部分相干光经像差光学系统的传输和光谱特性研究
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摘要
激光束的聚焦和光谱特性是现代光学研究的主要内容,对现代光学理论和激光技术的发展具有重要意义。本文从部分相干光的传输理论出发,以模拟实际多模激光的一类典型部分相干光——高斯-谢尔模型(GSM)光束为主要研究对象,对部分相干光束通过有像差光学系统的传输特性和光谱变化进行了深入研究。
介绍了研究光束传输变换的基本理论方法,包括矩阵光学方法和衍射积分方法。阐述了描述部分相干光束的数学-物理模型,包括高斯-谢尔模型(GSM)光束、准单色矢量高斯-谢尔模型光束即准单色部分偏振高斯-谢尔模型(PGSM)光束和有扭曲的各向同性高斯-谢尔模型(TGSM)光束。在此基础上,本文进行的主要工作有:
根据光学系统的传输矩阵和部分相干光的传输理论,推出了GSM光束通过光阑像散透镜的传输公式。通过数值分析计算表明,被光阑像散透镜聚焦的高斯-谢尔模型光束的轴上光强分布、轴上最大光强和轴上最大光强位置与透镜的像散、光场的相关性、光阑截断参数和菲涅耳数有关。详细分析了这些参数对GSM光束聚焦特性的影响。
基于空间-时间域中互强度的传输理论和BCP矩阵处理方法,首次研究了PGSM光束通过光阑球差透镜的传输变换特性,推导出了PGSM光束传输表达式,可以对PGSM光束偏振和光强的传输变化进行分析。数值计算结果表明,系统球差影响PGSM光束的轴上光强分布和偏振度。同时对PGSM光束通过光阑球差透镜分离系统的焦移和焦开关进行了研究,着重分析了球差和相关参数对焦开关的影响。
从部分空间相干光的传输理论出发,对被光阑像散透镜聚焦GSM光束轴上的光谱变化和光谱开关作了研究。对实际光学透镜,除了空间相关诱导的光谱变化外,透镜像散也会诱导光谱变化。像散会使光谱开关出现的位置发生变化,随着像散增大到一定程度,光谱开关出现的位置会明显向聚焦几何焦面方向移动。特别是当像散系数C6大到一定程度,光谱开关会消失。
采用衍射积分方法,分析了扭曲高斯谢尔-模型光束被光阑衍射诱导的光谱变化和光谱开关。着重强调扭曲因子μ对光谱变化和光谱开关的影响。结果表明,扭曲因子可以改变出现光谱开关的临界位置,并且扭曲因子μ可使光谱的最小值Smin增加、光谱跃迁量Δ减小。无像差GSM光束的光谱可以作为TGSM光束的一种特殊情况μ=0。
The focusing and spectral properties of laser beam are topics of current interest, which play an important role in development of the modern optics theory and laser technologies. Starting from the propagation law of partially coherent light and using a typical partially coherent light, i.e., Gaussian Schell-model (GSM) beam describing the multimode laser in practice, I present in this dissertation the research results on propagation properties and spectral changes of partially coherent light passing through an optical system with aberration.
A comprehensive review of the basic analytical methods for the beam transformation including the matrix optics method and diffraction integral method is summarized. And several beam models for the partially coherent beam are introduced, which include GSM beam, partially polarized Gaussian Schell-model (PGSM) beam and isotropic twisted Gaussian Schell-model (TGSM) beam et al. Based on the above theory and methods, the main works of this thesis are listed as follows:
Starting from the transfer matrix of optical system and propagation law of partially coherent light, the expression of GSM beam passing through an astigmatic aperture lens is derived. It is shown that the axial irradiance distribution, the maximum axial irradiance and its position of focused GSM beams by an astigmatic aperture lens depend upon the astigmatism of the lens, the coherence of partially coherent light, the truncation parameter of the aperture and Fresnel number. The numerical calculation results are given to illustrate how these parameters affect the focusing property.
Starting from the propagation law of partially coherent light and beam coherence-polarization (BCP) matrix approach, the properties of PGSM beams through an aperture lens with spherical aberration are studied. The propagation equations of PGSM beams are derived, which enable us to study the axial polarization changes and irradiance distributions of PGSM beams through an aperture lens with spherical aberration. Detailed numerical results show that the spherical aberration affects axial polarization and irradiance distributions. At the same time, the focal shift and focal switch of PGSM beams passing through a system with the aperture and spherically aberrated lens separated is studied in detail. Our main attention is focused on the effect of spherical aberration and partial coherence on the focal shift and focal switch of PGSM beams.
Starting from the propagation law of partially coherent light, the spectral shifts and spectral switches of GSM beams focused by an astigmatic aperture lens are studied. As compared with the aberration-free case, where the spectral change is only correlation-induced, the astigmatism of lens affects the spectral behavior of GSM beams. The astigmatism of lens can change the position where the spectral switch appears, and the position shifts towards the focal plane obviously. However, the spectral switch disappears when the astigmatism is big enough.
Basing on the diffraction integral method, the spectral changes and spectral switches of TGSM beams diffracted by an aperture are studied. The influence of the twist factor on spectral changes and spectral switches of TGSM beams is emphasized. It is shown that the twist factor can change the critical position where the spectral switch takes place. And the spectral minimum Smin increases and transition height ? decreases with increasing twist factor. In addition, Spectrum of GSM beams without aberration through an aperture can be treated as special case ofμ=0.
介绍了研究光束传输变换的基本理论方法,包括矩阵光学方法和衍射积分方法。阐述了描述部分相干光束的数学-物理模型,包括高斯-谢尔模型(GSM)光束、准单色矢量高斯-谢尔模型光束即准单色部分偏振高斯-谢尔模型(PGSM)光束和有扭曲的各向同性高斯-谢尔模型(TGSM)光束。在此基础上,本文进行的主要工作有:
根据光学系统的传输矩阵和部分相干光的传输理论,推出了GSM光束通过光阑像散透镜的传输公式。通过数值分析计算表明,被光阑像散透镜聚焦的高斯-谢尔模型光束的轴上光强分布、轴上最大光强和轴上最大光强位置与透镜的像散、光场的相关性、光阑截断参数和菲涅耳数有关。详细分析了这些参数对GSM光束聚焦特性的影响。
基于空间-时间域中互强度的传输理论和BCP矩阵处理方法,首次研究了PGSM光束通过光阑球差透镜的传输变换特性,推导出了PGSM光束传输表达式,可以对PGSM光束偏振和光强的传输变化进行分析。数值计算结果表明,系统球差影响PGSM光束的轴上光强分布和偏振度。同时对PGSM光束通过光阑球差透镜分离系统的焦移和焦开关进行了研究,着重分析了球差和相关参数对焦开关的影响。
从部分空间相干光的传输理论出发,对被光阑像散透镜聚焦GSM光束轴上的光谱变化和光谱开关作了研究。对实际光学透镜,除了空间相关诱导的光谱变化外,透镜像散也会诱导光谱变化。像散会使光谱开关出现的位置发生变化,随着像散增大到一定程度,光谱开关出现的位置会明显向聚焦几何焦面方向移动。特别是当像散系数C6大到一定程度,光谱开关会消失。
采用衍射积分方法,分析了扭曲高斯谢尔-模型光束被光阑衍射诱导的光谱变化和光谱开关。着重强调扭曲因子μ对光谱变化和光谱开关的影响。结果表明,扭曲因子可以改变出现光谱开关的临界位置,并且扭曲因子μ可使光谱的最小值Smin增加、光谱跃迁量Δ减小。无像差GSM光束的光谱可以作为TGSM光束的一种特殊情况μ=0。
The focusing and spectral properties of laser beam are topics of current interest, which play an important role in development of the modern optics theory and laser technologies. Starting from the propagation law of partially coherent light and using a typical partially coherent light, i.e., Gaussian Schell-model (GSM) beam describing the multimode laser in practice, I present in this dissertation the research results on propagation properties and spectral changes of partially coherent light passing through an optical system with aberration.
A comprehensive review of the basic analytical methods for the beam transformation including the matrix optics method and diffraction integral method is summarized. And several beam models for the partially coherent beam are introduced, which include GSM beam, partially polarized Gaussian Schell-model (PGSM) beam and isotropic twisted Gaussian Schell-model (TGSM) beam et al. Based on the above theory and methods, the main works of this thesis are listed as follows:
Starting from the transfer matrix of optical system and propagation law of partially coherent light, the expression of GSM beam passing through an astigmatic aperture lens is derived. It is shown that the axial irradiance distribution, the maximum axial irradiance and its position of focused GSM beams by an astigmatic aperture lens depend upon the astigmatism of the lens, the coherence of partially coherent light, the truncation parameter of the aperture and Fresnel number. The numerical calculation results are given to illustrate how these parameters affect the focusing property.
Starting from the propagation law of partially coherent light and beam coherence-polarization (BCP) matrix approach, the properties of PGSM beams through an aperture lens with spherical aberration are studied. The propagation equations of PGSM beams are derived, which enable us to study the axial polarization changes and irradiance distributions of PGSM beams through an aperture lens with spherical aberration. Detailed numerical results show that the spherical aberration affects axial polarization and irradiance distributions. At the same time, the focal shift and focal switch of PGSM beams passing through a system with the aperture and spherically aberrated lens separated is studied in detail. Our main attention is focused on the effect of spherical aberration and partial coherence on the focal shift and focal switch of PGSM beams.
Starting from the propagation law of partially coherent light, the spectral shifts and spectral switches of GSM beams focused by an astigmatic aperture lens are studied. As compared with the aberration-free case, where the spectral change is only correlation-induced, the astigmatism of lens affects the spectral behavior of GSM beams. The astigmatism of lens can change the position where the spectral switch appears, and the position shifts towards the focal plane obviously. However, the spectral switch disappears when the astigmatism is big enough.
Basing on the diffraction integral method, the spectral changes and spectral switches of TGSM beams diffracted by an aperture are studied. The influence of the twist factor on spectral changes and spectral switches of TGSM beams is emphasized. It is shown that the twist factor can change the critical position where the spectral switch takes place. And the spectral minimum Smin increases and transition height ? decreases with increasing twist factor. In addition, Spectrum of GSM beams without aberration through an aperture can be treated as special case ofμ=0.
引文
1. E. Wolf. Coherence and radiometry [J]. J. Opt. Soc. Am. 1978, 68: 6-17.
2. E. Collett, E. Wolf. Is complete coherence necessary for the generation of highly directional light beams? [J]. Opt. Lett. 1978, 2: 27-29.
3. E. Wolf, E. Collett. Partially coherent sources which produce the same far-field intensity distribution as a laser [J]. Opt. Commun. 1978, 25: 293-296.
4. J.T. Foley, M.S. Zubairy. The directional of Gaussian-Schell-model beams [J]. Opt. Commun. 1978, 26: 297-300.
5. P.D. Santis, F. Gori, G. Guattari, C. Palma. An example of a Collett-Wolf source [J]. Opt. Commun. 1979, 29: 256-260.
6. J.D. Farina, L.M. Narducci, E. Collett. Generation of highly directional beams from a globally incoherent source [J]. Opt. Commun. 1980, 32: 203-208.
7. F. Gori. Mode propagation of the field generated by Collett-Wolf Schell-Model sources [J]. Opt. Commun. 1983,.46: 149-154.
8. G. Gbur, E. Wolf. Sources of arbitrary states of coherence that generate completely coherent fields outside the source. [J]. Opt. Lett. 1997, 22: 943-946.
9. F. Gori, M. Santarsiero. Intensity-based modal analysis of partially coherent beams with Hermite-Gaussian modes [J]. Opt. Lett. 1998, 23: 989-991.
10. A.T. Friberg, T.D. Visser, E. Wolf. A reciprocity inequality for Gaussian Schell-model beams and some of its consequences [J]. Opt. Lett. 2000, 25: 366-368.
11. S.A. Ponomarenko, E. Wolf. Light beams with minimum phase space product [J]. Opt. Lett. 2000, 25:
663-665.
12. T.D. Visser, A.T. Friberg, E. Phase-space inequality for partially coherent optical beams [J]. Opt. Commun. 2001, 187: 1-6.
13. T. Shirai, E. Wolf. Spatial coherence properties of the far field of a class of partially coherent beams which have the same directionality as a fully coherent laser beam [J]. Opt. Commun, 2002.204: 25-31.
14. F. Gori. Collet-Wolf sources and multimode lasers [J]. Opt. Commun. 1980, 34: 301-305.
15. R. Simon, E.C.G. Sudarshan, and N. Mukunda. Generalized ray in first-order optics: Transformation properties of Gaussian Schell-model fields [J]. Phys. Rev. A 1984, 29: 3273-3279.
16. A.T. Friberg, R.J. Sodol Propagation parameters of Gaussian Schell-model beams [J]. Opt. Commun. 1982, 41: 383-387.
17. A.T. Friberg, J. Turunen. Imaging of Gaussian Schell-model sources [J]. J. Opt. Soc. Am. A 1988, 5: 713-719.
18. R. Gase. The multimode laser radiation as a Gaussian Schell-model beam [J]. J. Mod. Opt. 1991, 38: 1107-1115.
19. E. Wolf. Invariance of spectrum of light on propagation [J]. Phys. Rev. Lett. 1986, 56: 1370-1372.
20. G. M. Morris, D. Faklis. Effects of source correlation on the spectrum of light [J]. Opt. Commun. 1987,62: 5-11.
21. D. Faklis, G. M. Morris. Spectral shifts produced by source correlations [J]. Opt. Lett. 1988, 13: 4-6.
22. L. Mandel, E. Wolf. Optical Coherence and Quantum Optics [J]. Cambridge University Press, Cambridge. 1995.
23. C. Palma, G. Cincotti, et al.. Spectral shift of a Gaussian Schell-model beam beyond a thin lens [J]. IEEE J. Quantum Electron. 1998, 34: 378-383.
24. C. Palma, G. Cincotti. Spectral shifts of a partially coherent field after passing through a lens [J]. Opt. Lett. 1997, 22: 671-672.
25. H.C. Kandpal, A. Wasan, J.S Vaishya. Spectroscopy of partially coherent fields at geometrical-image plane and Fourier transform plane of a lens [J]. Opt. Commun. 1998, 149: 1-7.
26. E. Wolf. Redshifts and blueshifts of spectral lines caused by source correlation [J]. Opt. Commun. 1987, 62: 12-16.
27. F. Gori, G. Guattari, et al.. Observation of optical redshifts and blueshifts produced by source correlations [J]. Opt. Commun. 1988, 67: 1-4.
28. E. Wolf. Correlation-induced Doppler-like frequency shifts of spectral lines [J]. Phys. Rev. Lett. 1989,
63: 2220-2223.
29. H.C. Kandpal, J.S. Vaishya, K.C. Joshi. Simple experimental arrangement for observing spectral shifts due to source correlation [J]. Phys. Rev A 1987, 41: 4541-4542.
30. M.F. Bocko, D.H. Douglass, R.S. Knox. Observation of frequency shifts of spectral lines due to source correlations [J]. Phys. Rev. Lett. 1987, 58: 2649-2651.
31. Z. Dacic, E. Wolf. Changes in the spectrum of partially coherent light propagating in free space [J]. J. Opt. Soc. Am. A 1988, 5: 1118-1126.
32. F. Gori, G. Guattari, C. Palma. Observation of optical redshifts and blueshifts produced by source correlation [J]. Opt. Commun. 1988, 67: 1-4.
33. H.C. Kandpal, J.S. Vaishya, K.C. Joshi. Wolf shift and its application in spectroradiometry [J]. Opt. Commun. 1989, 73: 169-172.
34. E. Wolf, D.F.V. James. Correlation-induced spectral changes [J]. Rep. Prog. Phys. 1996, 59: 771-818.
35. D.F.V. James, E. Wolf. Some new aspects of Young’s interference experiment [J]. Phys. Lett. A 1991, 157: 6-10.
36. M. Santarsiero, F. Gori. Spectral changes in a Young’s interference pattern [J]. Phys. Lett. A 1992, 167: 123-128.
37. S. Vicalvi, S.G Schirripa, et al.. Experimental determination of the size of a source from spectral measurements [J]. Opt. Commun. 1996, 130: 241-244.
38. S.A. Ponomarenko, E. Wolf. Coherence properties of light in Young’s interference pattern formed with partially coherent light [J]. Opt. Commun. 1999, 170: 1-8
39. H.C. Kandpal, J.S. Vaishya. Experimental study of coherence properties of light fields in the region of superposition in Young’s interference experiment [J]. Opt. Commun. 2000, 186: 15-20.
40. J.T. Foley. The effect of an aperture on the spectrum of partially coherent light [J]. Opt. Commun. 1990,75: 347-352.
41. J.T. Foley. The effect of an aperture on the spectrum of partially coherent light [J]. J. Opt. Soc. Am. A 1991, 8: 1099-1105.
42. A. Wasan, H.C. Kandpal, D.S. Mehta, J.S. Vaishya, K.C. Joshi. Correlation-induced spectral changes on passing partially coherent light through an annular aperture [J]. Opt. Commun. 1995, 121: 89-94.
43. D.F.V. James, E. Wolf. Determination of the degree of coherence of light from spectroscopic measurements [J]. Opt. Commun. 1997, 145: 1-4.
44. Z. Lin, Z. Gu. Angular spectrum redistribution from a real image of a light as a secondary source [J]. Opt. Lett. 2001, 26: 663-665.
45. J.H. Walker, R.D. Saunders, J.K. Jackson, K.D. Results of a CCPR intercomparison of spectral irradiance measurements by national laboratories [J]. J. Res. Natl. Stand. Technol. 1991, 96: 647-668.
46. C. Palma, G. Cincotti, G. Guattari. Spectral changes in Gaussian cavity lasers [J]. IEEE J. Quant. Electron. 1998, 34: 1082-1088.
47. E. Wolf, T. Shirai, H. Chen, W. Wang. Coherence filters and their uses: 1.Basic theory and examples [J]. J. Mod. Opt. 1997, 44: 1345-1353.
48. T. Shirai, E. Wolf, H. Chen, W. Wang. Coherence filters and their uses: 2.One-dimensional realizations [J]. J. Mod. Opt. 1998, 45: 799-816.
49. E Wolf, Y Li. Conditions for the validity of the Debye integral representation of focused fields [J]. Opt. Commun. 1981, 39: 205-210.
50. Y Li, E Wolf. Focal shift in focused truncated Gaussian beams [J]. Opt. Commun. 1982, 42: 151-156.
51. Y Li. Dependence of the focal shift on Fresnel number and f number [J]. J. Opt. Soc. Am. A 1982, 72:
770-774.
52. Y Li, E Wolf.Three-dimensions intensity distribution near the focus in systems of different Fresnel numbers [J]. J. Opt. Soc. Am. A 1984, 1: 801-808.
53. Y Li. Oscillations and discontinuity in the focal shift of Gaussian laser beams [J]. J. Opt. Soc. Am. A 1986, 3: 1761-1765.
54. W H Carter, M F Aburdene. Focal shift in Laguerre-Gaussian beams [J]. J. Opt. Soc. Am. A 1987, 4: 1949-1952.
55. Y Li.Variations of the axial intensity pattern formed by a focused truncated Gaussian beam [J]. J. Opt. Soc. Am. A 1988, 68: 324-328.
56. P Andres, M Martinez-Corral, J Ojeda-Castaneda. Off-axis focal shift for rotationally nonsymmetric screens [J]. Opt Lett. 1993, 18: 1290-1292.
57. M Martínez-Corral, V Climent. Focal switch: a new effect in low-Fresnel-number systems [J]. Appl Opt 1996, 35: 24-7.
58. A T Friberg, T D Visser, W Wang, E Wolf. Focal shifts of converging diffracted waves of any state of spatial coherence [J]. Opt. Commun. 2001, 196: 1-7.
59. A Yoshida, T Asakura. Focusing a Gaussian laser beam without focal shift [J]. Opt. Commun. 1994, 109: 368-374.
60. A Yoshida, T Asakura. Propagation and focusing of Gaussian laser beams beyond conventional diffraction limit [J]. Opt. Commun. 1996, 123: 694-704.
61. G P Karamn, A V Duijl, J P Woerdman. Observation of a stronger focus due to spherical aberration [J]. J. Mod. Opt. 1998, 45: 2513-2517.
62. J Carlos, M Manuel, A Pedro, et al. Inverse focal shift: a new effect in truncated cylindrical waves [J]. J. Mod. Opt. 1999, 46: 129-144.
63. J Pu. Focusing Gausion beams by an annular lens with spherical aberration [J]. J. Mod. Opt. 1998, 45: 239-247.
64. J Pu, H Zhang. Intensity distribution of Gaussion beams focused by a lens with spherical aberration [J]. Opt. Commun. 1998, 151: 331-338.
65. J Pu, H Zhang. Aberrated lenses for generating flattened laser irradiance [J]. Appl. Opt. 1998, 37: 4200-4205.
66. 蒲继雄. 利用球差透镜获得超衍射极限聚焦[J]. 中国激光. 1999, A26:542-546.
67. B. Lü, B.Zhang, B.Cai. The integrated intensity of a Gaussian Schell-model beam focused by a lens [J]. Optik.1995, 101:42-46.
68. B. Lü, B. Zhang, B. Cai. The intensity distribution of a Gaussian Schell-model beam focused by an aperture lens [J]. J. Mod. Opt.1995, 42:523-540.
69. B. Lü, B. Zhang, B. Cai. Focusing of a Gaussian Schell-model beam through a circular lens [J]. J. Mod. Opt.1995, 42:289-298.
70. 吕百达,张彬,蔡邦维. 部分相干光聚焦场特性的分析[J]. 激光技术. 1996, 20:108-111.
71. W. Wang, A .T. Friberg, E Wolf. Focusing of partially coherent light in systems of large Fresnel numbers [J]. J. Opt. Soc. Am. A.1997, 14: 491-504.
72. J. Pu, S. Nemoto, H. Zhang. Reshaping Gaussian Schell-model beams to uniform profiles by lens spherical aberration [J]. J. Mod. Opt. 1999, 46:1611-1620.
73. J. Pu, S. Nemoto, W. Zhang. Axial intensity distribution of partially coherent light focused by a lens with spherical aberration [J]. J. Mod. Opt.2000, 47:605-612.
74. 潘留占,吕百达.部分相干光通过像散透镜的聚焦特性[J]. 激光技术. 2003,27:374-379.
75. J. Pu, H. Zhang, S. Nemoto. Spectral shifts and spectral switches of partially coherent light passing through an aperture [J]. Opt. Commun. 1999, 162: 57-63.
76. H.C. Kandpal. Experimental observation of the phenomenon of spectral switch [J]. J. Opt. A: Pure and Appl. Opt. 2001, 3: 296-299.
77. L Pan , B Lü. The spectral switch of partially coherent light in Young’s experiment [J]. IEEE J .Quant .Electron. 2001, 37:1377-1381.
78. B. Lü, L. Pan. Spectral switching of Gaussian Schell-model beams through an aperture lens [J]. IEEE J. Quant. Electron. 2002, 38:340-344.
79. B.K.Yadav, S.A.M Rizvi., H.C Kandpal. Experimental observation of spectral changes of partially coherent light in Young’s experiment [J]. J. Opt. A: Pure and Appl Opt. 2006, 8: 72-76.
80. M.S. Soskin, M.V. Vasnetsov. “Singular optics” Progress in Optics [J].2001, 42: 219-276.
81. G. Gbur, T.D. Visser, E. Wolf. Anomalous behavior of spectra near phase singularities of focused waves [J]. Phys. Rev. Lett. 2002, 88: 013901.
82. G. Gbur, T.D. Visser, E. Wolf. Singular behavior of the spectrum in the neighborhood of focus [J]. J. Opt. Soc. Am. A 2002, 19: 1694-1700.
83. S.A. Ponomarenko, E. Wolf. Spectral anomalies in a Fraunhofer diffraction pattern [J]. Opt. Lett. 2002, 27: 1211-1213.
84. J.T. Foley, E. Wolf. Phenomenon of spectral switches as a new effect in singular optics with polychromatic light [J]. J. Opt. Soc. Am. A 2002, 19: 2510-2516.
85. G. Popescu, A. Dogariu. Spectral anomalies at wave-front dislocations [J]. Phys. Rev. Lett. 2002, 88: 183902.
86. J. Pu, S. Nemoto. Spectral shifts of partially coherent beams focused by a lens with chromatic aberration [J]. Opt. Commun. 2002, 207: 1-5.
87. J. Pu, C. Cai, S. Nemoto. Chin. The spectral changes of partially coherent light focused by an aperture lens with chromatic aberration [J]. Opt. Lett. 2004, 2:239-242.
88. L. Pan, B. Lü.Spectral changes of Gaussian Schell-model beams passing through a dispersive lens [J]. Optik. 2003,114:485-490.
89. L.Pan, B. Lü. Spectral switches of polychromatic Gaussian beams passing through an astigmatic aperture lens [J]. Opt. Commun. 2004, 234: 1-6.
90. G. Zhao, X. Xiao, B. Lü.Effect of astigmatism on spectral switches of partially coherent beams [J]. Chinese Physics.2004, 13:2064-2070.
91. G. Zhao, B. Lü. Influence of aperture lens with spherical aberration on the spectral behaviour of polychromatic Gaussian Schell-model beams [J].Optik.2004, 115:181-186.
92. 肖希,吕百达.多色高斯-谢尔模型光束通过球差透镜的光谱变化[J]. 光学学报. 2005, 25:542-546.
93. 渠彪, 蒲继雄, 陈子阳. 部分相干光经色差透镜聚焦后的光谱开关现象[J]. 光电子·激光. 2006, 17:1142-1145.
94. B. Qu, J. Pu, Z. Chen. Experimental observation of spectral switch of partially coherent light focused by a lens with chromatic aberration [J]. Optics & Laser Technology.2007, 39:1226-1230.
95. R. Simon, N. Mukunda. Twisted Gaussian Schell-model beams [J]. J. Opt. Soc. Am. A .1993, 10:95-104.
96. A .T. Friberg, E. Tervonen, J. Turunen. Interpretation and experimental demonstration of twisted Gaussian Schell-model beams [J]. J. Opt. Soc. Am. A 1994,11:1818-1828
97. A.T. Friberg, E.Tervonen, J.Turunen .Focusing of twisted Gaussian Schell-model beams [J]. Opt. Commun. 1994, 106: 127-132.
98. Y Cai, Q Lin. Spectral shift of partially coherent twisted anisotropic Gaussian Schell-model beams in free space [J]. Opt. Commun. 2002, 204: 17-23.
99. Y. Cai, Y Huan, Q Lin. Spectral shift of partially coherent twisted anisotropic Gaussian-Schell-model beams focused by a thin lens [J]. J. Opt. A: Pure and Appl. Opt. 2003, 5:397–401.
100. Y. Cai, Q Lin. Focusing properties of partially coherent twisted anisotropic Gaussian–Schell model beams [J]. Opt. Commun. 2003, 215:239-245.
101. Y. Peng, B. Lü. Application of the Wigner distribution function to studying spectral changes of twisted anisotropic Gaussian Schell-Model beams [J]. Optik.2004, 115:322-328.
102. Y. Peng, B Lü. Diagonalization and symmetrization of anisotropic twisted Gaussian Schell-model beams [J]. Optik.2004, 115:1-6.
103. A Belanger. Beam propagation and ABCD ray matrices [J]. Opt. Lett. 1991, 16: 196-198.
104. 吕百达.强激光的传输与控制[M]. 北京: 国防工业出版社, 1999.
105. M. Born, E. Wolf. Principles of Optics, 7th (expanded) [M]. Cambridge University Press, Cambridge 1999.
106. M.J. Bastianns. Application of the Wigner distribution function to partially coherent light [J]. J. Opt. Soc. Am. A 1986, 3: 1227-1238.
107. H H Hopkins. Wave Theory of Aberration [M]. Oxford University Press, London 1995.
108. W H Swantner, W H Lowrey. Zernike-Tatian polynomials for interferogram reduction [J]. Appl.Opt. 1980, 19:161-163.
109. F. Gori. Matrix reatment for partially polarized partially coherent beams [J]. Opt. Lett. 1998, 23: 241-243.
110. F. Gori, M. Santarsiero, G. Piquero et al. Partially polarized Gaussian Schell-model beams [J]. J. Opt. A: Pure Appl. Opt. 2001, 3: 1-9.
111. J Alda, J Alonso, E Bernabeu. Characterization of aberrated laser beams [J]. J. Opt. Soc. Am. A 1997,14: 2737-2747.
112. X Gao. Focusing properties of the hyperbolic-cosine-Gaussion beam induced by phase plate [J]. Phys. lett. A 2006, 360:330-335.
2. E. Collett, E. Wolf. Is complete coherence necessary for the generation of highly directional light beams? [J]. Opt. Lett. 1978, 2: 27-29.
3. E. Wolf, E. Collett. Partially coherent sources which produce the same far-field intensity distribution as a laser [J]. Opt. Commun. 1978, 25: 293-296.
4. J.T. Foley, M.S. Zubairy. The directional of Gaussian-Schell-model beams [J]. Opt. Commun. 1978, 26: 297-300.
5. P.D. Santis, F. Gori, G. Guattari, C. Palma. An example of a Collett-Wolf source [J]. Opt. Commun. 1979, 29: 256-260.
6. J.D. Farina, L.M. Narducci, E. Collett. Generation of highly directional beams from a globally incoherent source [J]. Opt. Commun. 1980, 32: 203-208.
7. F. Gori. Mode propagation of the field generated by Collett-Wolf Schell-Model sources [J]. Opt. Commun. 1983,.46: 149-154.
8. G. Gbur, E. Wolf. Sources of arbitrary states of coherence that generate completely coherent fields outside the source. [J]. Opt. Lett. 1997, 22: 943-946.
9. F. Gori, M. Santarsiero. Intensity-based modal analysis of partially coherent beams with Hermite-Gaussian modes [J]. Opt. Lett. 1998, 23: 989-991.
10. A.T. Friberg, T.D. Visser, E. Wolf. A reciprocity inequality for Gaussian Schell-model beams and some of its consequences [J]. Opt. Lett. 2000, 25: 366-368.
11. S.A. Ponomarenko, E. Wolf. Light beams with minimum phase space product [J]. Opt. Lett. 2000, 25:
663-665.
12. T.D. Visser, A.T. Friberg, E. Phase-space inequality for partially coherent optical beams [J]. Opt. Commun. 2001, 187: 1-6.
13. T. Shirai, E. Wolf. Spatial coherence properties of the far field of a class of partially coherent beams which have the same directionality as a fully coherent laser beam [J]. Opt. Commun, 2002.204: 25-31.
14. F. Gori. Collet-Wolf sources and multimode lasers [J]. Opt. Commun. 1980, 34: 301-305.
15. R. Simon, E.C.G. Sudarshan, and N. Mukunda. Generalized ray in first-order optics: Transformation properties of Gaussian Schell-model fields [J]. Phys. Rev. A 1984, 29: 3273-3279.
16. A.T. Friberg, R.J. Sodol Propagation parameters of Gaussian Schell-model beams [J]. Opt. Commun. 1982, 41: 383-387.
17. A.T. Friberg, J. Turunen. Imaging of Gaussian Schell-model sources [J]. J. Opt. Soc. Am. A 1988, 5: 713-719.
18. R. Gase. The multimode laser radiation as a Gaussian Schell-model beam [J]. J. Mod. Opt. 1991, 38: 1107-1115.
19. E. Wolf. Invariance of spectrum of light on propagation [J]. Phys. Rev. Lett. 1986, 56: 1370-1372.
20. G. M. Morris, D. Faklis. Effects of source correlation on the spectrum of light [J]. Opt. Commun. 1987,62: 5-11.
21. D. Faklis, G. M. Morris. Spectral shifts produced by source correlations [J]. Opt. Lett. 1988, 13: 4-6.
22. L. Mandel, E. Wolf. Optical Coherence and Quantum Optics [J]. Cambridge University Press, Cambridge. 1995.
23. C. Palma, G. Cincotti, et al.. Spectral shift of a Gaussian Schell-model beam beyond a thin lens [J]. IEEE J. Quantum Electron. 1998, 34: 378-383.
24. C. Palma, G. Cincotti. Spectral shifts of a partially coherent field after passing through a lens [J]. Opt. Lett. 1997, 22: 671-672.
25. H.C. Kandpal, A. Wasan, J.S Vaishya. Spectroscopy of partially coherent fields at geometrical-image plane and Fourier transform plane of a lens [J]. Opt. Commun. 1998, 149: 1-7.
26. E. Wolf. Redshifts and blueshifts of spectral lines caused by source correlation [J]. Opt. Commun. 1987, 62: 12-16.
27. F. Gori, G. Guattari, et al.. Observation of optical redshifts and blueshifts produced by source correlations [J]. Opt. Commun. 1988, 67: 1-4.
28. E. Wolf. Correlation-induced Doppler-like frequency shifts of spectral lines [J]. Phys. Rev. Lett. 1989,
63: 2220-2223.
29. H.C. Kandpal, J.S. Vaishya, K.C. Joshi. Simple experimental arrangement for observing spectral shifts due to source correlation [J]. Phys. Rev A 1987, 41: 4541-4542.
30. M.F. Bocko, D.H. Douglass, R.S. Knox. Observation of frequency shifts of spectral lines due to source correlations [J]. Phys. Rev. Lett. 1987, 58: 2649-2651.
31. Z. Dacic, E. Wolf. Changes in the spectrum of partially coherent light propagating in free space [J]. J. Opt. Soc. Am. A 1988, 5: 1118-1126.
32. F. Gori, G. Guattari, C. Palma. Observation of optical redshifts and blueshifts produced by source correlation [J]. Opt. Commun. 1988, 67: 1-4.
33. H.C. Kandpal, J.S. Vaishya, K.C. Joshi. Wolf shift and its application in spectroradiometry [J]. Opt. Commun. 1989, 73: 169-172.
34. E. Wolf, D.F.V. James. Correlation-induced spectral changes [J]. Rep. Prog. Phys. 1996, 59: 771-818.
35. D.F.V. James, E. Wolf. Some new aspects of Young’s interference experiment [J]. Phys. Lett. A 1991, 157: 6-10.
36. M. Santarsiero, F. Gori. Spectral changes in a Young’s interference pattern [J]. Phys. Lett. A 1992, 167: 123-128.
37. S. Vicalvi, S.G Schirripa, et al.. Experimental determination of the size of a source from spectral measurements [J]. Opt. Commun. 1996, 130: 241-244.
38. S.A. Ponomarenko, E. Wolf. Coherence properties of light in Young’s interference pattern formed with partially coherent light [J]. Opt. Commun. 1999, 170: 1-8
39. H.C. Kandpal, J.S. Vaishya. Experimental study of coherence properties of light fields in the region of superposition in Young’s interference experiment [J]. Opt. Commun. 2000, 186: 15-20.
40. J.T. Foley. The effect of an aperture on the spectrum of partially coherent light [J]. Opt. Commun. 1990,75: 347-352.
41. J.T. Foley. The effect of an aperture on the spectrum of partially coherent light [J]. J. Opt. Soc. Am. A 1991, 8: 1099-1105.
42. A. Wasan, H.C. Kandpal, D.S. Mehta, J.S. Vaishya, K.C. Joshi. Correlation-induced spectral changes on passing partially coherent light through an annular aperture [J]. Opt. Commun. 1995, 121: 89-94.
43. D.F.V. James, E. Wolf. Determination of the degree of coherence of light from spectroscopic measurements [J]. Opt. Commun. 1997, 145: 1-4.
44. Z. Lin, Z. Gu. Angular spectrum redistribution from a real image of a light as a secondary source [J]. Opt. Lett. 2001, 26: 663-665.
45. J.H. Walker, R.D. Saunders, J.K. Jackson, K.D. Results of a CCPR intercomparison of spectral irradiance measurements by national laboratories [J]. J. Res. Natl. Stand. Technol. 1991, 96: 647-668.
46. C. Palma, G. Cincotti, G. Guattari. Spectral changes in Gaussian cavity lasers [J]. IEEE J. Quant. Electron. 1998, 34: 1082-1088.
47. E. Wolf, T. Shirai, H. Chen, W. Wang. Coherence filters and their uses: 1.Basic theory and examples [J]. J. Mod. Opt. 1997, 44: 1345-1353.
48. T. Shirai, E. Wolf, H. Chen, W. Wang. Coherence filters and their uses: 2.One-dimensional realizations [J]. J. Mod. Opt. 1998, 45: 799-816.
49. E Wolf, Y Li. Conditions for the validity of the Debye integral representation of focused fields [J]. Opt. Commun. 1981, 39: 205-210.
50. Y Li, E Wolf. Focal shift in focused truncated Gaussian beams [J]. Opt. Commun. 1982, 42: 151-156.
51. Y Li. Dependence of the focal shift on Fresnel number and f number [J]. J. Opt. Soc. Am. A 1982, 72:
770-774.
52. Y Li, E Wolf.Three-dimensions intensity distribution near the focus in systems of different Fresnel numbers [J]. J. Opt. Soc. Am. A 1984, 1: 801-808.
53. Y Li. Oscillations and discontinuity in the focal shift of Gaussian laser beams [J]. J. Opt. Soc. Am. A 1986, 3: 1761-1765.
54. W H Carter, M F Aburdene. Focal shift in Laguerre-Gaussian beams [J]. J. Opt. Soc. Am. A 1987, 4: 1949-1952.
55. Y Li.Variations of the axial intensity pattern formed by a focused truncated Gaussian beam [J]. J. Opt. Soc. Am. A 1988, 68: 324-328.
56. P Andres, M Martinez-Corral, J Ojeda-Castaneda. Off-axis focal shift for rotationally nonsymmetric screens [J]. Opt Lett. 1993, 18: 1290-1292.
57. M Martínez-Corral, V Climent. Focal switch: a new effect in low-Fresnel-number systems [J]. Appl Opt 1996, 35: 24-7.
58. A T Friberg, T D Visser, W Wang, E Wolf. Focal shifts of converging diffracted waves of any state of spatial coherence [J]. Opt. Commun. 2001, 196: 1-7.
59. A Yoshida, T Asakura. Focusing a Gaussian laser beam without focal shift [J]. Opt. Commun. 1994, 109: 368-374.
60. A Yoshida, T Asakura. Propagation and focusing of Gaussian laser beams beyond conventional diffraction limit [J]. Opt. Commun. 1996, 123: 694-704.
61. G P Karamn, A V Duijl, J P Woerdman. Observation of a stronger focus due to spherical aberration [J]. J. Mod. Opt. 1998, 45: 2513-2517.
62. J Carlos, M Manuel, A Pedro, et al. Inverse focal shift: a new effect in truncated cylindrical waves [J]. J. Mod. Opt. 1999, 46: 129-144.
63. J Pu. Focusing Gausion beams by an annular lens with spherical aberration [J]. J. Mod. Opt. 1998, 45: 239-247.
64. J Pu, H Zhang. Intensity distribution of Gaussion beams focused by a lens with spherical aberration [J]. Opt. Commun. 1998, 151: 331-338.
65. J Pu, H Zhang. Aberrated lenses for generating flattened laser irradiance [J]. Appl. Opt. 1998, 37: 4200-4205.
66. 蒲继雄. 利用球差透镜获得超衍射极限聚焦[J]. 中国激光. 1999, A26:542-546.
67. B. Lü, B.Zhang, B.Cai. The integrated intensity of a Gaussian Schell-model beam focused by a lens [J]. Optik.1995, 101:42-46.
68. B. Lü, B. Zhang, B. Cai. The intensity distribution of a Gaussian Schell-model beam focused by an aperture lens [J]. J. Mod. Opt.1995, 42:523-540.
69. B. Lü, B. Zhang, B. Cai. Focusing of a Gaussian Schell-model beam through a circular lens [J]. J. Mod. Opt.1995, 42:289-298.
70. 吕百达,张彬,蔡邦维. 部分相干光聚焦场特性的分析[J]. 激光技术. 1996, 20:108-111.
71. W. Wang, A .T. Friberg, E Wolf. Focusing of partially coherent light in systems of large Fresnel numbers [J]. J. Opt. Soc. Am. A.1997, 14: 491-504.
72. J. Pu, S. Nemoto, H. Zhang. Reshaping Gaussian Schell-model beams to uniform profiles by lens spherical aberration [J]. J. Mod. Opt. 1999, 46:1611-1620.
73. J. Pu, S. Nemoto, W. Zhang. Axial intensity distribution of partially coherent light focused by a lens with spherical aberration [J]. J. Mod. Opt.2000, 47:605-612.
74. 潘留占,吕百达.部分相干光通过像散透镜的聚焦特性[J]. 激光技术. 2003,27:374-379.
75. J. Pu, H. Zhang, S. Nemoto. Spectral shifts and spectral switches of partially coherent light passing through an aperture [J]. Opt. Commun. 1999, 162: 57-63.
76. H.C. Kandpal. Experimental observation of the phenomenon of spectral switch [J]. J. Opt. A: Pure and Appl. Opt. 2001, 3: 296-299.
77. L Pan , B Lü. The spectral switch of partially coherent light in Young’s experiment [J]. IEEE J .Quant .Electron. 2001, 37:1377-1381.
78. B. Lü, L. Pan. Spectral switching of Gaussian Schell-model beams through an aperture lens [J]. IEEE J. Quant. Electron. 2002, 38:340-344.
79. B.K.Yadav, S.A.M Rizvi., H.C Kandpal. Experimental observation of spectral changes of partially coherent light in Young’s experiment [J]. J. Opt. A: Pure and Appl Opt. 2006, 8: 72-76.
80. M.S. Soskin, M.V. Vasnetsov. “Singular optics” Progress in Optics [J].2001, 42: 219-276.
81. G. Gbur, T.D. Visser, E. Wolf. Anomalous behavior of spectra near phase singularities of focused waves [J]. Phys. Rev. Lett. 2002, 88: 013901.
82. G. Gbur, T.D. Visser, E. Wolf. Singular behavior of the spectrum in the neighborhood of focus [J]. J. Opt. Soc. Am. A 2002, 19: 1694-1700.
83. S.A. Ponomarenko, E. Wolf. Spectral anomalies in a Fraunhofer diffraction pattern [J]. Opt. Lett. 2002, 27: 1211-1213.
84. J.T. Foley, E. Wolf. Phenomenon of spectral switches as a new effect in singular optics with polychromatic light [J]. J. Opt. Soc. Am. A 2002, 19: 2510-2516.
85. G. Popescu, A. Dogariu. Spectral anomalies at wave-front dislocations [J]. Phys. Rev. Lett. 2002, 88: 183902.
86. J. Pu, S. Nemoto. Spectral shifts of partially coherent beams focused by a lens with chromatic aberration [J]. Opt. Commun. 2002, 207: 1-5.
87. J. Pu, C. Cai, S. Nemoto. Chin. The spectral changes of partially coherent light focused by an aperture lens with chromatic aberration [J]. Opt. Lett. 2004, 2:239-242.
88. L. Pan, B. Lü.Spectral changes of Gaussian Schell-model beams passing through a dispersive lens [J]. Optik. 2003,114:485-490.
89. L.Pan, B. Lü. Spectral switches of polychromatic Gaussian beams passing through an astigmatic aperture lens [J]. Opt. Commun. 2004, 234: 1-6.
90. G. Zhao, X. Xiao, B. Lü.Effect of astigmatism on spectral switches of partially coherent beams [J]. Chinese Physics.2004, 13:2064-2070.
91. G. Zhao, B. Lü. Influence of aperture lens with spherical aberration on the spectral behaviour of polychromatic Gaussian Schell-model beams [J].Optik.2004, 115:181-186.
92. 肖希,吕百达.多色高斯-谢尔模型光束通过球差透镜的光谱变化[J]. 光学学报. 2005, 25:542-546.
93. 渠彪, 蒲继雄, 陈子阳. 部分相干光经色差透镜聚焦后的光谱开关现象[J]. 光电子·激光. 2006, 17:1142-1145.
94. B. Qu, J. Pu, Z. Chen. Experimental observation of spectral switch of partially coherent light focused by a lens with chromatic aberration [J]. Optics & Laser Technology.2007, 39:1226-1230.
95. R. Simon, N. Mukunda. Twisted Gaussian Schell-model beams [J]. J. Opt. Soc. Am. A .1993, 10:95-104.
96. A .T. Friberg, E. Tervonen, J. Turunen. Interpretation and experimental demonstration of twisted Gaussian Schell-model beams [J]. J. Opt. Soc. Am. A 1994,11:1818-1828
97. A.T. Friberg, E.Tervonen, J.Turunen .Focusing of twisted Gaussian Schell-model beams [J]. Opt. Commun. 1994, 106: 127-132.
98. Y Cai, Q Lin. Spectral shift of partially coherent twisted anisotropic Gaussian Schell-model beams in free space [J]. Opt. Commun. 2002, 204: 17-23.
99. Y. Cai, Y Huan, Q Lin. Spectral shift of partially coherent twisted anisotropic Gaussian-Schell-model beams focused by a thin lens [J]. J. Opt. A: Pure and Appl. Opt. 2003, 5:397–401.
100. Y. Cai, Q Lin. Focusing properties of partially coherent twisted anisotropic Gaussian–Schell model beams [J]. Opt. Commun. 2003, 215:239-245.
101. Y. Peng, B. Lü. Application of the Wigner distribution function to studying spectral changes of twisted anisotropic Gaussian Schell-Model beams [J]. Optik.2004, 115:322-328.
102. Y. Peng, B Lü. Diagonalization and symmetrization of anisotropic twisted Gaussian Schell-model beams [J]. Optik.2004, 115:1-6.
103. A Belanger. Beam propagation and ABCD ray matrices [J]. Opt. Lett. 1991, 16: 196-198.
104. 吕百达.强激光的传输与控制[M]. 北京: 国防工业出版社, 1999.
105. M. Born, E. Wolf. Principles of Optics, 7th (expanded) [M]. Cambridge University Press, Cambridge 1999.
106. M.J. Bastianns. Application of the Wigner distribution function to partially coherent light [J]. J. Opt. Soc. Am. A 1986, 3: 1227-1238.
107. H H Hopkins. Wave Theory of Aberration [M]. Oxford University Press, London 1995.
108. W H Swantner, W H Lowrey. Zernike-Tatian polynomials for interferogram reduction [J]. Appl.Opt. 1980, 19:161-163.
109. F. Gori. Matrix reatment for partially polarized partially coherent beams [J]. Opt. Lett. 1998, 23: 241-243.
110. F. Gori, M. Santarsiero, G. Piquero et al. Partially polarized Gaussian Schell-model beams [J]. J. Opt. A: Pure Appl. Opt. 2001, 3: 1-9.
111. J Alda, J Alonso, E Bernabeu. Characterization of aberrated laser beams [J]. J. Opt. Soc. Am. A 1997,14: 2737-2747.
112. X Gao. Focusing properties of the hyperbolic-cosine-Gaussion beam induced by phase plate [J]. Phys. lett. A 2006, 360:330-335.