光学涡旋场的产生方法、衍射特性及其应用研究
|
摘要
光学涡旋(Optical Vortices)是一种具有螺旋型波前结构和确定的光子轨道角动量的特殊光场,近年来,受到科学界的重视,并被广泛的研究,目前已经发展成为现代光学的一个新的研究领域;已经在光学微操纵、原子光学、生物医学、非线性光学、光学信息传输等领域得到了重要而广泛的应用。本论文重点对光学涡旋的产生方法、衍射特性及其实际应用中的有关问题进行理论与实验研究。主要研究内容和结果如下:
1.总结论述了光学涡旋的数学描述、产生方法及在近轴情况下光学涡旋场的轨道角动量特性。
2.分析了阶梯型螺旋相位板产生的涡旋光场的涡旋特性,分别给出了实现最大总轨道角动量输出、最小总轨道角动量、最大主光学涡旋轨道角动量和高纯度的光学涡旋场输出的条件。为螺旋相位板的设计和实际应用提供了参考依据。
3.从理论上解释了利用具有相位调制偏差的液晶空间光调制器产生周期性强度调制光学涡旋场的原因,并提出利用这种方法可以检测液晶空间光调制器的相位偏差。
4.分析了螺旋相位滤波系统的一些特性,提出利用这种方法产生任意形状以及任意排列的光学涡旋场,为我们研究微观颗粒在阵列光学涡旋场中的受力以及阵列光学涡旋场的传播动力学提供了实验基础。
5.在用螺旋相位板进行光学径向希尔伯特变换的基础上,提出了一种利用拉盖尔-高斯空间滤波器来实现光学径向希尔伯特变换的新方法,并从理论与实验上证实了该方法的可行性。理论与实验结果表明利用这种方法能够有效的增强物体的边缘信息,提高对比度。
Optical vortices are intriguing special optical structures with helical (or spiral)wave fronts, which attract much attention for their well-defined orbital angularmomentum(OAM) properties. This kind of special optical field has been applied inmany fields that include optical micromanipulation, atomic optics, biomedicine,nonlinear optics, or quantum information processing. In this thesis, we explored thegeneration mehtods of optical vortices, their diffractive properties and applications.The major content and result are as follows:
1. We made a description of optical vortices, introduced some method to generateoptical vortices and analyzed the angular momentum of the optical vortices underparaxial condition.
2. We analyzed the vortex properties of the field generated by multi-level stepspiral phase plate, and gave the condition for generation of optical vortices withmaximal OAM, minimal OAM and high purity, which provide us some usefulparameters for designing the spiral phase plate and its applications.
3. We explained the relationship between modulation depth of optical vortices andthe phase deviation of the spatial light modulator in theory. This theory provide apossible approach to measure the phase deviation of SLM.
4. We analyzed the properties of the helical phase spatial filtering system andproposed a new method to generate optical vortices with any shape and array byuse of helical phase spatial filtering. This method offers an advanceduser-interactive functionality and high adaptability, which are important forapplications in study of optical micromanipulation of a mixture ofmicrostructures, optically induced photonic lattices, and lattice of optical vortexsoliton.
5. We introduced a new method to implement radial Hilbert transform by use oflaguerre-gaussian spatial filters and demonstrated the feasibility of this method intheory and experiments. The result implied that using this method can enhancethe edge information of the image effectively and advanced the contrast.
1.总结论述了光学涡旋的数学描述、产生方法及在近轴情况下光学涡旋场的轨道角动量特性。
2.分析了阶梯型螺旋相位板产生的涡旋光场的涡旋特性,分别给出了实现最大总轨道角动量输出、最小总轨道角动量、最大主光学涡旋轨道角动量和高纯度的光学涡旋场输出的条件。为螺旋相位板的设计和实际应用提供了参考依据。
3.从理论上解释了利用具有相位调制偏差的液晶空间光调制器产生周期性强度调制光学涡旋场的原因,并提出利用这种方法可以检测液晶空间光调制器的相位偏差。
4.分析了螺旋相位滤波系统的一些特性,提出利用这种方法产生任意形状以及任意排列的光学涡旋场,为我们研究微观颗粒在阵列光学涡旋场中的受力以及阵列光学涡旋场的传播动力学提供了实验基础。
5.在用螺旋相位板进行光学径向希尔伯特变换的基础上,提出了一种利用拉盖尔-高斯空间滤波器来实现光学径向希尔伯特变换的新方法,并从理论与实验上证实了该方法的可行性。理论与实验结果表明利用这种方法能够有效的增强物体的边缘信息,提高对比度。
Optical vortices are intriguing special optical structures with helical (or spiral)wave fronts, which attract much attention for their well-defined orbital angularmomentum(OAM) properties. This kind of special optical field has been applied inmany fields that include optical micromanipulation, atomic optics, biomedicine,nonlinear optics, or quantum information processing. In this thesis, we explored thegeneration mehtods of optical vortices, their diffractive properties and applications.The major content and result are as follows:
1. We made a description of optical vortices, introduced some method to generateoptical vortices and analyzed the angular momentum of the optical vortices underparaxial condition.
2. We analyzed the vortex properties of the field generated by multi-level stepspiral phase plate, and gave the condition for generation of optical vortices withmaximal OAM, minimal OAM and high purity, which provide us some usefulparameters for designing the spiral phase plate and its applications.
3. We explained the relationship between modulation depth of optical vortices andthe phase deviation of the spatial light modulator in theory. This theory provide apossible approach to measure the phase deviation of SLM.
4. We analyzed the properties of the helical phase spatial filtering system andproposed a new method to generate optical vortices with any shape and array byuse of helical phase spatial filtering. This method offers an advanceduser-interactive functionality and high adaptability, which are important forapplications in study of optical micromanipulation of a mixture ofmicrostructures, optically induced photonic lattices, and lattice of optical vortexsoliton.
5. We introduced a new method to implement radial Hilbert transform by use oflaguerre-gaussian spatial filters and demonstrated the feasibility of this method intheory and experiments. The result implied that using this method can enhancethe edge information of the image effectively and advanced the contrast.
引文
1. Sheldon Green eds., Fluid Vortices, (Kluwer Academic Publishers, Dordrecht, Netherlands, 1995).
2. L. Davis, Natural Disasters, Facts on File Science Library (Facts on File, new York 2002).
3. L.M. Pismen, Vortices in Nonlinear Fields, Oxford Science Publications (Clarendon Press, Oxford, 1999).
4. M.W. Beijersbergen, R.P.C. Coerwinkel, and J.P. Woerdman, “Helical-wavefront laser beams produced by a spiral phase plate,” Opt. Comm. 112, 321-327 (1994).
5. L. Allen, M. W. Beijersbergen, R. J. Spreeuw and J. P. Woerdman. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phy. Rev. A. 45(11):8185-8189, 1992.
6. S. M. Barnett and L. Allen. Orbital angular momentum and nonparaxial light beams . Opt. Commun. 110:679-688, 1994.
7. K.T. Gahagan and G.A. Swartzlander Jr., “Trapping of Low-index Microparticles in an Optical Vortex,” J. Opt. Soc. Am. B 15, 524-534 (1998).
8. C.S. Buer, K.T. Gahagan, G.A. Swartzlander Jr., and P.J. Weathers, “Insertion of Microscopic Objects Through Plant Cell Walls Using Laser Microsurgery,”Biotechnology and Bioengineering 60, 348-355(1998).
9. C.S. Buer, K.T. Gahagan, G.A. Swartzlander Jr., and P.J. Weathers, “Differences in optical trapping prompt investigations of Agrobacterium surface chacteristics,” Journal of Industrial Microbiology and Biotechnology 21, 233-236 (1998).
10. A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Conversion of topological charge of optical vortices in a parametric frequency converter,” Opt. Comm. 140, 273-276 (1997).
11. S. Ramo, J.R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, (Wiley, New York, NY, 1965).
12. E. Abramochkin and V. Volostnikov, “Spiral-Type Beams,” Opt. Comm. 73, 403 (1989).
13. L.A. Lugiato, C. Oldano, and L.M. Narducci, “Cooperative frequency locking and stationary spatial structures in lasers,” J. Opt. Soc. Am. B 5, 879-888 (1988).
14. J.F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165-190 (1974).
15. M.V. Berry, “Singularities in Waves and Rays,” in Physics of defects, Les Houches Sessions XXXV, R. Balian, M. Kleman, and J.P Poirier, eds., (North Holland, Amsterdam, 1981), pp. 453-543.
16. N.B. Baranova, B. Ya. Zel'dovich, A.V. Mamaev, N.F. Pilipetski, and V.V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis'ma Zh. Eksp. Teor. Fiz., 33, 206 (1981) [JETP Lett., 33, 195 (1981)].
17. N.B. Baranova, A.V. Mamaev, N.F. Pilipetski, V.V. Shkunov, and B. Ya. Zel'dovich, “Wave-front dislocations:topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525-528 (1983).
18. I. Freund, N. Shvartsman, and V. Freilikher, “Optical Dislocation networks in highly random media,” Opt. Comm. 101, 247-264 (1993).
19. T. Ackemann, E. Kriege, and W. Lange, “Phase singularities via nonlinear beam propagation in Sodium vapor,” Opt. Comm. 115, 339-346 (1995).
20. G.A. Swartzlander Jr. and C.T. Law, “Optical Vortex Solitons Observed in Kerr Nonlinear Media,” Phys. Rev. Lett. 69, 2503-2506 (1992).
21. A.W. Snyder, L. Poladian, and D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789-791 (1992).
22. F.S. Roux, “Dynamical behavior of optical vortices,” J. Opt. Soc. Am. B 12, 1215-1221 (1995).
23. G. Idebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73-87 (1993).
24. Guang-Hoon-Kim et al., “An array of phase singularities in a self-defocusing medium,” Opt. Comm. 147, 131-137 (1998).
25. D. Rozas, Z.S. Sacks, and G.A. Swartzlander Jr., “Experimental Observation of Fluidlike Motion of Optical Vortices,” Phys. Rev. Lett. 79, 3399-3402 (1997).
26. D. Rozas and G.A. Swartzlander Jr., “Observed rotational enhancement of nonlinear optical vortices,” Opt. Lett. 25, 126-128 (2000).
27. L.G. Gouy, “Sur une propriete nouvelle des ondes luminineuses,” Compt. Rend. Acad. Sci. Paris 110, 1251-1253 (1890).
28. L.G. Gouy, “Sur la propagation anomale des ondes,” Ann. Chim. Phys. Ser. 6 24, 145-213 (1891).
29. M.W. Beijersbergen, L. Allen, H.E.L.O. van der Veen, and J.P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Comm. 96, 123-132 (1996).
30. A.Y. Bekshaev, M.S. Soskin, M.V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. A 20, 1635-1643 (2003).
31. M. Vasnetsov and K. Staliunas, eds., Optical Vortices, vol. 228, Horizons in World Physics, (Nova Science, Huntington, NY, 1999).
32. C.T. law, X. Zhang, and G.A. Swartzlander Jr., “Waveguiding properties of optical vortex solitons,” Opt. Lett. 25, 55-57 (2000).
33. K.T. Gahagan and G.A. Swartzlander Jr., “Optical Vortex Trapping of Particles,” Opt. Lett. 21, 827-829 (1996).
34. K. Dholakia, J. Soneson, E.M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
35. S.A. Tatarkova, A.E. Carruthers, K. Dholakia, “One-dimensional optically bound arrays of microscopic particles,” Phys. Rev. Lett. 89, 283901 (2002).
36. G. Molina-Terriza, J. Recolons, L. Torner, “The curious arithmetic of optical vortices,” Opt. Lett. 25, 1135-1137 (2000).
37. I.D. Maleev and G.A. Swartzlander Jr., “Composite optical vortices,” J. Opt. Soc. Am. B 20, 1169-1176 (2003).
38. M. Born and E. Wolf, Principles of Optics-corrected 7th ed., (Cambridge University Press, Cambridge, UK, 2002).
39. R. Simon and G.S. Agarwal, “Wigner representation of Laguerre-Gaussian beams,” Opt. Lett. 25, 1313-1315 (2000).
40. R. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 10, 95-109 (1993).
41. Z. Bouchal and J. Perina, “Non-diffracting beams with controlled spatial coherence,” J. of Mod. Opt. 49, 1673-1689 (2002).
42. G.V. Bogatyryova, et al., “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28, 878-880 (2003).
43. B.J. Thompson and E. Wolf, “Two-beam interference with. partially coherent light”,J. Opt. Soc. Am. 47, 895 (1957).
44. D. Palacios, I.M. Maleev, A.S. Marathay, and G.A. Swartzlander Jr., “Spatial Correlation Singularity of a Vortex Field,” Phys. Rev. Lett. 92, 143905 (2004).
45. G. Gbur and T.D. Visser, “Coherence vortices in partially coherent beams,” Opt. Comm. 222, 117 (2003).
46. T.D. Visser, Gbur, E. Wolf, “Effect of the state of coherence on the threedimensional spectral intensity distribution near focus,” Opt. Comm. 213, 13-19 (2002).
47. G. Popescu and A. Dogariu, “Spectral anomlies at wave-front dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
48. G.A. Swartzlander Jr. and J. Schmidt, “Temporal Correlation Vortices and Topological Dispersion,” Phys. Rev. Lett. 93, 093901(4) (2004)
49. G.A. Swartzlander Jr., “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497 (2001).
50. David Palacios, David Rozas, and Grover A. Swartzlander Jr., “Observed Scattering into a Dark Optical Vortex Core,” Phys. Rev. Lett. 88, 103902 (2002).
51. R. A. Beth, ‘Mechanical detection and measurement of the angular momentum of light', Phys. Rev. 50, 115–127 (1936).
52. 魏光辉,朱宝亮,“激光束光学”。
53. J. Durnin. Exact solutions of nondiffraction beams. I. The scarlar teory. JOSA A, 4: 651-654, 1987.
54. J. Durnin, J. J. Miceli, J. H. Eberly, Diffraction –free beams. Phy. Rev. Lett., 58: 1499-1501, 1987.
55. J. Arlt, K. Dholakia, J. Soneson and E. M. Wright. Optical diploe traps and atomic waveguides based on Bessel light beams. Phys. Rev. A, 63:063602, 2001.
56. Yin J P, et al., Doughnut-beam-induced Sisyphus cooling in atomic guiding and collimation. J. Opt. Soc. Am B, 15(8):2235, 1998.
57. J. Arlt, K. Dholakia, Generation of high-order Bessel beams by use of an axicon. Opt. Commun., 177: 297-301, 2000
58. M. Lax, W. H. Louisell and W. B. McKnight, “From Maxwell to paraxial wave optics”, Phys. Rev. A. 11, 1365–1370 (1975)
59. H. A. Haus. Waves and Fields in Optoelectronics. (Prentice-Hall, Englewood Cliffs, NJ, 1984)
60. M. W. Beijersbergen, L. Allen, H. Vanderveen, J. P. Woerdman: Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum. Optics Commun. 96:123-132, 1993.
61. N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17: 221-223,1992.
62. J. Arlt, K. Dholakia, L. Allen and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45: 1231-1237, 1998.
63. Cheng-Shan Guo, Xuan Liu, Xiuyun Ren, Hui-Tian Wang. Optimal Annular Computer-Generated Holograms for Generation of Optical vortices. J. Opt. Soc. Am. A, 22(2): 385-390, 2005
64. G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen and M. J. Padgett. “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate”,Opt. Comm. 127: 183-188, 1996.
65. Jennifer E. Curtis and David G. Grier, “Structure of optical vortices”, Phys. Rev. Lett. 90, 133901 (2003).
66. Steven Sundbeck and Ilya Gruzberg and David G. Grier, “Structure and scaling of helical modes of light”, Opt. Lett. 30, 477-479 (2005).
67. M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. Hulst, Local observations of phase singularities in optical fields in waveguide structures. Phys. Rev. Lett. 85: 294-297, 2000.
68. R. M. Jenkins, J. Banerji, A. R. Davies, The generation of optical vortices and shape preserving vortex arrays in hollow multimode waveguides. J. Opt. A 3: 527–532, 2001.
69. Arlee V. Smith and Darrell J. Armstrong. Generation of vortex beams by an image-rotating optical parametric oscillator. Opt. Exp. 11(8):868-873, 2003.
70. J. M. Vaughan and D. V. Willetts. “Interference properties of a light beam having a helical wave surface”Opt. Comm.30: 263-267, 1979.
71. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Hasman. The formation of laser beams with pure azimuthal or radial polarization. Applied Physics Letters 77:3322-3324, 2000.
72. R. Oron, N. Davidson, A. A. Friesem, F. Hasman: Efficient formation of pure helical laser beams. Optics Communications 182:205-208, 2000.
73. V. Yu. Bazhenov, m.V. Vasnetsov, and M.S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis'ma Zh. Eksp. Teor. Fiz. 52, 1037-1039 (1990) [JETP Lett. 52, 429-431 (1990)].
74. Jennifer E. Curtis and David G. Grier. Modulated optical vortices. Opt. Lett. 28: 872-874, 2003.
75. Jennifer E. Curtis, Brian A. Koss, and David G. Grier. Dynamic Holographic Optical Tweezers. Opt. Commun. 207: 169-175, 2002.
76. Cheng-Shan Guo, Xuan Liu, Jing-Liang He, Hui-Tian Wang,” Optimal annulus structures of optical vortices”, Optics Express. 12. 4625-4634 (2004).
77. K. Ladavac and D. G. Grier,”Colloidal hydrodynamic coupling in concentric optical vortices”, Europhys. Lett., 70, 548-554 (2005)
78. Carmel Rotschild, Shachaf Zommer, Shulamit Moed, Oren Hershcovitz, and Stephen G. Lipson. Adjustable spiral phase plate. Applied Optics, 43(12): 2397-2399, 2004
79. J.A. Davis, D.E. McNamra, D.M. Cottrell, J. Campos, “Image processing with the radial Hilbert transform: theory and experiments ”Opt. Lett. 25 (2000) 99.
80. S. Fuerhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “spiral phase contrast imaging in microscopy”, Opt. Express 13, 689-694 (2005).
81. A. Jesacher, S. Fuerhapter, S. Bernet, and M. Ritsch-Marte, “Shadow Effects in Spiral Phase Contrast Microscopy”,Phys. Rev. Lett. 94, 233902 (2005).
82. Severin Fürhapter, Alexander Jesacher, Stefan Bernet, and Monika Ritsch-Marte, “Spiral interferometry”, Opt. Lett. 30 (2005) 1953
83. Cheng-Shan Guo, Xin Cheng, Xiu-Yun Ren, Jian-Ping Ding, Hui-Tian Wang, “Optical vortex phase-shifting digital holography”, Optics Express. 12, 5166-5171(2004).
84. G. Foo, D. M. Palacios, and G. A. Swartzlander, Jr. “Optical vortex coronagraph,” Opt. Lett. 30, 3308-3310 (2005).
85. C. S. Guo Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. Vol. 244, 233-344 (2006).
86. Q. Wang, X. W. Sun, P. Shum, “Dynamic switching of optical vortices with dynamic gamma-correction liquid crystal spiral phase plate,” Opt. Express 13, 10285-10291 (2005)
87. Cheng-Shan Guo, Dong-Mei Xue, Yu-Jing Han and Lu-Zhong Cai, “Optimal phase steps of multi-level spiral phase plates”, Opt. Lett. (Submitted).
88. L. B. Lesem, P. M. Hirsch and J. A. Jordan, Jr., “Generation of discrete point holograms”,J. Opt. Soc. Am. 58, 729A, 1968.
89. Jeffrey A. Davis and Joel B. Bentley,” Azimuthal prism effect with partially blocked vortex-producing lenses”, Opt. Lett. 30, 3204-3206, 2005.
90. A. Kastler, Rev. Opt. 29, 308 (1950).
91. H. Wolter, Ann. Phys. 7, 341 (1950).
92. A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, “Fractional Hilbert transform”, Opt. Lett. 21, 281 (1996).
93. Cheng-Shan Guo, Yu-Jing Han, Jian-Bo Xu and Jian-Ping Ding, “Radial Hilbert
transform with Laguerre-gaussian spatial filters”, Opt. Lett. Vol. 31, No. 10, 1394-1396 (2006).
2. L. Davis, Natural Disasters, Facts on File Science Library (Facts on File, new York 2002).
3. L.M. Pismen, Vortices in Nonlinear Fields, Oxford Science Publications (Clarendon Press, Oxford, 1999).
4. M.W. Beijersbergen, R.P.C. Coerwinkel, and J.P. Woerdman, “Helical-wavefront laser beams produced by a spiral phase plate,” Opt. Comm. 112, 321-327 (1994).
5. L. Allen, M. W. Beijersbergen, R. J. Spreeuw and J. P. Woerdman. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phy. Rev. A. 45(11):8185-8189, 1992.
6. S. M. Barnett and L. Allen. Orbital angular momentum and nonparaxial light beams . Opt. Commun. 110:679-688, 1994.
7. K.T. Gahagan and G.A. Swartzlander Jr., “Trapping of Low-index Microparticles in an Optical Vortex,” J. Opt. Soc. Am. B 15, 524-534 (1998).
8. C.S. Buer, K.T. Gahagan, G.A. Swartzlander Jr., and P.J. Weathers, “Insertion of Microscopic Objects Through Plant Cell Walls Using Laser Microsurgery,”Biotechnology and Bioengineering 60, 348-355(1998).
9. C.S. Buer, K.T. Gahagan, G.A. Swartzlander Jr., and P.J. Weathers, “Differences in optical trapping prompt investigations of Agrobacterium surface chacteristics,” Journal of Industrial Microbiology and Biotechnology 21, 233-236 (1998).
10. A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Conversion of topological charge of optical vortices in a parametric frequency converter,” Opt. Comm. 140, 273-276 (1997).
11. S. Ramo, J.R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, (Wiley, New York, NY, 1965).
12. E. Abramochkin and V. Volostnikov, “Spiral-Type Beams,” Opt. Comm. 73, 403 (1989).
13. L.A. Lugiato, C. Oldano, and L.M. Narducci, “Cooperative frequency locking and stationary spatial structures in lasers,” J. Opt. Soc. Am. B 5, 879-888 (1988).
14. J.F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165-190 (1974).
15. M.V. Berry, “Singularities in Waves and Rays,” in Physics of defects, Les Houches Sessions XXXV, R. Balian, M. Kleman, and J.P Poirier, eds., (North Holland, Amsterdam, 1981), pp. 453-543.
16. N.B. Baranova, B. Ya. Zel'dovich, A.V. Mamaev, N.F. Pilipetski, and V.V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis'ma Zh. Eksp. Teor. Fiz., 33, 206 (1981) [JETP Lett., 33, 195 (1981)].
17. N.B. Baranova, A.V. Mamaev, N.F. Pilipetski, V.V. Shkunov, and B. Ya. Zel'dovich, “Wave-front dislocations:topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525-528 (1983).
18. I. Freund, N. Shvartsman, and V. Freilikher, “Optical Dislocation networks in highly random media,” Opt. Comm. 101, 247-264 (1993).
19. T. Ackemann, E. Kriege, and W. Lange, “Phase singularities via nonlinear beam propagation in Sodium vapor,” Opt. Comm. 115, 339-346 (1995).
20. G.A. Swartzlander Jr. and C.T. Law, “Optical Vortex Solitons Observed in Kerr Nonlinear Media,” Phys. Rev. Lett. 69, 2503-2506 (1992).
21. A.W. Snyder, L. Poladian, and D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789-791 (1992).
22. F.S. Roux, “Dynamical behavior of optical vortices,” J. Opt. Soc. Am. B 12, 1215-1221 (1995).
23. G. Idebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73-87 (1993).
24. Guang-Hoon-Kim et al., “An array of phase singularities in a self-defocusing medium,” Opt. Comm. 147, 131-137 (1998).
25. D. Rozas, Z.S. Sacks, and G.A. Swartzlander Jr., “Experimental Observation of Fluidlike Motion of Optical Vortices,” Phys. Rev. Lett. 79, 3399-3402 (1997).
26. D. Rozas and G.A. Swartzlander Jr., “Observed rotational enhancement of nonlinear optical vortices,” Opt. Lett. 25, 126-128 (2000).
27. L.G. Gouy, “Sur une propriete nouvelle des ondes luminineuses,” Compt. Rend. Acad. Sci. Paris 110, 1251-1253 (1890).
28. L.G. Gouy, “Sur la propagation anomale des ondes,” Ann. Chim. Phys. Ser. 6 24, 145-213 (1891).
29. M.W. Beijersbergen, L. Allen, H.E.L.O. van der Veen, and J.P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Comm. 96, 123-132 (1996).
30. A.Y. Bekshaev, M.S. Soskin, M.V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. A 20, 1635-1643 (2003).
31. M. Vasnetsov and K. Staliunas, eds., Optical Vortices, vol. 228, Horizons in World Physics, (Nova Science, Huntington, NY, 1999).
32. C.T. law, X. Zhang, and G.A. Swartzlander Jr., “Waveguiding properties of optical vortex solitons,” Opt. Lett. 25, 55-57 (2000).
33. K.T. Gahagan and G.A. Swartzlander Jr., “Optical Vortex Trapping of Particles,” Opt. Lett. 21, 827-829 (1996).
34. K. Dholakia, J. Soneson, E.M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
35. S.A. Tatarkova, A.E. Carruthers, K. Dholakia, “One-dimensional optically bound arrays of microscopic particles,” Phys. Rev. Lett. 89, 283901 (2002).
36. G. Molina-Terriza, J. Recolons, L. Torner, “The curious arithmetic of optical vortices,” Opt. Lett. 25, 1135-1137 (2000).
37. I.D. Maleev and G.A. Swartzlander Jr., “Composite optical vortices,” J. Opt. Soc. Am. B 20, 1169-1176 (2003).
38. M. Born and E. Wolf, Principles of Optics-corrected 7th ed., (Cambridge University Press, Cambridge, UK, 2002).
39. R. Simon and G.S. Agarwal, “Wigner representation of Laguerre-Gaussian beams,” Opt. Lett. 25, 1313-1315 (2000).
40. R. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 10, 95-109 (1993).
41. Z. Bouchal and J. Perina, “Non-diffracting beams with controlled spatial coherence,” J. of Mod. Opt. 49, 1673-1689 (2002).
42. G.V. Bogatyryova, et al., “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28, 878-880 (2003).
43. B.J. Thompson and E. Wolf, “Two-beam interference with. partially coherent light”,J. Opt. Soc. Am. 47, 895 (1957).
44. D. Palacios, I.M. Maleev, A.S. Marathay, and G.A. Swartzlander Jr., “Spatial Correlation Singularity of a Vortex Field,” Phys. Rev. Lett. 92, 143905 (2004).
45. G. Gbur and T.D. Visser, “Coherence vortices in partially coherent beams,” Opt. Comm. 222, 117 (2003).
46. T.D. Visser, Gbur, E. Wolf, “Effect of the state of coherence on the threedimensional spectral intensity distribution near focus,” Opt. Comm. 213, 13-19 (2002).
47. G. Popescu and A. Dogariu, “Spectral anomlies at wave-front dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
48. G.A. Swartzlander Jr. and J. Schmidt, “Temporal Correlation Vortices and Topological Dispersion,” Phys. Rev. Lett. 93, 093901(4) (2004)
49. G.A. Swartzlander Jr., “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497 (2001).
50. David Palacios, David Rozas, and Grover A. Swartzlander Jr., “Observed Scattering into a Dark Optical Vortex Core,” Phys. Rev. Lett. 88, 103902 (2002).
51. R. A. Beth, ‘Mechanical detection and measurement of the angular momentum of light', Phys. Rev. 50, 115–127 (1936).
52. 魏光辉,朱宝亮,“激光束光学”。
53. J. Durnin. Exact solutions of nondiffraction beams. I. The scarlar teory. JOSA A, 4: 651-654, 1987.
54. J. Durnin, J. J. Miceli, J. H. Eberly, Diffraction –free beams. Phy. Rev. Lett., 58: 1499-1501, 1987.
55. J. Arlt, K. Dholakia, J. Soneson and E. M. Wright. Optical diploe traps and atomic waveguides based on Bessel light beams. Phys. Rev. A, 63:063602, 2001.
56. Yin J P, et al., Doughnut-beam-induced Sisyphus cooling in atomic guiding and collimation. J. Opt. Soc. Am B, 15(8):2235, 1998.
57. J. Arlt, K. Dholakia, Generation of high-order Bessel beams by use of an axicon. Opt. Commun., 177: 297-301, 2000
58. M. Lax, W. H. Louisell and W. B. McKnight, “From Maxwell to paraxial wave optics”, Phys. Rev. A. 11, 1365–1370 (1975)
59. H. A. Haus. Waves and Fields in Optoelectronics. (Prentice-Hall, Englewood Cliffs, NJ, 1984)
60. M. W. Beijersbergen, L. Allen, H. Vanderveen, J. P. Woerdman: Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum. Optics Commun. 96:123-132, 1993.
61. N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17: 221-223,1992.
62. J. Arlt, K. Dholakia, L. Allen and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45: 1231-1237, 1998.
63. Cheng-Shan Guo, Xuan Liu, Xiuyun Ren, Hui-Tian Wang. Optimal Annular Computer-Generated Holograms for Generation of Optical vortices. J. Opt. Soc. Am. A, 22(2): 385-390, 2005
64. G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen and M. J. Padgett. “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate”,Opt. Comm. 127: 183-188, 1996.
65. Jennifer E. Curtis and David G. Grier, “Structure of optical vortices”, Phys. Rev. Lett. 90, 133901 (2003).
66. Steven Sundbeck and Ilya Gruzberg and David G. Grier, “Structure and scaling of helical modes of light”, Opt. Lett. 30, 477-479 (2005).
67. M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. Hulst, Local observations of phase singularities in optical fields in waveguide structures. Phys. Rev. Lett. 85: 294-297, 2000.
68. R. M. Jenkins, J. Banerji, A. R. Davies, The generation of optical vortices and shape preserving vortex arrays in hollow multimode waveguides. J. Opt. A 3: 527–532, 2001.
69. Arlee V. Smith and Darrell J. Armstrong. Generation of vortex beams by an image-rotating optical parametric oscillator. Opt. Exp. 11(8):868-873, 2003.
70. J. M. Vaughan and D. V. Willetts. “Interference properties of a light beam having a helical wave surface”Opt. Comm.30: 263-267, 1979.
71. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Hasman. The formation of laser beams with pure azimuthal or radial polarization. Applied Physics Letters 77:3322-3324, 2000.
72. R. Oron, N. Davidson, A. A. Friesem, F. Hasman: Efficient formation of pure helical laser beams. Optics Communications 182:205-208, 2000.
73. V. Yu. Bazhenov, m.V. Vasnetsov, and M.S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis'ma Zh. Eksp. Teor. Fiz. 52, 1037-1039 (1990) [JETP Lett. 52, 429-431 (1990)].
74. Jennifer E. Curtis and David G. Grier. Modulated optical vortices. Opt. Lett. 28: 872-874, 2003.
75. Jennifer E. Curtis, Brian A. Koss, and David G. Grier. Dynamic Holographic Optical Tweezers. Opt. Commun. 207: 169-175, 2002.
76. Cheng-Shan Guo, Xuan Liu, Jing-Liang He, Hui-Tian Wang,” Optimal annulus structures of optical vortices”, Optics Express. 12. 4625-4634 (2004).
77. K. Ladavac and D. G. Grier,”Colloidal hydrodynamic coupling in concentric optical vortices”, Europhys. Lett., 70, 548-554 (2005)
78. Carmel Rotschild, Shachaf Zommer, Shulamit Moed, Oren Hershcovitz, and Stephen G. Lipson. Adjustable spiral phase plate. Applied Optics, 43(12): 2397-2399, 2004
79. J.A. Davis, D.E. McNamra, D.M. Cottrell, J. Campos, “Image processing with the radial Hilbert transform: theory and experiments ”Opt. Lett. 25 (2000) 99.
80. S. Fuerhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “spiral phase contrast imaging in microscopy”, Opt. Express 13, 689-694 (2005).
81. A. Jesacher, S. Fuerhapter, S. Bernet, and M. Ritsch-Marte, “Shadow Effects in Spiral Phase Contrast Microscopy”,Phys. Rev. Lett. 94, 233902 (2005).
82. Severin Fürhapter, Alexander Jesacher, Stefan Bernet, and Monika Ritsch-Marte, “Spiral interferometry”, Opt. Lett. 30 (2005) 1953
83. Cheng-Shan Guo, Xin Cheng, Xiu-Yun Ren, Jian-Ping Ding, Hui-Tian Wang, “Optical vortex phase-shifting digital holography”, Optics Express. 12, 5166-5171(2004).
84. G. Foo, D. M. Palacios, and G. A. Swartzlander, Jr. “Optical vortex coronagraph,” Opt. Lett. 30, 3308-3310 (2005).
85. C. S. Guo Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. Vol. 244, 233-344 (2006).
86. Q. Wang, X. W. Sun, P. Shum, “Dynamic switching of optical vortices with dynamic gamma-correction liquid crystal spiral phase plate,” Opt. Express 13, 10285-10291 (2005)
87. Cheng-Shan Guo, Dong-Mei Xue, Yu-Jing Han and Lu-Zhong Cai, “Optimal phase steps of multi-level spiral phase plates”, Opt. Lett. (Submitted).
88. L. B. Lesem, P. M. Hirsch and J. A. Jordan, Jr., “Generation of discrete point holograms”,J. Opt. Soc. Am. 58, 729A, 1968.
89. Jeffrey A. Davis and Joel B. Bentley,” Azimuthal prism effect with partially blocked vortex-producing lenses”, Opt. Lett. 30, 3204-3206, 2005.
90. A. Kastler, Rev. Opt. 29, 308 (1950).
91. H. Wolter, Ann. Phys. 7, 341 (1950).
92. A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, “Fractional Hilbert transform”, Opt. Lett. 21, 281 (1996).
93. Cheng-Shan Guo, Yu-Jing Han, Jian-Bo Xu and Jian-Ping Ding, “Radial Hilbert
transform with Laguerre-gaussian spatial filters”, Opt. Lett. Vol. 31, No. 10, 1394-1396 (2006).