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Advances in Optics and Photonics

Advances in Optics and Photonics

| BRINGING REVIEWS AND TUTORIALS TO LIGHT

  • Editor: Bahaa E. A. Saleh
  • Vol. 3, Iss. 2 — Jun. 30, 2011

Optics InfoBase > Advances in Optics and Photonics > Volume 3 > Issue 2 > Orbital angular momentum: origins, behavior and applications

Orbital angular momentum: origins, behavior and applications

Alison M. Yao and Miles J. Padgett  »View Author Affiliations


Advances in Optics and Photonics, Vol. 3, Issue 2, pp. 161-204 (2011)
http://dx.doi.org/10.1364/AOP.3.000161


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Abstract

As they travel through space, some light beams rotate. Such light beams have angular momentum. There are two particularly important ways in which a light beam can rotate: if every polarization vector rotates, the light has spin; if the phase structure rotates, the light has orbital angular momentum (OAM), which can be many times greater than the spin. Only in the past 20 years has it been realized that beams carrying OAM, which have an optical vortex along the axis, can be easily made in the laboratory. These light beams are able to spin microscopic objects, give rise to rotational frequency shifts, create new forms of imaging systems, and behave within nonlinear material to give new insights into quantum optics.

© 2011 OSA

OCIS Codes
(050.4865) Diffraction and gratings : Optical vortices
(260.6042) Physical optics : Singular optics

ToC Category:
Physical Optics

History
Original Manuscript: October 8, 2010
Revised Manuscript: January 5, 2011
Manuscript Accepted: January 5, 2011
Published: May 15, 2011

Virtual Issues
(2011) Advances in Optics and Photonics

Citation
Alison M. Yao and Miles J. Padgett, "Orbital angular momentum: origins, behavior and applications," Adv. Opt. Photon. 3, 161-204 (2011)
http://www.opticsinfobase.org/aop/abstract.cfm?URI=aop-3-2-161


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References

  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre–Gaussian laser modes," Phys. Rev. A 45, 8185‒8189 (1992). [CrossRef]
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, 1995.
  3. L. Allen, M. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291‒372 (1999).
  4. J. W. Simmons and M. J. Guttmann, States, Waves, and Photons: a Modern Introduction to Light, Addison-Wesley, 1970.
  5. M. J. Padgett and L. Allen, "The Poynting vector in Laguerre–Gaussian laser modes," Opt. Commun. 121, 36‒40 (1995). [CrossRef]
  6. J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, "Direct measurement of the skew angle of the Poynting vector in a helically phased beam," Opt. Express 14, 11919‒11924 (2006). [CrossRef]
  7. S. Barnett and L. Allen, "Orbital angular momentum and non paraxial light beams," Opt. Commun. 110, 670‒678 (1994). [CrossRef]
  8. Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, "Spin-to-orbital angular momentum conversion in a strongly focused optical beam," Phys. Rev. Lett. 99, 073901 (2007). [CrossRef]
  9. T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Angular momentum of a strongly focused Gaussian beam," J. Opt. A. Pure Appl. Opt. 10, 115005 (2008). [CrossRef]
  10. S. M. Barnett, "Optical angular-momentum flux," J. Opt. B Quantum Semiclass. Opt. 4, 7‒16 (2002). [CrossRef]
  11. J. Poynting, "The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light," Proc. R. Soc. Lond. A Ser. A 82, 560‒567 (1909). [CrossRef]
  12. R. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115‒125 (1936). [CrossRef]
  13. J. D. Jackson, Classical Electrodynamics, 3rd ed., Wiley, 1999.
  14. P. Dirac, "Quantised singularities in the electromagnetic field," Proc. R. Soc. Lond. A 133, 60‒72 (1931). [CrossRef]
  15. J. F. Nye and M. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165‒190 (1974). [CrossRef]
  16. M. Berry, J. Nye, and F. Wright, "The elliptic umbilic diffraction catastrophe," Phil. Trans. R. Soc. Lond. 291, 453‒484 (1979). [CrossRef]
  17. J. M. Vaughan and D. Willetts, "Interference properties of a light-beam having a helical wave surface," Opt. Commun. 30, 263‒267 (1979). [CrossRef]
  18. C. Tamm, "Frequency locking of 2 transverse optical modes of a laser," Phys. Rev. A 38, 5960‒5963 (1988). [CrossRef]
  19. C. Tamm and C. Weiss, "Bistability and optical switching of spatial patterns in a laser," J. Opt. Soc. Am. B 7, 1034‒1038 (1990). [CrossRef]
  20. L. A. Lugiato, F. Prati, L. M. Narducci, and G.-L. Oppo, "Spontaneous breaking of the cylindrical symmetry in lasers," Opt. Commun. 69, 387‒392 (1989). [CrossRef]
  21. L. A. Lugiato, G.-L. Oppo, J. R. Tredicce, L. M. Narducci, and M. A. Pernigo, "Instability and spatial complexity in a laser," J. Opt. Soc. Am. B 7, 1019‒1033 (1990). [CrossRef]
  22. M. Brambilla, F. Battipiede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090‒5113 (1991). [CrossRef]
  23. M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Prati, A. J. Kent, G.-L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, "Dynamical transverse laser patterns. I. Theory," Phys. Rev. A 49, 1427‒1451 (1994). [CrossRef]
  24. A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, J. R. Tredicce, M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Prati, A. J. Kent, and G.-L. Oppo, "Dynamical transverse laser patterns. II. Experiments," Phys. Rev. A 49, 1452‒1466 (1994). [CrossRef]
  25. G. D’Alessandro and G.-L. Oppo, "Gauss–Laguerre modes: a sensible basis for laser dynamics," Opt. Commun. 88, 130‒136 (1992). [CrossRef]
  26. P. Coullet, G. Gil, and F. Rocca, "Optical vortices," Opt. Commun. 73, 403‒408 (1989). [CrossRef]
  27. V. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser-beams with screw dislocations in their wave-fronts," JETP. Lett. 52, 429‒431 (1990).
  28. M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A 456, 2059‒2079 (2000). [CrossRef]
  29. J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21‒27 (2001). [CrossRef]
  30. K. O’Holleran, M. Padgett, and M. Dennis, "Topology of optical vortex lines formed by the interference of three, four, and five plane waves," Opt. Express 14, 3039‒3044 (2006). [CrossRef]
  31. J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, 1st ed., Taylor & Francis, 1999.
  32. K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, "Fractality of light’s darkness," Phys. Rev. Lett. 100, 053902 (2008). [CrossRef]
  33. M. V. Berry and M. R. Dennis, "Knotted and linked phase singularities in monochromatic waves," Proc. R. Soc. Lond. A 457, 2251‒2263 (2001). [CrossRef]
  34. K. O’Holleran, M. Dennis, and M. Padgett, "Topology of light’s darkness," Phys. Rev. Lett. 102, 143902 (2009). [CrossRef]
  35. G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305‒310 (2007). [CrossRef]
  36. S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299‒315 (2008). [CrossRef]
  37. M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112, 321‒327 (1994). [CrossRef]
  38. G. A. Turnbull, D. A. Roberson, G. M. Smith, L. Allen, and M. J. Padgett, "Generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate," Opt. Commun. 127, 183‒188 (1996). [CrossRef]
  39. S. Oemrawsingh, J. van Houwelingen, E. Eliel, J. P. Woerdman, E. Verstegen, J. Kloosterboer, and G. ’t Hooft, "Production and characterization of spiral phase plates for optical wavelengths," Appl. Optics 43, 688‒694 (2004). [CrossRef]
  40. K. Sueda, G. Miyaji, N. Miyanaga, and M. Nakatsuka, "Laguerre–Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses," Opt. Express 12, 3548‒3553 (2004). [CrossRef]
  41. A. E. Siegman, Lasers, University Science Books, 1986.
  42. M. Kolobov, ed., Quantum Imaging, Springer, 2007.
  43. J. Durnin, J. J. Miceli Jr., and J. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499‒1501 (1987). [CrossRef]
  44. J. Gutiérrez-Vega, M. Iturbe-Castillo, and S. Chávez-Cerda, "Alternative formulation for invariant optical fields: Mathieu beams," Opt. Lett. 25, 1493‒1495 (2000). [CrossRef]
  45. V. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985‒990 (1992). [CrossRef]
  46. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. Wegener, "Laser beams with phase singularities," Opt. Quantum. Electron 24, S951‒S962 (1992). [CrossRef]
  47. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. White, "Generation of optical phase singularities by computer-generated holograms," Opt. Lett. 17, 221‒223 (1992). [CrossRef]
  48. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "Parametric downconversion for light beams possessing orbital angular momentum," Phys. Rev. A 59, 3950‒3952 (1999). [CrossRef]
  49. M. Dennis, K. O’Holleran, and M. Padgett, "Singular optics: optical vortices and polarization singularities," Prog. Opt. 53, 293‒363 (2009).
  50. R. W. Gerchberg and W. Saxton, "Practical algorithm for determination of phase from image and diffraction plane pictures," Optik 35, 237‒246 (1972).
  51. A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, "Near-perfect hologram reconstruction with a spatial light modulator," Opt. Express 16, 2597‒2603 (2008). [CrossRef]
  52. J. Kirk and A. Jones, "Phase-only complex-valued spatial filter," J. Opt. Soc. Am. 61, 1023‒1028 (1971). [CrossRef]
  53. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005). [CrossRef]
  54. M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, "Isolated optical vortex knots," Nat. Phys. 6, 118‒121 (2010). [CrossRef]
  55. B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, "Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces," Phys. Rev. A 81, 043844 (2010). [CrossRef]
  56. M. W. Beijersbergen, L. Allen, H. van der Veen, and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123‒132 (1993). [CrossRef]
  57. N. González, G. Molina-Terriza, and J. Torres, "How a Dove prism transforms the orbital angular momentum of a light beam," Opt. Express 14, 9093‒9102 (2006). [CrossRef]
  58. G. A. Swartzlander and R. I. Hernandez-Aranda, "Optical Rankine vortex and anomalous circulation of light," Phys. Rev. Lett. 99, 163901 (2007). [CrossRef]
  59. G. A. Swartzlander, "Peering into darkness with a vortex spatial filter," Opt. Lett. 26, 497‒499 (2001). [CrossRef]
  60. G. Foo, D. M. Palacios, and G. A. Swartzlander, "Optical vortex coronagraph," Opt. Lett. 30, 3308‒3310 (2005). [CrossRef]
  61. G. Gbur, T. Visser, and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002). [CrossRef]
  62. M. V. Berry, "Coloured phase singularities," New J. Phys. 4, 66 (2002). [CrossRef]
  63. M. V. Berry, "Exploring the colours of dark light," New J. Phys. 4, 74 (2002). [CrossRef]
  64. J. Leach and M. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 154 (2003). [CrossRef]
  65. J. Courtial, K. Dholakia, D. Robertson, L. Allen, and M. J. Padgett, "Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum," Phys. Rev. Lett. 80, 3217‒3219 (1998). [CrossRef]
  66. B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, "Utilization of photon orbital angular momentum in the low-frequency radio domain," Phys. Rev. Lett. 99, 087701 (2007). [CrossRef]
  67. S. Sasaki and I. Mcnulty, "Proposal for generating brilliant x-ray beams carrying orbital angular momentum," Phys. Rev. Lett. 100, 124801 (2008). [CrossRef]
  68. M. Uchida and A. Tonomura, "Generation of electron beams carrying orbital angular momentum," Nature 464, 737‒739 (2010). [CrossRef]
  69. H. T. J. Verbeeck and P. Schattschneider, "Production and application of electron vortex beams," Nature 467, 301‒304 (2010). [CrossRef]
  70. K. Volke-Sepúlveda, A. O. Santillán, and R. R. Boullosa, "Transfer of angular momentum to matter from acoustical vortices in free space," Phys. Rev. Lett. 100, 024302 (2008). [CrossRef]
  71. K. D. Skeldon, C. Wilson, M. Edgar, and M. J. Padgett, "An acoustic spanner and its associated rotational doppler shift," New J. Phys. 10, 013018 (2008). [CrossRef]
  72. H. He, M. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826‒829 (1995). [CrossRef]
  73. N. Simpson, K. Dholakia, L. Allen, and M. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner," Opt. Lett. 22, 52‒54 (1997). [CrossRef]
  74. D. Grier, "A revolution in optical manipulation," Nature 424, 810‒816 (2003). [CrossRef]
  75. M. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World 10, 35‒38 (1997).
  76. M. Friese, T. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348‒350 (1998). [CrossRef]
  77. A. O’Neil, I. MacVicar, L. Allen, and M. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002). [CrossRef]
  78. L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912 (2001). [CrossRef]
  79. H. Luo, Z. Ren, W. Shu, and S. Wen, "Reversed propagation dynamics of Laguerre–Gaussian beams in left-handed materials," Phys. Rev. A 77, 023812 (2008). [CrossRef]
  80. J. Courtial and M. Padgett, "Limit to the orbital angular momentum per unit energy in a light beam that can be focused onto a small particle," Opt. Commun. 173, 269‒274 (2000). [CrossRef]
  81. E. Higurashi, H. Ukita, H. Tanaka, and O. Ohguchi, "Optically induced rotation of anisotropic micro-objects fabricated by surface micromachining," Appl. Phys. Lett. 64, 2209‒2210 (1994). [CrossRef]
  82. M. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547‒549 (2001). [CrossRef]
  83. G. Knoner, S. Parkin, T. A. Nieminen, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Integrated optomechanical microelements," Opt. Express 15, 5521‒5530 (2007). [CrossRef]
  84. K. Ladavac and D. Grier, "Micro-optomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144‒1149 (2004). [CrossRef]
  85. J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, "An optically driven pump for microfluidics," Lab Chip 6, 735‒739 (2006). [CrossRef]
  86. M. Babiker, W. L. Power, and L. Allen, "Light-induced torque on moving atoms," Phys. Rev. Lett. 73, 1239‒1242 (1994). [CrossRef]
  87. L. Allen, M. Babiker, and W. L. Power, "Azimuthal Dopper-shift in light-beams with orbital angular momentum," Opt. Commun. 112, 141‒144 (1994). [CrossRef]
  88. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel optical trap of atoms with a doughnut beam," Phys. Rev. Lett. 78, 4713‒4716 (1997). [CrossRef]
  89. J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre–Gaussian and Bessel light beams," Appl. Phys. B: Lasers and Optics 71, 549‒554 (2000). [CrossRef]
  90. K. Gahagan and G. A. Swartzlander, "Optical vortex trapping of particles," Opt. Lett. 21, 827‒829 (1996). [CrossRef]
  91. M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized rotation of atoms from photons with orbital angular momentum," Phys. Rev. Lett. 97, 170406 (2006). [CrossRef]
  92. R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, "Topological stability of stored optical vortices," Phys. Rev. Lett. 98, 203601 (2007). [CrossRef]
  93. D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaître, J. Bloch, C. Tejedor, and L. Viña, "Persistent currents and quantized vortices in a polariton superfluid," Nat. Phys. 6, 527‒533 (2010). [CrossRef]
  94. M. J. Padgett and J. Courtial, "Poincare-sphere equivalent for light beams containing orbital angular momentum," Opt. Lett. 24, 430‒432 (1999). [CrossRef]
  95. E. Galvez, P. Crawford, H. Sztul, M. Pysher, P. Haglin, and R. Williams, "Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum," Phys. Rev. Lett. 90, 203901 (2003). [CrossRef]
  96. L. Allen, J. Courtial, and M. Padgett, "Matrix formulation for the propagation of light beams with orbital and spin angular momenta," Phys. Rev. E 60, 7497‒7503 (1999). [CrossRef]
  97. F. Araoka, T. Verbiest, K. Clays, and A. Persoons, "Interactions of twisted light with chiral molecules: an experimental investigation," Phys. Rev. A 71, 055401 (2005). [CrossRef]
  98. L. Allen and M. Padgett, "Equivalent geometric transformations for spin and orbital angular momentum of light," J. Mod. Opt. 54, 487‒491 (2007). [CrossRef]
  99. B. Garetz and S. Arnold, "Variable frequency-shifting of circularly polarized laser-radiation via a rotating half-wave retardation plate," Opt. Commun. 31, 1‒3 (1979). [CrossRef]
  100. B. Garetz, "Angular Dopper effect," J. Opt. Soc. Am. 71, 609‒611 (1981). [CrossRef]
  101. G. Nienhuis, "Doppler effect induced by rotating lenses," Opt. Commun. 132, 8‒14 (1996). [CrossRef]
  102. J. Courtial, D. Robertson, K. Dholakia, L. Allen, and M. Padgett, "Rotational frequency shift of a light beam," Phys. Rev. Lett. 81, 4828‒4830 (1998). [CrossRef]
  103. G. Molina-Terriza, J. Torres, and L. Torner, "Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum," Phys. Rev. Lett. 88, 013601 (2001). [CrossRef]
  104. R. V. Jones, "Rotary ‘aether drag’," Proc. R. Soc. Lond. A 349, 423‒439 (1976). [CrossRef]
  105. M. A. Player, "On the dragging of the plane of polarization of light propagating in a rotating medium," Proc. R. Soc. Lond. A 349, 441‒445 (1976). [CrossRef]
  106. G. Nienhuis, J. P. Woerdman, and I. Kuscer, "Magnetic and mechanical Faraday effects," Phys. Rev. A 46, 7079‒7092 (1992). [CrossRef]
  107. R. V. Jones, "‘Fresnel aether drag’ in a transversely moving medium," Proc. R. Soc. Lond. A 328, 337‒352 (1972). [CrossRef]
  108. M. Padgett, G. Whyte, J. Girkin, A. Wright, L. Allen, P. Ohberg, and S. M. Barnett, "Polarization and image rotation induced by a rotating dielectric rod: an optical angular momentum interpretation," Opt. Lett. 31, 2205‒2207 (2006). [CrossRef]
  109. J. Leach, A. J. Wright, J. B. Gotte, J. M. Girkin, L. Allen, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, "‘Aether drag’ and moving images," Phys. Rev. Lett. 100, 153902 (2008). [CrossRef]
  110. L. Gil, K. Emilsson, and G.-L. Oppo, "Dynamics of spiral waves in a spatially inhomogenous Hopf bifurcation," Phys. Rev. A 45, R567‒R570 (1992). [CrossRef]
  111. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, "Observation of vortex lattices in Bose–Einstein condensates," Science 292, 476‒479 (2001). [CrossRef]
  112. G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503‒2506 (1992). [CrossRef]
  113. W. Firth and D. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450‒2453 (1997). [CrossRef]
  114. D. Skryabin and W. Firth, "Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media," Phys. Rev. E 58, 3916‒3930 (1998). [CrossRef]
  115. A. Desyatnikov, Y. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291‒391 (2005).
  116. K. Dholakia, N. Simpson, M. Padgett, and L. Allen, "Second-harmonic generation and the orbital angular momentum of light," Phys. Rev. A 54, R3742‒R3745 (1996). [CrossRef]
  117. J. Courtial, K. Dholakia, L. Allen, and M. Padgett, "Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes," Phys. Rev. A 56, 4193‒4196 (1997). [CrossRef]
  118. A. Beranskis, A. Matijoius, A. Piskarskas, V. Smilgeviius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273‒276 (1997). [CrossRef]
  119. R. Ghosh and L. Mandel, "Observation of nonclassical effects in the interference of two photons," Phys. Rev. Lett. 59, 1903‒1905 (1987). [CrossRef]
  120. D. P. Caetano, M. P. Almeida, P. H. S. Ribeiro, J. A. O. Huguenin, B. C. dos Santos, and A. Z. Khoury, "Conservation of orbital angular momentum in stimulated downconversion," Phys. Rev. A 66, 041801(R) (2002). [CrossRef]
  121. M. Marinelli, J. A. O. Huguenin, P. Nussenzveig, and A. Z. Khoury, "Orbital angular momentum exchange in an optical parametric oscillator," Phys. Rev. A 70, 013812 (2004). [CrossRef]
  122. G.-L. Oppo, A. J. Scroggie, and W. J. Firth, "Characterization, dynamics and stabilization of diffractive domain walls and dark ring cavity solitons in parametric oscillators," Phys. Rev. E 63, 066209 (2001). [CrossRef]
  123. A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777‒780 (1935). [CrossRef]
  124. J. Howell, R. Bennink, S. Bentley, and R. Boyd, "Realization of the Einstein–Podolsky–Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion," Phys. Rev. Lett. 92, 210403 (2004). [CrossRef]
  125. P. G. Kwiat, A. Steinberg, and R. Chiao, "High-visibility interference in a Bell-inequality experiment for energy and time," Phys. Rev. A 47, R2472‒R2475 (1993). [CrossRef]
  126. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313‒316 (2001). [CrossRef]
  127. S. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. Eliel, G. ’t Hooft, and J. P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005). [CrossRef]
  128. J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, "Quantum correlations in optical angle-orbital angular momentum variables," Science 329, 662‒665 (2010). [CrossRef]
  129. J. S. Bell, "On the Einstein Podolsky Rosen paradox," Physics 1, 195‒200 (1964).
  130. A. Aspect, J. Dalibard, and G. Roger, "Experimental test of Bell’s inequalities using time-varying analyzers," Phys. Rev. Lett. 49, 1804‒1807 (1982). [CrossRef]
  131. J. Leach, B. Jack, J. Romero, M. Ritsch-Marte, R. Boyd, A. Jha, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces," Opt. Express 17, 8287‒8293 (2009). [CrossRef]
  132. A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 240401 (2002). [CrossRef]
  133. G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, "Triggered qutrits for quantum communication protocols," Phys. Rev. Lett. 92, 167903 (2004). [CrossRef]
  134. J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005). [CrossRef]
  135. E. Nagali, F. Sciarrino, F. D. Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, "Quantum information transfer from spin to orbital angular momentum of photons," Phys. Rev. Lett. 103, 013601 (2009). [CrossRef]
  136. E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, "Spin–orbit hybrid entanglement of photons and quantum contextuality," Phys. Rev. A 82, 022115 (2010). [CrossRef]
  137. L. Deng, H. Wang, and K. Wang, "Quantum CNOT gates with orbital angular momentum and polarization of single-photon quantum logic," J. Opt. Soc. Am. B 24, 2517‒2520 (2007). [CrossRef]
  138. L. Marrucci, C. Manzo, and D. Paparo, "Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media," Phys. Rev. Lett. 96, 163905 (2006). [CrossRef]
  139. G. Biener, A. Niv, V. Kleiner, and E. Hasman, "Formation of helical beams by use of Pancharatnam-Berry phase optical elements," Opt. Lett. 27, 1875‒1877 (2002). [CrossRef]
  140. G. Calvo and A. Picón, "Spin-induced angular momentum switching," Opt. Lett. 32, 838‒840 (2007). [CrossRef]
  141. E. Nagali, L. Sansoni, F. Sciarrino, F. D. Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, "Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence," Nat. Photonics 3, 720‒723 (2009). [CrossRef]
  142. E. Brasselet, N. Murazawa, and H. Misawa, "Optical vortices from liquid crystal droplets," Phys. Rev. Lett. 103, 103903 (2009). [CrossRef]
  143. S. Khonina, V. Kotlyar, and V. Soifer, "Diffraction optical elements matched to the Gauss–Laguerre modes," Opt. Spectrosc. 85, 636‒644 (1998).
  144. S. Khonina, V. Kotlyar, R. Skidanov, V. Soifer, P. Laakkonen, and J. Turunen, "Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element," Opt. Commun. 175, 301‒308 (2000). [CrossRef]
  145. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, "Free-space information transfer using light beams carrying orbital angular momentum," Opt. Express 12, 5448‒5456 (2004). [CrossRef]
  146. I. V. Basistiy, V. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422‒428 (1993). [CrossRef]
  147. M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, "Laser modes with helical wave-fronts," Phys. Rev. A 49, 3119‒3122 (1994). [CrossRef]
  148. M. Soskin, V. Gorshkov, M. Vasnetsov, J. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064‒4075 (1997). [CrossRef]
  149. I. V. Basistiy, V. Slyusar, M. S. Soskin, M. V. Vasnetsov, and A. Bekshaev, "Manifestation of the rotational Doppler effect by use of an off-axis optical vortex beam," Opt. Lett. 28, 1185‒1187 (2003). [CrossRef]
  150. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002). [CrossRef]
  151. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon," Phys. Rev. Lett. 92, 013601 (2004). [CrossRef]
  152. J. Arlt, "Handedness and azimuthal energy flow of optical vortex beams," J. Mod. Opt. 50, 1573‒1580 (2003).
  153. D. Ghai, P. Senthilkumaran, and R. Sirohi, "Single-slit diffraction of an optical beam with phase singularity," Opt. Lasers Eng. 47, 123‒126 (2009). [CrossRef]
  154. H. Sztul and R. Alfano, "Double-slit interference with Laguerre–Gaussian beams," Opt. Lett. 31, 999‒1001 (2006). [CrossRef]
  155. G.C.G. Berkhout and M. W. Beijersbergen, "Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects," Phys. Rev. Lett. 101, 100801 (2008). [CrossRef]
  156. J. M. Hickmann, E. J. S. Fonseca, W.C. Soares, and S. Chavez-Cerda, "Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum," Phys. Rev. Lett. 105, 053904 (2010). [CrossRef]
  157. E. Yao, S. Franke-Arnold, J. Courtial, S. Barnett, and M. Padgett, "Fourier relationship between angular position and optical orbital angular momentum," Opt. Express 14, 9071‒9076 (2006). [CrossRef]
  158. G. Forbes and M. Alonso, "Measures of spread for periodic distributions and the associated uncertainty relations," Am. J. Phys. 69, 340‒347 (2001). [CrossRef]
  159. S. Franke-Arnold, S. M. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, "Uncertainty principle for angular position and angular momentum," New J. Phys. 6, 103 (2004). [CrossRef]
  160. O. Bryngdahl, "Geometrical transformations in optics," J. Opt. Soc. Am. 64, 1092‒1099 (1974). [CrossRef]
  161. W. Hossack, A. Darling, and A. Dahdouh, "Coordinate transformations with multiple computer-generated optical-elements," J. Mod. Opt. 34, 1235‒1250 (1987). [CrossRef]
  162. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, "Efficient sorting of orbital angular momentum states of light," Phys. Rev. Lett. 105, 153601 (2010). [CrossRef]
  163. L. Torner, J. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873‒881 (2005). [CrossRef]
  164. S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral phase contrast imaging in microscopy," Opt. Express 13, 689‒694 (2005). [CrossRef]
  165. S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral interferometry," Opt. Lett. 30, 1953‒1955 (2005). [CrossRef]
  166. S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, "Quantitative imaging of complex samples by spiral phase contrast microscopy," Opt. Express 14, 3792‒3805 (2006). [CrossRef]
  167. B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, "Holographic ghost imaging and the violation of a Bell inequality," Phys. Rev. Lett. 103, 083602 (2009). [CrossRef]
  168. J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander Jr., "Experimental verification of an optical vortex coronagraph," Phys. Rev. Lett. 97, 053901 (2006). [CrossRef]
  169. G. Swartzlander, E. Ford, R. Abdul-Malik, L. Close, M. Peters, D. Palacios, and D. Wilson, "Astronomical demonstration of an optical vortex coronagraph," Opt. Express 16, 10200‒10207 (2008). [CrossRef]
  170. M. Harwit, "Photon orbital angular momentum in astrophysics," Astrophys. J. 597, 1266‒1270 (2003). [CrossRef]

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