. R. Simon and N. Mukunda. Iwasawa decomposition in first-order optics, universal treatment ofshape-invariant propagation for coherent and partially coherent beams. J. Opt. Soc. Am. A,15,2146-2155,1998.
77. R. Simon and N. Mukunda. Optical phase space, Wigner representation, and invariant qualityparameters. J. Opt. Soc. Am. A,17,2440-2463,2000.
78. A. T. Friberg, E. Tervonen and J. Turunen. Interpretation and experimental decomposition oftwisted Gaussian Schell-model beams. J. Opt. Soc. Am. A,11,1818-1826,1994.
79. G. Nemes and A. E. Siegman. Measurement of all ten second-order moments of an astigmatic beamby the use of rotating simple astigmatic (anamorphic) optics. J. Opt. Soc. Am. A,11,2257-2264,1994.
80. M. J. Bastiaans. Wigner distribution function applied to twisted Gaussian light propagating infirst-order optical systems. J. Opt. Soc. Am. A17,2475-2480,2000.
81. G. Ding and B. Lu. Propagation of twisted Gaussian Schell-model beams through a misalignedfirst-order optical system. J. Mod. Opt.48,1617-1621,2001.
82. Y. Cai, Q. Lin and O. Korotkova. Ghost imaging with twisted Gaussian Schell-model beam. Opt.Express,17,2453-2464,2009.
83. C. Zhao, Y. Cai and O. Korotkova. Radiation force of scalar and electromagnetic twisted GaussianSchell-model beams. Opt. Express,17,21472-21487,2009.
84. F. Wang and Y. Cai. Second-order statistics of a twisted Gaussian Schell-model beam in turbulentatmosphere. Opt. Express,18,24661-24672,2010.
85. R. J. Fante. In Progress in optics, edited by E Wolf (Elsevier, Amsterdam), Vol XXII,343-398.1985.
86. D. F. V. James. Change of polarization of light beams on propagation in free space. J. Opt. Soc. Am.A,11,1641-1643,1994.
87. F. Gori. Matrix treatment for partially polarized, partially coherent beams. Opt. Lett.23,241-243,1998.
88. E. Wolf. Unified theory of coherence and polarization of random electromagnetic beams. Phy. Lett.A,312,263-267,2003.
89. E. Wolf. Correlation-induced changes in the degree of polarization, the degree of coherence and thespectrum of random electromagnetic beams on propagation. Opt. Lett.28,1078-1080,2003.
90. F. Gori, M Santarsiero, R Borghi and E. Wolf. Effects of coherence on the degree of polarization ina Young interference pattern. Opt. Lett.31,688-690,2006.
91. T. Shirai, O. Korotkova and E. Wolf. A method of generating electromagnetic GaussianSchell-model beams. J. Opt. A, Pure Appl. Opt.7,232-237,2003.
92. H. Roychowdhury and E. Wolf. Determination of the electric cross-spectral density matrix of arandom electromagnetic beam. Opt. Commun.226,57-60,2003.
93. E. Wolf. Polarization of a spatially fully coherent electromagnetic beam. J. Mod. Opt.51,757-759,2004.
94. O. Korotkova, M. Salem and E. Wolf. Beam conditions for radiation generated by anelectromagnetic Gaussian Schell-model source. Opt. Lett.29,1173-1175,2004.
95. T. Shirai and E. Wolf. Coherence and polarization of electromagnetic beams modulated by randomphase screens and their changes on propagation in free space. J. Opt. Soc. Am. A,21,1907-1916,2004.
96. Z. Chen and J. Pu. Propagation characteristics of aberrant stochastic electromagnetic beams in aturbulent atmosphere. J. Opt. A, Pure Appl. Opt.9,1123-1130,2007.
97. Y. Zhu, D. Zhao and X. Du. Propagation of stochastic Gaussian-Schell model array beams inturbulent atmosphere. Opt. Express,16,18437-18442,2008.
98. E. Shchepakina and O. Korotkova. Second-order statistics of stochastic electromagnetic beamspropagating through non-Kolmogorov turbulence. Opt. Express,18,10650-10658,2010.
99. S. Yu, Z. Chen, T. Wang, G. Wu, H. Guo and W. Gu. Beam wander of electromagneticGaussian-Schell model beams propagating in atmospheric turbulence. Appl. Opt.51,7581-7585,2012.
100. F. Gori. M. Santarsiero, G. Piquero, R. Borghi, A. Mondello and R. Simon. Partially polarizedGaussian Schell-model beams. J. Opt. A, Pure Appl. Opt.3,1-9,2001.
101. G. Piquero, R. Borghi and M. Santarsiero. Gaussian Schell-model beams propagating throughpolarization gratings. J. Opt. Soc. Am. A,18,1399-1405,2001.
102. T. Set l, M. Kaivola and A. T. Friberg. Degree of Polarization in Near Fields of Thermal Sources,Effects of Surface Waves. Phys. Rev. Lett.88,123902,2002.
103. O. Korotkova, M. Salem and E. Wolf. The far-zone behavior of the degree of polarization ofelectromagnetic beams propagating through atmospheric turbulence. Opt. Commun.233,225-230,2004.
104. O. Korotkova and E. Wolf. Changes in the state of polarization of a random electromagnetic beamon propagation. Opt. Commun.246,35-43,2005.
105. Y. Cai and O. Korotkova. Twist phase-induced polarization changes in electromagnetic GaussianSchell-model beams. Appl. Phys. B,96,499-507,2009.
106. L. Zhang, F. Wang Y. Cai and O. Korotkova. Degree of paraxiality of a stochastic electromagneticGaussian Schell-model beam. Opt. Commun.284,1111-1117,2011.
107. Y. Shen, L. Liu, C. Zhao, Y. Yuan and Y. Cai. Second-order moments of an electromagneticGaussian Schell-model beam in a uniaxial crystal. J. Opt. Soc. Am. A,31,238-245,2014.
108. L. C. Andrews, R. L. Phillips and C. Y. Hopen. Laser Beam Scintillation with Applications. SPIEPress, Washington,2001.
109. T. Shirai, A. Dogariu, and E. Wolf. Mode analysis of spreading of partially coherent beamspropagating through atmospheric turbulence. J. Opt. Soc. Am. A,20,1094-1102,2003.
110. H. T. Eyyubo lu and Y. Baykal. Reciprocity of Cos-Gaussian and Cosh-Gaussian laser beams inturbulent atmosphere. Opt. Express12,4659-4674,2004.
111. H. T. Eyyubo lu. Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere. Opt.Commun.245,37-47,2005.
112. A. Peleg and J. V. Moloney. Scintillation index for two Gaussian laser beams with differentwavelengths in weak atmospheric turbulence. J. Opt. Soc. Am. A,23,3114-3122,2006.
113. Y. Cai. Propagation of Various Flat-Topped Beams in a Turbulent Atmosphere. J. Opt. A: PureAppl. Opt.8,537-545,2006.
114. Y. Cai and S. He. Propagation of various dark hollow beams in a turbulent atmosphere. Opt.Express,14,1353-1367,2006.
115. Y. Dan. and B. Zhang. Beam propagation factor of partially coherent flat-topped beams in aturbulent atmosphere. Opt. Express,16,15563-15575,2008.
116. X. Ji and E. Zhang and B. Lü. Spectral properties of chirped Gaussian pulsed beams propagatingthrough the turbulent atmosphere. J. Mod. Opt.54,541-553,2007.
117. Y. Gu, O. Korotkova and G. Gbur. Scintillation of nonuniformly polarized beams in atmosphericturbulence. Opt. Lett.34,2261-2263,2009.
118. S. Zhu, Y. Cai and O. Korotkova. Propagation factor of a stochastic electromagnetic GaussianSchell-model beam. Opt. Express,18,12587-12598,2010.
119. S. Zhu and Y. Cai. M2-factor of a truncated electromagnetic Gaussian Schell-model beam. Appl.Phys. B,103,971-984,2011.
120. F. Wang, Y. Cai, Y. Dong and O. Korotkova. Experimental generation of a radially polarized beamwith controllable spatial coherence. Appl. Phys. Lett.100,04,1108,2012.
121. G. Wu and Y. Cai. Detection of a semi-rough target in turbulent atmosphere by a partially coherentbeam. Opt. Lett.36,1939-1942,2011.
122. Y. Gu and G. Gbur. Scintillation of nonuniformly correlated beams in atmospheric turbulence. Opt.Lett.38,1395-1397,2013.
123. G. Piquero, F. Gori, P. Romnini, M. Santarsiero, R. Borghi and A. Mondello. Synthesis of partiallypolarized Gaussian Schell-Model sources. Opt. Commun.208,9-16,2002.
124. F. Gori, M. Santarsiero, R. Borghi and V. Ramírez-Sánchez. Realizability condition forelectromagnetic Schell-model sources. J. Opt. Soc. Am. A,25,1016-1021,2008.
125. B. Kanseri and H. C. Kandpal. Experimental determination of electric cross-spectral density matrixand generalized Stokes parameters for a laser beam. Opt. Lett.33,2410-2412,2008.
126. F. Wang, G. Wu, X. Liu, S. Zhu and Y Cai. Experimental measurement of the beam parameters ofan electromagnetic Gaussian Schell-modelsource. Opt. Lett.36,2722-2724,2011.
127. S. Zhu and Y. Cai. M2-factor of a stochastic electromagnetic beam in a Gaussian cavity. Opt.Express,18,27567-27581,2010.
128. S. Zhu and Y. Cai. Spectral shift of a twisted electromagnetic Gaussian Schell-model beam focusedby a thin lens. Appl. Phys. B,99,317-323,2010.
129. S. Zhu, F Zhou, Y. Cai and L. Zhang. Thermal lens effect induced changes of polarization,coherence and spectrum of a stochastic electromagnetic beam in a Gaussian cavity. Appl. Phys. B,102,953-061,2010.
130. S. Zhu and Y. Cai. Degree of polarization of a twisted electromagnetic Gaussian Schell-modelbeam in a Gaussian cavity filled with gain media. Prog. Electromagn. Res. B,21,171-187,2010.
131. F. Zhou, S. Zhu and Y. Cai. Spectral shift of a partially coherent electromagnetic GaussianSchell-model beam propagating through tissue. J. Mod. Opt.58,38-44,2011.
132. F. Wang, S. Zhu, X. Hu and Y. Cai. Coincidence fractional Fourier transform with a stochasticelectromagnetic Gaussian Schell-model beam. Opt. Commun.284,5275-5280,2011.
133. S. Zhu, L. Liu, Y. Chen and Y. Cai. State of polarization and propagation factor of a stochasticelectromagnetic beam in a gradient-index fiber. J. Opt. Soc. Am. A,30,2306-2313,2013.
134. R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang and Y. Cai. Statistical properties of a Laguerre-GaussianSchell-model beam in turbulent atmosphere. Opt. Express,22,1871-1883,2014.
135. Y. Mushiake, K. Matzumurra and N. Nakajima. Generation of radially polarized optical beammode by laser oscillation. Proc. IEEE.60,1107-1109,1972.
136. A. V. Nesterov, V. G. Niziev and V. P. Yakunin. Generation of high-power radially polarized beam.J. Phys. D: Appl. Phys.32,2871,1999.
137. Y. Kozawa and S. Sato. Generation of a radially polarized laser beam by use of a conical Brewsterprism. Opt Lett.30,3063365,2005.
138. K. Yonezawa, Y. Kozawa and S. Sato. Geneartion of a radially polarized laser beam by use of thebirefringence of a c cut Nd:YVO4crystal. Opt. Lett.31,2151-2153.2006.
139. G Machavariani, Y. Lumer, I. Moshe, et al. Birefringence induced bifocusing forslection of radiallyor azimuthally polarized laser modes. Appl. Opt.46,3304-3310,2007.
140. S. C. Tidwell, D. H Ford, W. D. Kimura. Efficient radially polarized laser beam generation with adouble interferometer. Appl. Opt.32,5222-5229.1993.
141. A. V. Nesterov and V. G. Niziev. Laser beams with axially symmetric polarization. J. Phys. D: Appl.Phys.33,1-6,2006.
142. R. Dorn, S. Quabis and G. Leuchs. Sharper focus for a radially polarized light beam. Phys. Rev.Lett.91,233901,2003.
143. S Quabis, R Dorn, M Elberler, et al. Focusing light into a tighter spot. Opt. Commun.179,1-7,2000.
144. X. Li, T. H. Lan, C. H. Tien and M. Gu. Three-dimensional orientation-unlimited polarizationencryption by a single optically configured vectorial beam. Nat. Commun.3,998,2012.
145. P. Zijlstra, J. W. M. Chon and M Gu. Five-dimensional optical recording mediated by surfaceplasmons in gold nanorods. Nature,459,410-4132009.
146. Q. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt.Photonics,1,1-57,2009.
147. K. S. Youngworth and T. G. Brown. Focusing of high numerical aperture cylindrical-vector beams.Opt. Express,7,77-87,2000.
148. D. P. Biss and T. G. Brown. Cylindrical vector beam focusing through a dielectric interface. Opt.Express,9,490-497,2001.
149. Q. Zhan and J. R. Lege.r Focus shaping using cylindrical vector beams. Opt. Express,10,324-331,2002.
150. W. Chen and Q. Zhan. Three dimensional focus shaping with cylindrical vector beams. Opt.Commun.265,411-417,2006.
151. P. Wróbel, J. Pniewski, T. J. Antosiewicz and T. Szoplik. Focusing radially polarized light by aconcentrically corrugated silver film without a hole. Phys. Rev. Lett.102,183902,2009.
152. H. Wang, L. Shi, B. Lukyanchuk, C. J. R. Sheppard and C. T. Chong. Creation of a needle oflongitudinally polarized light in vacuum using binary optics. Nat. Photonics,2,501-505,2008.
153. W. Chen, D. C. Abeysinghe, R. L. Nelson and Q. Zhan. Plasmonic lens made of multipleconcentric metallic rings under radially polarized illumination. Nano Lett.9,4320-4325,2009.
154. Y. Dong, F. Wang, C. Zhao and Y. Cai. Effect of spatial coherence on propagation, tight focusing,and radiation forces of an azimuthally polarized beam. Phys. Rev. A,86,013840,2009.
155. Y. Dong, F. Feng, Y. Chen, C. Zhao, and Y. Cai. Statistical properties of a nonparaxial cylindricalvector partially coherent field in free space. Opt. Express,20,15908-15927,2012.
156. G. Wu, F. Wang, and Y. Cai. Coherence and polarization properties of a radially polarized beamwith variable spatial coherence. Opt. Express,20,28301-28318,2012.
157. F. Wang, X. Liu, L. Liu, Y. Yuan and Y. Cai. Experimental study of the scintillation index of aradially polarized beam with controllable spatial coherence. Appl. Phys. Lett.103,091102,2013.
158. Q. Zhan. Trapping metallic Rayleigh particles with radial polarization. Opt. Express,12,3377-3382,2004.
159. Y. Q. Zhao, Q. Zhan, Y. L. Zhang, et al. Creation of a three dimensional optical chain forcontrollable particle delivery. Opt. Lett.30,848-850,2005.
160. M. Meier, V. Romano and T. Feurer. Material processing with pulsed radially and azimuthallypolarized laser radiation. Appl. Phys. A,86,329-334,2007.
161. S. Zhu, X. Zhu, L. Liu, F. Wang and Y. Cai. Theoretical and experimental studies of the spectralchanges of a polychromatic partially coherent radially polarized beam. Opt. Express,21,27682-27696,2013.
162. X. Zhu, G. Wu, L. Liu, S. Zhu and Y. Cai. Statistical properties of a partially coherent radiallypolarized beam propagating through an astigmatic optical system. Opti. Commun.316,132-139,2014.
1. S. Wang and D. Zhao, Matrix Optics, CHEP&Springer,2000.
2. H. Kogelnik and T. Li. Laser Beams and Resonators. Appl. Opt.5,1550,1966.
3. A. Gerrard and J. M. Burch. Introduction to Matrix Methods in Optics (Wiley, London),119-122,1975.
4. S. A. Collins. lens-systems diffraction integral written in terms of matrix optics. J. Opt. Soc. Am.60,1168-1177,1970.
5.王仕璠，朱自强，现代光学原理，电子科技大学出版社1998.
6. M. Born and E. Wolf. Principles of Optics. Pergamon,1980.
7. E. Wigner. On the quantum correction for thermodynamic equilibrium. Phys Rev.40,749-759,1932.
8. M. J. Bastiaans. The Wigner distribution function of partially coherent light. Optical Acta,28,1215,1981.
9. Z. I. Feizulin and Y. A. Kravtsov. Broadening of a laser beam in a turbulent medium. Radiophys.Quantum Electron.10,33-35,1967.
10. C. Y. Young, Y. V. Gilchrest and B. R. Macon. Turbulence-induced beam spreading of higher-ordermode optical waves. Opt. Eng.41,1097-1103,2002.
11. T. Shirai, A. Dogariu and E. Wolf. Mode analysis of spreading of partially coherent beamspropagating through turbulent atmosphere. J. Opt. Soc. Am.20,1094-1102,2003.
12. J. C. Leader, Atmospheric propagation of partially coherent radiation. J. Opt. Soc. Am.68,175-185,1978.
13. S. C. H. Wang and M. A. Plonus. Optical beam propagation for a partially coherent source in theturbulent atmosphere. J. Opt. Soc. Am.69,1297-1304,1979.
14. T. Shirai, A. Dogariu, and E. Wolf. Mode analysis of spreading of partially coherent beamspropagating through atmospheric turbulence. J. Opt. Soc. Am. A20,1094-1102,2003.
15. H. T. Eyyubo lu and Y. Baykal. Reciprocity of Cos-Gaussian and Cosh-Gaussian laser beams inturbulent atmosphere. Opt. Express,12,4659-4674,2004.
16. Y. Cai and S. He. Propagation of a partially coherent twisted anisotropic Gaussian Schell-modelbeam in a turbulent atmosphere. Appl. Phys. Lett.89,041117,2006.
17. Y. Cai, S. He. Propagation of various dark hollow beams in a turbulent atmosphere, Opt. Express,14,1353-1367,2006.
18. Y. Baykal, H. T. Eyyubo lu. Scintillation characteristics of cosh-Gaussian beams. Appl. Opt.46,1099-1106,2007.
19. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyubo lu and Y. Baykal. M2-factor of coherent and partiallycoherent dark hollow beams propagating in turbulent atmosphere. Opt. Express,17,17344-17356,2009.
20. S. Zhu, Y. Cai and O. Korotkova. Propagation factor of a stochastic electromagnetic GaussianSchell-model Beam. Opt. Express,18,12587-12598,2010.
21. A. E. Siegman. New developments in laser resonators, SPIE,1224,2-14,1990.
22. R. Martinez-Herrero, P. M. Mejias and M. Arias. Parametric characterization of coherent,lowest-order Gaussian beams propagating through hard-edge apertures, Opt. Lett.20,124-126,1995.
23. C. Pare, P. A. Belanger. Propagation analysis of the truncated second-order moment. Proc. SPIE.104-111,1996.
24. S. Amarande, A. Giesen and H. Hugel. Propagation analysis of self-convergent beam width andcharacterization of hard-edge diffracted beams. Appl. Opt.39,3914-3924,2000.
25. L. Mandel and E. Wolf. Optical coherence and Quantum Optics. Cambridge University Press,1995.
26. A. T. Friberg and J. Turunen. Imaging of Gaussian Schell-model sources. J. Opt. Soc. Am. A,5,713-719,1988.
27. E. Wolf. Unified theory of coherence and polarization of random electromagnetic beams. Phy. Lett.A,312,263-267,2003.
28. Y. Cai, O. Korotkova, H. T. Eyyuboglu and Y. Baykal. Active laser radar systems with stochasticelectromagnetic beams in turbulent atmosphere. Opt. Express,16,15835-15846,2008.
29. Z. Tong, O. Korotkova, Y. Cai, H. T. Eyyuboglu and Y. Baykal. Correlation properties of randomelectromagnetic beams in laser resonators. Appl. Phys. B,97,849-857,2009.
30. O. Korotkova, Y. Cai, E. Watson. Stochastic electromagnetic beams for LIDAR systems operatingthrough turbulent atmosphere. Appl. Phys. B,94,681-690,2009.
31. C. Zhao, Y. Cai and O. Korotkova. Radiation force of scalar and electromagnetic twisted GaussianSchell-model beams. Opt. Express,17,21472-21487,2009.
32. S. Zhu and Y. Cai. M2-factor of a stochastic electromagnetic beam in a Gaussian cavity. Opt.Express,18,27567-27581,2010.
33. H. M. Ozaktas, Z. Zalevsky and M. A. Kutay. The fractional Fourier transform with applications inoptics and signal processing. New York: Wiley,88-92,2001.
34. T. Alieva, M. J. Bastiaans and M. L. Calvo. Fractional transforms in optical information processing.EURASIPJ. Appl. Signal Process,1498-1519,2005.
35. D. Mendlovic and H. M. Ozaktas. Fractional Fourier transforms and their optical implementation: I.J. Opt. Soc. Am. A,10,1875-1881,1993.
36. H. M. Ozaktas and D. Mendlovic. Fractional Fourier transforms and their optical implementation:II, J. Opt. Soc. Am. A,10,2522-2531,1993.
37. A. W. Lohmann. Image rotation, Wigner rotation, and the fractional Fourier transform. J. Opt. Soc.Am. A,10,2181-2186,1993.
38. D. Mendlovic, H. M. Ozaktas and A. W. Lohmann. Graded index fibers, Wigner-distributionfunctions, and the fractional Fourier transforms. Appl. Opt.33,6188-6193,1994.
1. M. Born and E. Wolf. Principles of Optics. Pergamon,1980.
2. E. Wolf. Invariance of the spectrum of light on propagation. Phys. Rev. Lett.56,1370-1372,1986.
3. L. Mandel and E. Wolf. Optical coherence and Quantum Optics. Cambridge University Press,1995.
4. Z. Mei and O. Korotkova. Random sources generating ring-shaped beams. Opt. Lett.38,91-93,2013.
5. F. Wang, X. Liu, Y. Yuan and Y. Cai. Experimental generation of partially coherent beams withdifferent complex degrees of coherence. Opt. Lett.38,1814-1816,2013.
6. Y. Chen, F. Wang, L. Liu, C. Zhao and Y. Cai. Generation and propagation of a partially coherentvector beam with special correlation functions. Phys. Rev. A,89,013801,2014.
7. E. Collett and E. Wolf. Is complete spatial coherence necessary for the generation of highlydirectional light beams? Opt. Lett.2,27-29,1978.
8. J. T. Foley and M. S. Zubairy. The directionality of Gaussian Schell-model beams. Opt. Commun.26,297-300,1978.
9. A. T. Friberg and J. Turunen. Imaging of Gaussian Schell-model sources. J. Opt. Soc. Am. A,5,713-720,1988.
10. J. Wu. Propagation of a Gaussian-Schell beam through turbulent media. J. Mod. Opt.37,671-684,1990.
11. Y. Li and E. Wolf. Radiation from anisotropic Gaussian Schell-model sources. Opt. Lett.7,256-258,1982.
12. F. Gori. Mode propagation of the field generated by Collett-Wolf Schell-model sources. Opt.Commun.46,149-154,1983.
13. R. Simon, E. C. G. Sudarshan and N. Mukunda. Anisotropic Gaussian Schell-model beams,Passage through optical systems and associated invariants. Phys. Rev. A,31,2419-2434,1985.
14. M. Santarsiero, F. Gori and R. Borghi. Spreading properties of beams radiated by partially coherentSchell-model sources. J. Opt. Soc. Am. A,16,106-112,1999.
15. Y. Cai, Q. Lin and D. Ge. Propagation of partially coherent twisted anisotropic GaussianSchell-model beams in dispersive and absorbing media. J. Opt. Soc. Am. A,19,2036-2042,2002.
16. Y. Cai and S. He. Propagation of a partially coherent twisted anisotropic Gaussian Schell-modelbeam in a turbulent atmosphere. Appl. Phys. Lett.89,041117,2006.
17. M. Yao, Y. Cai and H. T. Eyyuboglu. Evolution of the degree of polarization of an electromagneticGaussian Schell-model beam in a Gaussian cavity. Opt. Lett.33,2266-2268,2008.
18. A. T. Friberg, E. Tervonen and J. Turunen. Interpretation and experimental decomposition oftwisted Gaussian Schell-model beams. J. Opt. Soc. Am. A,11,1818-1826,1994.
19. G. Nemes and A. E. Siegman. Measurement of all ten second-order moments of an astigmatic beamby the use of rotating simple astigmatic (anamorphic) optics. J. Opt. Soc. Am. A,11,2257-2264,1994.
20. F. Wang and Y. Cai. Experimental generation of a partially coherent flat-topped beam. Opt. Lett.33,1795-1797,2008.
21. M. J. Bastiaans. Wigner distribution function applied to twisted Gaussian light propagating infirst-order optical systems. J. Opt. Soc. Am. A,17,2475-2480,2000.
22. Q. Lin and Y. Cai. Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schellmodel beams. Opt. Lett.27,216-218,2002.
23. S. Zhu, Y. Chen and Y. Cai. Experimental determination of the radius of curvature of an isotropicGaussian Schell-model beam. J. Opt. Soc. Am. A,30,887-891,2013.
24. F. Wang, S. Zhu and Y. Cai. Experimental study of the focusing properties of a GaussianSchell-model vortex beam. Opt. Lett.36,3281-3283,2011.
25. S. Zhu, C. Zhao, Y. Chen and Y. Cai. Experimental generation of a polychromatic partiallycoherent dark hollow beam. Optik,124,5271-5273,2013.
26. Y. Cai and S. Zhu. Orbital angular moment of a partially coherent beam propagating through anastigmatic ABCD optical system with loss or gain. Opt. Lett.39,1968-1971,2014.
27. E. Wolf and E. Collett. Partially coherent sources which produce same far-field intensitydistribution as a laser. Opt. Commun.25,293-296,1978.
28. X. Ji and X. Li. Effective radius of curvature of partially coherent Hermite–Gaussian beamspropagating through atmospheric turbulence. J. Opt.12,035403,2010.
29. G. Gbur and T. D. Visser. Coherence vortices in partially coherent beams. Opt. Commun.222,117-125,2003.
30. J. Serna and J. M. Movilla. Orbital angular momentum of partially coherent beams. Opt. Lett.26,405-407,2001.
31. F. Gori, G. Guattari and C. Padovani. Bessel-Gauss beams. Opt. Commun.64,491-495,1987.
32. Y. Cai, X. Lu and Q. Lin. Hollow Gaussian beams and their propagation properties, Opt. Lett.28,1084-1086,2003.
33. Q. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt.Photonics,1,1-57,2009.
34. J. Yin, W. Gao and Y. Zhu. Generation of dark hollow beams and their applications. in: E. Wolf(Ed.). Progress in Optics,44.119-204,2003.
35. I. Manek, Y. B. Ovehinnikov and R. Grimm. Generation of a hollow laser beam for atom trappingusing an axicon. Opt. Commun.147,67-70,1998.
36. C. Zhao, Y. Cai, F. Wang, X. Lu and Y. Wang. Generation of a high-quality partially coherent darkhollow beam with a multimode fiber. Opt. Lett.33,1389-1391,2008.
37. C. Zhao, Y. Cai, X. Lu and H. T. Eyyubo lu. Radiation force of coherent and partially coherentflat-topped beams on a Rayleigh particle. Opt. Express,17,1753-765,2009.
38. S. A. Amarande. Beam propagation factor and the kurtosis parameter of flattened Gaussian beams.Opt. Commun.129,311-317,1996.
39. P. Zhou, Z. Liu, X. Xu and X. Chu. Propagation of coherently combined flattened laser beam arrayin turbulent atmosphere. Opt. Laser Tech.41,403-407,2009.
40. F. Gori. Flattened gaussian beams. Opt. Commun.107,335-341,1994.
41. R. Borghi and M. Santarsiero. Modal decomposition of partially coherent flat-topped beamsproduced by multimode lasers. Opt. Lett.23,313-315,1998.
42. Y. Li. Light beams with flat-topped profiles. Opt. Lett.27,1007-1009,2003.
43. Y. Cai. Propagation of various flat-topped beams in a turbulent atmosphere. J. Opt. A: Pure Appl.Opt.8,537,2006.
44. F. Wang and Y. Cai. Experimental generation of a partially coherent flat-topped beam. Opt. Lett.33,1795-1797,2008.
45. E. Wolf. Invariance of the spectrum of light on propagation. Phys. Rev. Lett.56,1370-1372,1986.
46. H. C. Kandpal, A. Wasan, J. S. Vaishya, E. S. R. Gopal, M. Singh, B. B. Sanwal and R. Sagar.Application of spatial coherence spectroscopy for determining the angular diameters of stars.feasibility experiment. Indian J. Pure Appl. Phys.36,665-674,1998.
1. E. Wolf. Introduction to the Theory of Coherence and Polarization of Light. Cambridge U. Press,2007.
2. D. F. V. James. Change of polarization of light beams on propagation in free space. J. Opt. Soc. Am.A,11,1641-1643,1994.
3. F. Gori. Matrix treatment for partially polarized, partially coherent beams. Opt. Lett.23,241-243,1998.
4. T. Set l, M. Kaivola and A. T. Friberg. Degree of polarization in near fields of thermal sources,effects of surface waves. Phys. Rev. Lett.88,123902,2002.
5. E. Wolf. Unified theory of coherence and polarization of random electromagnetic beams. Phy. Lett.A,312,263-267,2003.
6. E. Wolf. Correlation-induced changes in the degree of polarization, the degree of coherence and thespectrum of random electromagnetic beams on propagation. Opt. Lett.28,1078-1080,2003.
7. O. Korotkova and E. Wolf. Changes in the state of polarization of a random electromagnetic beamon propagation. Opt. Commun.246,35-43,2005.
8. M. Yao, Y. Cai and H. T. Eyyuboglu. Evolution of the degree of polarization of an electromagneticGaussian Schell-model beam in a Gaussian cavity. Opt. Lett.33,2266-2268,2008.
9. S. Zhu, Y. Cai and O. Korotkova. Propagation factor of a stochastic electromagnetic GaussianSchell-model beam. Opt. Express,18,12587-12598,2010.
10. M. Lahiri and E. Wolf. Theory of refraction and reflection with partially coherent electromagneticbeams. Phys. Rev. A,86,43815,2012.
11. R. Dorn, S. Quabis and G. Leuchs. Sharper focus for a radially polarized light beam. Phys. Rev.Lett.91,233901,2003.
12. Q. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt.Photonics,1,1-57,2009.
13. F. Wang, X. Liu, L. Liu, Y. Yuan and Y. Cai. Experimental study of the scintillation index of aradially polarized beam with controllable spatial coherence. Appl. Phys. Lett.103,091102,2013.
14. F. Wang, Y. Cai, Y. Dong and O. Korotkova. Experimental generation of a radially polarized beamwith controllable spatial coherence. Appl. Phys. Lett.100,051108,2012.
15. Q. Lin and Y. Cai. Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schellmodel beams. Opt. Lett.27,216-218,2002.
16. B. Kanseri, S. Rath and H. C. Kandpal. Determination of the beam coherence-polarization matrixof a random electromagnetic beam. IEEE J. Quantum Electron.45,1163-1167,2009.
17. H. C. Kandpal, A. Wasan, J. S. Vaishya, E. S. R. Gopal, M. Singh, B. B. Sanwal and R. Sagar.Application of spatial coherence spectroscopy for determining the angular diameters of stars:feasibility experiment. Indian J. Pure Appl. Phys.36,665-674,1998.
18. Y. Cai, Q. Lin and D. Ge. Propagation of partially coherent twisted anisotropic GaussianSchell-model beams in dispersive and absorbing media. J. Opt. Soc. Am. A,19,2036-2042,2002.
19. B. K. Yadav and H. C. Kandpal. Spectral anomalies of polychromatic DHGB and its applicationsin FSO. J. Lightwave Technol.29,960-966,2011.
20. D. Mendlovic and H. M. Ozaktas, Fractional Fourier transforms and their optical implementation: I.J. Opt. Soc. Am. A,10,1875-1881,1993.
21. H. M. Ozaktas and D. Mendlovic. Fractional Fourier transforms and their optical implementation:II, J. Opt. Soc. Am. A,10,2522-2531,1993.
22. A. W. Lohmann. Image rotation, Wigner rotation, and the fractional Fourier transform. J. Opt. Soc.Am. A,10,2181-2186,1993.
23. D. Mendlovic, H. M. Ozaktas and A. W. Lohmann. Graded index fibers, Wigner-distributionfunctions, and the fractional Fourier transforms. Appl. Opt.33,6188-6193,1994.
24. H. M. Ozaktas, Z. Zalevsky and M. A. Kutay. The fractional Fourier transform with applications inoptics and signal processing. New York: Wiley,88-92,2001.
25. T. Alieva, M. J. Bastiaans, M. L. Calvo. Fractional transforms in optical information processing.EURASIPJ. Appl. Signal Process,1498,2005.
26. Y. Cai and S. Zhu. Coincidence fractional Fourier transform implemented with partially coherentlight radiation. J. Opt. Soc. Am. A,22,1798-1804,2005.
27. Y. Cai. Propagation of various flat-topped beams in a turbulent atmosphere. J. Opt. A: Pure Appl.Opt.8,537,2006.
28. P. Zijlstra, J. W. M. Chon and M Gu. Five-dimensional optical recording mediated by surfaceplasmons in gold nanorods. Nature,459,410-413,2009.
29. W. Gao. Changes of polarization of light beams on propagation through tissue. Opt. Commun.260,749-754,2006.
30. M. J. Schmitt and G. Kumar. Turbulent nature of refractive-index variations in biological tissue.Opt. Lett.21,1310-1312,1996.
31. G. P. Agrawal, A. K. Ghatak and C. L. Mehta. Propagation of partially coherent beam throughSelfoc fibers. Opt. Commun.12,333-337,1974.
32. G. P. Agarwal. Fiber-Optic Communication Systems,3rd ed. Wiley,2002.
33. A. Gamliel and G. P. Agrawal. Wolf effect in homogenous and inhomogenous media. J. Opt. Soc.Am. A,7,2184-2192.1990.
34. H. Roychowdhury, G. P. Agarwal and E. Wolf. Changes in the spectrum, in the spectral degree ofpolarization, and in the spectral degree of coherence of a partially coherent beam propagatingthrough a gradient-index fiber. J. Opt. Soc. Am. A,23,940-948,2006.
35. C. Zhao, Y. Cai, F. Wang, X. Lu and Y. Wang. Generation of a high-quality partially coherent darkhollow beam with a multimode fiber. Opt. Lett.33,1389-1391,2008.
36. S. Zhu, C. Zhao, Y. Chen, and Y. Cai. Experimental generation of a polychromatic partiallycoherent dark hollow beam. Optik,124,5271-5273.2013.
37. O. Korotkova and E. Wolf. Changes in the state of polarization of a random electromagnetic beamon propagation. Opt. Commun.246,35-43,2005.
38. E. Siegman. New developments in laser resonators. Proc. SPIE1224,2-14,1990.
39. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti and P. Vahimaa. Spreading properties of beamsradiated by partially coherent Schell-model sources. J. Opt. Soc. Am. A16,106-112,1999.
40. J. Serna, R. Martinez-Herrero and P. M. Mejfas. Parametric characterization of general partiallycoherent beams propagating through ABCD optical systems. J. Opt. Soc. Am. A,8,1094-1098,1991.
1. S. De Silvestri, V. Magni, O Svelto, et. al. Lasers with super-Gaussian mirrors. IEEE J. QuantumElectron.26,1500-1509,1990.
2. P. A. Belanger, R. L. Lachance and C. Pare. Super-Gaussian output from a CO2laser by using agraded-phase mirror resonator. Opt. Lett.17,739-741,1992.
3. Y. Mushiake, K. Matzumurra and N. Nakajima. Generation of radially polarized optical beammode by laser oscillation. Proc. IEEE60,1107-1109,1972.
4. M. Yao, Y Cai and H. T. Eyyuboglu. Evolution of the degree of polarization of an electromagneticGaussian Schell-model beam in a Gaussian cavity. Opt. Lett.33,2266-2268,2008.
5. Z. Tong, O. Korotkova, Y. Cai, H. T. Eyyuboglu and Y. Baykal. Correlation properties of randomelectromagnetic beams in laser resonators. Appl. Phys. B,97,849-857,2009.
6. A. G. Fox and T. Li. Resonate modes in a maser interferometer. Bell Syst. Tech. J.40,453-488,1961.
7. E. Wolf. Spatial coherence of resonant modes in a maser interferometer. Phys. Lett.,3,166-168,1963.
8. E. Wolf and G. S. Agarwal. Coherence theory of laser resonator Modes. J. Opt. Soc. Am. A,1,541-546,1984.
9. F. Gori. Propagation of the mutual intensity through a periodic structure Atti Fond. Giorgio Ronchi,35,434-447,1980.
10. P. Desantis, A. Mascello, C. Palma and M. R. Perrone. Coherence growth of laser radiation inGaussian cavities. IEEE J. Quantum Electron.32,802-812,1996.
11. C. Palma, G. Cardone and G. Cincotti. Spectral changes in Gaussian-cavity lasers. IEEE J.Quantum Electron.34,1082-1088,1998.
12. E. Wolf. Unified theory of coherence and polarization of random electromagnetic beams. Phy. Lett.A,312,263-267,2003.
13. H. Roychowdhury and E. Wolf. Determination of the electric cross-spectral density matrix of arandom electromagnetic beam. Opt. Commun.226,57-60,2003.
14. S. Zhu, Y. Cai and O. Korotkova. Propagation factor of a stochastic electromagnetic GaussianSchell-model beam. Opt. Express,18,12587-12598,2010.
15. F. Wang, G. Wu, X. Liu, S. Zhu and Y. Cai. Experimental measurement of the beam parameters ofan electromagnetic Gaussian Schell-modelsource. Opt. Lett.36,2722-2724,2011.
16. S. Zhu, F. Zhou, Y. Cai and L. Zhang. Thermal lens effect induced changes of polarization,coherence and spectrum of a stochastic electromagnetic beam in a Gaussian cavity. Appl. Phys. B,102,953-961,2011.
17. S. Zhu and Y. Cai. Degree of polarization of a twisted electromagnetic Gaussian Schell-modelbeam in a Gaussian cavity filled with gain media. Prog. Electromagn. Res. B,21,171-187,2010.
18. S. Zhu and Y. Cai. M2-factor of a stochastic electromagnetic beam in a Gaussian cavity. Opt.Express,18,27567-27581,2010.
19. J. P. Gordon, R. C. C. Leite, R. S. Moore, et. al. Long-transient effects in lasers with inserted liquidsamples, J. Appl. Phys.36,3-8,1965.
20. J. Stone. Measurements of the absorption of light in low-loss liquids. J. Opt. Soc. Am.62,327-333,1972.
21. C. Hu and J. R. Whinnery. New thermooptical measurement method and a comparison with othermethods. Appl. Opt.12,72-79,1973.
22. S. J. Sheldon, L. V. Knight, and J. M. Thorne. Laser-induced thermal lens effect, a new theoreticalmodel. Appl. Opt.21,1663-1669,1982.
23. T. Xu and S. Wang. Propagation of Ince-Gaussian beams in a thermal lens medium. Opt. Commun.265,1-5,2006.
24. Z. Tong and O. Korotkova. Stochastic electromagnetic beams in positive-and negative-phasematerials. Opt. Lett.35,175-177,2010.
25. J. Deschamps, D. Courjon and J. Bulabois. Gaussian Schell-model sources,an example and someperspectives. J. Opt. Soc. Am.73,256-261,1983
26. R. Simon, E. C. G. Sudarshan, and N. Mukunda. Anisotropic Gaussian Schell-model beams,passage through optical systems and associated invariants. Phys. Rev. A,31,2419-2434,1985.
27. A. T. Friberg and J. Turnnen. Algebraic and graphical propagation methods for Gaussian Schell-model beams. Opt. Eng.25,857-864,1986
28. Q. Lin and Y. Cai. Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schellmodel beams. Opt. Lett.27,216-218,2002.
29. F. Gori, M. Santarsiero and A. Sona. The change of width for a partially coherent beam on paraxialpropagation. Opt. Commun.82,197-203,1991.
30. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti and P. Vahimaa. Spreading properties of beamsradiated by partially coherent Schell-model sources. J. Opt. Soc. Am. A,16,106-112,1999.
31. E. Siegman. New developments in laser resonators. Proc. SPIE1224,2-14,1990.
32. M. J. Bastiaans. Application of the Wigner distribution function to partially coherent light. J. Opt.Soc. Am. A3,1227-1239,1986.
33. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti and P. Vahimaa. Spreading properties of beamsradiated by partially coherent Schell-model sources. J. Opt. Soc. Am. A16,106-112,1999.
34. J. Serna, R. Martinez-Herrero and P. M. Mejfas. Parametric characterization of general partiallycoherent beams propagating through ABCD optical systems. J. Opt. Soc. Am. A,8,1094-1098,1991.
35. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyubo lu, Y. Baykal and O. Korotkova. M2-factor of coherent andpartially coherent dark hollow beams propagating in turbulent atmosphere. Opt. Express,17,17344-17356,2009.
36. F. Wang and Y. Cai. Second-order statistics of a twisted Gaussian Schell-model beam in turbulentatmosphere. Opt. Express,18,24661-24672,2010.
1. L. C. Andrews and R. L. Phillips. Laser beam propagation through random media. SPIE Press,2005.
2.饶瑞中，光在湍流大气中的传播，安徽科学技术出版社，第一版，2005.
3.张逸新，迟泽英，光波在大气中的传输与成像，国防工业出版社，第一版，1997.
4. V. I. T atarskii. The effect of the turbulent atmosphere on wave propagation. IPST Catalog5391,1971.
5. R. J. Hill. Modified spectrum of atmospheric fluctuation and its application to optical propagation,J. Opt. Soc. Am.68,892-905,1978.
6. G. R. Ochs and R. J. Hill. Optical-scintillation method of measuring turbulence inner scale. Appl.Opt.24,2430-2432,1985.
7. J. C. Ricklin and F. M. Davidson. Atmospheric turbulence effects on a partially coherent Gaussianbeam, implications for free-space laser communication. J. Opt. Soc. Am. A,19,1794-1802,2002.
8. Y. Cai and S. Zhu. Ghost interference with partially coherent radiation. Opt. Lett.29,2716-2718,2004.
9. P. Zhou, Z. Liu X. Xu and X. Chu. Propagation of coherently combined flattened laser beam arrayin turbulent atmosphere. Opt. Laser, Tech.41,403-407,2009.
10. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyubo lu, Y. Baykal and O. Korotkova. M2-factor of coherent andpartially coherent dark hollow beams propagating in turbulent atmosphere, Opt. Express,20,17344-17356,2009.
11. S. Zhu, Y. Cai and O. Korotkova. Propagation factor of a stochastic electromagnetic GaussianSchell-model beam. Opt. Express,18,12587-12598,2010.
12. A. N. Kolmogorov. The local structure of turbulence in an incompressible viscous fluid for verylarge Reynolds numbers. C.R.(Doki) Acad. Sci. U.S.S.R.30,301-305,1941.
13. V. I. Tatarski. Wave propagation in a random medium. New York, McGraw-Hill Book Company,142-165,1961.
14. Y. Cai and S. He. Propagation of a partially coherent twisted anisotropic Gaussian Schell-modelbeam in a turbulent atmosphere. Appl. Phys. Lett.89,04,1117,2006.
15. Y. Cai, O. Korotkova, H. T. Eyyuboglu and Y. Baykal. Active laser radar systems with stochasticelectromagnetic beams in turbulent atmosphere. Opt. Express,6,15834-15846,2008.
16. H. T. Yura and S. G. Hanson. Optical beam wave propagation through complex optical systems. J.Opt. Soc. Am.4,1931-1948,1987.
17. Y. Yuan, Y. Cai, H. T. Eyyuboglu, Y. Baykal and J. Chen. Propagation factor of partially coherentflat-topped beam array in free space and turbulent atmosphere. Opt. Laser Eng.50,752-759,2012
18. S. Du, Y. Yuan, C. Liang and Y. Cai. Second-order moments of a multi-Gaussian Schell-modelbeam in a turbulent atmosphere. Opt. Laser Tech.50,14-19,2013.
19. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti and P. Vahimaa. Spreading properties of beamsradiated by partially coherent Schell-model sources. J. Opt. Soc. Am. A,16,106-112,1999.
20. Y. Li. Dependence of the focal shift on Fresnel number and f number. J. Opt. Soc. Am.72,770-774,1982.
21. X. Liu and J. Pu. Focal shift and focal switch of partially coherent light in dual-focus systems. Opt.Commun.252,262-267,2005.
22. F. Wang, Y. Cai and O. Korotkova. Experimental observation of focal shifts in focused partiallycoherent beams. Opt. Commun.282,3408-2412,2009.
23. J. Pu, H. Zhang and S. Nemoto. Spectral shifts and spectral switches of partially coherent lightpassing through an aperture. Opt. Commun.162,57-63,1999.
24. J. J. Wen and M. A. Breazeale. A diffraction beam field expressed as the superposition of Gaussianbeams. J. Acoust. Soc. Am.83,1752-1756,1988.
25. Y. Cai and L. Hu. Propagation of partially coherent twisted anisotropic Gaussian Schell-modelbeams through an apertured astigmatic optical system. Opt. Lett.31,685-687,2006.
26. F. Wang, Y. Cai and Q. Lin. Experimental observation of truncated fractional Fourier transform fora partially coherent Gaussian Schell-model beam. J. Opt. Soc. Am. A,25,2001-2010,2008.
1. R. Dorn, S. Quabis and G. Leuchs. Sharper focus for a radially polarized light beam. Phys. Rev.Lett.91,233901,2003.
2. Q. Zhan. Trapping metallic Rayleigh particles with radial polarization. Opt. Express,12,3377-3382,2004.
3. W. Chen, D. C. Abeysinghe, R. L. Nelson and Q. Zhan. Plasmonic lens made of multipleconcentric metallic rings under radially polarized illumination. Nano Lett.9,4320-4325,2009.
4. P. Zijlstra, J. W. M. Chon and M. Gu. Five-dimensional optical recording mediated by surfaceplasmons in gold nanorods. Nature,459,410-4132009.
5. X. Li, T. H. Lan, C. H. Tien and M. Gu. Three-dimensional orientation-unlimited polarizationencryption by a single optically configured vectorial beam. Nat. Commun.3,998,2012.
6. Y. Mushiake, K. Matzumurra and N. Nakajima. Generation of radially polarized optical beammode by laser oscillation. Proc. IEEE60,1107-1109,1972.
7. A. V. Nesterov, V. G. Niziev and V. P. Yakunin. Generation of high-power radially polarized beam.J. Phys. D: Appl. Phys.32,2871,1999.
8. Y. Kozawa and S. Sato. Generation of a radially polarized laser beam by use of a conical Brewsterprism. Opt Lett.30,3063-3065,2005.
9. K. Yonezawa, Y. Kozawa and S. Sato. Geneartion of a radially polarized laser beam by use of thebirefringence of a c cut Nd:YVO4crystal. Opt. Lett.31,2151-2153.2006.
10. G Machavariani, Y. Lumer, I. Moshe, et al. Birefringence induced bifocusing forslection of radiallyor azimuthally polarized laser modes. Appl. Opt.46,3304-3310,2007.
11. S. C. Tidwell, D. H Ford and W. D. Kimura. Efficient radially polarized laser beam generation witha double interferometer. Appl. Opt.32,5222-5229.1993.
12. A. V. Nesterov and V. G. Niziev. Laser beams with axially symmetric polarization. J. Phys. D: Appl.Phys.33,1-6,2006.
13. F. Wang, Y. Cai, Y. Dong and O. Korotkova. Experimental generation of a radially polarized beamwith controllable spatial coherence. Appl. Phys. Lett.100,041108,2012.
14. Q. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt.Photonics,1,1-57,2009.
15. S. Quabis, R Dorn, M Elberler, et al. Focusing light into a tighter spot. Opt. Commun.179,1-7,2000.
16. Y. Cai, Q. Lin, H. T. Eyyuboglu and Y. Baykal. Average irradiance and polarization properties of aradially or azimuthally polarized beam in a turbulent atmosphere. Opt. Express,16,7665-7673,2008.
17. Y. Gu, O. Korotkova and G. Gbur. Scintillation of nonuniformly polarized beams in atmosphericturbulence. Opt Lett.34,2261-2263,2009.
18. W. Cheng, J. W. Haus and Q. Zhan. Propagation of vector vortex beams through a turbulentatmosphere. Opt. Express,17,17829-17836,2009.
19. F. Wang, X. Liu, L. Liu, Y. Yuan and Y. Cai. Experimental study of the scintillation index of aradially polarized beam with controllable spatial coherence. Appl. Phys. Lett.103,091102,2013.
20. Y. Dong, F. Wang, C. Zhao and Y. Cai. Effect of spatial coherence on propagation, tight focusing,and radiation forces of an azimuthally polarized beam. Phys. Rev. A,86,013840,2009.
21. Y. Zhang, B. Ding and T. Suyama. Trapping two types of particles using a double-ring-shapedradially polarized beam. Phys. Rev. A,81,023831,2010.
22. Y. Dong, F. Feng, Y. Chen, C. Zhao, and Y. Cai. Statistical properties of a nonparaxial cylindricalvector partially coherent field in free space. Opt. Express,20,15908-15927,2012.
23. G. Wu, F. Wang and Y. Cai. Coherence and polarization properties of a radially polarized beamwith variable spatial coherence. Opt. Express,20,28301-28318,2012.
24. L. Huang, H. Guo, J. Li, L. Ling, B. Feng and Z. Li. Optical trapping of gold nanoparticles bycylindrical vector beam. Opt. Lett.37,1694-1696.2012.
25. R. Chen, Y. Dong, F. Wang and Y. Cai. Statistical properties of a cylindrical vector partiallycoherent beam in turbulent atmosphere. Appl. Phys. B,112,247-259,2013.
26. S. Zhu, X. Zhu, L. Liu, F. Wang and Y. Cai. Theoretical and experimental studies of the spectralchanges of a polychromatic partially coherent radially polarized beam. Opt. Express,21,27682-27696,2013.
27. X. Zhu, G. Wu, L. Liu, S. Zhu and Y. Cai. Statistical properties of a partially coherent radiallypolarized beam propagating through an astigmatic optical system. Opt. Commun.316,132-139,2014.
28. Q. Lin and Y. Cai. Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schellmodel beams. Opt. Lett.27,216-218,2002.
29. C. Palma, G. Cincotti and G. Guattari. Spectral shift of a Gaussian Schell-model beam beyond athin lens. IEEE J. Quantum Electron.34,378-383,1998.
30. H. Mashaal, A. Goldstein, D. Feuermann and J. M. Gordon. First direct measurement of the spatialcoherence of sunlight. Opt. Lett.37,3516-3518,2012.
31. F. Wang, Y. Cai and Q. Lin. Experimental observation of truncated fractional Fourier transform fora partially coherent Gaussian Schell-model beam. J. Opt. Soc. Am. A,25,2001-2010,2008.
32. L. Pan, M. Sun, C. Ding, Z. Zhao and B. Lu. Effects of astigmatism on spectra, coherence andpolarization of stochastic electromagnetic beams passing through an astigmatic optical system. Opt.Express,17,7310-7321,2009.
33. O. Korotkova and E. Wolf. Changes in the state of polarization of a random electromagnetic beamon propagation. Opt. Commun.246,35-43,2005.
34. S. A. Ponomarenko and E. Wolf. Coherence properties of light in Young's interference patternformed with partially coherent light. Opt. Commun.170,1-8,1999.
35. G. Gbur, T. D. Visser and E. Wolf. Complete destructive interference of partially coherent fields.Opt. Commun.239,15-23,2004.
36. T. Set l, J. Tervo and A. T. Friberg. Contrasts of Stokes parameters in Young's interferenceexperiment and electromagnetic degree of coherence. Opt. Lett.31,2669-2671,2006.
37. G. S. Agarwal, A. Dogariu, T. D Visser and E. Wolf. Generation of complete coherence in Young'sinterference experiment with random mutually uncorrelated electromagnetic beams. Opt. Lett.30,120-122,2006.
38. Y. Li, H. Lee and E. Wolf. Spectra, coherence and polarization in Young's interference patternformed by stochastic electromagnetic beams. Opt. Commun.265,63-72,2006.
39. J. J. Wen and M. A. Breazeale. A diffraction beam field expressed as the superposition of Gaussianbeams. J. Acoust. Soc. Am.83,1752-1756,1988.
40. Y. Cai and L. Hu. Propagation of partially coherent twisted anisotropic Gaussian Schell-modelbeams through an apertured astigmatic optical system. Opt. Lett.31,685-687,2006.
41. S. Zhu and Y. Cai. M2-factor of a truncated electromagnetic Gaussian Schell-model beam. Appl.Phys. B,103,971-984,2011.
2. A. L. Schawlow and C. H. Townes. Infrared and optical masers. Phys. Rev.112,1940-1949,1958.
3. T. H. Maiman. Stimulated optical radiation in ruby. Nature,187,493-494,1960.
4.邓锡铭,王之江.光学量子放大器.科学通报,11,25-29,1961.
5. G. Fox and T. Li. Resonant modes in a maser interferometer. Bell Sys. Tech. J.40,450-456,1961.
6. H. Kogelnik. Imaging of optical modes-resonators with internal lenses. Bell Sys. Tech. J.44,455-462,1965.
7. S. A. Collins. Lens-systems diffraction integral written in terms of matrix optics. J. Opt. Soc. Am.60,1168-1177,1970.
8. Q. Lin and Y. Cai. Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schellmodel beams. Opt. Lett.27,216-218,2002.
9. Y. Cai and S. He. Propagation of a partially coherent twisted anisotropic Gaussian Schell-modelbeam in a turbulent atmosphere. Appl. Phys. Lett.89,04,1117,2006.
10. M. Yao, Y. Cai and H T Eyyuboglu. Evolution of the degree of polarization of an electromagneticGaussian Schell-model beam in a Gaussian cavity. Opt. Lett.33,2266-2268,2008.
11. P. Belland and J. P. Crenn. Changes in the characteristics of a Gaussian beam weakly diffracted bya circular aperture. Appl. Opt.21,522-527,1982.
12. W. H. Carter and M. F. Aburdene. Focal shift in Laguerre-Gaussian beams. J. Opt. Soc. Am. A,4,1949-1952,1987.
13. A. E. Siegman. Hermite-gaussian functions of complex argument as optical-beam eigen functions.J. Opt. Soc. Am. A,63,1093-1094,1973.
14. F. Gori. Flattened gaussian beams. Opt. Commun.107,335-341,1994.
15. R. Borghi. Elegant Laguerre-Gauss beams as a new tool for describing axisymmetric flattenedGaussian beams. J. Opt. Soc. Am. A,18,1627-1633,2001.
16. Y. Li. Light beams with flat-topped profiles. Opt. Lett.27,1007-1009,2003.
17. F. Gori, G. Guattari and C. Padovani. Bessel-Gauss beams. Opt. Commun.64,491-495,1987.
18. S. Marksteiner, C. M. Savage, P. Zoller and S. Rolston. Coherent atomic waveguides from hollowoptical fibers. quantized atomic motion. Phys. Rev. A,50,2680-2690,1994.
19. M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman and E. A. Cornell.Laser-guided atoms in hollow-core optical fibers Phys. Rev. Lett.75,3253-3256,1995.
20. H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee and W. Jhe. Laser spectroscopy of atoms guidingby evanescent waves in micro-sized hollow optical fibers. Phys. Rev. Lett.76,4500-4503,1996.
21. J. Yin and Y. Zhu. LP01-mode output beam from a micro-sized hollow optical fiber. A simpletheoretical model and its applications in atom optics. J. Appl. Phys.85,2473-2481,1999.
22. X. Xu, V. G. Minogin, K. Lee, Y. Wang and W. Jhe. Guiding cold atoms in a hollow laser beam.Phys. Rev. A,60,4796-4804,1999.
23. M. Born and E. Wolf. Principles of Optics. Pergamon,1980.
24. L. Mandel and E.Wolf. Optical coherence and Quantum Optics. Cambridge University Press,1995.
25.王云山.激光转镜扫描光束的优化和光斑特性分析.光电子激光,8,287-290,1997.
26. E. Wolf. Coherent-mode representation of Gaussian Schell-model sources and of their radiationfields. J. Opt. Soc. Am.72,923-928,1982.
27. E. Wolf. New theory of partial coherence in the space-frequency domain. II. Steady-state fields andhigher-order correlations. J. Opt. Soc. Am. A,3,76-85,1986.
28. E. Wolf and G. S. Agarwal. Coherence theory of laser resonator modes. J. Opt. Soc. Am. A,1,541-546,1984.
29. J. W. Goodman. Statistical Optics. Wiley, New York,1985.
30. E. Collett and E. Wolf. Is complete spatial coherence necessary for the generation of highlydirectional light beams? Opt. Lett.2,27-29,1978.
31. J. T. Foley and M. S. Zubairy. The directionality of Gaussian Schell-model beams. Opt. Commun.26,297-300,1978.
32. R. Grella. Synhesis of generalized Collett-Wolf sources. J. Optics (Paris),13,127-131,1982.
33. C. Palma and G. Cincotti. Spatial behavior of the Wolf effect in free propagation for GaussianSchell-model beams. J. Opt. Soc. Am. A,14,1885-1889,1997.
34. M. Santarsiero, F. Gori and R. Borghi. Spreading properties of beams radiated by partially coherentSchell-model sources. J. Opt. Soc. Am. A,16,106-112,1999.
35. A. T. Friberg and J. Turunen. Imaging of Gaussian Schell-model sources. J. Opt. Soc. Am. A,5,713-720,1988.
36. R. Simon, E. C. G. Sudarshan and N. Mukunda. Anisotropic Gaussian Schell-model beams passagethrough optical systems and associated invariants. Phys. Rev. A,31,2419-2434,1985.
37. J. Wu. Propagation of a Gaussian-Schell beam through turbulent media. J. Mod. Opt.37,671-684,1990.
38. Y. Cai and Q. Lin. Propagation of partially coherent twisted anisotropic Gaussian-Schell modelbeams through misaligned optical systems. Opt. Commun.211,1-8,2002.
39. Y. Cai, Q. Lin and D. Ge. Propagation of partially coherent twisted anisotropic GaussianSchell-model beams in dispersive and absorbing media. J. Opt. Soc. Am. A,19,2036-2042,2002.
40. Y. Cai and L. Hu. Propagation of partially coherent twisted anisotropic Gaussian Schell-modelbeams through an apertured astigmatic optical system. Opt. Lett.31,685-687,2006.
41. Y. Cai and U. Peschel. Second-harmonic generation by an astigmatic partially coherent beam. Opt.Express,15,15480-15492,2007.
42. F. Wang and Y. Cai. Second-order statistics of a twisted Gaussian Schell-model beam in turbulentatmosphere. Opt. Express,18,24661-24672,2010.
43. W. H. Carter and M. Bertolotti. An analysis of the far-field coherence and radiant intensity of lightscattered from liquid crystals. J. Opt. Soc. Am. A,68,329-333,1978.
44. P. D. Santis, F. Gori, G. Guattari and C. Palma. An example of a collett-wolf source. Opt. Commun.29,256-260,1979.
45. J. D. Farina, L.M. Narducci and E. Collet. Generation of highly directional beams from a globallyincoherent source. Opt. Commun.32,203-207,1980.
46. E. Tervonen, A.T. Friberg and J. Turunen. Gaussian Schell-model beams generated with syntheticacousto-optic holograms. J. Opt. Soc. Am. A,9,796-803,1992.
47. S. N. Dixit, I. M. Thomas and B.W. Woods. Random phase plates for beam smoothing on the Novalaser. Appl. Opt.32,2543-2554,1993.
48. F. Gori and M. Santarsiero.Devising genuine spatial correlation functions. Opt. Lett.32,3531-3533,2007.
49. J. Deshamps, D. Courjon and J. Bulabois. Gaussian Schell-model sources, an example and someperspectives. J. Opt. Soc. Am.73,256-261,1983.
50. H. Lajunen and T. Saastamoinen. Propagation characteristics of partially coherent beams withspatially varying correlations. Opt. Lett.36,4104-4106,2011.
51. Z. Tong and O. Korotkova. Nonuniformly correlated light beams in uniformly correlated media.Opt. Lett.37,3240-3242,2012.
52. Z. Mei and O. Korotkova. Random sources generating ring-shaped beams. Opt. Lett.38,91-93,2013.
53. F. Wang, X. Liu, Y. Yuan and Y. Cai. Experimental generation of partially coherent beams withdifferent complex degrees of coherence. Opt. Lett.38,1814-1816,2013.
54. F. Wang, X. Liu, L. Liu, Y. Yuan and Y. Cai, Experimental study of the scintillation index of aradially polarized beam with controllable spatial coherence. Appl. Phys. Lett.103,091102,2013.
55. Y. Chen, F. Wang L. Liu, C. Zhao and Y. Cai. Generation and propagation of a partially coherentvector beam with special correlation functions. Phys. Rev. A,89,013801,2014.
56. E. Wolf. Invariance of the spectrum of light on propagation. Phys. Rev. Lett.56,1370-1372,1986.
57. D. Fkalis and G. M. Morris. Spectral shifts produced by source correlations. Opt. Lett.13,4-6,1988.
58. J. Pu, H. Zhang and S. Nemoto. Spectral shifts and spectral switches of partially coherent lightpassing through an aperture. Opt. Commun.162,57-63,1999.
59. L. Pan and B. Lü. Spectral switches of polychromatic Gaussian beams passing through anastigmatic aperture lens. Opt. Commun.234,13-22,2004.
60. C. Ding, L. Pan and B. Lü. Effect of turbulence on the spectral switches of diffracted spatially andspectrally partially coherent pulsed beams in atmospheric turbulence. J. Opt. A: Pure Appl. Opt.11,105404,2009.
61. L. Pan, Z. Zhao, C. Ding and B. Lü. Effect of polarization on spectral switches in the diffraction ofstochastic electromagnetic beams. Appl. Phys. Lett.95,181112,2009.
62. H. C. Kandpal, A. Wasan, J. S. Vaishya, E. S. R. Gopal, M. Singh, B. B. Sanwal and R. Sagar.Application of spatial coherence spectroscopy for determining the angular diameters of stars:feasibility experiment. Indian J. Pure Appl. Phys.36,665-674,1998.
63. H. C. Kandpal. Experimental observation of the phenomenon of spectral switch. J. Opt. A: Pureand Appl. Opt.3,296-299,2001.
64. B. K. Yadav and H. C. Kandpal. Spectral anomalies of polychromatic DHGB and its applicationsin FSO. J. Lightwave Technol.29,960-966,2011.
65. A. Gerrard and J. M. Burch. Introduction to matrix methods in optics. London. New York, JohnWilly&Sons,1975.
66. J. Turunen and A.T. Friberg. Matrix representation of Gaussian Schell-model beams in opticalsystem, Opt. Laser. Technol.18,259-267,1986.
67. S. Wang and D. Zhao. Matrix Optics, CHEP&Springer,2000.
68. J. W. Goodman. Introduction to Fourier optics. London. New York, John Willy&Sons,1974.
69. R. Martinez-Herrero, P. M. Mejias, M. Sanchez and J. L. H. Neira. Third-and fourth-orderparametric characterization of partially coherent beams propagation through ABCD optical systems.Opt. Quantum. Electron.24, S1021-S1026,1992.
70. M. J. Bastiaans. The Wigner distribution function applied to optical signals and systems. Opt.Commun.25,26-30,1978.
71. M. J. Bastiaans. Wigner distribution function and its application to first-order optics. J. Opt. Soc.Am.69,1710-1716,1979.
72. M. J. Bastiaans. The Wigner distributions function of partially coherent light. J. Mod. Opt.28,1215-1224,1981.
73. R. Simon and N. Mukunda. Twisted Gaussian Schell-model beams. J. Opt. Soc. Am. A,10,95-109,1993.
74. D. Ambrosini, V. Bagini, F. Gori and M. Santarsiero. Twisted Gaussian Schell-model beams, asuperposition model. J. Mod. Opt.41,1391-1399,1994.
75. R. Simon, A. T. Friberg and E. Wolf. Transfer of radiance by twisted Gaussian Schell-model beamsin paraxial systems. Pure Appl. Opt.5,331,1996.
76. R. Simon and N. Mukunda. Iwasawa decomposition in first-order optics, universal treatment ofshape-invariant propagation for coherent and partially coherent beams. J. Opt. Soc. Am. A,15,2146-2155,1998.
77. R. Simon and N. Mukunda. Optical phase space, Wigner representation, and invariant qualityparameters. J. Opt. Soc. Am. A,17,2440-2463,2000.
78. A. T. Friberg, E. Tervonen and J. Turunen. Interpretation and experimental decomposition oftwisted Gaussian Schell-model beams. J. Opt. Soc. Am. A,11,1818-1826,1994.
79. G. Nemes and A. E. Siegman. Measurement of all ten second-order moments of an astigmatic beamby the use of rotating simple astigmatic (anamorphic) optics. J. Opt. Soc. Am. A,11,2257-2264,1994.
80. M. J. Bastiaans. Wigner distribution function applied to twisted Gaussian light propagating infirst-order optical systems. J. Opt. Soc. Am. A17,2475-2480,2000.
81. G. Ding and B. Lu. Propagation of twisted Gaussian Schell-model beams through a misalignedfirst-order optical system. J. Mod. Opt.48,1617-1621,2001.
82. Y. Cai, Q. Lin and O. Korotkova. Ghost imaging with twisted Gaussian Schell-model beam. Opt.Express,17,2453-2464,2009.
83. C. Zhao, Y. Cai and O. Korotkova. Radiation force of scalar and electromagnetic twisted GaussianSchell-model beams. Opt. Express,17,21472-21487,2009.
84. F. Wang and Y. Cai. Second-order statistics of a twisted Gaussian Schell-model beam in turbulentatmosphere. Opt. Express,18,24661-24672,2010.
85. R. J. Fante. In Progress in optics, edited by E Wolf (Elsevier, Amsterdam), Vol XXII,343-398.1985.
86. D. F. V. James. Change of polarization of light beams on propagation in free space. J. Opt. Soc. Am.A,11,1641-1643,1994.
87. F. Gori. Matrix treatment for partially polarized, partially coherent beams. Opt. Lett.23,241-243,1998.
88. E. Wolf. Unified theory of coherence and polarization of random electromagnetic beams. Phy. Lett.A,312,263-267,2003.
89. E. Wolf. Correlation-induced changes in the degree of polarization, the degree of coherence and thespectrum of random electromagnetic beams on propagation. Opt. Lett.28,1078-1080,2003.
90. F. Gori, M Santarsiero, R Borghi and E. Wolf. Effects of coherence on the degree of polarization ina Young interference pattern. Opt. Lett.31,688-690,2006.
91. T. Shirai, O. Korotkova and E. Wolf. A method of generating electromagnetic GaussianSchell-model beams. J. Opt. A, Pure Appl. Opt.7,232-237,2003.
92. H. Roychowdhury and E. Wolf. Determination of the electric cross-spectral density matrix of arandom electromagnetic beam. Opt. Commun.226,57-60,2003.
93. E. Wolf. Polarization of a spatially fully coherent electromagnetic beam. J. Mod. Opt.51,757-759,2004.
94. O. Korotkova, M. Salem and E. Wolf. Beam conditions for radiation generated by anelectromagnetic Gaussian Schell-model source. Opt. Lett.29,1173-1175,2004.
95. T. Shirai and E. Wolf. Coherence and polarization of electromagnetic beams modulated by randomphase screens and their changes on propagation in free space. J. Opt. Soc. Am. A,21,1907-1916,2004.
96. Z. Chen and J. Pu. Propagation characteristics of aberrant stochastic electromagnetic beams in aturbulent atmosphere. J. Opt. A, Pure Appl. Opt.9,1123-1130,2007.
97. Y. Zhu, D. Zhao and X. Du. Propagation of stochastic Gaussian-Schell model array beams inturbulent atmosphere. Opt. Express,16,18437-18442,2008.
98. E. Shchepakina and O. Korotkova. Second-order statistics of stochastic electromagnetic beamspropagating through non-Kolmogorov turbulence. Opt. Express,18,10650-10658,2010.
99. S. Yu, Z. Chen, T. Wang, G. Wu, H. Guo and W. Gu. Beam wander of electromagneticGaussian-Schell model beams propagating in atmospheric turbulence. Appl. Opt.51,7581-7585,2012.
100. F. Gori. M. Santarsiero, G. Piquero, R. Borghi, A. Mondello and R. Simon. Partially polarizedGaussian Schell-model beams. J. Opt. A, Pure Appl. Opt.3,1-9,2001.
101. G. Piquero, R. Borghi and M. Santarsiero. Gaussian Schell-model beams propagating throughpolarization gratings. J. Opt. Soc. Am. A,18,1399-1405,2001.
102. T. Set l, M. Kaivola and A. T. Friberg. Degree of Polarization in Near Fields of Thermal Sources,Effects of Surface Waves. Phys. Rev. Lett.88,123902,2002.
103. O. Korotkova, M. Salem and E. Wolf. The far-zone behavior of the degree of polarization ofelectromagnetic beams propagating through atmospheric turbulence. Opt. Commun.233,225-230,2004.
104. O. Korotkova and E. Wolf. Changes in the state of polarization of a random electromagnetic beamon propagation. Opt. Commun.246,35-43,2005.
105. Y. Cai and O. Korotkova. Twist phase-induced polarization changes in electromagnetic GaussianSchell-model beams. Appl. Phys. B,96,499-507,2009.
106. L. Zhang, F. Wang Y. Cai and O. Korotkova. Degree of paraxiality of a stochastic electromagneticGaussian Schell-model beam. Opt. Commun.284,1111-1117,2011.
107. Y. Shen, L. Liu, C. Zhao, Y. Yuan and Y. Cai. Second-order moments of an electromagneticGaussian Schell-model beam in a uniaxial crystal. J. Opt. Soc. Am. A,31,238-245,2014.
108. L. C. Andrews, R. L. Phillips and C. Y. Hopen. Laser Beam Scintillation with Applications. SPIEPress, Washington,2001.
109. T. Shirai, A. Dogariu, and E. Wolf. Mode analysis of spreading of partially coherent beamspropagating through atmospheric turbulence. J. Opt. Soc. Am. A,20,1094-1102,2003.
110. H. T. Eyyubo lu and Y. Baykal. Reciprocity of Cos-Gaussian and Cosh-Gaussian laser beams inturbulent atmosphere. Opt. Express12,4659-4674,2004.
111. H. T. Eyyubo lu. Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere. Opt.Commun.245,37-47,2005.
112. A. Peleg and J. V. Moloney. Scintillation index for two Gaussian laser beams with differentwavelengths in weak atmospheric turbulence. J. Opt. Soc. Am. A,23,3114-3122,2006.
113. Y. Cai. Propagation of Various Flat-Topped Beams in a Turbulent Atmosphere. J. Opt. A: PureAppl. Opt.8,537-545,2006.
114. Y. Cai and S. He. Propagation of various dark hollow beams in a turbulent atmosphere. Opt.Express,14,1353-1367,2006.
115. Y. Dan. and B. Zhang. Beam propagation factor of partially coherent flat-topped beams in aturbulent atmosphere. Opt. Express,16,15563-15575,2008.
116. X. Ji and E. Zhang and B. Lü. Spectral properties of chirped Gaussian pulsed beams propagatingthrough the turbulent atmosphere. J. Mod. Opt.54,541-553,2007.
117. Y. Gu, O. Korotkova and G. Gbur. Scintillation of nonuniformly polarized beams in atmosphericturbulence. Opt. Lett.34,2261-2263,2009.
118. S. Zhu, Y. Cai and O. Korotkova. Propagation factor of a stochastic electromagnetic GaussianSchell-model beam. Opt. Express,18,12587-12598,2010.
119. S. Zhu and Y. Cai. M2-factor of a truncated electromagnetic Gaussian Schell-model beam. Appl.Phys. B,103,971-984,2011.
120. F. Wang, Y. Cai, Y. Dong and O. Korotkova. Experimental generation of a radially polarized beamwith controllable spatial coherence. Appl. Phys. Lett.100,04,1108,2012.
121. G. Wu and Y. Cai. Detection of a semi-rough target in turbulent atmosphere by a partially coherentbeam. Opt. Lett.36,1939-1942,2011.
122. Y. Gu and G. Gbur. Scintillation of nonuniformly correlated beams in atmospheric turbulence. Opt.Lett.38,1395-1397,2013.
123. G. Piquero, F. Gori, P. Romnini, M. Santarsiero, R. Borghi and A. Mondello. Synthesis of partiallypolarized Gaussian Schell-Model sources. Opt. Commun.208,9-16,2002.
124. F. Gori, M. Santarsiero, R. Borghi and V. Ramírez-Sánchez. Realizability condition forelectromagnetic Schell-model sources. J. Opt. Soc. Am. A,25,1016-1021,2008.
125. B. Kanseri and H. C. Kandpal. Experimental determination of electric cross-spectral density matrixand generalized Stokes parameters for a laser beam. Opt. Lett.33,2410-2412,2008.
126. F. Wang, G. Wu, X. Liu, S. Zhu and Y Cai. Experimental measurement of the beam parameters ofan electromagnetic Gaussian Schell-modelsource. Opt. Lett.36,2722-2724,2011.
127. S. Zhu and Y. Cai. M2-factor of a stochastic electromagnetic beam in a Gaussian cavity. Opt.Express,18,27567-27581,2010.
128. S. Zhu and Y. Cai. Spectral shift of a twisted electromagnetic Gaussian Schell-model beam focusedby a thin lens. Appl. Phys. B,99,317-323,2010.
129. S. Zhu, F Zhou, Y. Cai and L. Zhang. Thermal lens effect induced changes of polarization,coherence and spectrum of a stochastic electromagnetic beam in a Gaussian cavity. Appl. Phys. B,102,953-061,2010.
130. S. Zhu and Y. Cai. Degree of polarization of a twisted electromagnetic Gaussian Schell-modelbeam in a Gaussian cavity filled with gain media. Prog. Electromagn. Res. B,21,171-187,2010.
131. F. Zhou, S. Zhu and Y. Cai. Spectral shift of a partially coherent electromagnetic GaussianSchell-model beam propagating through tissue. J. Mod. Opt.58,38-44,2011.
132. F. Wang, S. Zhu, X. Hu and Y. Cai. Coincidence fractional Fourier transform with a stochasticelectromagnetic Gaussian Schell-model beam. Opt. Commun.284,5275-5280,2011.
133. S. Zhu, L. Liu, Y. Chen and Y. Cai. State of polarization and propagation factor of a stochasticelectromagnetic beam in a gradient-index fiber. J. Opt. Soc. Am. A,30,2306-2313,2013.
134. R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang and Y. Cai. Statistical properties of a Laguerre-GaussianSchell-model beam in turbulent atmosphere. Opt. Express,22,1871-1883,2014.
135. Y. Mushiake, K. Matzumurra and N. Nakajima. Generation of radially polarized optical beammode by laser oscillation. Proc. IEEE.60,1107-1109,1972.
136. A. V. Nesterov, V. G. Niziev and V. P. Yakunin. Generation of high-power radially polarized beam.J. Phys. D: Appl. Phys.32,2871,1999.
137. Y. Kozawa and S. Sato. Generation of a radially polarized laser beam by use of a conical Brewsterprism. Opt Lett.30,3063365,2005.
138. K. Yonezawa, Y. Kozawa and S. Sato. Geneartion of a radially polarized laser beam by use of thebirefringence of a c cut Nd:YVO4crystal. Opt. Lett.31,2151-2153.2006.
139. G Machavariani, Y. Lumer, I. Moshe, et al. Birefringence induced bifocusing forslection of radiallyor azimuthally polarized laser modes. Appl. Opt.46,3304-3310,2007.
140. S. C. Tidwell, D. H Ford, W. D. Kimura. Efficient radially polarized laser beam generation with adouble interferometer. Appl. Opt.32,5222-5229.1993.
141. A. V. Nesterov and V. G. Niziev. Laser beams with axially symmetric polarization. J. Phys. D: Appl.Phys.33,1-6,2006.
142. R. Dorn, S. Quabis and G. Leuchs. Sharper focus for a radially polarized light beam. Phys. Rev.Lett.91,233901,2003.
143. S Quabis, R Dorn, M Elberler, et al. Focusing light into a tighter spot. Opt. Commun.179,1-7,2000.
144. X. Li, T. H. Lan, C. H. Tien and M. Gu. Three-dimensional orientation-unlimited polarizationencryption by a single optically configured vectorial beam. Nat. Commun.3,998,2012.
145. P. Zijlstra, J. W. M. Chon and M Gu. Five-dimensional optical recording mediated by surfaceplasmons in gold nanorods. Nature,459,410-4132009.
146. Q. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt.Photonics,1,1-57,2009.
147. K. S. Youngworth and T. G. Brown. Focusing of high numerical aperture cylindrical-vector beams.Opt. Express,7,77-87,2000.
148. D. P. Biss and T. G. Brown. Cylindrical vector beam focusing through a dielectric interface. Opt.Express,9,490-497,2001.
149. Q. Zhan and J. R. Lege.r Focus shaping using cylindrical vector beams. Opt. Express,10,324-331,2002.
150. W. Chen and Q. Zhan. Three dimensional focus shaping with cylindrical vector beams. Opt.Commun.265,411-417,2006.
151. P. Wróbel, J. Pniewski, T. J. Antosiewicz and T. Szoplik. Focusing radially polarized light by aconcentrically corrugated silver film without a hole. Phys. Rev. Lett.102,183902,2009.
152. H. Wang, L. Shi, B. Lukyanchuk, C. J. R. Sheppard and C. T. Chong. Creation of a needle oflongitudinally polarized light in vacuum using binary optics. Nat. Photonics,2,501-505,2008.
153. W. Chen, D. C. Abeysinghe, R. L. Nelson and Q. Zhan. Plasmonic lens made of multipleconcentric metallic rings under radially polarized illumination. Nano Lett.9,4320-4325,2009.
154. Y. Dong, F. Wang, C. Zhao and Y. Cai. Effect of spatial coherence on propagation, tight focusing,and radiation forces of an azimuthally polarized beam. Phys. Rev. A,86,013840,2009.
155. Y. Dong, F. Feng, Y. Chen, C. Zhao, and Y. Cai. Statistical properties of a nonparaxial cylindricalvector partially coherent field in free space. Opt. Express,20,15908-15927,2012.
156. G. Wu, F. Wang, and Y. Cai. Coherence and polarization properties of a radially polarized beamwith variable spatial coherence. Opt. Express,20,28301-28318,2012.
157. F. Wang, X. Liu, L. Liu, Y. Yuan and Y. Cai. Experimental study of the scintillation index of aradially polarized beam with controllable spatial coherence. Appl. Phys. Lett.103,091102,2013.
158. Q. Zhan. Trapping metallic Rayleigh particles with radial polarization. Opt. Express,12,3377-3382,2004.
159. Y. Q. Zhao, Q. Zhan, Y. L. Zhang, et al. Creation of a three dimensional optical chain forcontrollable particle delivery. Opt. Lett.30,848-850,2005.
160. M. Meier, V. Romano and T. Feurer. Material processing with pulsed radially and azimuthallypolarized laser radiation. Appl. Phys. A,86,329-334,2007.
161. S. Zhu, X. Zhu, L. Liu, F. Wang and Y. Cai. Theoretical and experimental studies of the spectralchanges of a polychromatic partially coherent radially polarized beam. Opt. Express,21,27682-27696,2013.
162. X. Zhu, G. Wu, L. Liu, S. Zhu and Y. Cai. Statistical properties of a partially coherent radiallypolarized beam propagating through an astigmatic optical system. Opti. Commun.316,132-139,2014.
1. S. Wang and D. Zhao, Matrix Optics, CHEP&Springer,2000.
2. H. Kogelnik and T. Li. Laser Beams and Resonators. Appl. Opt.5,1550,1966.
3. A. Gerrard and J. M. Burch. Introduction to Matrix Methods in Optics (Wiley, London),119-122,1975.
4. S. A. Collins. lens-systems diffraction integral written in terms of matrix optics. J. Opt. Soc. Am.60,1168-1177,1970.
5.王仕璠，朱自强，现代光学原理，电子科技大学出版社1998.
6. M. Born and E. Wolf. Principles of Optics. Pergamon,1980.
7. E. Wigner. On the quantum correction for thermodynamic equilibrium. Phys Rev.40,749-759,1932.
8. M. J. Bastiaans. The Wigner distribution function of partially coherent light. Optical Acta,28,1215,1981.
9. Z. I. Feizulin and Y. A. Kravtsov. Broadening of a laser beam in a turbulent medium. Radiophys.Quantum Electron.10,33-35,1967.
10. C. Y. Young, Y. V. Gilchrest and B. R. Macon. Turbulence-induced beam spreading of higher-ordermode optical waves. Opt. Eng.41,1097-1103,2002.
11. T. Shirai, A. Dogariu and E. Wolf. Mode analysis of spreading of partially coherent beamspropagating through turbulent atmosphere. J. Opt. Soc. Am.20,1094-1102,2003.
12. J. C. Leader, Atmospheric propagation of partially coherent radiation. J. Opt. Soc. Am.68,175-185,1978.
13. S. C. H. Wang and M. A. Plonus. Optical beam propagation for a partially coherent source in theturbulent atmosphere. J. Opt. Soc. Am.69,1297-1304,1979.
14. T. Shirai, A. Dogariu, and E. Wolf. Mode analysis of spreading of partially coherent beamspropagating through atmospheric turbulence. J. Opt. Soc. Am. A20,1094-1102,2003.
15. H. T. Eyyubo lu and Y. Baykal. Reciprocity of Cos-Gaussian and Cosh-Gaussian laser beams inturbulent atmosphere. Opt. Express,12,4659-4674,2004.
16. Y. Cai and S. He. Propagation of a partially coherent twisted anisotropic Gaussian Schell-modelbeam in a turbulent atmosphere. Appl. Phys. Lett.89,041117,2006.
17. Y. Cai, S. He. Propagation of various dark hollow beams in a turbulent atmosphere, Opt. Express,14,1353-1367,2006.
18. Y. Baykal, H. T. Eyyubo lu. Scintillation characteristics of cosh-Gaussian beams. Appl. Opt.46,1099-1106,2007.
19. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyubo lu and Y. Baykal. M2-factor of coherent and partiallycoherent dark hollow beams propagating in turbulent atmosphere. Opt. Express,17,17344-17356,2009.
20. S. Zhu, Y. Cai and O. Korotkova. Propagation factor of a stochastic electromagnetic GaussianSchell-model Beam. Opt. Express,18,12587-12598,2010.
21. A. E. Siegman. New developments in laser resonators, SPIE,1224,2-14,1990.
22. R. Martinez-Herrero, P. M. Mejias and M. Arias. Parametric characterization of coherent,lowest-order Gaussian beams propagating through hard-edge apertures, Opt. Lett.20,124-126,1995.
23. C. Pare, P. A. Belanger. Propagation analysis of the truncated second-order moment. Proc. SPIE.104-111,1996.
24. S. Amarande, A. Giesen and H. Hugel. Propagation analysis of self-convergent beam width andcharacterization of hard-edge diffracted beams. Appl. Opt.39,3914-3924,2000.
25. L. Mandel and E. Wolf. Optical coherence and Quantum Optics. Cambridge University Press,1995.
26. A. T. Friberg and J. Turunen. Imaging of Gaussian Schell-model sources. J. Opt. Soc. Am. A,5,713-719,1988.
27. E. Wolf. Unified theory of coherence and polarization of random electromagnetic beams. Phy. Lett.A,312,263-267,2003.
28. Y. Cai, O. Korotkova, H. T. Eyyuboglu and Y. Baykal. Active laser radar systems with stochasticelectromagnetic beams in turbulent atmosphere. Opt. Express,16,15835-15846,2008.
29. Z. Tong, O. Korotkova, Y. Cai, H. T. Eyyuboglu and Y. Baykal. Correlation properties of randomelectromagnetic beams in laser resonators. Appl. Phys. B,97,849-857,2009.
30. O. Korotkova, Y. Cai, E. Watson. Stochastic electromagnetic beams for LIDAR systems operatingthrough turbulent atmosphere. Appl. Phys. B,94,681-690,2009.
31. C. Zhao, Y. Cai and O. Korotkova. Radiation force of scalar and electromagnetic twisted GaussianSchell-model beams. Opt. Express,17,21472-21487,2009.
32. S. Zhu and Y. Cai. M2-factor of a stochastic electromagnetic beam in a Gaussian cavity. Opt.Express,18,27567-27581,2010.
33. H. M. Ozaktas, Z. Zalevsky and M. A. Kutay. The fractional Fourier transform with applications inoptics and signal processing. New York: Wiley,88-92,2001.
34. T. Alieva, M. J. Bastiaans and M. L. Calvo. Fractional transforms in optical information processing.EURASIPJ. Appl. Signal Process,1498-1519,2005.
35. D. Mendlovic and H. M. Ozaktas. Fractional Fourier transforms and their optical implementation: I.J. Opt. Soc. Am. A,10,1875-1881,1993.
36. H. M. Ozaktas and D. Mendlovic. Fractional Fourier transforms and their optical implementation:II, J. Opt. Soc. Am. A,10,2522-2531,1993.
37. A. W. Lohmann. Image rotation, Wigner rotation, and the fractional Fourier transform. J. Opt. Soc.Am. A,10,2181-2186,1993.
38. D. Mendlovic, H. M. Ozaktas and A. W. Lohmann. Graded index fibers, Wigner-distributionfunctions, and the fractional Fourier transforms. Appl. Opt.33,6188-6193,1994.
1. M. Born and E. Wolf. Principles of Optics. Pergamon,1980.
2. E. Wolf. Invariance of the spectrum of light on propagation. Phys. Rev. Lett.56,1370-1372,1986.
3. L. Mandel and E. Wolf. Optical coherence and Quantum Optics. Cambridge University Press,1995.
4. Z. Mei and O. Korotkova. Random sources generating ring-shaped beams. Opt. Lett.38,91-93,2013.
5. F. Wang, X. Liu, Y. Yuan and Y. Cai. Experimental generation of partially coherent beams withdifferent complex degrees of coherence. Opt. Lett.38,1814-1816,2013.
6. Y. Chen, F. Wang, L. Liu, C. Zhao and Y. Cai. Generation and propagation of a partially coherentvector beam with special correlation functions. Phys. Rev. A,89,013801,2014.
7. E. Collett and E. Wolf. Is complete spatial coherence necessary for the generation of highlydirectional light beams? Opt. Lett.2,27-29,1978.
8. J. T. Foley and M. S. Zubairy. The directionality of Gaussian Schell-model beams. Opt. Commun.26,297-300,1978.
9. A. T. Friberg and J. Turunen. Imaging of Gaussian Schell-model sources. J. Opt. Soc. Am. A,5,713-720,1988.
10. J. Wu. Propagation of a Gaussian-Schell beam through turbulent media. J. Mod. Opt.37,671-684,1990.
11. Y. Li and E. Wolf. Radiation from anisotropic Gaussian Schell-model sources. Opt. Lett.7,256-258,1982.
12. F. Gori. Mode propagation of the field generated by Collett-Wolf Schell-model sources. Opt.Commun.46,149-154,1983.
13. R. Simon, E. C. G. Sudarshan and N. Mukunda. Anisotropic Gaussian Schell-model beams,Passage through optical systems and associated invariants. Phys. Rev. A,31,2419-2434,1985.
14. M. Santarsiero, F. Gori and R. Borghi. Spreading properties of beams radiated by partially coherentSchell-model sources. J. Opt. Soc. Am. A,16,106-112,1999.
15. Y. Cai, Q. Lin and D. Ge. Propagation of partially coherent twisted anisotropic GaussianSchell-model beams in dispersive and absorbing media. J. Opt. Soc. Am. A,19,2036-2042,2002.
16. Y. Cai and S. He. Propagation of a partially coherent twisted anisotropic Gaussian Schell-modelbeam in a turbulent atmosphere. Appl. Phys. Lett.89,041117,2006.
17. M. Yao, Y. Cai and H. T. Eyyuboglu. Evolution of the degree of polarization of an electromagneticGaussian Schell-model beam in a Gaussian cavity. Opt. Lett.33,2266-2268,2008.
18. A. T. Friberg, E. Tervonen and J. Turunen. Interpretation and experimental decomposition oftwisted Gaussian Schell-model beams. J. Opt. Soc. Am. A,11,1818-1826,1994.
19. G. Nemes and A. E. Siegman. Measurement of all ten second-order moments of an astigmatic beamby the use of rotating simple astigmatic (anamorphic) optics. J. Opt. Soc. Am. A,11,2257-2264,1994.
20. F. Wang and Y. Cai. Experimental generation of a partially coherent flat-topped beam. Opt. Lett.33,1795-1797,2008.
21. M. J. Bastiaans. Wigner distribution function applied to twisted Gaussian light propagating infirst-order optical systems. J. Opt. Soc. Am. A,17,2475-2480,2000.
22. Q. Lin and Y. Cai. Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schellmodel beams. Opt. Lett.27,216-218,2002.
23. S. Zhu, Y. Chen and Y. Cai. Experimental determination of the radius of curvature of an isotropicGaussian Schell-model beam. J. Opt. Soc. Am. A,30,887-891,2013.
24. F. Wang, S. Zhu and Y. Cai. Experimental study of the focusing properties of a GaussianSchell-model vortex beam. Opt. Lett.36,3281-3283,2011.
25. S. Zhu, C. Zhao, Y. Chen and Y. Cai. Experimental generation of a polychromatic partiallycoherent dark hollow beam. Optik,124,5271-5273,2013.
26. Y. Cai and S. Zhu. Orbital angular moment of a partially coherent beam propagating through anastigmatic ABCD optical system with loss or gain. Opt. Lett.39,1968-1971,2014.
27. E. Wolf and E. Collett. Partially coherent sources which produce same far-field intensitydistribution as a laser. Opt. Commun.25,293-296,1978.
28. X. Ji and X. Li. Effective radius of curvature of partially coherent Hermite–Gaussian beamspropagating through atmospheric turbulence. J. Opt.12,035403,2010.
29. G. Gbur and T. D. Visser. Coherence vortices in partially coherent beams. Opt. Commun.222,117-125,2003.
30. J. Serna and J. M. Movilla. Orbital angular momentum of partially coherent beams. Opt. Lett.26,405-407,2001.
31. F. Gori, G. Guattari and C. Padovani. Bessel-Gauss beams. Opt. Commun.64,491-495,1987.
32. Y. Cai, X. Lu and Q. Lin. Hollow Gaussian beams and their propagation properties, Opt. Lett.28,1084-1086,2003.
33. Q. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt.Photonics,1,1-57,2009.
34. J. Yin, W. Gao and Y. Zhu. Generation of dark hollow beams and their applications. in: E. Wolf(Ed.). Progress in Optics,44.119-204,2003.
35. I. Manek, Y. B. Ovehinnikov and R. Grimm. Generation of a hollow laser beam for atom trappingusing an axicon. Opt. Commun.147,67-70,1998.
36. C. Zhao, Y. Cai, F. Wang, X. Lu and Y. Wang. Generation of a high-quality partially coherent darkhollow beam with a multimode fiber. Opt. Lett.33,1389-1391,2008.
37. C. Zhao, Y. Cai, X. Lu and H. T. Eyyubo lu. Radiation force of coherent and partially coherentflat-topped beams on a Rayleigh particle. Opt. Express,17,1753-765,2009.
38. S. A. Amarande. Beam propagation factor and the kurtosis parameter of flattened Gaussian beams.Opt. Commun.129,311-317,1996.
39. P. Zhou, Z. Liu, X. Xu and X. Chu. Propagation of coherently combined flattened laser beam arrayin turbulent atmosphere. Opt. Laser Tech.41,403-407,2009.
40. F. Gori. Flattened gaussian beams. Opt. Commun.107,335-341,1994.
41. R. Borghi and M. Santarsiero. Modal decomposition of partially coherent flat-topped beamsproduced by multimode lasers. Opt. Lett.23,313-315,1998.
42. Y. Li. Light beams with flat-topped profiles. Opt. Lett.27,1007-1009,2003.
43. Y. Cai. Propagation of various flat-topped beams in a turbulent atmosphere. J. Opt. A: Pure Appl.Opt.8,537,2006.
44. F. Wang and Y. Cai. Experimental generation of a partially coherent flat-topped beam. Opt. Lett.33,1795-1797,2008.
45. E. Wolf. Invariance of the spectrum of light on propagation. Phys. Rev. Lett.56,1370-1372,1986.
46. H. C. Kandpal, A. Wasan, J. S. Vaishya, E. S. R. Gopal, M. Singh, B. B. Sanwal and R. Sagar.Application of spatial coherence spectroscopy for determining the angular diameters of stars.feasibility experiment. Indian J. Pure Appl. Phys.36,665-674,1998.
1. E. Wolf. Introduction to the Theory of Coherence and Polarization of Light. Cambridge U. Press,2007.
2. D. F. V. James. Change of polarization of light beams on propagation in free space. J. Opt. Soc. Am.A,11,1641-1643,1994.
3. F. Gori. Matrix treatment for partially polarized, partially coherent beams. Opt. Lett.23,241-243,1998.
4. T. Set l, M. Kaivola and A. T. Friberg. Degree of polarization in near fields of thermal sources,effects of surface waves. Phys. Rev. Lett.88,123902,2002.
5. E. Wolf. Unified theory of coherence and polarization of random electromagnetic beams. Phy. Lett.A,312,263-267,2003.
6. E. Wolf. Correlation-induced changes in the degree of polarization, the degree of coherence and thespectrum of random electromagnetic beams on propagation. Opt. Lett.28,1078-1080,2003.
7. O. Korotkova and E. Wolf. Changes in the state of polarization of a random electromagnetic beamon propagation. Opt. Commun.246,35-43,2005.
8. M. Yao, Y. Cai and H. T. Eyyuboglu. Evolution of the degree of polarization of an electromagneticGaussian Schell-model beam in a Gaussian cavity. Opt. Lett.33,2266-2268,2008.
9. S. Zhu, Y. Cai and O. Korotkova. Propagation factor of a stochastic electromagnetic GaussianSchell-model beam. Opt. Express,18,12587-12598,2010.
10. M. Lahiri and E. Wolf. Theory of refraction and reflection with partially coherent electromagneticbeams. Phys. Rev. A,86,43815,2012.
11. R. Dorn, S. Quabis and G. Leuchs. Sharper focus for a radially polarized light beam. Phys. Rev.Lett.91,233901,2003.
12. Q. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt.Photonics,1,1-57,2009.
13. F. Wang, X. Liu, L. Liu, Y. Yuan and Y. Cai. Experimental study of the scintillation index of aradially polarized beam with controllable spatial coherence. Appl. Phys. Lett.103,091102,2013.
14. F. Wang, Y. Cai, Y. Dong and O. Korotkova. Experimental generation of a radially polarized beamwith controllable spatial coherence. Appl. Phys. Lett.100,051108,2012.
15. Q. Lin and Y. Cai. Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schellmodel beams. Opt. Lett.27,216-218,2002.
16. B. Kanseri, S. Rath and H. C. Kandpal. Determination of the beam coherence-polarization matrixof a random electromagnetic beam. IEEE J. Quantum Electron.45,1163-1167,2009.
17. H. C. Kandpal, A. Wasan, J. S. Vaishya, E. S. R. Gopal, M. Singh, B. B. Sanwal and R. Sagar.Application of spatial coherence spectroscopy for determining the angular diameters of stars:feasibility experiment. Indian J. Pure Appl. Phys.36,665-674,1998.
18. Y. Cai, Q. Lin and D. Ge. Propagation of partially coherent twisted anisotropic GaussianSchell-model beams in dispersive and absorbing media. J. Opt. Soc. Am. A,19,2036-2042,2002.
19. B. K. Yadav and H. C. Kandpal. Spectral anomalies of polychromatic DHGB and its applicationsin FSO. J. Lightwave Technol.29,960-966,2011.
20. D. Mendlovic and H. M. Ozaktas, Fractional Fourier transforms and their optical implementation: I.J. Opt. Soc. Am. A,10,1875-1881,1993.
21. H. M. Ozaktas and D. Mendlovic. Fractional Fourier transforms and their optical implementation:II, J. Opt. Soc. Am. A,10,2522-2531,1993.
22. A. W. Lohmann. Image rotation, Wigner rotation, and the fractional Fourier transform. J. Opt. Soc.Am. A,10,2181-2186,1993.
23. D. Mendlovic, H. M. Ozaktas and A. W. Lohmann. Graded index fibers, Wigner-distributionfunctions, and the fractional Fourier transforms. Appl. Opt.33,6188-6193,1994.
24. H. M. Ozaktas, Z. Zalevsky and M. A. Kutay. The fractional Fourier transform with applications inoptics and signal processing. New York: Wiley,88-92,2001.
25. T. Alieva, M. J. Bastiaans, M. L. Calvo. Fractional transforms in optical information processing.EURASIPJ. Appl. Signal Process,1498,2005.
26. Y. Cai and S. Zhu. Coincidence fractional Fourier transform implemented with partially coherentlight radiation. J. Opt. Soc. Am. A,22,1798-1804,2005.
27. Y. Cai. Propagation of various flat-topped beams in a turbulent atmosphere. J. Opt. A: Pure Appl.Opt.8,537,2006.
28. P. Zijlstra, J. W. M. Chon and M Gu. Five-dimensional optical recording mediated by surfaceplasmons in gold nanorods. Nature,459,410-413,2009.
29. W. Gao. Changes of polarization of light beams on propagation through tissue. Opt. Commun.260,749-754,2006.
30. M. J. Schmitt and G. Kumar. Turbulent nature of refractive-index variations in biological tissue.Opt. Lett.21,1310-1312,1996.
31. G. P. Agrawal, A. K. Ghatak and C. L. Mehta. Propagation of partially coherent beam throughSelfoc fibers. Opt. Commun.12,333-337,1974.
32. G. P. Agarwal. Fiber-Optic Communication Systems,3rd ed. Wiley,2002.
33. A. Gamliel and G. P. Agrawal. Wolf effect in homogenous and inhomogenous media. J. Opt. Soc.Am. A,7,2184-2192.1990.
34. H. Roychowdhury, G. P. Agarwal and E. Wolf. Changes in the spectrum, in the spectral degree ofpolarization, and in the spectral degree of coherence of a partially coherent beam propagatingthrough a gradient-index fiber. J. Opt. Soc. Am. A,23,940-948,2006.
35. C. Zhao, Y. Cai, F. Wang, X. Lu and Y. Wang. Generation of a high-quality partially coherent darkhollow beam with a multimode fiber. Opt. Lett.33,1389-1391,2008.
36. S. Zhu, C. Zhao, Y. Chen, and Y. Cai. Experimental generation of a polychromatic partiallycoherent dark hollow beam. Optik,124,5271-5273.2013.
37. O. Korotkova and E. Wolf. Changes in the state of polarization of a random electromagnetic beamon propagation. Opt. Commun.246,35-43,2005.
38. E. Siegman. New developments in laser resonators. Proc. SPIE1224,2-14,1990.
39. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti and P. Vahimaa. Spreading properties of beamsradiated by partially coherent Schell-model sources. J. Opt. Soc. Am. A16,106-112,1999.
40. J. Serna, R. Martinez-Herrero and P. M. Mejfas. Parametric characterization of general partiallycoherent beams propagating through ABCD optical systems. J. Opt. Soc. Am. A,8,1094-1098,1991.
1. S. De Silvestri, V. Magni, O Svelto, et. al. Lasers with super-Gaussian mirrors. IEEE J. QuantumElectron.26,1500-1509,1990.
2. P. A. Belanger, R. L. Lachance and C. Pare. Super-Gaussian output from a CO2laser by using agraded-phase mirror resonator. Opt. Lett.17,739-741,1992.
3. Y. Mushiake, K. Matzumurra and N. Nakajima. Generation of radially polarized optical beammode by laser oscillation. Proc. IEEE60,1107-1109,1972.
4. M. Yao, Y Cai and H. T. Eyyuboglu. Evolution of the degree of polarization of an electromagneticGaussian Schell-model beam in a Gaussian cavity. Opt. Lett.33,2266-2268,2008.
5. Z. Tong, O. Korotkova, Y. Cai, H. T. Eyyuboglu and Y. Baykal. Correlation properties of randomelectromagnetic beams in laser resonators. Appl. Phys. B,97,849-857,2009.
6. A. G. Fox and T. Li. Resonate modes in a maser interferometer. Bell Syst. Tech. J.40,453-488,1961.
7. E. Wolf. Spatial coherence of resonant modes in a maser interferometer. Phys. Lett.,3,166-168,1963.
8. E. Wolf and G. S. Agarwal. Coherence theory of laser resonator Modes. J. Opt. Soc. Am. A,1,541-546,1984.
9. F. Gori. Propagation of the mutual intensity through a periodic structure Atti Fond. Giorgio Ronchi,35,434-447,1980.
10. P. Desantis, A. Mascello, C. Palma and M. R. Perrone. Coherence growth of laser radiation inGaussian cavities. IEEE J. Quantum Electron.32,802-812,1996.
11. C. Palma, G. Cardone and G. Cincotti. Spectral changes in Gaussian-cavity lasers. IEEE J.Quantum Electron.34,1082-1088,1998.
12. E. Wolf. Unified theory of coherence and polarization of random electromagnetic beams. Phy. Lett.A,312,263-267,2003.
13. H. Roychowdhury and E. Wolf. Determination of the electric cross-spectral density matrix of arandom electromagnetic beam. Opt. Commun.226,57-60,2003.
14. S. Zhu, Y. Cai and O. Korotkova. Propagation factor of a stochastic electromagnetic GaussianSchell-model beam. Opt. Express,18,12587-12598,2010.
15. F. Wang, G. Wu, X. Liu, S. Zhu and Y. Cai. Experimental measurement of the beam parameters ofan electromagnetic Gaussian Schell-modelsource. Opt. Lett.36,2722-2724,2011.
16. S. Zhu, F. Zhou, Y. Cai and L. Zhang. Thermal lens effect induced changes of polarization,coherence and spectrum of a stochastic electromagnetic beam in a Gaussian cavity. Appl. Phys. B,102,953-961,2011.
17. S. Zhu and Y. Cai. Degree of polarization of a twisted electromagnetic Gaussian Schell-modelbeam in a Gaussian cavity filled with gain media. Prog. Electromagn. Res. B,21,171-187,2010.
18. S. Zhu and Y. Cai. M2-factor of a stochastic electromagnetic beam in a Gaussian cavity. Opt.Express,18,27567-27581,2010.
19. J. P. Gordon, R. C. C. Leite, R. S. Moore, et. al. Long-transient effects in lasers with inserted liquidsamples, J. Appl. Phys.36,3-8,1965.
20. J. Stone. Measurements of the absorption of light in low-loss liquids. J. Opt. Soc. Am.62,327-333,1972.
21. C. Hu and J. R. Whinnery. New thermooptical measurement method and a comparison with othermethods. Appl. Opt.12,72-79,1973.
22. S. J. Sheldon, L. V. Knight, and J. M. Thorne. Laser-induced thermal lens effect, a new theoreticalmodel. Appl. Opt.21,1663-1669,1982.
23. T. Xu and S. Wang. Propagation of Ince-Gaussian beams in a thermal lens medium. Opt. Commun.265,1-5,2006.
24. Z. Tong and O. Korotkova. Stochastic electromagnetic beams in positive-and negative-phasematerials. Opt. Lett.35,175-177,2010.
25. J. Deschamps, D. Courjon and J. Bulabois. Gaussian Schell-model sources,an example and someperspectives. J. Opt. Soc. Am.73,256-261,1983
26. R. Simon, E. C. G. Sudarshan, and N. Mukunda. Anisotropic Gaussian Schell-model beams,passage through optical systems and associated invariants. Phys. Rev. A,31,2419-2434,1985.
27. A. T. Friberg and J. Turnnen. Algebraic and graphical propagation methods for Gaussian Schell-model beams. Opt. Eng.25,857-864,1986
28. Q. Lin and Y. Cai. Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schellmodel beams. Opt. Lett.27,216-218,2002.
29. F. Gori, M. Santarsiero and A. Sona. The change of width for a partially coherent beam on paraxialpropagation. Opt. Commun.82,197-203,1991.
30. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti and P. Vahimaa. Spreading properties of beamsradiated by partially coherent Schell-model sources. J. Opt. Soc. Am. A,16,106-112,1999.
31. E. Siegman. New developments in laser resonators. Proc. SPIE1224,2-14,1990.
32. M. J. Bastiaans. Application of the Wigner distribution function to partially coherent light. J. Opt.Soc. Am. A3,1227-1239,1986.
33. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti and P. Vahimaa. Spreading properties of beamsradiated by partially coherent Schell-model sources. J. Opt. Soc. Am. A16,106-112,1999.
34. J. Serna, R. Martinez-Herrero and P. M. Mejfas. Parametric characterization of general partiallycoherent beams propagating through ABCD optical systems. J. Opt. Soc. Am. A,8,1094-1098,1991.
35. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyubo lu, Y. Baykal and O. Korotkova. M2-factor of coherent andpartially coherent dark hollow beams propagating in turbulent atmosphere. Opt. Express,17,17344-17356,2009.
36. F. Wang and Y. Cai. Second-order statistics of a twisted Gaussian Schell-model beam in turbulentatmosphere. Opt. Express,18,24661-24672,2010.
1. L. C. Andrews and R. L. Phillips. Laser beam propagation through random media. SPIE Press,2005.
2.饶瑞中，光在湍流大气中的传播，安徽科学技术出版社，第一版，2005.
3.张逸新，迟泽英，光波在大气中的传输与成像，国防工业出版社，第一版，1997.
4. V. I. T atarskii. The effect of the turbulent atmosphere on wave propagation. IPST Catalog5391,1971.
5. R. J. Hill. Modified spectrum of atmospheric fluctuation and its application to optical propagation,J. Opt. Soc. Am.68,892-905,1978.
6. G. R. Ochs and R. J. Hill. Optical-scintillation method of measuring turbulence inner scale. Appl.Opt.24,2430-2432,1985.
7. J. C. Ricklin and F. M. Davidson. Atmospheric turbulence effects on a partially coherent Gaussianbeam, implications for free-space laser communication. J. Opt. Soc. Am. A,19,1794-1802,2002.
8. Y. Cai and S. Zhu. Ghost interference with partially coherent radiation. Opt. Lett.29,2716-2718,2004.
9. P. Zhou, Z. Liu X. Xu and X. Chu. Propagation of coherently combined flattened laser beam arrayin turbulent atmosphere. Opt. Laser, Tech.41,403-407,2009.
10. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyubo lu, Y. Baykal and O. Korotkova. M2-factor of coherent andpartially coherent dark hollow beams propagating in turbulent atmosphere, Opt. Express,20,17344-17356,2009.
11. S. Zhu, Y. Cai and O. Korotkova. Propagation factor of a stochastic electromagnetic GaussianSchell-model beam. Opt. Express,18,12587-12598,2010.
12. A. N. Kolmogorov. The local structure of turbulence in an incompressible viscous fluid for verylarge Reynolds numbers. C.R.(Doki) Acad. Sci. U.S.S.R.30,301-305,1941.
13. V. I. Tatarski. Wave propagation in a random medium. New York, McGraw-Hill Book Company,142-165,1961.
14. Y. Cai and S. He. Propagation of a partially coherent twisted anisotropic Gaussian Schell-modelbeam in a turbulent atmosphere. Appl. Phys. Lett.89,04,1117,2006.
15. Y. Cai, O. Korotkova, H. T. Eyyuboglu and Y. Baykal. Active laser radar systems with stochasticelectromagnetic beams in turbulent atmosphere. Opt. Express,6,15834-15846,2008.
16. H. T. Yura and S. G. Hanson. Optical beam wave propagation through complex optical systems. J.Opt. Soc. Am.4,1931-1948,1987.
17. Y. Yuan, Y. Cai, H. T. Eyyuboglu, Y. Baykal and J. Chen. Propagation factor of partially coherentflat-topped beam array in free space and turbulent atmosphere. Opt. Laser Eng.50,752-759,2012
18. S. Du, Y. Yuan, C. Liang and Y. Cai. Second-order moments of a multi-Gaussian Schell-modelbeam in a turbulent atmosphere. Opt. Laser Tech.50,14-19,2013.
19. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti and P. Vahimaa. Spreading properties of beamsradiated by partially coherent Schell-model sources. J. Opt. Soc. Am. A,16,106-112,1999.
20. Y. Li. Dependence of the focal shift on Fresnel number and f number. J. Opt. Soc. Am.72,770-774,1982.
21. X. Liu and J. Pu. Focal shift and focal switch of partially coherent light in dual-focus systems. Opt.Commun.252,262-267,2005.
22. F. Wang, Y. Cai and O. Korotkova. Experimental observation of focal shifts in focused partiallycoherent beams. Opt. Commun.282,3408-2412,2009.
23. J. Pu, H. Zhang and S. Nemoto. Spectral shifts and spectral switches of partially coherent lightpassing through an aperture. Opt. Commun.162,57-63,1999.
24. J. J. Wen and M. A. Breazeale. A diffraction beam field expressed as the superposition of Gaussianbeams. J. Acoust. Soc. Am.83,1752-1756,1988.
25. Y. Cai and L. Hu. Propagation of partially coherent twisted anisotropic Gaussian Schell-modelbeams through an apertured astigmatic optical system. Opt. Lett.31,685-687,2006.
26. F. Wang, Y. Cai and Q. Lin. Experimental observation of truncated fractional Fourier transform fora partially coherent Gaussian Schell-model beam. J. Opt. Soc. Am. A,25,2001-2010,2008.
1. R. Dorn, S. Quabis and G. Leuchs. Sharper focus for a radially polarized light beam. Phys. Rev.Lett.91,233901,2003.
2. Q. Zhan. Trapping metallic Rayleigh particles with radial polarization. Opt. Express,12,3377-3382,2004.
3. W. Chen, D. C. Abeysinghe, R. L. Nelson and Q. Zhan. Plasmonic lens made of multipleconcentric metallic rings under radially polarized illumination. Nano Lett.9,4320-4325,2009.
4. P. Zijlstra, J. W. M. Chon and M. Gu. Five-dimensional optical recording mediated by surfaceplasmons in gold nanorods. Nature,459,410-4132009.
5. X. Li, T. H. Lan, C. H. Tien and M. Gu. Three-dimensional orientation-unlimited polarizationencryption by a single optically configured vectorial beam. Nat. Commun.3,998,2012.
6. Y. Mushiake, K. Matzumurra and N. Nakajima. Generation of radially polarized optical beammode by laser oscillation. Proc. IEEE60,1107-1109,1972.
7. A. V. Nesterov, V. G. Niziev and V. P. Yakunin. Generation of high-power radially polarized beam.J. Phys. D: Appl. Phys.32,2871,1999.
8. Y. Kozawa and S. Sato. Generation of a radially polarized laser beam by use of a conical Brewsterprism. Opt Lett.30,3063-3065,2005.
9. K. Yonezawa, Y. Kozawa and S. Sato. Geneartion of a radially polarized laser beam by use of thebirefringence of a c cut Nd:YVO4crystal. Opt. Lett.31,2151-2153.2006.
10. G Machavariani, Y. Lumer, I. Moshe, et al. Birefringence induced bifocusing forslection of radiallyor azimuthally polarized laser modes. Appl. Opt.46,3304-3310,2007.
11. S. C. Tidwell, D. H Ford and W. D. Kimura. Efficient radially polarized laser beam generation witha double interferometer. Appl. Opt.32,5222-5229.1993.
12. A. V. Nesterov and V. G. Niziev. Laser beams with axially symmetric polarization. J. Phys. D: Appl.Phys.33,1-6,2006.
13. F. Wang, Y. Cai, Y. Dong and O. Korotkova. Experimental generation of a radially polarized beamwith controllable spatial coherence. Appl. Phys. Lett.100,041108,2012.
14. Q. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt.Photonics,1,1-57,2009.
15. S. Quabis, R Dorn, M Elberler, et al. Focusing light into a tighter spot. Opt. Commun.179,1-7,2000.
16. Y. Cai, Q. Lin, H. T. Eyyuboglu and Y. Baykal. Average irradiance and polarization properties of aradially or azimuthally polarized beam in a turbulent atmosphere. Opt. Express,16,7665-7673,2008.
17. Y. Gu, O. Korotkova and G. Gbur. Scintillation of nonuniformly polarized beams in atmosphericturbulence. Opt Lett.34,2261-2263,2009.
18. W. Cheng, J. W. Haus and Q. Zhan. Propagation of vector vortex beams through a turbulentatmosphere. Opt. Express,17,17829-17836,2009.
19. F. Wang, X. Liu, L. Liu, Y. Yuan and Y. Cai. Experimental study of the scintillation index of aradially polarized beam with controllable spatial coherence. Appl. Phys. Lett.103,091102,2013.
20. Y. Dong, F. Wang, C. Zhao and Y. Cai. Effect of spatial coherence on propagation, tight focusing,and radiation forces of an azimuthally polarized beam. Phys. Rev. A,86,013840,2009.
21. Y. Zhang, B. Ding and T. Suyama. Trapping two types of particles using a double-ring-shapedradially polarized beam. Phys. Rev. A,81,023831,2010.
22. Y. Dong, F. Feng, Y. Chen, C. Zhao, and Y. Cai. Statistical properties of a nonparaxial cylindricalvector partially coherent field in free space. Opt. Express,20,15908-15927,2012.
23. G. Wu, F. Wang and Y. Cai. Coherence and polarization properties of a radially polarized beamwith variable spatial coherence. Opt. Express,20,28301-28318,2012.
24. L. Huang, H. Guo, J. Li, L. Ling, B. Feng and Z. Li. Optical trapping of gold nanoparticles bycylindrical vector beam. Opt. Lett.37,1694-1696.2012.
25. R. Chen, Y. Dong, F. Wang and Y. Cai. Statistical properties of a cylindrical vector partiallycoherent beam in turbulent atmosphere. Appl. Phys. B,112,247-259,2013.
26. S. Zhu, X. Zhu, L. Liu, F. Wang and Y. Cai. Theoretical and experimental studies of the spectralchanges of a polychromatic partially coherent radially polarized beam. Opt. Express,21,27682-27696,2013.
27. X. Zhu, G. Wu, L. Liu, S. Zhu and Y. Cai. Statistical properties of a partially coherent radiallypolarized beam propagating through an astigmatic optical system. Opt. Commun.316,132-139,2014.
28. Q. Lin and Y. Cai. Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schellmodel beams. Opt. Lett.27,216-218,2002.
29. C. Palma, G. Cincotti and G. Guattari. Spectral shift of a Gaussian Schell-model beam beyond athin lens. IEEE J. Quantum Electron.34,378-383,1998.
30. H. Mashaal, A. Goldstein, D. Feuermann and J. M. Gordon. First direct measurement of the spatialcoherence of sunlight. Opt. Lett.37,3516-3518,2012.
31. F. Wang, Y. Cai and Q. Lin. Experimental observation of truncated fractional Fourier transform fora partially coherent Gaussian Schell-model beam. J. Opt. Soc. Am. A,25,2001-2010,2008.
32. L. Pan, M. Sun, C. Ding, Z. Zhao and B. Lu. Effects of astigmatism on spectra, coherence andpolarization of stochastic electromagnetic beams passing through an astigmatic optical system. Opt.Express,17,7310-7321,2009.
33. O. Korotkova and E. Wolf. Changes in the state of polarization of a random electromagnetic beamon propagation. Opt. Commun.246,35-43,2005.
34. S. A. Ponomarenko and E. Wolf. Coherence properties of light in Young's interference patternformed with partially coherent light. Opt. Commun.170,1-8,1999.
35. G. Gbur, T. D. Visser and E. Wolf. Complete destructive interference of partially coherent fields.Opt. Commun.239,15-23,2004.
36. T. Set l, J. Tervo and A. T. Friberg. Contrasts of Stokes parameters in Young's interferenceexperiment and electromagnetic degree of coherence. Opt. Lett.31,2669-2671,2006.
37. G. S. Agarwal, A. Dogariu, T. D Visser and E. Wolf. Generation of complete coherence in Young'sinterference experiment with random mutually uncorrelated electromagnetic beams. Opt. Lett.30,120-122,2006.
38. Y. Li, H. Lee and E. Wolf. Spectra, coherence and polarization in Young's interference patternformed by stochastic electromagnetic beams. Opt. Commun.265,63-72,2006.
39. J. J. Wen and M. A. Breazeale. A diffraction beam field expressed as the superposition of Gaussianbeams. J. Acoust. Soc. Am.83,1752-1756,1988.
40. Y. Cai and L. Hu. Propagation of partially coherent twisted anisotropic Gaussian Schell-modelbeams through an apertured astigmatic optical system. Opt. Lett.31,685-687,2006.
41. S. Zhu and Y. Cai. M2-factor of a truncated electromagnetic Gaussian Schell-model beam. Appl.Phys. B,103,971-984,2011.