Cylindrical vector beams: From mathematical concepts to applications

Advances in Optics and Photonics

Volumn 1, Issue 1, 2009, Pages 1-57

  Zhan, Qiwen ^a  

^a UNIVERSITY OF DAYTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 65649130692     PISSN: None     EISSN: 19438206     Source Type: Journal    
DOI: 10.1364/AOP.1.000001     Document Type: Article

References (105)

1. D. Pohl, "Operation of a Ruby laser in the purely transverse electric mode TE01, " Appl. Phys. Lett. 20, 266-267 (1972).
2. Y. Mushiake, K. Matzumurra, and N. Nakajima, "Generation of radially polarized optical beam mode by laser oscillation, " Proc. IEEE 60, 1107-1109 (1972).
3. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light into a tighter spot, " Opt. Commun. 179, 1-7 (2000).
4. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam, " Phys. Rev. Lett. 91, 233901 (2003).
5. B. Jia, X. Gan, and M. Gu, "Direct measurement of a radially polarized focused evanescent field facilitated by a single LCD, " Opt. Express 13, 6821-6827 (2005).
6. B. Hao and J. Leger, "Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam, " Opt. Express 15, 3550-3556 (2007).
7. D. G. Hall, "Vector-beam solutions of Maxwell's wave equation, " Opt. Lett. 21, 9-11 (1996).
8. For example, J. M. Senior, Optical Fiber Communications (Prentice Hall, 1992).
9. F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams, " Opt. Commun. 64, 491-495 (1987).
10. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).
11. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).
12. Q. Zhan and J. R. Leger, "Focus shaping using cylindrical vector beams, " Opt. Express 10, 324-331 (2002).
13. M. E. Marhic and E. Garmire, "Low-order TE0q operation of a CO2 laser for transmission through circular metallic waveguides, " Appl. Phys. Lett. 38, 743-745 (1981).
14. T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. Anderson, and M. J. Rooks, "Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser, " Appl. Phys. Lett. 60, 1921-1923 (1992).
15. K. Yonezawa, Y. Kozawa, and S. Sato, "Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal, " Opt. Lett. 31, 2151-2153 (2006).
16. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel, and N. Davidson, "Birefringence-induced bifocusing for selection of radially or azimuthally polarized laser modes, " Appl. Opt. 46, 3304-3310 (2007).
17. K. Yonezawa, Y. Kozawa, and S. Sato, "Compact laser with radial polarization using birefringent laser medium, " Jpn. J. Appl. Phys., Part 1 46, 5160-5163 (2007).
18. J. F. Bisson, J. Li, K. Ueda, and Y. Senatsky, "Radially polarized ring and arc beams of a neodymium laser with an intra-cavity axicon, " Opt. Express 14, 3304-3311 (2006).
19. C.-C. Shih, "Radial polarization laser resonator, " U.S. patent 5,359,622 (Oct. 25, 1994).
20. Y. Kozawa and S. Sato, "Generation of a radially polarized laser beam by use of a conical Brewster prism, " Opt. Lett. 30, 3063-3065 (2005).
21. M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, "Multilayer polarizing grating mirror used for the generation of radial polarization inYb:YAG thin-disk lasers, " Opt. Lett. 32, 3272-3274 (2007).
22. V. G. Niziev, R. S. Chang, and A. V. Nesterov, "Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer, " Appl. Opt. 45, 8393-8399 (2006).
23. Q. Zhan and J. R. Leger, "Microellipsometer with radial symmetry, " Appl. Opt. 41, 4630-4637 (2002).
24. Q. Zhan and J. R. Leger, "Interferometric measurement of Berry's phase in space-variant polarization manipulations, " Opt. Commun. 213, 241-245 (2002).
25. C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S. G. Lipson, "Adjustable spiral phase plate, " Appl. Opt. 43, 2397-2399 (2004).
26. For example, the vortex phase plates from RPC Photonics (http:// www.rpcphotonics.com/).
27. Q. Zhan, "Cylindrical polarization symmetry for nondestructive nano-characterization, " Proc. SPIE 5045, 85-92 (2003).
28. K. J. Moh, X. C. Yuan, J. Bu, D. K.Y. Low, and R. E. Burge, "Direct noninterference cylindrical vector beam generation applied in the femtosecond regime, " Appl. Phys. Lett. 89, 251114 (2006).
29. R. Yamaguchi, T. Nose, and S. Sato, "Liquid crystal polarizers with axially symmetrical properties, " Jpn. J. Appl. Phys. Part 1 28, 1730-1731 (1989).
30. M. Stalder and M. Schadt, "Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters, " Opt. Lett. 21, 1948-1950 (1996).
31. For example, the ZPol from Nanophoton (http://www.nanophoton.jp/) and the radial polarizer from ARCoptix (http://www.arcoptix.com/).
32. M. R. Beversluis, L. Novotny, and S. J. Stranick, "Programmable vector point-spread function engineering, " Opt. Express 14, 2650-2656 (2006).
33. C. Ye, "Construction of an optical rotator using quarter-wave plates and an optical retarder, " Opt. Eng. 34, 3031-3035 (1995).
34. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, "Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams, " Opt. Commun. 281, 732-738 (2008).
35. A. K. Spilman and T. G. Brown, "Stress birefringent, space-variant wave plates for vortex illumination, " Appl. Opt. 46, 61-66 (2007).
36. S. C. McEldowney, D. M. Shemo, and R. A. Chipman, "Vortex retarders produced from photo-aligned liquid crystal polymers, " Opt. Express 16, 7295-7308 (2008).
37. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, "Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings, " Opt. Lett. 27, 285-287 (2002).
38. B. C. Lim, P. B. Phua, W. J. Lai, and M. H. Hong, "Fast switchable electro-optic radial polarization retarder, " Opt. Lett. 33, 950-952 (2008).
39. S. C. Tidwell, D. H. Ford, and W. D. Kimura, "Generating radially polarized beams interferometrically, " Appl. Opt. 29, 2234-2239 (1990).
40. N. Passilly, R. de Saint Denis, K. A-Ameur, F. Treussart, R. Hierle, and J. F. Roch, "Simple interferometric technique for generation of a radially polarized light beam, " J. Opt. Soc. Am. A 22, 984-991 (2005).
41. X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, "Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement, " Opt. Lett. 32, 3549-3551 (2007).
42. T. Grosjean, D. Courjon, and M. Spajer, "An all-fiber device for generating radially and other polarized light beams, " Opt. Commun. 203, 1-5 (2002).
43. G. Volpe, D. Petrov, "Generation of cylindrical vector beams with few-mode fibers excited by Laguerre-Gaussian beams, " Opt. Commun. 237, 89-95 (2004).
44. T. Hirayama, Y. Kozawa, T. Nakamura, and S. Sato, "Generation of a cylindrically symmetric, polarized laser beam with narrow linewidth and fine tunability, " Opt. Express 14, 12839-12845 (2006).
45. C. Sun and C. Liu, "Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation, " Opt. Lett. 28, 99-101 (2003).
46. W. Chen and Q. Zhan, "Three-dimensional focus shaping with cylindrical vector beams, " Opt. Commun. 265, 411-417 (2006).
47. E. Wolf, "Electromagnetic diffraction in optical systems I. An integral representation of the image field, " Proc. R. Soc. London Ser. A 253, 349-357 (1959).
48. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system, " Proc. R. Soc. London Ser. A 253, 358-379 (1959).
49. K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical vector beams, " Opt. Express 7, 77-87 (2000).
50. M. Gu, ed., Advanced Optical Imaging Theory, Vol. 75 of Springer Series in Optical Sciences (Springer-Verlag, 1999).
51. G. M. Lerman and U. Levy, "Effect of radial polarization and apodization on spot size under tight focusing conditions, " Opt. Express 16, 4567-4581 (2008).
52. C. J. R. Sheppard and A. Choudhury, "Annular pupils, radial polarization, and superresolution, " Appl. Opt. 43, 4322-4327 (2004).
53. S. F. Pereira, A. S. van de Nes, "Superresolution by means of polarisation, phase and amplitude pupil masks, " Opt. Commun. 234, 119-124 (2004).
54. J. Stadler, C. Stanciu, C. Stupperich, and A. J. Meixner, "Tighter focusing with a parabolic mirror, " Opt. Lett. 33, 681-683 (2008).
55. D. P. Biss, and T. G. Brown, "Polarization-vortex-driven second-harmonic generation, " Opt. Lett. 28, 923-925 (2003).
56. S. Carrasco, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Second-and third-harmonic generation with vector Gaussian beams, " J. Opt. Soc. Am. B 23, 2134-2141 (2006).
57. D. P. Biss, K. S. Youngworth, and T. G. Brown, "Dark-field imaging with cylindrical-vector beams, " Appl. Opt. 45, 470-479 (2006).
58. N. Bokor, N. Davidson, "Toward a spherical spot distribution with 4π focusing of radially polarized light, " Opt. Lett. 29, 1968-1970 (2004).
59. L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems, " Opt. Commun. 191, 161-172 (2001).
60. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules, " Phys. Rev. Lett. 86, 5251-5254 (2001).
61. N. Bokor, N. Davidson, "Generation of a hollow dark spherical spot by 4π focusing of a radially polarized Laguerre-Gaussian beam, " Opt. Lett. 31, 149-151 (2006).
62. S. Hell and J. Wichmann, "Breaking the diffraction resolution limit by stimulated emission: stimulated-emission depletion fluorescence microscopy, " Opt. Lett. 19, 780-782 (1994).
63. P. Török and P. Munro, "The use of Gauss-Laguerre vector beams in STED microscopy, " Opt. Express 12, 3605-3617 (2004).
64. H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, "Creation of a needle of longitudinally polarized light in vacuum using binary optics, " Nat. Photonics 2, 501-505 (2008).
65. A. F. Abouraddy and K. C. Toussaint, Jr., "Three-dimensional polarization control in microscopy, " Phys. Rev. Lett. 96, 153901 (2006).
66. T. D. Visser and J. T. Foley, "On the wavefront spacing of focused, radially polarized beams, " J. Opt. Soc. Am. A 22, 2527-2531 (2005).
67. H. Chen, Q. Zhan, Y. L. Zhang, and Y. P. Li, "The Gouy phase shift of the highly focused radially polarized beam, " Phys. Lett. A 371, 259-261 (2007).
68. L. G. Gouy, "Sur une propriété nouvelle des ondes lumineuses, " C. R. Acad. Sci. Paris. 110, 1251-1253 (1890).
69. Q. Zhan, "Second-order tilted wave interpretation of the Gouy phase shift under high numerical aperture uniform illumination, " Opt. Commun. 242, 351-360 (2004).
70. J. Cheng and X. S. Xie, "Green's function formulation for third-harmonic generation microscopy, " J. Opt. Soc. Am. B 19, 1604-1610 (2002).
71. J. Cheng, A. Volkmer, and X. S. Xie, "Theoretical and experimental characterization of coherent anti-Stokes Raman scattering microscopy, " J. Opt. Soc. Am. B 19, 1363-1375 (2002).
72. Y. Yang and Q. Zhan, "Third-harmonic generation microscopy with tightly focused radial polarization, " J. Opt. A 10, 125103 (2008).
73. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and Gratings (Spinger-Verlag, 1988).
74. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays, " Nature 391, 667-669 (1998).
75. N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limit imaging with a silver superlens, " Science 308, 534-537 (2005).
76. X. Luo and T. Ishihara, "Surface plasmon resonant interference nanolithography technique, " Appl. Phys. Lett. 84, 4780-4782 (2004).
77. Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing surface plasmons with a plasmonic lens, " Nano Lett. 5, 1726-1729 (2005).
78. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, "Subwavelength focusing and guiding of surface plasmons, " Nano Lett. 5, 1399-1402 (2005).
79. W. Chen and Q. Zhan, "Optimal plasmonic focusing with radial polarization, " Proc. SPIE 6450, 64500D (2007).
80. H. Kano, S. Mizuguchi, and S. Kawata, "Excitation of surface-plasmon polaritons by a focused laser beam, " J. Opt. Soc. Am. B 15, 1381-1386 (1998).
81. Q. Zhan, "Evanescent Bessel beam generation via surface plasmon resonance by radially polarized beam, " Opt. Lett. 31, 1726-1728 (2006).
82. W. Chen and Q. Zhan, "Realization of evanescent Bessel beam via surface plasmon interference excited by radially polarized beam" Opt. Lett. (to be published).
83. A. Bouhelier, F. Ignatovich, A. Bruyant, C. Huang, G. Colas des Francs, J.-C. Weeber, A. Dereux, G. P. Wiederrecht, and L. Novotny, "Surface plasmon interference excited by tightly focused laser beams, " Opt. Lett. 32, 2535-2537 (2007).
84. A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy, " J. Microsc. 210, 220-224 (2003).
85. W. Chen and Q. Zhan, "Numerical study of an apertureless near field scanning optical microscope probe under radial polarization illumination, " Opt. Express 15, 4106-4111 (2007).
86. W. Chen and Q. Zhan, "Field enhancement analysis of an apertureless near field scanning optical microscope probe with finite element method, " Chin. Opt. Lett. 5, 709-711 (2007).
87. Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization, " Opt. Express 12, 3377-3382 (2004).
88. H. Kawauchi, K. Yonezawa, Y. Kozawa, and S. Sato, "Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam, " Opt. Lett. 32, 1839-1841 (2007).
89. Y. Q. Zhao, Q. Zhan, Y. L. Zhang, and Y. P. Li, "Creation of a three-dimensional optical chain for controllable particle delivery, " Opt. Lett. 30, 848-850 (2005).
90. Q. Zhan, "Optical radiation forces on a dielectric sphere produced by highly focused cylindrical vector beams, " J. Opt. A, Pure Appl. Opt. 5, 229-232 (2003).
91. Q. Zhan, "Trapping nanoparticles with cylindrical polarization, " Proc. SPIE 5514, 275-282 (2004).
92. J. R. Zurita-Sanchez and L. Novotny, "Multipolar interband absorption in a semiconductor quantum dot. II. Magnetic dipole enhancement, " J. Opt. Soc. Am. B 19, 2722-2726 (2002).
93. E. M. Furst and A. P. Gast, "Micromechanics of dipolar chains using optical tweezers, " Phys. Rev. Lett. 82, 4130-4133 (1999).
94. Y. B. Du and P. Tong, "Light scattering properties of paramagnetic particles, " J. Chem. Phys. 107, 355-362 (1997).
95. V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency, " J. Phys. D 32, 1455-1461 (1999).
96. M. Meier, V. Romano, and T. Feurer, "Material processing with pulsed radially and azimuthally polarized laser radiation, " Appl. Phys. A 86, 329-334 (2007).
97. Y. Cai, Q. Lin, H. T. Eyyuboglu, and Y. Baykal, "Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere, " Opt. Express 16, 7665-7673 (2008).
98. W. Cheng, J. W. Haus, and Q. Zhan, "Propagation of scalar and vector vortex beams through turbulent atmosphere, " Proc. SPIE 7200 (to be published).
99. J. W. Haus, Z. Mozumder, and Q. Zhan, "Azimuthal modulation instability for a cylindrically polarized wave in a nonlinear Kerr Medium, " Opt. Express 14, 4757-4764 (2006).
100. G. Chang, C. J. Divin, C. H. Liu, S. L. Williamson, A. Galvanauskas, and T. B. Norris, "Generation of radially polarized terahertz pulses via velocity-mismatched optical rectification, " Opt. Lett. 32, 433-435 (2007).
101. Q. Cao and J. Jahns, "Azimuthally polarized surface plasmons as effective terahertz waveguides, " Opt. Express 13, 511-518 (2005).
102. Q. Zhan, "Properties of circularly polarization vortex beams, " Opt. Lett. 31, 867-869 (2006).
103. F. Gori, "Polarization basis for vortex beams, " J. Opt. Soc. Am. A 18, 1612-1617 (2001).
104. R. Borghi and M. Santarsiero, "Nonparaxial propagation of spirally polarized optical beams, " J. Opt. Soc. Am. A 21, 2029-2037 (2004).
105. R. Borghi, M. Santarsiero, and M. A. Alonso, "Highly focused spirally polarized beams, " J. Opt. Soc. Am. A 22, 1420-1431 (2005).