光场偏振参量演化特性与精细结构理论研究
|
摘要
现代光学技术越来越依赖偏振光自身携带的丰富信息作为探测和感知物质世界的手段。偏振参量是电磁场的光强、相位、光谱等参量之外的重要自由度,主要指光的偏振度(总能量中完全偏振成分所占比重)和偏振态两个方面。对它们行为特性的准确掌握是有效利用偏振信息的基本前提,这使得从理论层面研究偏振参量若干规律成为发展偏振光学技术不能回避的问题。本文就光场偏振度随光传播、散射等过程的纵向演化特性和偏振态在空间中精细分布结构进行研究。
对于偏振度的演化特性,详细探讨了导致偏振度演化的机理。首先选取准均匀随机介质作为模型研究光经过该类介质散射后偏振度的角分布情况。在将标量散射利用矢量角谱方法推广到矢量散射后,重点分析了随机介质统计参数尤其是折射率空间相干性因素所起的主要作用,并指出相干性因素是引起偏振度演化的原因之一。在此基础上,将偏振度演化机制的研究延伸到具有相似性的部分相干光源辐射场。本文从引进交叉偏振度概念入手,指出相干性效应并非导致偏振度演化的唯一因素。通过构造了两个具有相同相干性、相同偏振度、不同交叉偏振度的光源并证实这样一组光源的辐射远场仍然具有不同的偏振度,即交叉偏振效应同样导致偏振度演化,澄清了对于偏振度演化机制的认识。另外以交叉偏振度作为工具,提出一种定义三维光场偏振度的方法。注意到偏振度反映光垂直分量间相关性本质,这种相关性由于正交关系在振幅上得不到反映,而必须以光强相关的形式出现。提出通过将交叉偏振度从二维场推广到三维场的方法来间接得到三维光场偏振度。
对于偏振态精细结构的研究主要围绕随空间位置变化偏振态分布的产生及分布中偏振奇异点的分析展开。在阐明用线型和圆型双折射器件调制偏振椭圆度和方位角原理的基础上,提出通过将两束沿不同方向调制光束叠加的方法来实现二维偏振椭圆分布。讨论了当两叠加光束之间相关性不同时得到的偏振态分布,发现光束间相关性显著影响偏振度、偏振态等分布。接着研究了两个有相位涡旋调制光束叠加后偏振椭圆场的分布情况。借助奇异光学理论对偏振椭圆场进行了整体性分析,讨论了圆偏振点附近椭圆方位角包络线的形态以及小幅扰动下圆偏振点的运动情况。分析了扰动作用下奇异点拓扑稳定性导致的方位角包络线拉伸与压缩效应和由此引起的圆偏振点形态之间的转化。高数值孔径系统焦点区是另一个可能出现复杂光场结构的场所。为此用数值模拟方法研究了非均匀偏振入射光被高数值孔径聚焦后焦点附近区域能量、相位、偏振奇异点的分布。计算过程采用了快速傅立叶变换方法解决矢量衍射积分在无对称性条件下计算复杂度高、计算量大的问题,使任意偏振分布的聚焦计算耗时量显著降低。首先计算了几种不同偏振分布聚焦后焦点附近三维空间的能量和相位分布,发现焦斑形状、各分量能量比重、能量中心位置等对入射偏振分布都是敏感的,这有助于通过偏振性质对焦点特性精确控制,而相位分布有助于分析能量暗区附近的结构。接着计算了焦点附近的圆偏振和线偏振分布,发现圆偏振产生更易受到入射光相位涡旋的影响,而对一般的非均匀偏振敏感度不高。发现圆偏振和线偏振的共同特征是它们都分布于三维空间的曲线上或二维空间的点上,且可以在比波长更小的空间尺度上发生变化,这与奇异光学理论有很好的吻合。
本文对偏振度演化和偏振态分布的研究结论在较广范围内对偏振光的应用有一定价值。特别是在需要对偏振光进行复杂加工、变换的场合,有助于预测可能得到的结果和分析出现的现象,对需要综合利用偏振光多自由度发展新的成像和探测技术方面也有一定帮助。
Modern optical techniques make more and more frequent use of information extracted with the help of polarized light. Polarization parameters, like light intensities, phase and spectrum do, provide very important available freedoms including the degree of polarization (DP) and the state of polarization (SP) of polarized part in light. The knowledges of these parameters are fundamental prerequisite to make efficient use of them. It is thus of radical importance for developing polarization engineering techniques to theoretically scrutinize how these polariza-tion parameters behavior. In this thesis we theoretically study the the longitudinal evolution of the degree of polarization during processes like radiation from light sources and scattering from random medium and the spatial fine structure of SP in light fields.
For evolution properties, our mainly concern is the mechanism that induces the change of DP. We first studied the angular distribution of DP in light scattered from a quasi-homogeneous random medium. Based on the generalization of scalar scattering to its vectorial counterpart using the method of angular spectrum, we analyzed the effect of spatial correlation of refractive index on the DP and pointed out that correlation effect predominantly contributes to the change of DP. Keeping in mind that there are similarities between scattering and radiation problems, our analysis naturally saturated to the fard fields radiated from partially coherent lights sources. We demonstrated that for radiation problems, there is another effect beyond the coherence ef-fect that induces the change of DP, and it is called cross-polarizaiton effect. This was proved by considering a group of light sources that have the same degrees of polarization, the same spatial degrees of coherence but with different degrees of cross-polarization to confirm that they gener-ate beams with different DP. These results clarified the question of what mechanisms are indeed responsible for the evolution of DP. Using the degree of cross-polarization as a tool, we also supposed a procedure for constructing a physically sound definition of the DP for three dimen-sional light fields. This could be achieved by first generalizing the degree of cross-polarization to the three dimensional case then using it at coincident points as the usual DP.
As for the fine structure of SP, we concentrated mainly on the possible methods generat-ing a space-variant polarization distribution. For this task, we demonstrated that two kinds of birefringent devices, one of linear type and the other circular type could modulate SP in one dimension. Two beams of light each modulated this way could superpose to generate a two-dimensional distribution. It was found that the correlation properties between these two beams have an evident modulation on the distribution of poalrization parameters. A particular example of polarization distribution generated by superposing two modulated beam which contain phase vortices was studies. The embedded polarization singularities, namely, points where the polar-ization is circular and curves where the polarization is linear were analyzed in the framework of singular optics. These singularities were found to have topological stabilities under small per-turbations. Perturbations could drag and compress the streamlines of polarization major axis and induce the trasformation of the morphologies of these line from one type to another. The other arena where light fields could have fine structure is the focal region of a high numerical aperture system. We numericall simulated the energy, the phase and the polarization distribu-tions of some types of non-uniformly polarized incident light. A fast FFT numerical method was adopted to achieve fast computations. It was found that the shape and orientation of the focal spot, the energy ratio between the three components are all sensitive to the polarization distribution across the aperture. These results may shed lights on the possibility of intentionally controlling the focal spot with polarization engineering. The generation of polarization singu-larities which lie on curves in space and points in planes, was found sensitive to the existence of phase vortex in the aperture. The variations of these singularities were found to be able to take place in scales much smaller than the wavelength of light. All these numerical results agree well with theories.
The researches and results presented in this thesis will be of value in a broader regime of applications using polarized light. In particular, they may be of help in giving prediction to possible results and analyzing emerged various phenomena in situations where complex manip-ulation of polarized light are needed. For situations multiple degrees of freedom of polarization parameters are engaged they may also find potential values.
对于偏振度的演化特性,详细探讨了导致偏振度演化的机理。首先选取准均匀随机介质作为模型研究光经过该类介质散射后偏振度的角分布情况。在将标量散射利用矢量角谱方法推广到矢量散射后,重点分析了随机介质统计参数尤其是折射率空间相干性因素所起的主要作用,并指出相干性因素是引起偏振度演化的原因之一。在此基础上,将偏振度演化机制的研究延伸到具有相似性的部分相干光源辐射场。本文从引进交叉偏振度概念入手,指出相干性效应并非导致偏振度演化的唯一因素。通过构造了两个具有相同相干性、相同偏振度、不同交叉偏振度的光源并证实这样一组光源的辐射远场仍然具有不同的偏振度,即交叉偏振效应同样导致偏振度演化,澄清了对于偏振度演化机制的认识。另外以交叉偏振度作为工具,提出一种定义三维光场偏振度的方法。注意到偏振度反映光垂直分量间相关性本质,这种相关性由于正交关系在振幅上得不到反映,而必须以光强相关的形式出现。提出通过将交叉偏振度从二维场推广到三维场的方法来间接得到三维光场偏振度。
对于偏振态精细结构的研究主要围绕随空间位置变化偏振态分布的产生及分布中偏振奇异点的分析展开。在阐明用线型和圆型双折射器件调制偏振椭圆度和方位角原理的基础上,提出通过将两束沿不同方向调制光束叠加的方法来实现二维偏振椭圆分布。讨论了当两叠加光束之间相关性不同时得到的偏振态分布,发现光束间相关性显著影响偏振度、偏振态等分布。接着研究了两个有相位涡旋调制光束叠加后偏振椭圆场的分布情况。借助奇异光学理论对偏振椭圆场进行了整体性分析,讨论了圆偏振点附近椭圆方位角包络线的形态以及小幅扰动下圆偏振点的运动情况。分析了扰动作用下奇异点拓扑稳定性导致的方位角包络线拉伸与压缩效应和由此引起的圆偏振点形态之间的转化。高数值孔径系统焦点区是另一个可能出现复杂光场结构的场所。为此用数值模拟方法研究了非均匀偏振入射光被高数值孔径聚焦后焦点附近区域能量、相位、偏振奇异点的分布。计算过程采用了快速傅立叶变换方法解决矢量衍射积分在无对称性条件下计算复杂度高、计算量大的问题,使任意偏振分布的聚焦计算耗时量显著降低。首先计算了几种不同偏振分布聚焦后焦点附近三维空间的能量和相位分布,发现焦斑形状、各分量能量比重、能量中心位置等对入射偏振分布都是敏感的,这有助于通过偏振性质对焦点特性精确控制,而相位分布有助于分析能量暗区附近的结构。接着计算了焦点附近的圆偏振和线偏振分布,发现圆偏振产生更易受到入射光相位涡旋的影响,而对一般的非均匀偏振敏感度不高。发现圆偏振和线偏振的共同特征是它们都分布于三维空间的曲线上或二维空间的点上,且可以在比波长更小的空间尺度上发生变化,这与奇异光学理论有很好的吻合。
本文对偏振度演化和偏振态分布的研究结论在较广范围内对偏振光的应用有一定价值。特别是在需要对偏振光进行复杂加工、变换的场合,有助于预测可能得到的结果和分析出现的现象,对需要综合利用偏振光多自由度发展新的成像和探测技术方面也有一定帮助。
Modern optical techniques make more and more frequent use of information extracted with the help of polarized light. Polarization parameters, like light intensities, phase and spectrum do, provide very important available freedoms including the degree of polarization (DP) and the state of polarization (SP) of polarized part in light. The knowledges of these parameters are fundamental prerequisite to make efficient use of them. It is thus of radical importance for developing polarization engineering techniques to theoretically scrutinize how these polariza-tion parameters behavior. In this thesis we theoretically study the the longitudinal evolution of the degree of polarization during processes like radiation from light sources and scattering from random medium and the spatial fine structure of SP in light fields.
For evolution properties, our mainly concern is the mechanism that induces the change of DP. We first studied the angular distribution of DP in light scattered from a quasi-homogeneous random medium. Based on the generalization of scalar scattering to its vectorial counterpart using the method of angular spectrum, we analyzed the effect of spatial correlation of refractive index on the DP and pointed out that correlation effect predominantly contributes to the change of DP. Keeping in mind that there are similarities between scattering and radiation problems, our analysis naturally saturated to the fard fields radiated from partially coherent lights sources. We demonstrated that for radiation problems, there is another effect beyond the coherence ef-fect that induces the change of DP, and it is called cross-polarizaiton effect. This was proved by considering a group of light sources that have the same degrees of polarization, the same spatial degrees of coherence but with different degrees of cross-polarization to confirm that they gener-ate beams with different DP. These results clarified the question of what mechanisms are indeed responsible for the evolution of DP. Using the degree of cross-polarization as a tool, we also supposed a procedure for constructing a physically sound definition of the DP for three dimen-sional light fields. This could be achieved by first generalizing the degree of cross-polarization to the three dimensional case then using it at coincident points as the usual DP.
As for the fine structure of SP, we concentrated mainly on the possible methods generat-ing a space-variant polarization distribution. For this task, we demonstrated that two kinds of birefringent devices, one of linear type and the other circular type could modulate SP in one dimension. Two beams of light each modulated this way could superpose to generate a two-dimensional distribution. It was found that the correlation properties between these two beams have an evident modulation on the distribution of poalrization parameters. A particular example of polarization distribution generated by superposing two modulated beam which contain phase vortices was studies. The embedded polarization singularities, namely, points where the polar-ization is circular and curves where the polarization is linear were analyzed in the framework of singular optics. These singularities were found to have topological stabilities under small per-turbations. Perturbations could drag and compress the streamlines of polarization major axis and induce the trasformation of the morphologies of these line from one type to another. The other arena where light fields could have fine structure is the focal region of a high numerical aperture system. We numericall simulated the energy, the phase and the polarization distribu-tions of some types of non-uniformly polarized incident light. A fast FFT numerical method was adopted to achieve fast computations. It was found that the shape and orientation of the focal spot, the energy ratio between the three components are all sensitive to the polarization distribution across the aperture. These results may shed lights on the possibility of intentionally controlling the focal spot with polarization engineering. The generation of polarization singu-larities which lie on curves in space and points in planes, was found sensitive to the existence of phase vortex in the aperture. The variations of these singularities were found to be able to take place in scales much smaller than the wavelength of light. All these numerical results agree well with theories.
The researches and results presented in this thesis will be of value in a broader regime of applications using polarized light. In particular, they may be of help in giving prediction to possible results and analyzing emerged various phenomena in situations where complex manip-ulation of polarized light are needed. For situations multiple degrees of freedom of polarization parameters are engaged they may also find potential values.
引文
[1]Stokes G G. On the composition and resolution of streams of polarized light from dif-ferent sources. Trans. Cambridge Philos. Soc.,1852,9:399-416.
[2]Born M, Wolf E. Principles of Optics.7th ed., Cambridge:Cambridge University Press, 1999.
[3]Kovac J M, Leitch E M, Pryke C, et al. Detection of polarization in the cosmic microwave background using DASI. Nature,2002,420(6917):772.
[4]Berry M V, Dennis M R, Jr R L L. Polarization singularities in the clear sky. New. J. Phys.,2004,6:162.
[5]Hannay J H. Polarization of sky light from a canopy atmosphere. New. J. Phys.,2004, 6:197.
[6]Mandel L, Wolf E. Optical Coherence and Quantum Optics. Cambridge:Cambridge University Press,1995.
[7]Setala T, Shevchenko A, Kaivola M, et al. Polarization time and length for random optical beams. Phys. Rev. A,2008,78(3):033817.
[8]Egan W G, Johnson W R, Whitehead V S. Terrestial polarization imagery obtained from the space shuttle:characterization and interpretation. Appl. Opt.,1991,30(4):435-442.
[9]Kleinlogel S, White A G. The secret world of shrimps:polarisation vision at its best. PLoS ONE,2008,3:e2190.
[10]Rowe M P, E N Pugh J, Tyo J S, et al. Polarization-difference imaging:a biolog-ically inspired technique for observation through scattering media. Opt. Lett.,1995, 20(6):608-610.
[11]Tyo J S, Rowe M P, E N Pugh J, et al. Target detection in optically scattering media by polarization-difference imaging. Appl. Opt.,1996,35(11):1855-1870.
[12]Tyo J S. Enhancement of the point-spread function for imaging in scattering media by use of polarization-difference imaging. J. Opt. Soc. Am. A,2000,17(1):1-10.
[13]Treibitz T, Schechner Y Y. Active polarization descattering. IEEE Trans. PAMI,2009, 31(3):385-399.
[14]Hielscher A, Eick A, Mourant J, et al. Diffuse backscattering Mueller matricesof highly scattering media. Opt. Express,1997,1(13):441-453.
[15]Oka K, Kato T. Spectroscopic polarimetry with a channeled spectrum. Opt. Lett.,1999, 24(21):1475-1477.
[16]Hagen N, Oka K, Dereniak E L. Snapshot Mueller matrix spectropolarimeter. Opt. Lett., 2007,32(15):2100-2102.
[17]VanWiggeren G D, Roy R. Communication with dynamically fluctuating states of light polarization. Phys. Rev. Lett.,2002,88(9):097903.
[18]Andrews M R, Mitra P P, deCarvalho R. Tripling the capacity of wireless communica-tions using electromagnetic polarization. Nature,2001,409(6818):316-318.
[19]Dorn R, Quabis S, Leuchs G. Sharper focus for a radially polarized light beam. Phys. Rev. Lett.,2003,91(23):233901.
[20]Leuchs G, Quabis S. Tailored polarization patterns for performance optimization of optical devices. J. Mod. Opt.,2006,53(5-6):787-797.
[21]Lindlein N, Quabis S, Peschel U, et al. High numerical aperture imaging with different polarization patterns. Opt. Express,2007,15(9):5827-5842.
[22]Chi W, Chu K, George N. Polarization coded aperture. Opt. Express,2006, 14(15):6634-6642.
[23]Lindfors K, Priimagi A, Setala T, et al. Local polarization of tightly focused unpolarized light. Nature Photonics,2007,1(4):228-231.
[24]James D F V. Change of polarization of light beams on propagation in free space. J. Opt. Soc. Am. A,1994,11(5):1641-1643.
[25]Nye J F. Natural Focusing and Fine Structure of Light. Bristol, UK:IOP Publishing, 1999.
[26]Bliokh K Y, Niv A, Kleiner V, et al. Singular polarimetry:Evolution of polarizationsin-gularities in electromagnetic wavespropagating in a weakly anisotropic medium. Opt. Express,2008,16(2):695-709.
[27]Wozniak W A, Kurzynowski P. Compact spatial polariscope for light polarization state analysis. Opt. Express,2008,16(14):10471-10479.
[28]Flossmann F, O'Holleran K, Dennis M R, et al. Polarization Singularities in 2D and 3D Speckle Fields. Phys. Rev. Lett.,2008,100(20):203902.
[29]Buinyi I O, Denisenko V G, Soskin M S. Topological structure in polarization re-solved conoscopic patterns for nematic liquid crystal cells. Opt. Commun.,2009, 282(2):143-155.
[30]Wiener N. Generalized harmonic analysis. Acta Math.,1930,55:182.
[31]Wolf E. Optics in terms of observable quantities. Nuovo Cimento,1954,12(6):884-888.
[32]Wolf E. Coherence properties of partially polarized electromagnetic radiation. Nuovo Cimento,1959,13(6):1165-1181.
[33]Wolf E. Correlation-induced Doppler-type frequency shifts of spectral lines. Phys. Rev. Lett.,1989,63(20):2220-2223.
[34]Gori F, Santarsiero M, Vicalvi S, et al. Beam coherence-polarization matrix. Pure Appl. Opt,1998,7(5):941-951.
[35]Wolf E. Unified theory of coherence and polarization of random electro magnetic beams. Phys. Lett. A,2003,312(5-6):263-267.
[36]Wolf E. Polarization invariance in beam propagation. Opt. Lett.,2007, 32(23):3400-3401.
[37]Zhao D, Wolf E. Light beams whose degree of polarization does not change on propa-gation. Opt. Commun.,2008,281(11):3067-3070.
[38]Wolf E. Can a light beam be considered to be the sum of a completely polarized and a completely unpolarized beam? Opt. Lett.,2008,33(7):642-644.
[39]Lahiri M, Wolf E. Cross-spectral density matrices of polarized light beams. Opt. Lett., 2009,34(5):557-559.
[40]Lahiri M, Korotkova O, Wolf E. Polarization and coherence properties of a beam formed by superposition of a pair of stochastic electromagnetic beams. Opt. Commun.,2008, 281(20):5073-5077.
[41]Gori F, Santarsiero M. Devising genuine spatial correlation functions. Opt. Lett.,2007, 32(24):3531-3533.
[42]Martinez-Herrero R, Mejias P M, Gori F. Genuine cross-spectral densities and pseudo-modal expansions. Opt. Lett.,2009,34(9):1399-1401.
[43]Gori F. Partially correlated sources with complete polarization. Opt. Lett.,2008, 33(23):2818-2820.
[44]Korotkova O, Wolf E. Changes in the state of polarization of a random electromagnetic beam on propagation. Opt. Commun.,2005,246(1-3):35-43.
[45]Korotkova O, Hoover B G, Gamiz V L, et al. Coherence and polarization properties of far fields generated by quasi-homogeneous planar electromagnetic sources. J. Opt. Soc. Am. A,2005,22(11):2547-2556.
[46]Korotkova O, Salem M, Wolf E. The far-zone behavior of the degree of polarization of random electromagnetic beams propagating through atmospheric turbulence. Opt. Commun.,2004,233(4-6):225-230.
[47]Salem M, Korotkova O, Wolf E. Can two planar sources with the same sets of Stokes parameters generate beams with different degrees of polarization? Opt. Lett.,2006, 31(20):3025-3027.
[48]Yao M, Cai Y, Eyyuboglu H T, et al. Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity. Opt. Lett.,2008, 33(19):2266-2268.
[49]Du X, Zhao D. Criterion for keeping completely unpolarized or completely polarized stochastic electromagnetic Gaussian Schell-model beams on propagation. Opt. Express, 2008,16(20):16172-16180.
[50]Korotkova O, Wolf E. Generalized Stokes parameters of random electromagneticbeams. Opt. Lett.,2005,30(2):198-200.
[51]Shirai T, Wolf E. Correlation between intensity fluctuations in stochastic electromagnetic beams of any state of coherence and polarization. Opt. Commun.,2007,272(2):289-292.
[52]Xin Y, Chen Y, Zhao Q, et al. Effect of cross-polarization of electromagnetic source on the degree of polarization of generated beam. Opt. Commun.,2008,281(8):1954-1957.
[53]Volkov S N, James D F V, Shirai T, et al. Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams. J. Opt. A:Pure Appl. Opt,2008, 10(5):055001 (4pp).
[54]Du X, Zhao D. Changes in generalized Stokes parameters of stochastic electromagnetic beams on propagation through ABCD optical systems and in the turbulent atmosphere. Opt. Commun.,2008,281(24):5968-5972.
[55]Pu J, Korotkova O. Propgation of the degree of cross-polarization of a stochas-tic electromagnetic beam through the turbulent atmosphere. Opt. Commun.,2009, 282(9):1691-1698.
[56]Luis A. Degree of polarization for three-dimensional fields as a distance between corre-lation matrix. Opt. Commun.,2005,253(1-3):10-14.
[57]Setala T, Kaivola M, Friberg A T. Degree of polarization in near fields of thermal sources: effects of surface waves. Phys. Rev. Lett.,2002,88(12):123902.
[58]Setala T, Shevchenko A, Kaivola M, et al. Degree of polarization for optical near fields. Phys. Rev. E,2002,66(1):016615.
[59]Lindfors K, Setala T, Kaivola M, et al. Degree of polarization in tightly focused optical fields. J. Opt. Soc. Am. A,2005,22(3):561-568.
[60]Ellis J, Dogariu A, Ponomarenko S, et al. Degree of polarization of statistically stationary electromagnetic fields. Opt. Commun.,2005,248:333-337.
[61]Bohren C F, Huffman D R. Absorption and scattering of light by small particles. Wein-heim:WILEY-VCH Verlag GmbH & Co. KGaA,2004.
[62]Berg M J, Sorensen C M, Chakrabarti A. Reflection symmetry of a sphere's internal field and its consequences on scattering:a microphysical approach. J. Opt. Soc. Am. A, 2008,25(1):98-107.
[63]Freund I, Soskin M S, Mokhun A I. Elliptic critical points in paraxial optical fields. Opt. Commun.,2002,208(4-6):223-253.
[64]Urbach H P, Pereira S F. Field in focus with a maximum longitudinal electric component. Phys. Rev. Lett.,2008,100(12):123904.
[65]Gori F. Polarization basis for vortex beams. J. Opt. Soc. Am. A,2001,18(7):1612-1617.
[66]Passilly N, Saint Denis R, Ait-Ameur K, et al. Simple interferometric technique for generation of a radially polarized light beam. J. Opt. Soc. Am. A,2005,22(5):984-991.
[67]Kozawa Y, Sato S. Generation of a radially polarized laser beam by use of a conical Brewster prism. Opt. Lett.,2005,30(22):3063-3065.
[68]Wang X L, Ding J, Ni W J, et al. Generation of arbitrary vector beams with a spa-tial light modulator and a common path interferometric arrangement. Opt. Lett.,2007, 32(24):3549-3551.
[69]Xin Y, Chen Y, Zhao Q. Coherent and incoherent polarization encoding of electromag-netic fields. Opt. Commun.,2009,282(7):1260-1264.
[70]Schoonover R W, Visser T D. Creating polarization singularities with an N-pinhole interferometer. Phys. Rev. A,2009,79(4):043809.
[71]Dennis M R. Polarization singularity anisotropy:determining monstardom. Opt. Lett., 2008,33(22):2572-2574.
[72]Dennis M R, Hamilton A C, Courtial J. Superoscillation in speckle patterns. Opt. Lett., 2008,33(24):2976-2978.
[73]Zhu Y, Zhao D. Generalized Stokes parameters of a stochastic electromagnetic beam propagating through a paraxial ABCD optical system. J. Opt. Soc. Am. A,2008, 25(8):1944-1948.
[74]Zhao D, Zhu Y. Generalized formulas for stochastic electromagnetic beams on inverse propagation through nonsymmetrical optical systems. Opt. Lett.,2009,34(7):884-886.
[75]Chowdhury D R, Bhattacharya K, Chakroborty A K, et al. Possibility of an Optical Focal Shift with Polarization Masks. Appl. Opt.,2003,42(19):3819-3826.
[76]Chowdhury D R, Bhattacharya K, Chakraborty A K, et al. Polarization-Based Compen-sation of Astigmatism. Appl. Opt.,2004,43(4):750-755.
[77]Hao B, Leger J. Polarization beam shaping. Appl. Opt.,2007,46(33):8211-8217.
[78]Hao B, Burch J, Leger J. Smallest flattop focus by polarization engineering. Appl. Opt., 2008,47(16):2931-2940.
[79]Martinez-Corral M, Martinez-Cuenca R, Escobar I, et al. Reduction of focus size in tightly focused linearly polarized beams. Appl. Phys. Lett.,2004,85(19):4319-4321.
[80]Dijk T, Visser T D. Evolution of singularities in a partially coherent vortex beam. J. Opt. Soc. Am. A,2009,26(4):741-744.
[81]Dijk T, Schouten H F, Visser T D. Coherence singularities in the field generated by partially coherent sources. Phys. Rev. A,2009,79(3):033805.
[82]Silverman R A. Scattering of plane waves by locally homogeneous dielectric noise. Proc. Cambridge Philos. Soc.,1958,54:530-537.
[83]Fischer D G, Wolf E. Theory of diffraction tomography for quasi-homogeneous random objects. Opt. Commun.,1997,133(1-6):17-21.
[84]Lahiri M, Wolf E, Fischer D G, et al. Determination of correlation functions of scatter-ing potentials of stochstic media from scattering experiments. Phys. Rev. Lett.,2009, 102(12):123901.
[85]Schoonover R W, Rutherford J M, Keller O, et al. Non-local constituitive relations and the quasi-homogeneous approximation. Phys. Lett. A,2005,342(5-6):363-367.
[86]Visser T D, Fischer D G, Wolf E. Scattering of light from quasi-homogeneous sources on quasi-homogeneous media. J. Opt. Soc. Am. A,2006,23(7):1631-1638.
[87]Priest R G, Meier S R. Polarimetric microfacet scattering theory with applications to absorptive and reflective surfaces. Opt. Eng.,2002,41(5):988-993.
[88]Leskova T A, Maradudin A A, Lopez J. Coherence of light scattered from a randomly rough surface. Phys. Rev. E,2005,71(3):036606.
[89]Xin Y, Chen Y, Zhao Q, et al. Beam radiated from quasi-homogeneous uniformly polar-ized electromagnetic source scattering on quasi-homogeneous media. Opti. Commun., 2007,278(2):247-252.
[90]Chen C G, Konkola P T, Ferrera J, et al. Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations. J. Opt. Soc. Am. A,2002, 19(2):404-412.
[91]Tsang L, Kong J A, Ding K H. Scattering of electromagnetic waves:Theory and appli-cations. First ed., New York:John Wiley & Sons, Inc,2000.
[92]Samson J C. Descriptions of the polarization states of vector processes:application to ULF magnetic fields. Geophys. J. R. Astron. Soc.,1973,34:403.
[93]Roychowdhury H, Korotkova O. Realizability conditions for electromagnetic Gaussian-Schell model sources. Opt. Commun.,2005,249:379-385.
[94]Pu J, Korotkova O, Wolf E. Invariance and noninvariance of the spectra of stochastic electromagnetic beams on propogation. Opt. Lett.,2006,31(14):2097-2099.
[95]Pu J, Korotkova O, Wolf E. Polarization-induced spectral changes on propagation of stochastic electromagnetic beams. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics),2007,75(5):056610.
[96]Wolf E, Foley J T, Gori F. Frequency shifts of spectral lines produced by scattering from spatially random media. J. Opt. Soc. Am. A,1989,6(8):1142-1149.
[97]Wolf E. Far-zone spectral isotropy in weak scattering on spatially random media. J. Opt. Soc. Am. A,1997,14(10):2820-2823.
[98]Zhao D, Korotkova O, Wolf E. Application of correlation-induced spectral changes to inverse scattering. Opt. Lett.,2007,32(24):3483-3485.
[99]Gatti A, Brambilla E, Bache M, et al. Ghost Imaging with Thermal Light:Comparing Entanglement and Classical Correlation. Phys. Rev. Lett.,2004,93(9):093602.
[100]Cai Y, Zhu S Y. Ghost interference with partially coherent radiation. Opt. Lett.,2004, 29(23):2716-2718.
[101]Cai Y, Zhu S Y. Ghost imaging with incoherent and partially coherent light radiation. Phys. Rev. E,2005,71(5):056607.
[102]Cai Y, Wang F. Lensless imaging with partially coherent light. Opt. Lett.,2007, 32(3):205-207.
[103]Chen X H, Liu Q, Luo K H, et al. Lensless ghost imaging with true thermal light. Opt. Lett.,2009,34(5):695-697.
[104]Ellis J, Dogariu A. Complex degree of mutual polarization. Opt. Lett.,2004, 29(6):536-538.
[105]Roychowdhury H, Wolf E. Statistical similarity and the physical significance of com-plete spatial coherence and complete polarization of random electromagnetic beams. Optics Communications,2005,248(4-6):327-332.
[106]Gao W. Changes of polarization of light beams on propagation through tissue. Opt. Commun.,2006,260(2):749-754.
[107]Gao W, Korotkova O. Changes in the state of polarization of a random electromagnetic beam propagating through tissue. Opt. Commun.,2007,270(2):474-478.
[108]Salem M, Wolf E. Coherence-induced polarization changes in light beams. Opt. Lett., 2008,33(11):1180-1182.
[109]Korotkova O, Wolf E. Spectral degree of coherence of a random three-dimensional electromagnetic field. J. Opt. Soc. Am. A,2004,21(12):2382-2385.
[110]Chernyshov A A, Felde C V, Bogatyryova H V, et al. Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components. Journal of Optics A:Pure and Applied Optics,2009, 11(9):094010.
[111]Flossmann F, Schwarz U T, Maier M, et al. Polarization Singularities from Unfolding an Optical Vortex through a Birefringent Crystal. Phys. Rev. Lett.,2005,95(25):253901.
[112]Berry M V, Hannay J H. Umbilic points on Gaussian random surfaces. Journal of Physics A:Mathematical and General,1977,10(11):1809-1821.
[113]Zhang Z, Pu J, Wang X. Focusing of partially coherent Bessel-Gaussian beams through a high-numerical-aperture objective. Opt. Lett.,2008,33(1):49-51.
[114]Chen B, Zhang Z, Pu J. Tight focusing of partially coherent and circularly polarized vortex beams. J. Opt. Soc. Am. A,2009,26(4):862-869.
[115]Chen B, Pu J. Tight focusing of elliptically polarized vortex beams. Appl. Opt.,2009, 48(7):1288-1294.
[116]Schoonover R W, Visser T D. Polarization singularities of focused, radially polarized fields. Opt. Express,2006,14(12):5733-5745.
[117]Leutenegger M, Rao R, Leitgeb R A, et al. Fast focus field calculations. Opt. Express, 2006,14(23):11277-11291.
[118]Boruah B, Neil M. Focal field computation of an arbitrarily polarized beam using fast Fourier transforms. Optics Communications,2009,282(24):4660-4667.
[119]Lerman G M, Levy U. Tight focusing of spatially variant vector optical fields with elliptical symmetry of linear polarization. Opt. Lett.,2007,32(15):2194-2196.
[120]Lerman G M, Lilach Y, Levy U. Demonstration of spatially inhomogeneous vector beams with elliptical symmetry. Opt. Lett.,2009,34(11):1669-1671.
[121]Pu J, Lu B. Focal shifts in focused nonuniformly polarized beams. J. Opt. Soc. Am. A, 2001,18(11):2760-2766.
[122]Berry M V. The electric and magnetic polarization singularities of paraxial waves. Jour-nal of Optics A:Pure and Applied Optics,2004,6(5):475-481.
[123]Zhao Y, Edgar J S, Jeffries G D M, et al. Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam. Physical Review Letters,2007,99(7):073901.
[124]Govyadinov A A, Panasyuk G Y, Schotland J C. Phaseless Three-Dimensional Optical Nanoimaging. Physical Review Letters,2009,103(21):213901.
[2]Born M, Wolf E. Principles of Optics.7th ed., Cambridge:Cambridge University Press, 1999.
[3]Kovac J M, Leitch E M, Pryke C, et al. Detection of polarization in the cosmic microwave background using DASI. Nature,2002,420(6917):772.
[4]Berry M V, Dennis M R, Jr R L L. Polarization singularities in the clear sky. New. J. Phys.,2004,6:162.
[5]Hannay J H. Polarization of sky light from a canopy atmosphere. New. J. Phys.,2004, 6:197.
[6]Mandel L, Wolf E. Optical Coherence and Quantum Optics. Cambridge:Cambridge University Press,1995.
[7]Setala T, Shevchenko A, Kaivola M, et al. Polarization time and length for random optical beams. Phys. Rev. A,2008,78(3):033817.
[8]Egan W G, Johnson W R, Whitehead V S. Terrestial polarization imagery obtained from the space shuttle:characterization and interpretation. Appl. Opt.,1991,30(4):435-442.
[9]Kleinlogel S, White A G. The secret world of shrimps:polarisation vision at its best. PLoS ONE,2008,3:e2190.
[10]Rowe M P, E N Pugh J, Tyo J S, et al. Polarization-difference imaging:a biolog-ically inspired technique for observation through scattering media. Opt. Lett.,1995, 20(6):608-610.
[11]Tyo J S, Rowe M P, E N Pugh J, et al. Target detection in optically scattering media by polarization-difference imaging. Appl. Opt.,1996,35(11):1855-1870.
[12]Tyo J S. Enhancement of the point-spread function for imaging in scattering media by use of polarization-difference imaging. J. Opt. Soc. Am. A,2000,17(1):1-10.
[13]Treibitz T, Schechner Y Y. Active polarization descattering. IEEE Trans. PAMI,2009, 31(3):385-399.
[14]Hielscher A, Eick A, Mourant J, et al. Diffuse backscattering Mueller matricesof highly scattering media. Opt. Express,1997,1(13):441-453.
[15]Oka K, Kato T. Spectroscopic polarimetry with a channeled spectrum. Opt. Lett.,1999, 24(21):1475-1477.
[16]Hagen N, Oka K, Dereniak E L. Snapshot Mueller matrix spectropolarimeter. Opt. Lett., 2007,32(15):2100-2102.
[17]VanWiggeren G D, Roy R. Communication with dynamically fluctuating states of light polarization. Phys. Rev. Lett.,2002,88(9):097903.
[18]Andrews M R, Mitra P P, deCarvalho R. Tripling the capacity of wireless communica-tions using electromagnetic polarization. Nature,2001,409(6818):316-318.
[19]Dorn R, Quabis S, Leuchs G. Sharper focus for a radially polarized light beam. Phys. Rev. Lett.,2003,91(23):233901.
[20]Leuchs G, Quabis S. Tailored polarization patterns for performance optimization of optical devices. J. Mod. Opt.,2006,53(5-6):787-797.
[21]Lindlein N, Quabis S, Peschel U, et al. High numerical aperture imaging with different polarization patterns. Opt. Express,2007,15(9):5827-5842.
[22]Chi W, Chu K, George N. Polarization coded aperture. Opt. Express,2006, 14(15):6634-6642.
[23]Lindfors K, Priimagi A, Setala T, et al. Local polarization of tightly focused unpolarized light. Nature Photonics,2007,1(4):228-231.
[24]James D F V. Change of polarization of light beams on propagation in free space. J. Opt. Soc. Am. A,1994,11(5):1641-1643.
[25]Nye J F. Natural Focusing and Fine Structure of Light. Bristol, UK:IOP Publishing, 1999.
[26]Bliokh K Y, Niv A, Kleiner V, et al. Singular polarimetry:Evolution of polarizationsin-gularities in electromagnetic wavespropagating in a weakly anisotropic medium. Opt. Express,2008,16(2):695-709.
[27]Wozniak W A, Kurzynowski P. Compact spatial polariscope for light polarization state analysis. Opt. Express,2008,16(14):10471-10479.
[28]Flossmann F, O'Holleran K, Dennis M R, et al. Polarization Singularities in 2D and 3D Speckle Fields. Phys. Rev. Lett.,2008,100(20):203902.
[29]Buinyi I O, Denisenko V G, Soskin M S. Topological structure in polarization re-solved conoscopic patterns for nematic liquid crystal cells. Opt. Commun.,2009, 282(2):143-155.
[30]Wiener N. Generalized harmonic analysis. Acta Math.,1930,55:182.
[31]Wolf E. Optics in terms of observable quantities. Nuovo Cimento,1954,12(6):884-888.
[32]Wolf E. Coherence properties of partially polarized electromagnetic radiation. Nuovo Cimento,1959,13(6):1165-1181.
[33]Wolf E. Correlation-induced Doppler-type frequency shifts of spectral lines. Phys. Rev. Lett.,1989,63(20):2220-2223.
[34]Gori F, Santarsiero M, Vicalvi S, et al. Beam coherence-polarization matrix. Pure Appl. Opt,1998,7(5):941-951.
[35]Wolf E. Unified theory of coherence and polarization of random electro magnetic beams. Phys. Lett. A,2003,312(5-6):263-267.
[36]Wolf E. Polarization invariance in beam propagation. Opt. Lett.,2007, 32(23):3400-3401.
[37]Zhao D, Wolf E. Light beams whose degree of polarization does not change on propa-gation. Opt. Commun.,2008,281(11):3067-3070.
[38]Wolf E. Can a light beam be considered to be the sum of a completely polarized and a completely unpolarized beam? Opt. Lett.,2008,33(7):642-644.
[39]Lahiri M, Wolf E. Cross-spectral density matrices of polarized light beams. Opt. Lett., 2009,34(5):557-559.
[40]Lahiri M, Korotkova O, Wolf E. Polarization and coherence properties of a beam formed by superposition of a pair of stochastic electromagnetic beams. Opt. Commun.,2008, 281(20):5073-5077.
[41]Gori F, Santarsiero M. Devising genuine spatial correlation functions. Opt. Lett.,2007, 32(24):3531-3533.
[42]Martinez-Herrero R, Mejias P M, Gori F. Genuine cross-spectral densities and pseudo-modal expansions. Opt. Lett.,2009,34(9):1399-1401.
[43]Gori F. Partially correlated sources with complete polarization. Opt. Lett.,2008, 33(23):2818-2820.
[44]Korotkova O, Wolf E. Changes in the state of polarization of a random electromagnetic beam on propagation. Opt. Commun.,2005,246(1-3):35-43.
[45]Korotkova O, Hoover B G, Gamiz V L, et al. Coherence and polarization properties of far fields generated by quasi-homogeneous planar electromagnetic sources. J. Opt. Soc. Am. A,2005,22(11):2547-2556.
[46]Korotkova O, Salem M, Wolf E. The far-zone behavior of the degree of polarization of random electromagnetic beams propagating through atmospheric turbulence. Opt. Commun.,2004,233(4-6):225-230.
[47]Salem M, Korotkova O, Wolf E. Can two planar sources with the same sets of Stokes parameters generate beams with different degrees of polarization? Opt. Lett.,2006, 31(20):3025-3027.
[48]Yao M, Cai Y, Eyyuboglu H T, et al. Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity. Opt. Lett.,2008, 33(19):2266-2268.
[49]Du X, Zhao D. Criterion for keeping completely unpolarized or completely polarized stochastic electromagnetic Gaussian Schell-model beams on propagation. Opt. Express, 2008,16(20):16172-16180.
[50]Korotkova O, Wolf E. Generalized Stokes parameters of random electromagneticbeams. Opt. Lett.,2005,30(2):198-200.
[51]Shirai T, Wolf E. Correlation between intensity fluctuations in stochastic electromagnetic beams of any state of coherence and polarization. Opt. Commun.,2007,272(2):289-292.
[52]Xin Y, Chen Y, Zhao Q, et al. Effect of cross-polarization of electromagnetic source on the degree of polarization of generated beam. Opt. Commun.,2008,281(8):1954-1957.
[53]Volkov S N, James D F V, Shirai T, et al. Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams. J. Opt. A:Pure Appl. Opt,2008, 10(5):055001 (4pp).
[54]Du X, Zhao D. Changes in generalized Stokes parameters of stochastic electromagnetic beams on propagation through ABCD optical systems and in the turbulent atmosphere. Opt. Commun.,2008,281(24):5968-5972.
[55]Pu J, Korotkova O. Propgation of the degree of cross-polarization of a stochas-tic electromagnetic beam through the turbulent atmosphere. Opt. Commun.,2009, 282(9):1691-1698.
[56]Luis A. Degree of polarization for three-dimensional fields as a distance between corre-lation matrix. Opt. Commun.,2005,253(1-3):10-14.
[57]Setala T, Kaivola M, Friberg A T. Degree of polarization in near fields of thermal sources: effects of surface waves. Phys. Rev. Lett.,2002,88(12):123902.
[58]Setala T, Shevchenko A, Kaivola M, et al. Degree of polarization for optical near fields. Phys. Rev. E,2002,66(1):016615.
[59]Lindfors K, Setala T, Kaivola M, et al. Degree of polarization in tightly focused optical fields. J. Opt. Soc. Am. A,2005,22(3):561-568.
[60]Ellis J, Dogariu A, Ponomarenko S, et al. Degree of polarization of statistically stationary electromagnetic fields. Opt. Commun.,2005,248:333-337.
[61]Bohren C F, Huffman D R. Absorption and scattering of light by small particles. Wein-heim:WILEY-VCH Verlag GmbH & Co. KGaA,2004.
[62]Berg M J, Sorensen C M, Chakrabarti A. Reflection symmetry of a sphere's internal field and its consequences on scattering:a microphysical approach. J. Opt. Soc. Am. A, 2008,25(1):98-107.
[63]Freund I, Soskin M S, Mokhun A I. Elliptic critical points in paraxial optical fields. Opt. Commun.,2002,208(4-6):223-253.
[64]Urbach H P, Pereira S F. Field in focus with a maximum longitudinal electric component. Phys. Rev. Lett.,2008,100(12):123904.
[65]Gori F. Polarization basis for vortex beams. J. Opt. Soc. Am. A,2001,18(7):1612-1617.
[66]Passilly N, Saint Denis R, Ait-Ameur K, et al. Simple interferometric technique for generation of a radially polarized light beam. J. Opt. Soc. Am. A,2005,22(5):984-991.
[67]Kozawa Y, Sato S. Generation of a radially polarized laser beam by use of a conical Brewster prism. Opt. Lett.,2005,30(22):3063-3065.
[68]Wang X L, Ding J, Ni W J, et al. Generation of arbitrary vector beams with a spa-tial light modulator and a common path interferometric arrangement. Opt. Lett.,2007, 32(24):3549-3551.
[69]Xin Y, Chen Y, Zhao Q. Coherent and incoherent polarization encoding of electromag-netic fields. Opt. Commun.,2009,282(7):1260-1264.
[70]Schoonover R W, Visser T D. Creating polarization singularities with an N-pinhole interferometer. Phys. Rev. A,2009,79(4):043809.
[71]Dennis M R. Polarization singularity anisotropy:determining monstardom. Opt. Lett., 2008,33(22):2572-2574.
[72]Dennis M R, Hamilton A C, Courtial J. Superoscillation in speckle patterns. Opt. Lett., 2008,33(24):2976-2978.
[73]Zhu Y, Zhao D. Generalized Stokes parameters of a stochastic electromagnetic beam propagating through a paraxial ABCD optical system. J. Opt. Soc. Am. A,2008, 25(8):1944-1948.
[74]Zhao D, Zhu Y. Generalized formulas for stochastic electromagnetic beams on inverse propagation through nonsymmetrical optical systems. Opt. Lett.,2009,34(7):884-886.
[75]Chowdhury D R, Bhattacharya K, Chakroborty A K, et al. Possibility of an Optical Focal Shift with Polarization Masks. Appl. Opt.,2003,42(19):3819-3826.
[76]Chowdhury D R, Bhattacharya K, Chakraborty A K, et al. Polarization-Based Compen-sation of Astigmatism. Appl. Opt.,2004,43(4):750-755.
[77]Hao B, Leger J. Polarization beam shaping. Appl. Opt.,2007,46(33):8211-8217.
[78]Hao B, Burch J, Leger J. Smallest flattop focus by polarization engineering. Appl. Opt., 2008,47(16):2931-2940.
[79]Martinez-Corral M, Martinez-Cuenca R, Escobar I, et al. Reduction of focus size in tightly focused linearly polarized beams. Appl. Phys. Lett.,2004,85(19):4319-4321.
[80]Dijk T, Visser T D. Evolution of singularities in a partially coherent vortex beam. J. Opt. Soc. Am. A,2009,26(4):741-744.
[81]Dijk T, Schouten H F, Visser T D. Coherence singularities in the field generated by partially coherent sources. Phys. Rev. A,2009,79(3):033805.
[82]Silverman R A. Scattering of plane waves by locally homogeneous dielectric noise. Proc. Cambridge Philos. Soc.,1958,54:530-537.
[83]Fischer D G, Wolf E. Theory of diffraction tomography for quasi-homogeneous random objects. Opt. Commun.,1997,133(1-6):17-21.
[84]Lahiri M, Wolf E, Fischer D G, et al. Determination of correlation functions of scatter-ing potentials of stochstic media from scattering experiments. Phys. Rev. Lett.,2009, 102(12):123901.
[85]Schoonover R W, Rutherford J M, Keller O, et al. Non-local constituitive relations and the quasi-homogeneous approximation. Phys. Lett. A,2005,342(5-6):363-367.
[86]Visser T D, Fischer D G, Wolf E. Scattering of light from quasi-homogeneous sources on quasi-homogeneous media. J. Opt. Soc. Am. A,2006,23(7):1631-1638.
[87]Priest R G, Meier S R. Polarimetric microfacet scattering theory with applications to absorptive and reflective surfaces. Opt. Eng.,2002,41(5):988-993.
[88]Leskova T A, Maradudin A A, Lopez J. Coherence of light scattered from a randomly rough surface. Phys. Rev. E,2005,71(3):036606.
[89]Xin Y, Chen Y, Zhao Q, et al. Beam radiated from quasi-homogeneous uniformly polar-ized electromagnetic source scattering on quasi-homogeneous media. Opti. Commun., 2007,278(2):247-252.
[90]Chen C G, Konkola P T, Ferrera J, et al. Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations. J. Opt. Soc. Am. A,2002, 19(2):404-412.
[91]Tsang L, Kong J A, Ding K H. Scattering of electromagnetic waves:Theory and appli-cations. First ed., New York:John Wiley & Sons, Inc,2000.
[92]Samson J C. Descriptions of the polarization states of vector processes:application to ULF magnetic fields. Geophys. J. R. Astron. Soc.,1973,34:403.
[93]Roychowdhury H, Korotkova O. Realizability conditions for electromagnetic Gaussian-Schell model sources. Opt. Commun.,2005,249:379-385.
[94]Pu J, Korotkova O, Wolf E. Invariance and noninvariance of the spectra of stochastic electromagnetic beams on propogation. Opt. Lett.,2006,31(14):2097-2099.
[95]Pu J, Korotkova O, Wolf E. Polarization-induced spectral changes on propagation of stochastic electromagnetic beams. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics),2007,75(5):056610.
[96]Wolf E, Foley J T, Gori F. Frequency shifts of spectral lines produced by scattering from spatially random media. J. Opt. Soc. Am. A,1989,6(8):1142-1149.
[97]Wolf E. Far-zone spectral isotropy in weak scattering on spatially random media. J. Opt. Soc. Am. A,1997,14(10):2820-2823.
[98]Zhao D, Korotkova O, Wolf E. Application of correlation-induced spectral changes to inverse scattering. Opt. Lett.,2007,32(24):3483-3485.
[99]Gatti A, Brambilla E, Bache M, et al. Ghost Imaging with Thermal Light:Comparing Entanglement and Classical Correlation. Phys. Rev. Lett.,2004,93(9):093602.
[100]Cai Y, Zhu S Y. Ghost interference with partially coherent radiation. Opt. Lett.,2004, 29(23):2716-2718.
[101]Cai Y, Zhu S Y. Ghost imaging with incoherent and partially coherent light radiation. Phys. Rev. E,2005,71(5):056607.
[102]Cai Y, Wang F. Lensless imaging with partially coherent light. Opt. Lett.,2007, 32(3):205-207.
[103]Chen X H, Liu Q, Luo K H, et al. Lensless ghost imaging with true thermal light. Opt. Lett.,2009,34(5):695-697.
[104]Ellis J, Dogariu A. Complex degree of mutual polarization. Opt. Lett.,2004, 29(6):536-538.
[105]Roychowdhury H, Wolf E. Statistical similarity and the physical significance of com-plete spatial coherence and complete polarization of random electromagnetic beams. Optics Communications,2005,248(4-6):327-332.
[106]Gao W. Changes of polarization of light beams on propagation through tissue. Opt. Commun.,2006,260(2):749-754.
[107]Gao W, Korotkova O. Changes in the state of polarization of a random electromagnetic beam propagating through tissue. Opt. Commun.,2007,270(2):474-478.
[108]Salem M, Wolf E. Coherence-induced polarization changes in light beams. Opt. Lett., 2008,33(11):1180-1182.
[109]Korotkova O, Wolf E. Spectral degree of coherence of a random three-dimensional electromagnetic field. J. Opt. Soc. Am. A,2004,21(12):2382-2385.
[110]Chernyshov A A, Felde C V, Bogatyryova H V, et al. Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components. Journal of Optics A:Pure and Applied Optics,2009, 11(9):094010.
[111]Flossmann F, Schwarz U T, Maier M, et al. Polarization Singularities from Unfolding an Optical Vortex through a Birefringent Crystal. Phys. Rev. Lett.,2005,95(25):253901.
[112]Berry M V, Hannay J H. Umbilic points on Gaussian random surfaces. Journal of Physics A:Mathematical and General,1977,10(11):1809-1821.
[113]Zhang Z, Pu J, Wang X. Focusing of partially coherent Bessel-Gaussian beams through a high-numerical-aperture objective. Opt. Lett.,2008,33(1):49-51.
[114]Chen B, Zhang Z, Pu J. Tight focusing of partially coherent and circularly polarized vortex beams. J. Opt. Soc. Am. A,2009,26(4):862-869.
[115]Chen B, Pu J. Tight focusing of elliptically polarized vortex beams. Appl. Opt.,2009, 48(7):1288-1294.
[116]Schoonover R W, Visser T D. Polarization singularities of focused, radially polarized fields. Opt. Express,2006,14(12):5733-5745.
[117]Leutenegger M, Rao R, Leitgeb R A, et al. Fast focus field calculations. Opt. Express, 2006,14(23):11277-11291.
[118]Boruah B, Neil M. Focal field computation of an arbitrarily polarized beam using fast Fourier transforms. Optics Communications,2009,282(24):4660-4667.
[119]Lerman G M, Levy U. Tight focusing of spatially variant vector optical fields with elliptical symmetry of linear polarization. Opt. Lett.,2007,32(15):2194-2196.
[120]Lerman G M, Lilach Y, Levy U. Demonstration of spatially inhomogeneous vector beams with elliptical symmetry. Opt. Lett.,2009,34(11):1669-1671.
[121]Pu J, Lu B. Focal shifts in focused nonuniformly polarized beams. J. Opt. Soc. Am. A, 2001,18(11):2760-2766.
[122]Berry M V. The electric and magnetic polarization singularities of paraxial waves. Jour-nal of Optics A:Pure and Applied Optics,2004,6(5):475-481.
[123]Zhao Y, Edgar J S, Jeffries G D M, et al. Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam. Physical Review Letters,2007,99(7):073901.
[124]Govyadinov A A, Panasyuk G Y, Schotland J C. Phaseless Three-Dimensional Optical Nanoimaging. Physical Review Letters,2009,103(21):213901.