部分相干光相关诱导的光谱变化与光谱开关
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摘要
光谱分析是最重要的科学分析手段之一。在光谱分析中，经常假定光在自由空间传输中其光谱保持不变。在最近十多年，这一被认为是理所当然的假定受到了质疑。1986年，美国著名的光学专家Wolf教授证明：当光源的光谱相干度满足所谓的定标定律时，从光源发出的光在传输中才保持光谱不变。反之，从违反定标定律的光源发出的光在传输过程中，其光谱将会发生变化。这种现象称为相关诱导的光谱变化。之后，人们还发现，当满足定标定律的部分相干光被光阑衍射时，在衍射光场也会出现光谱变化。这种光谱变化有时也称为衍射诱导的光谱变化。
在一般情况下，由两个相同发光光谱的点光源发出的光在迭加区的归一化光谱与两个点光源的归一化光谱不同。在迭加区的归一化光谱被两个点光源之间的相干性调制了。当两个点光源是非相干的，迭加光场观测到的归一化光谱才等于点光源的归一化光谱。
准均匀光源是自然界和实验室常见的光源。可以得到从准均匀光源发出的光在远场的光谱与光源光谱之间的关系。结果表明，在一般情况下，在远场的归一化光谱并不等于光源的归一化光谱，而是依赖于光源的光谱相干度和观测方向。为了使准均匀光源的归一化发光光谱保持传输不变性，光源的光谱相干度必须满足如下式子：
μ(r′)=h(kr′)， (1)式中，r′为光源平面两点r_1和r_2的位置矢量差，即r′=r_2-r_1。k=ω/c是波数，c为真空中的光速。
(1)式就是定标定律。应用这个定标定律，我们能判断从准均匀光源发出的光的光谱是否发生变化。庆幸的是，自然界和实验室某些常见的光源都满足定标定
四少11大学博士学位论文
律
高斯一谢尔模型(GSM)光束是一种特殊的部分相干光束。GSM光束的光强
分布和空间相干度分布均为高斯分布的部分相干光束。我们研究了宽频带GSM光
束在传输中的光谱变化。当GSM光束在自由空间中传输，其光谱在一般情况下也
会发生变化。这种光谱变化依赖于GSM光源的半径w0和有效相干宽度外与频率。
的依赖关系。为了使GSM光束在传输中保持光谱不变，GSM光源的有效相干宽度
内(。)必须满足
W。
一，~血、_甘
on吸口少j二二-气二二二二二二二二二
““了，，一1
(2)
式中，假设GSM光束的半径w0与频率无关，夕是一正常数。
根据光线传输矩阵的传输公式，我们还推导了GSM光束经过ABCD光线传输
矩阵描述的光学系统的传输公式。据此，我们可以发现:GSM光束经过光学系统
传输之后，其光谱也会发生变化。这种光谱变化不仅取决于GSM光束的参数，而
且还取决于光学系统的光线传输矩阵元。作为一个特殊的例子，我们研究了GSM
光束经过色差光学透镜的聚焦。结果发现，光学透镜适量的色差就导致了聚焦光场
的光谱发生显著的变化。并且，这种光谱变化还与GSM光束的相干度有关，GSM
光束的相干度愈低，色差对聚焦光场光谱的影响就愈小。
完全相干光被衍射光栅的衍射是一个熟知的光学过程。但是，当部分相干光被
衍射光栅的衍射时，部分相干光的空间相干度对衍射光束的影响如何却不清楚。我
们研究了GSM光束经过全息光栅的衍射。我们发现当一束GSM光束经过全息光
栅衍射，在衍射光场得到了三束GSM光束，即零级GSM光束和士1级GSM光束。
零级GSM光束的光谱变化与GSM光束在自由空间中传输时的光谱变化情况相同。
而士1级的光谱却发生了很大的变化。这种光谱变化不仅依赖于全息光栅的频率;
而且还依赖于GSM光源的半径和空间相干度。
当满足定标定律的宽频带部分相干光被光阑衍射时，在衍射光场的光谱与光阑
处光的光谱不同。我们发现，在衍射光场的近场和远场的光谱均发生了变化。这种
光谱变化取决于衍射光阑处部分相干光的空间相干度。在衍射光场的近场，光谱分
裂成两个峰。通过测量光谱位移与:/:。的变化关系，我们发现，在一般情况下，
光谱位移随着:/z0的变化而呈现缓慢的变化。但是，当:/z0等于某特殊值时，光
四川大学博士学位论文
谱位移从红移(或蓝移)快速地变成蓝移(或红移)。这种光谱位移的快速变化的
现象就是光谱开关。
我们还研究了另一类型的部分相干光被光阑衍射时，在衍射光场的远场发生的
光谱变化。理论结果表明，在远场处的光谱也发生变化，并且光谱位移随着光阑处
部分相干光的空间相干度的改变而呈现缓慢的变化。但是，当光阑处的部分相干光
的空间相干度等于某一特定值时，在远场也发生光谱开关。另外，在远场的轴外点
也出现光谱开关。并且，在不同的衍射角v的光谱探测器(输出口)出现光谱开关
所对应的空间相干度不同。据此，我们提出了lxN光谱开关。在这种光谱开关中，
通过控制输入口(衍射光阑)的空间相干度，使特定衍射角的输出口发生光谱位移
的快速变化(即光谱开关)。
我们所获得的光谱开关的理论结果己被印度国家物理实验室H.c.KandPal博士
等人实验证实。
The spectral analysis of radiation is one of most important analytic methods in science. Implicit in its use is the assumption that the spectrum of light does not change as the radiation propagates in free space. This assumption has been called into question for past ten years. In 1986, Professor Wolf, a famous optics researcher of America, showed that only when the spectral degree of coherence of a source satisfies the so-called scaling law, does the spectrum of the radiation from the source keep the spectral invariance during its propagation. Conversely, when the source does not satisfy the scaling law, the spectrum of the radiation from the source will experience spectral change. This kind of phenomenon is termed correlation-induced spectral changes. Later it is also found that when partially coherent light whose spectral degree of coherence satisfies the scaling law is diffracted by an aperture, the spectrum of the light in the diffracted field will be changed as well. This kind of spectral changes somet
imes is called the diffraction-induced spectral changes.
Generally the normalized spectrum of the radiation generated by two point sources, with the same normalized spectrum, is different from the normalized spectrum of each source. The normalized spectrum of the light at the superposition of region is modulated by the correlation of the two sources. Only when the two sources are completely uncorrelated, is the normalized spectrum of the light of the superposition region equal to the normalized spectrum of each source.
Quasi-homogenous sources are frequently encountered in nature and laboratory. The relation between the spectrum of the light in the far zone radiated from the source and the spectrum of the source has been derived. It is shown that the normalized spectrum of the light in the far zone is not equal to the normalized spectrum of the source, but is dependent on the spectral degree of coherence of the source and the observed direction. To ensure the normalized spectrum of the light radiated from the quasi-homogenous source be the same throughout the far zone, the spectral degree of coherence of the source should satisfy following equation:
here, r' denotes the vector difference between the two points r, and r2 , i.e., r'= r2 -r1. k = ω/ c is the wave-number associated with the frequency ω . c is the light speed in vacuum.
Formula (1) is just the scaling law. Based on formula (1), we can judge that the spectrum of radiation from a source changes or not. Fortunately some of most commonly occurring sources found in the nature and in laboratory satisfy formula (1).
A Gaussian Schell-model (GSM) beam is one special kind of partially coherent beam. Both the intensity distribution and the coherence distribution of the GSM beam are Gaussian distribution. We have studied the spectral changes of a GSM beam during its propagation. It is shown that even when a GSM beam propagates in free space, its normalized spectrum will change. The spectral changes are dependent on the frequency dependence of the GSM source radius w0 and of the effective coherence
width σ0 (ω) . To keep the spectral invariance of the GSM beam propagating in the free space, the effective coherence width σ0 (ω) should be
here w0 is assumed to be independent of frequency ω , and y is a positive constant.
Based on the ray matrix method, the generalized formulas for describing the propagation of a GSM beam through an optical system of ABCD ray matrix are derived. It is shown that in general the spectral changes also take place as the beam propagates through the optical system, and the spectral changes are not only dependent on the parameters of the GSM beam, but also on the elements of the ray matrix of the optical system. As a special example, the focusing of a GSM beam by a lens with chromatic aberration is presented. We show that suitable chromatic aberration of the lens will lead to remarkable spectral changes of the light near the focus. The spectral changes also depend on the coherence, the lower coherence of th
在一般情况下，由两个相同发光光谱的点光源发出的光在迭加区的归一化光谱与两个点光源的归一化光谱不同。在迭加区的归一化光谱被两个点光源之间的相干性调制了。当两个点光源是非相干的，迭加光场观测到的归一化光谱才等于点光源的归一化光谱。
准均匀光源是自然界和实验室常见的光源。可以得到从准均匀光源发出的光在远场的光谱与光源光谱之间的关系。结果表明，在一般情况下，在远场的归一化光谱并不等于光源的归一化光谱，而是依赖于光源的光谱相干度和观测方向。为了使准均匀光源的归一化发光光谱保持传输不变性，光源的光谱相干度必须满足如下式子：
μ(r′)=h(kr′)， (1)式中，r′为光源平面两点r_1和r_2的位置矢量差，即r′=r_2-r_1。k=ω/c是波数，c为真空中的光速。
(1)式就是定标定律。应用这个定标定律，我们能判断从准均匀光源发出的光的光谱是否发生变化。庆幸的是，自然界和实验室某些常见的光源都满足定标定
四少11大学博士学位论文
律
高斯一谢尔模型(GSM)光束是一种特殊的部分相干光束。GSM光束的光强
分布和空间相干度分布均为高斯分布的部分相干光束。我们研究了宽频带GSM光
束在传输中的光谱变化。当GSM光束在自由空间中传输，其光谱在一般情况下也
会发生变化。这种光谱变化依赖于GSM光源的半径w0和有效相干宽度外与频率。
的依赖关系。为了使GSM光束在传输中保持光谱不变，GSM光源的有效相干宽度
内(。)必须满足
W。
一，~血、_甘
on吸口少j二二-气二二二二二二二二二
““了，，一1
(2)
式中，假设GSM光束的半径w0与频率无关，夕是一正常数。
根据光线传输矩阵的传输公式，我们还推导了GSM光束经过ABCD光线传输
矩阵描述的光学系统的传输公式。据此，我们可以发现:GSM光束经过光学系统
传输之后，其光谱也会发生变化。这种光谱变化不仅取决于GSM光束的参数，而
且还取决于光学系统的光线传输矩阵元。作为一个特殊的例子，我们研究了GSM
光束经过色差光学透镜的聚焦。结果发现，光学透镜适量的色差就导致了聚焦光场
的光谱发生显著的变化。并且，这种光谱变化还与GSM光束的相干度有关，GSM
光束的相干度愈低，色差对聚焦光场光谱的影响就愈小。
完全相干光被衍射光栅的衍射是一个熟知的光学过程。但是，当部分相干光被
衍射光栅的衍射时，部分相干光的空间相干度对衍射光束的影响如何却不清楚。我
们研究了GSM光束经过全息光栅的衍射。我们发现当一束GSM光束经过全息光
栅衍射，在衍射光场得到了三束GSM光束，即零级GSM光束和士1级GSM光束。
零级GSM光束的光谱变化与GSM光束在自由空间中传输时的光谱变化情况相同。
而士1级的光谱却发生了很大的变化。这种光谱变化不仅依赖于全息光栅的频率;
而且还依赖于GSM光源的半径和空间相干度。
当满足定标定律的宽频带部分相干光被光阑衍射时，在衍射光场的光谱与光阑
处光的光谱不同。我们发现，在衍射光场的近场和远场的光谱均发生了变化。这种
光谱变化取决于衍射光阑处部分相干光的空间相干度。在衍射光场的近场，光谱分
裂成两个峰。通过测量光谱位移与:/:。的变化关系，我们发现，在一般情况下，
光谱位移随着:/z0的变化而呈现缓慢的变化。但是，当:/z0等于某特殊值时，光
四川大学博士学位论文
谱位移从红移(或蓝移)快速地变成蓝移(或红移)。这种光谱位移的快速变化的
现象就是光谱开关。
我们还研究了另一类型的部分相干光被光阑衍射时，在衍射光场的远场发生的
光谱变化。理论结果表明，在远场处的光谱也发生变化，并且光谱位移随着光阑处
部分相干光的空间相干度的改变而呈现缓慢的变化。但是，当光阑处的部分相干光
的空间相干度等于某一特定值时，在远场也发生光谱开关。另外，在远场的轴外点
也出现光谱开关。并且，在不同的衍射角v的光谱探测器(输出口)出现光谱开关
所对应的空间相干度不同。据此，我们提出了lxN光谱开关。在这种光谱开关中，
通过控制输入口(衍射光阑)的空间相干度，使特定衍射角的输出口发生光谱位移
的快速变化(即光谱开关)。
我们所获得的光谱开关的理论结果己被印度国家物理实验室H.c.KandPal博士
等人实验证实。
The spectral analysis of radiation is one of most important analytic methods in science. Implicit in its use is the assumption that the spectrum of light does not change as the radiation propagates in free space. This assumption has been called into question for past ten years. In 1986, Professor Wolf, a famous optics researcher of America, showed that only when the spectral degree of coherence of a source satisfies the so-called scaling law, does the spectrum of the radiation from the source keep the spectral invariance during its propagation. Conversely, when the source does not satisfy the scaling law, the spectrum of the radiation from the source will experience spectral change. This kind of phenomenon is termed correlation-induced spectral changes. Later it is also found that when partially coherent light whose spectral degree of coherence satisfies the scaling law is diffracted by an aperture, the spectrum of the light in the diffracted field will be changed as well. This kind of spectral changes somet
imes is called the diffraction-induced spectral changes.
Generally the normalized spectrum of the radiation generated by two point sources, with the same normalized spectrum, is different from the normalized spectrum of each source. The normalized spectrum of the light at the superposition of region is modulated by the correlation of the two sources. Only when the two sources are completely uncorrelated, is the normalized spectrum of the light of the superposition region equal to the normalized spectrum of each source.
Quasi-homogenous sources are frequently encountered in nature and laboratory. The relation between the spectrum of the light in the far zone radiated from the source and the spectrum of the source has been derived. It is shown that the normalized spectrum of the light in the far zone is not equal to the normalized spectrum of the source, but is dependent on the spectral degree of coherence of the source and the observed direction. To ensure the normalized spectrum of the light radiated from the quasi-homogenous source be the same throughout the far zone, the spectral degree of coherence of the source should satisfy following equation:
here, r' denotes the vector difference between the two points r, and r2 , i.e., r'= r2 -r1. k = ω/ c is the wave-number associated with the frequency ω . c is the light speed in vacuum.
Formula (1) is just the scaling law. Based on formula (1), we can judge that the spectrum of radiation from a source changes or not. Fortunately some of most commonly occurring sources found in the nature and in laboratory satisfy formula (1).
A Gaussian Schell-model (GSM) beam is one special kind of partially coherent beam. Both the intensity distribution and the coherence distribution of the GSM beam are Gaussian distribution. We have studied the spectral changes of a GSM beam during its propagation. It is shown that even when a GSM beam propagates in free space, its normalized spectrum will change. The spectral changes are dependent on the frequency dependence of the GSM source radius w0 and of the effective coherence
width σ0 (ω) . To keep the spectral invariance of the GSM beam propagating in the free space, the effective coherence width σ0 (ω) should be
here w0 is assumed to be independent of frequency ω , and y is a positive constant.
Based on the ray matrix method, the generalized formulas for describing the propagation of a GSM beam through an optical system of ABCD ray matrix are derived. It is shown that in general the spectral changes also take place as the beam propagates through the optical system, and the spectral changes are not only dependent on the parameters of the GSM beam, but also on the elements of the ray matrix of the optical system. As a special example, the focusing of a GSM beam by a lens with chromatic aberration is presented. We show that suitable chromatic aberration of the lens will lead to remarkable spectral changes of the light near the focus. The spectral changes also depend on the coherence, the lower coherence of th
引文
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16． E.Wolf and D.F.V.James,"Comelation-induced spectral changes,"Rep.Prog.Phys.59,771-818(1996) .
17． J.T.Foley,"The effect of an aperture on the spectrum of partially coherent light,"Opt.Commun.75,347-352(1990)
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20． D. F. V James and E Wolf, "Spectral changes produced in Young's interference experiment," Opt Commun. 81,150-154(1991)
21． D.F.V,James and E.Wolf,"Some new aspects of Young's interference experiment",Phys.Lett A 157,6-10(1991)
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25． L.Mandel and E.Wolf,Optical Coherence and Quantum Optics(Cambrige University Press,Cambrige, 1995) Chapter4．
26． Z.Lin and Z.Gu,"Angular spectrum redistribution from a real image of a light as a secondary source,"Opt. Lett. 26,663-665 (2001)
27． Y.Ohtsuka,"Spectrum invaniance for a particular class of optical fields propagated in far zone,"Opt.Rev.2, 347-351(1995)
28． Z.Jiang,R.Jacquemin,Q.Lu,and W.Eberhardt,"Spectral shifts of ultrashort pulsed Gaussian beam,"Opt. Commun. 138,253-256(1997)
29． E.Wolf,T.Shirai,H.Chen,and W.Wang,"Coherence filters and their uses:1,Basic theory and examples," J.Mod. Opt 44,1345-1353 (1997)
30． T. Shirai,E.Wolf,H.Chen,and W.Wang,"Coherence filters and their uses:2． One-dimensional realizations,"J.Mod.Opt. 45,799-816(1998)
31． J.H.Walker,R.D.Saunders,J.K.Jackson,and K.D.Mielenz,"Results of a CCPR intercomparison of spectral inadiance measurements by national laboratonies,"J.Res.Natl.Stand.Technol.96,647-668 (1991)
32 J.R.Moore,"Source of enor in spectroradiometry,"Light Res.Technol,12,213-220(1980) .
33． J.Pu, H.Zhang and S. Nemoto, "Spectral shifts and spectral switches of partially coherent light passing
through an aperture,Opt .Commun.162, 57-63 (1999) .
34． J. Pu and S. Nemoto, "Spectral shifts and spectral switches in diffraction of partially coherent.light by a circular aperture,"IEEE J.Quant.Electron.36, 1407-1411 (2000)
35． J. Pu and S.Nemoto,"Spectral changs and x N spectral switches in diffraction of partially coherent light by an aperture,"J.Opt.Soc,Am.A19,339-334(2002) .
36． H.C.Kandpal,''Experimental observation of the phenomenon of spectral switch,"J.Opt.A:Pure and Appl.Opt.3,296-299(2001)
37． H.C.Kandpal,S.Anand,and J.S.Vaishya,"Experimental observation of phenomenon of spectral switch for a class of partially coherent light ,"IEEE J.Quant.Electron.38,336-339(2002) .
38． S.Anand,B.K.Yadav,and H.C.Kandpal,"Experimental study of the phenomenon of 1xN spectral switch due to diffraction of partially coherent light ,"J.Opt.Soc .Am.A19,2223-2228(2002) .
39． L.Pan and B.Lu,"The spectral switch of partially coherent light in Young's experiment,"IEEE J.Quant. Electron.37,1377-1381(2001) .
40． B.Lu and L.Pan, "Spectral switching of Gaussian Schell-model beams passing through an aperture lens," IEEE J.Quant Electron.38, 340-344 (2002)
41． G Gbur,T.D.Visser,and E.Wolf,"Anomalous behavior of spectra near phase singulrities of focused waves,"Phys.Rev.Lett.88,013901 (2002) .
41 G.Gbur,T.D.Visser,and E.Wolf,"Sigular behavior of the spectrum in the neighborhood of focus,"J.Opt. Soc.Am A19, 1694-1700(2002)
43． G Popescu and A.Dogariu,"Spectral anomalies at wave-front dislocations,"Phys.Rev.Lett.88,183902 (2002)
44． S.A.Ponomarenko and E.Wolf,"Spectral anomalies in a Fraunhofer diffraction pattem,"Opt.Lett.27, 1211-1213(2002)
45． J. T. Foley and E.Wolf,"Phenomen of spectral switches as a new effect in singular optics with polychromatic light,".Opt.Soc.Am.A 19,2510-2516(2002)
46． J.Pu and S. Nemoto, "The effect of spectral correlations on spectral switches in the diffraction of partially coherent light,"J. Opt Soc Am A (revised version)
47． R.Gase,"The multimode laser radiation as a Gaussian Schell-model beam,"J.Mod.Opt.38,1107-1115 (1991) .
48． J. T. Foley and M.Wang,"A theoretical analysis of coherence-induced spectral shift experiments of Kandpal,Vaishya,and Joshi,"J.Res.Natl.Stand.Technol. 99,267-280(1994)
49． A.T.Friberg and E.Wolf,"Relationships between the complex degrees of coherence in the spece-time and in the space-frequency domains,"Opt.Lett.20,623-625(1995) .
50． A.Gamliel and E.Wolf,"Spectral modulation by control of source correlations,"Opt.Commun.65,91-96 (1988)
51． M.Bom and E.Wolf,Principles of Optics,7th (expanded)edition(Cambridge University Press,Cambridge,1999) ,Chapter 10．
52 E.W.Marchand and E.Wolf,"Radiometry with sources of any state of coherence,"J.Opt.Soc.Am.64, 1219-1226(1974) .
53． W.H.Carter and E.Wolf,"Coherence and radiometry with quasihomogeneous planar sources,"J.Opt. Soc,Am.67,785-796(1977) .
54． J.T.Foley and M.S.Zubairy,"The directionality of Gaussian Schell-model beams,"Opt.Commun.26, 297-300(1978)
55． A.T.Friberg and R.J.Sudol,"Propagation parameters of Gaussian Schell-model beams,"Opt.Commun. 41,383-387(1982)
56． A T.Friberg and R.J.Sudol,"The spatial coherence properties of Gaussian Schell-model beams,"Opt. Acta 30,1075-1097(1983)
57． AT.Friberg and J.Turunen,"Imaging of Gaussian Schell-model sources,"J.Opt.Soc.Am.A5,713-720 (1988)
58． J.Pu,"Waist location and Rayleigh range for Gaussian Schell model beams,"J.Opt.(Paris)22,157-159 (1991)
59． GGbur and E.Wolf,"The Rayleigh range of Gaussian Schell-model beams,"J.Mod.Opt.48,1735-1741 (2001)
60． J.Pu,"Beam quality changes of Gaussian Schell-model beams propagating through axicons,"Opt.& Quantum Electronics30, 265-270(1998)
61． J.Pu, "A simple procedure for tracing Gaussian Schell-model beams through optical systems,"Optik 99, 120-122(1995)
62 R,Simon,N.Mukunda,and E.C.G.Sudarshan,Partially coherent beams and a generalized ABCD-law," Opt, Commun 65,322-328(1988)
63． B.Lu,B.Zhag,and B.Cai,"Focusing of a Gaussian Schell-model beam through a circular lens,"J.Mod. Opt.42,289-298(1995)
64． Q.He,J.Turunen,and A.T.Friberg,"Propagation and imaging experiments with Gaussian Schell-model
beams,"Opt.Commun 67,245-250(1988)
65． P.D.Santis,F.Gori,G Guattari,and C.Palma,"Anexample of Collett-Wolf source,"Opt. Commun 29, 256-260(1979)
66． E Tervonen,A T Friberg,and J.Turunen,"Gaussian Schell-model beams generated with synthetic acousto-optic holograms,"J.Opt.Soc,Am.A9,796-803(1992) .
67． O.E,Martinez,"Matrix formalism for pulse compressors,"IEEE J.Quant.Electron.24,2530-2536 (1988)
68． O.E.Martinez,"Matrix formalism for disperive laser cavities,"IEEE J.Quant .Electron.25, 296-300 (1989)
69． A.G.Kostenbauder,"Ray-pulse matrices:a rational treatment for dispersive optical systems,"IEEE J. Quant Electron 16, 1148-1157(1990) .
70． Z.L.Horvath and Z.Bor,"Focusing of femtosecond pulses having gaussian spatial distribution,"Opt. Communm100, 6-12(1993)
71． A Yariv,"Imaging of coherent.fields through thr lenslike systems,"Opt.Lett,19, 1607-1608(1994)
72 Z.Mitreska,Lj,Janicijevic,and B.Veljanoski,"Hemite-Gaussian beam transformation by thin hologram grating",Optik 88; 1-6(1991)
73． Lj,Janicijevic,J.Mozer,M.Jonoska,and R.Bejtullahu,"The hyperbolic hologram and its Fresnel diffraction characteristics,"Optik 69,94-104(1985) .
74． Lj,Janicijevic,"The elliptical Gaussian wave transformation due to diffration by an elliptical hologram," Opt,Quantum Electron.17, 125-138(1985)
75． N.Streibl,"Beam shaping with optical anray generator," J.Mod.Opt,36,1559-1573(1989) .
76． R,Szwaykowski and V.Amizon,"Talbot anray illuminator with multilevel phase grating,"Appl,Opt.33, 1109-1114(1993)
77． T.Yatagai,S.Kawai,and H. Huang,"Optical computing and interconmects,"Proc ,IEEE 84 ,828-852 (1996)
78． M.Mitchell,Z.Chen,M.Shih,and M.Segev,"Self-trapping of partially spatially incoherent Light,"Phys. Rev.Lett.77,490-493 (1996)
79． M.Mitchell and M.Segev,"Self-trapping of incoherent white light,"Nature 387,880-883(1997) .
80． J.Pu and H Zhang,"Propagation of Gaussian Schell-model beams through a thin hologram grating," Optik 106,115-118(1997)
81． G.W.Goodman,Introduction to Fourier Optics(McGraw-Hill,New York,1968) Chapter 4．
82 J.Pu, "Spectral shifts of partially coherent light produced by passing through an annular aperture,",J.Opt. (Paris) 24,141-144(1993)
83． J. D. Farina, L M.Nanducci, and E.Collett, "Generation of highly directional beams from a globally incoherent source,"Opt. Commun. 32,203-208(1980)
84． F.Scudieri,M.Bertolotti,and R.Bartolini,"Light scattered by a liquid crystal:a new quasi-themal source," Appl.Opt.131,181-185(1974)
85． M. Bartolotti,F. Scudieri, and S.Verginelli,"Spatial coherene of light scattered by media wtih large comelation length of refractive index fluctuations,"Appl.Opt,15,1842-1844(1976)
86． Y Ohtsuka, "Modulation effects of a sound wave on the mutual coherence function of light," Opt. Commun.17,234-237(1976)
87． Y.Ohtsuka,"Modulation of optical coherence by ultrasonic waves,"J.Opt.Soc,Am.A3,1247-1257 (1986) .
88． J.Turunen,E.Tervonen,and A.T.Friberg,"Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,"J.Appl.Phys.67,49-59(1990) .
89． S.A.Collins,"Lens-system diffraction integral written in tems of matrix optics,"J.Opt.Soc,Am.60,1168-1177(1970)
90． G.W.Goodman,Introduction to Fourier Optics(McGraw-Hill,New York,1968) pp 119-120．
91． M.Bom and E.Wolf,Principles of Optics ,7th(expanded)edition(Cambridge University Press,Cambridge, 1999) Sec.852．
2 E.Wolf,"Non-cosmological redshift of spectral lines",Nature 326,363-265(1987) .
3． E.Wolf,"Redshifts and blueshifts of spectral lines caused by source conelation,"Opt,Commun.62,12-16(1987) .
4． H.C.Kandpal,J.S.Vaishya,K.Saxena,and K.C.Joshi,"Intensity distribution across a source from spectral measurements,"J.Mod.Opt.42,455-464(1995) .
5． H.C.Kandpal,J.S.Vaishya,and K.C.Joshi,"Wolf shift and its application in spectroradiometry,"Opt. Commun.73, 169-172(1989) .
6． E.Wolf,"Comelation-induced Doppler-like frequency shifts of spectral lines," Phys.Rev.Lett.63,2220-2223(1989)
7． D.Faklis and G.M.Momis,"Spectral shifts produced by source comelations,"Opt,Lett.13,4-6(1988) .
8． GM.Momis and D.Faklis,"Effects of source conelation on the spectrum of light,"Opt.Commun,62,5-11(1987) .
9． M.F.Bocko,D.H.Douglass, and R.S.Knox,"Observation of frequency shifts of spectral lines due to source conelations,"Phys,Rev.Lett.58,2649-2651 (1987) .
10． Z.Dacic and E.Wolf,"Changes in the spectrum of partially coherent light propagating in free space,"J.Opt. Soc Am.A 5,1118-1126(1988) .
11． F.Gori,G Guattari,and C.Palma,"Observation of optical redshifts and blueshifts produced by source conelation,"Opt,Commun.67,1-4(1988)
12． G Indebetouw,"Shnthesis of polychromatic light sources with arbitrary degree of coherence:some experiments,"J.Mod.Opt,36,251-259(1989)
13． C.Palma,G.Cincotti,and G.Guattari,"Spectral shift of a Gaussian Schell-model beam beyond a thin lens," IEEE.J.Quant Button 34,378-383(1998)
14． C Palma, G Cincotti,and G Guattari,"Spectral changes in Gaussian cavity lasers," IEEE J.Quant. Electron.34,1082-1088(1998)
15． C,Palma and G Cincotti,"Spectral shifts of a partially coherent field after passing through a lens,"Opt.Lett. 22,671-672, (1997)
16． E.Wolf and D.F.V.James,"Comelation-induced spectral changes,"Rep.Prog.Phys.59,771-818(1996) .
17． J.T.Foley,"The effect of an aperture on the spectrum of partially coherent light,"Opt.Commun.75,347-352(1990)
18． J.T.Foky,"The effect of an aperture on the spectrum of partially coherent light",J.Opt.Soc.Am.A 8, 1099-1105(1991)
19． A.Wasan,H.C..Kandpal,D.S.Mehta,J.S. Vaishya,and K.C.Joshi,":Conelation-induced spectral changes on passing partially coherent light through an annular aperture,"Opt.Commun.121,89-94(1995) .
20． D. F. V James and E Wolf, "Spectral changes produced in Young's interference experiment," Opt Commun. 81,150-154(1991)
21． D.F.V,James and E.Wolf,"Some new aspects of Young's interference experiment",Phys.Lett A 157,6-10(1991)
21 D. F. V,James and E.Wolf,Detemination of the degree of coherence of light from spectroscopic measurements,"Opt.Commun.145,1-4(1997) .
23． S.A.Ponomarenko and E.Wolf,"Coherence properties of light in Young's interference pattem formed with partially coherent light,"Opt.Commun.170,1-8(1999)
24． S.Vicalvi,G.S.Spagnolo,and M.Santarsiero,"Experimental detemination of the size of a source from spectral measurements,"Opt.Commun,145,241-244(1996)
25． L.Mandel and E.Wolf,Optical Coherence and Quantum Optics(Cambrige University Press,Cambrige, 1995) Chapter4．
26． Z.Lin and Z.Gu,"Angular spectrum redistribution from a real image of a light as a secondary source,"Opt. Lett. 26,663-665 (2001)
27． Y.Ohtsuka,"Spectrum invaniance for a particular class of optical fields propagated in far zone,"Opt.Rev.2, 347-351(1995)
28． Z.Jiang,R.Jacquemin,Q.Lu,and W.Eberhardt,"Spectral shifts of ultrashort pulsed Gaussian beam,"Opt. Commun. 138,253-256(1997)
29． E.Wolf,T.Shirai,H.Chen,and W.Wang,"Coherence filters and their uses:1,Basic theory and examples," J.Mod. Opt 44,1345-1353 (1997)
30． T. Shirai,E.Wolf,H.Chen,and W.Wang,"Coherence filters and their uses:2． One-dimensional realizations,"J.Mod.Opt. 45,799-816(1998)
31． J.H.Walker,R.D.Saunders,J.K.Jackson,and K.D.Mielenz,"Results of a CCPR intercomparison of spectral inadiance measurements by national laboratonies,"J.Res.Natl.Stand.Technol.96,647-668 (1991)
32 J.R.Moore,"Source of enor in spectroradiometry,"Light Res.Technol,12,213-220(1980) .
33． J.Pu, H.Zhang and S. Nemoto, "Spectral shifts and spectral switches of partially coherent light passing
through an aperture,Opt .Commun.162, 57-63 (1999) .
34． J. Pu and S. Nemoto, "Spectral shifts and spectral switches in diffraction of partially coherent.light by a circular aperture,"IEEE J.Quant.Electron.36, 1407-1411 (2000)
35． J. Pu and S.Nemoto,"Spectral changs and x N spectral switches in diffraction of partially coherent light by an aperture,"J.Opt.Soc,Am.A19,339-334(2002) .
36． H.C.Kandpal,''Experimental observation of the phenomenon of spectral switch,"J.Opt.A:Pure and Appl.Opt.3,296-299(2001)
37． H.C.Kandpal,S.Anand,and J.S.Vaishya,"Experimental observation of phenomenon of spectral switch for a class of partially coherent light ,"IEEE J.Quant.Electron.38,336-339(2002) .
38． S.Anand,B.K.Yadav,and H.C.Kandpal,"Experimental study of the phenomenon of 1xN spectral switch due to diffraction of partially coherent light ,"J.Opt.Soc .Am.A19,2223-2228(2002) .
39． L.Pan and B.Lu,"The spectral switch of partially coherent light in Young's experiment,"IEEE J.Quant. Electron.37,1377-1381(2001) .
40． B.Lu and L.Pan, "Spectral switching of Gaussian Schell-model beams passing through an aperture lens," IEEE J.Quant Electron.38, 340-344 (2002)
41． G Gbur,T.D.Visser,and E.Wolf,"Anomalous behavior of spectra near phase singulrities of focused waves,"Phys.Rev.Lett.88,013901 (2002) .
41 G.Gbur,T.D.Visser,and E.Wolf,"Sigular behavior of the spectrum in the neighborhood of focus,"J.Opt. Soc.Am A19, 1694-1700(2002)
43． G Popescu and A.Dogariu,"Spectral anomalies at wave-front dislocations,"Phys.Rev.Lett.88,183902 (2002)
44． S.A.Ponomarenko and E.Wolf,"Spectral anomalies in a Fraunhofer diffraction pattem,"Opt.Lett.27, 1211-1213(2002)
45． J. T. Foley and E.Wolf,"Phenomen of spectral switches as a new effect in singular optics with polychromatic light,".Opt.Soc.Am.A 19,2510-2516(2002)
46． J.Pu and S. Nemoto, "The effect of spectral correlations on spectral switches in the diffraction of partially coherent light,"J. Opt Soc Am A (revised version)
47． R.Gase,"The multimode laser radiation as a Gaussian Schell-model beam,"J.Mod.Opt.38,1107-1115 (1991) .
48． J. T. Foley and M.Wang,"A theoretical analysis of coherence-induced spectral shift experiments of Kandpal,Vaishya,and Joshi,"J.Res.Natl.Stand.Technol. 99,267-280(1994)
49． A.T.Friberg and E.Wolf,"Relationships between the complex degrees of coherence in the spece-time and in the space-frequency domains,"Opt.Lett.20,623-625(1995) .
50． A.Gamliel and E.Wolf,"Spectral modulation by control of source correlations,"Opt.Commun.65,91-96 (1988)
51． M.Bom and E.Wolf,Principles of Optics,7th (expanded)edition(Cambridge University Press,Cambridge,1999) ,Chapter 10．
52 E.W.Marchand and E.Wolf,"Radiometry with sources of any state of coherence,"J.Opt.Soc.Am.64, 1219-1226(1974) .
53． W.H.Carter and E.Wolf,"Coherence and radiometry with quasihomogeneous planar sources,"J.Opt. Soc,Am.67,785-796(1977) .
54． J.T.Foley and M.S.Zubairy,"The directionality of Gaussian Schell-model beams,"Opt.Commun.26, 297-300(1978)
55． A.T.Friberg and R.J.Sudol,"Propagation parameters of Gaussian Schell-model beams,"Opt.Commun. 41,383-387(1982)
56． A T.Friberg and R.J.Sudol,"The spatial coherence properties of Gaussian Schell-model beams,"Opt. Acta 30,1075-1097(1983)
57． AT.Friberg and J.Turunen,"Imaging of Gaussian Schell-model sources,"J.Opt.Soc.Am.A5,713-720 (1988)
58． J.Pu,"Waist location and Rayleigh range for Gaussian Schell model beams,"J.Opt.(Paris)22,157-159 (1991)
59． GGbur and E.Wolf,"The Rayleigh range of Gaussian Schell-model beams,"J.Mod.Opt.48,1735-1741 (2001)
60． J.Pu,"Beam quality changes of Gaussian Schell-model beams propagating through axicons,"Opt.& Quantum Electronics30, 265-270(1998)
61． J.Pu, "A simple procedure for tracing Gaussian Schell-model beams through optical systems,"Optik 99, 120-122(1995)
62 R,Simon,N.Mukunda,and E.C.G.Sudarshan,Partially coherent beams and a generalized ABCD-law," Opt, Commun 65,322-328(1988)
63． B.Lu,B.Zhag,and B.Cai,"Focusing of a Gaussian Schell-model beam through a circular lens,"J.Mod. Opt.42,289-298(1995)
64． Q.He,J.Turunen,and A.T.Friberg,"Propagation and imaging experiments with Gaussian Schell-model
beams,"Opt.Commun 67,245-250(1988)
65． P.D.Santis,F.Gori,G Guattari,and C.Palma,"Anexample of Collett-Wolf source,"Opt. Commun 29, 256-260(1979)
66． E Tervonen,A T Friberg,and J.Turunen,"Gaussian Schell-model beams generated with synthetic acousto-optic holograms,"J.Opt.Soc,Am.A9,796-803(1992) .
67． O.E,Martinez,"Matrix formalism for pulse compressors,"IEEE J.Quant.Electron.24,2530-2536 (1988)
68． O.E.Martinez,"Matrix formalism for disperive laser cavities,"IEEE J.Quant .Electron.25, 296-300 (1989)
69． A.G.Kostenbauder,"Ray-pulse matrices:a rational treatment for dispersive optical systems,"IEEE J. Quant Electron 16, 1148-1157(1990) .
70． Z.L.Horvath and Z.Bor,"Focusing of femtosecond pulses having gaussian spatial distribution,"Opt. Communm100, 6-12(1993)
71． A Yariv,"Imaging of coherent.fields through thr lenslike systems,"Opt.Lett,19, 1607-1608(1994)
72 Z.Mitreska,Lj,Janicijevic,and B.Veljanoski,"Hemite-Gaussian beam transformation by thin hologram grating",Optik 88; 1-6(1991)
73． Lj,Janicijevic,J.Mozer,M.Jonoska,and R.Bejtullahu,"The hyperbolic hologram and its Fresnel diffraction characteristics,"Optik 69,94-104(1985) .
74． Lj,Janicijevic,"The elliptical Gaussian wave transformation due to diffration by an elliptical hologram," Opt,Quantum Electron.17, 125-138(1985)
75． N.Streibl,"Beam shaping with optical anray generator," J.Mod.Opt,36,1559-1573(1989) .
76． R,Szwaykowski and V.Amizon,"Talbot anray illuminator with multilevel phase grating,"Appl,Opt.33, 1109-1114(1993)
77． T.Yatagai,S.Kawai,and H. Huang,"Optical computing and interconmects,"Proc ,IEEE 84 ,828-852 (1996)
78． M.Mitchell,Z.Chen,M.Shih,and M.Segev,"Self-trapping of partially spatially incoherent Light,"Phys. Rev.Lett.77,490-493 (1996)
79． M.Mitchell and M.Segev,"Self-trapping of incoherent white light,"Nature 387,880-883(1997) .
80． J.Pu and H Zhang,"Propagation of Gaussian Schell-model beams through a thin hologram grating," Optik 106,115-118(1997)
81． G.W.Goodman,Introduction to Fourier Optics(McGraw-Hill,New York,1968) Chapter 4．
82 J.Pu, "Spectral shifts of partially coherent light produced by passing through an annular aperture,",J.Opt. (Paris) 24,141-144(1993)
83． J. D. Farina, L M.Nanducci, and E.Collett, "Generation of highly directional beams from a globally incoherent source,"Opt. Commun. 32,203-208(1980)
84． F.Scudieri,M.Bertolotti,and R.Bartolini,"Light scattered by a liquid crystal:a new quasi-themal source," Appl.Opt.131,181-185(1974)
85． M. Bartolotti,F. Scudieri, and S.Verginelli,"Spatial coherene of light scattered by media wtih large comelation length of refractive index fluctuations,"Appl.Opt,15,1842-1844(1976)
86． Y Ohtsuka, "Modulation effects of a sound wave on the mutual coherence function of light," Opt. Commun.17,234-237(1976)
87． Y.Ohtsuka,"Modulation of optical coherence by ultrasonic waves,"J.Opt.Soc,Am.A3,1247-1257 (1986) .
88． J.Turunen,E.Tervonen,and A.T.Friberg,"Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,"J.Appl.Phys.67,49-59(1990) .
89． S.A.Collins,"Lens-system diffraction integral written in tems of matrix optics,"J.Opt.Soc,Am.60,1168-1177(1970)
90． G.W.Goodman,Introduction to Fourier Optics(McGraw-Hill,New York,1968) pp 119-120．
91． M.Bom and E.Wolf,Principles of Optics ,7th(expanded)edition(Cambridge University Press,Cambridge, 1999) Sec.852．