Optics InfoBase > Advances in Optics and Photonics > Volume 3 > Issue 2 > Orbital angular momentum: origins, behavior and applications
Orbital angular momentum: origins, behavior and applicationsAlison M. Yao and Miles J. Padgett »View Author Affiliations
Alison M. Yao^{1}
and Miles J. Padgett^{2}
^{1}SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, UK ^{2}Department of Physics and Astronomy, SUPA, Kelvin Building, University of Glasgow, Glasgow G12 8QQ, Scotland, UK |
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
- 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]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, 1995.
- L. Allen, M. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291‒372 (1999).
- J. W. Simmons and M. J. Guttmann, States, Waves, and Photons: a Modern Introduction to Light, Addison-Wesley, 1970.
- M. J. Padgett and L. Allen, "The Poynting vector in Laguerre–Gaussian laser modes," Opt. Commun. 121, 36‒40 (1995). [CrossRef]
- 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]
- S. Barnett and L. Allen, "Orbital angular momentum and non paraxial light beams," Opt. Commun. 110, 670‒678 (1994). [CrossRef]
- 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]
- 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]
- S. M. Barnett, "Optical angular-momentum flux," J. Opt. B Quantum Semiclass. Opt. 4, 7‒16 (2002). [CrossRef]
- 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]
- R. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115‒125 (1936). [CrossRef]
- J. D. Jackson, Classical Electrodynamics, 3rd ed., Wiley, 1999.
- P. Dirac, "Quantised singularities in the electromagnetic field," Proc. R. Soc. Lond. A 133, 60‒72 (1931). [CrossRef]
- J. F. Nye and M. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165‒190 (1974). [CrossRef]
- M. Berry, J. Nye, and F. Wright, "The elliptic umbilic diffraction catastrophe," Phil. Trans. R. Soc. Lond. 291, 453‒484 (1979). [CrossRef]
- J. M. Vaughan and D. Willetts, "Interference properties of a light-beam having a helical wave surface," Opt. Commun. 30, 263‒267 (1979). [CrossRef]
- C. Tamm, "Frequency locking of 2 transverse optical modes of a laser," Phys. Rev. A 38, 5960‒5963 (1988). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. D’Alessandro and G.-L. Oppo, "Gauss–Laguerre modes: a sensible basis for laser dynamics," Opt. Commun. 88, 130‒136 (1992). [CrossRef]
- P. Coullet, G. Gil, and F. Rocca, "Optical vortices," Opt. Commun. 73, 403‒408 (1989). [CrossRef]
- V. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser-beams with screw dislocations in their wave-fronts," JETP. Lett. 52, 429‒431 (1990).
- M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A 456, 2059‒2079 (2000). [CrossRef]
- J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21‒27 (2001). [CrossRef]
- 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]
- J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, 1st ed., Taylor & Francis, 1999.
- K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, "Fractality of light’s darkness," Phys. Rev. Lett. 100, 053902 (2008). [CrossRef]
- 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]
- K. O’Holleran, M. Dennis, and M. Padgett, "Topology of light’s darkness," Phys. Rev. Lett. 102, 143902 (2009). [CrossRef]
- G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305‒310 (2007). [CrossRef]
- S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299‒315 (2008). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- A. E. Siegman, Lasers, University Science Books, 1986.
- M. Kolobov, ed., Quantum Imaging, Springer, 2007.
- J. Durnin, J. J. Miceli Jr., and J. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499‒1501 (1987). [CrossRef]
- 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]
- V. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985‒990 (1992). [CrossRef]
- 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]
- 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]
- 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]
- M. Dennis, K. O’Holleran, and M. Padgett, "Singular optics: optical vortices and polarization singularities," Prog. Opt. 53, 293‒363 (2009).
- R. W. Gerchberg and W. Saxton, "Practical algorithm for determination of phase from image and diffraction plane pictures," Optik 35, 237‒246 (1972).
- 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]
- J. Kirk and A. Jones, "Phase-only complex-valued spatial filter," J. Opt. Soc. Am. 61, 1023‒1028 (1971). [CrossRef]
- J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- G. A. Swartzlander and R. I. Hernandez-Aranda, "Optical Rankine vortex and anomalous circulation of light," Phys. Rev. Lett. 99, 163901 (2007). [CrossRef]
- G. A. Swartzlander, "Peering into darkness with a vortex spatial filter," Opt. Lett. 26, 497‒499 (2001). [CrossRef]
- G. Foo, D. M. Palacios, and G. A. Swartzlander, "Optical vortex coronagraph," Opt. Lett. 30, 3308‒3310 (2005). [CrossRef]
- G. Gbur, T. Visser, and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002). [CrossRef]
- M. V. Berry, "Coloured phase singularities," New J. Phys. 4, 66 (2002). [CrossRef]
- M. V. Berry, "Exploring the colours of dark light," New J. Phys. 4, 74 (2002). [CrossRef]
- J. Leach and M. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 154 (2003). [CrossRef]
- 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]
- 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]
- S. Sasaki and I. Mcnulty, "Proposal for generating brilliant x-ray beams carrying orbital angular momentum," Phys. Rev. Lett. 100, 124801 (2008). [CrossRef]
- M. Uchida and A. Tonomura, "Generation of electron beams carrying orbital angular momentum," Nature 464, 737‒739 (2010). [CrossRef]
- H. T. J. Verbeeck and P. Schattschneider, "Production and application of electron vortex beams," Nature 467, 301‒304 (2010). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- D. Grier, "A revolution in optical manipulation," Nature 424, 810‒816 (2003). [CrossRef]
- M. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World 10, 35‒38 (1997).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- M. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547‒549 (2001). [CrossRef]
- 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]
- K. Ladavac and D. Grier, "Micro-optomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144‒1149 (2004). [CrossRef]
- 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]
- M. Babiker, W. L. Power, and L. Allen, "Light-induced torque on moving atoms," Phys. Rev. Lett. 73, 1239‒1242 (1994). [CrossRef]
- 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]
- 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]
- 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]
- K. Gahagan and G. A. Swartzlander, "Optical vortex trapping of particles," Opt. Lett. 21, 827‒829 (1996). [CrossRef]
- 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]
- R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, "Topological stability of stored optical vortices," Phys. Rev. Lett. 98, 203601 (2007). [CrossRef]
- 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]
- M. J. Padgett and J. Courtial, "Poincare-sphere equivalent for light beams containing orbital angular momentum," Opt. Lett. 24, 430‒432 (1999). [CrossRef]
- 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]
- 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]
- 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]
- L. Allen and M. Padgett, "Equivalent geometric transformations for spin and orbital angular momentum of light," J. Mod. Opt. 54, 487‒491 (2007). [CrossRef]
- 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]
- B. Garetz, "Angular Dopper effect," J. Opt. Soc. Am. 71, 609‒611 (1981). [CrossRef]
- G. Nienhuis, "Doppler effect induced by rotating lenses," Opt. Commun. 132, 8‒14 (1996). [CrossRef]
- 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]
- 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]
- R. V. Jones, "Rotary ‘aether drag’," Proc. R. Soc. Lond. A 349, 423‒439 (1976). [CrossRef]
- 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]
- G. Nienhuis, J. P. Woerdman, and I. Kuscer, "Magnetic and mechanical Faraday effects," Phys. Rev. A 46, 7079‒7092 (1992). [CrossRef]
- R. V. Jones, "‘Fresnel aether drag’ in a transversely moving medium," Proc. R. Soc. Lond. A 328, 337‒352 (1972). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503‒2506 (1992). [CrossRef]
- W. Firth and D. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450‒2453 (1997). [CrossRef]
- 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]
- A. Desyatnikov, Y. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291‒391 (2005).
- 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]
- 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]
- 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]
- R. Ghosh and L. Mandel, "Observation of nonclassical effects in the interference of two photons," Phys. Rev. Lett. 59, 1903‒1905 (1987). [CrossRef]
- 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]
- 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]
- 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]
- A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777‒780 (1935). [CrossRef]
- 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]
- 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]
- A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313‒316 (2001). [CrossRef]
- 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]
- 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]
- J. S. Bell, "On the Einstein Podolsky Rosen paradox," Physics 1, 195‒200 (1964).
- 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]
- 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]
- A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 240401 (2002). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. Calvo and A. Picón, "Spin-induced angular momentum switching," Opt. Lett. 32, 838‒840 (2007). [CrossRef]
- 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]
- E. Brasselet, N. Murazawa, and H. Misawa, "Optical vortices from liquid crystal droplets," Phys. Rev. Lett. 103, 103903 (2009). [CrossRef]
- S. Khonina, V. Kotlyar, and V. Soifer, "Diffraction optical elements matched to the Gauss–Laguerre modes," Opt. Spectrosc. 85, 636‒644 (1998).
- 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]
- 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]
- 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]
- M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, "Laser modes with helical wave-fronts," Phys. Rev. A 49, 3119‒3122 (1994). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- J. Arlt, "Handedness and azimuthal energy flow of optical vortex beams," J. Mod. Opt. 50, 1573‒1580 (2003).
- 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]
- H. Sztul and R. Alfano, "Double-slit interference with Laguerre–Gaussian beams," Opt. Lett. 31, 999‒1001 (2006). [CrossRef]
- 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]
- 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]
- 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]
- G. Forbes and M. Alonso, "Measures of spread for periodic distributions and the associated uncertainty relations," Am. J. Phys. 69, 340‒347 (2001). [CrossRef]
- 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]
- O. Bryngdahl, "Geometrical transformations in optics," J. Opt. Soc. Am. 64, 1092‒1099 (1974). [CrossRef]
- W. Hossack, A. Darling, and A. Dahdouh, "Coordinate transformations with multiple computer-generated optical-elements," J. Mod. Opt. 34, 1235‒1250 (1987). [CrossRef]
- 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]
- L. Torner, J. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873‒881 (2005). [CrossRef]
- S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral phase contrast imaging in microscopy," Opt. Express 13, 689‒694 (2005). [CrossRef]
- S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral interferometry," Opt. Lett. 30, 1953‒1955 (2005). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- M. Harwit, "Photon orbital angular momentum in astrophysics," Astrophys. J. 597, 1266‒1270 (2003). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299‒315 (2008). [CrossRef]
- 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]
- L. Allen and M. Padgett, "Equivalent geometric transformations for spin and orbital angular momentum of light," J. Mod. Opt. 54, 487‒491 (2007). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- L. Allen, M. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291‒372 (1999).
- 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]
- 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]
- 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]
- 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]
- M. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World 10, 35‒38 (1997).
- 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]
- 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]
- M. J. Padgett and L. Allen, "The Poynting vector in Laguerre–Gaussian laser modes," Opt. Commun. 121, 36‒40 (1995). [CrossRef]
- 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]
- S. Barnett and L. Allen, "Orbital angular momentum and non paraxial light beams," Opt. Commun. 110, 670‒678 (1994). [CrossRef]
- M. Babiker, W. L. Power, and L. Allen, "Light-induced torque on moving atoms," Phys. Rev. Lett. 73, 1239‒1242 (1994). [CrossRef]
- 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]
- 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]
- 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]
- G. Forbes and M. Alonso, "Measures of spread for periodic distributions and the associated uncertainty relations," Am. J. Phys. 69, 340‒347 (2001). [CrossRef]
- 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]
- 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]
- J. Arlt, "Handedness and azimuthal energy flow of optical vortex beams," J. Mod. Opt. 50, 1573‒1580 (2003).
- 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]
- 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]
- 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]
- 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]
- 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]
- L. Allen, M. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291‒372 (1999).
- M. Babiker, W. L. Power, and L. Allen, "Light-induced torque on moving atoms," Phys. Rev. Lett. 73, 1239‒1242 (1994). [CrossRef]
- 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]
- 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]
- 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]
- S. Barnett and L. Allen, "Orbital angular momentum and non paraxial light beams," Opt. Commun. 110, 670‒678 (1994). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- S. M. Barnett, "Optical angular-momentum flux," J. Opt. B Quantum Semiclass. Opt. 4, 7‒16 (2002). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- V. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985‒990 (1992). [CrossRef]
- V. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser-beams with screw dislocations in their wave-fronts," JETP. Lett. 52, 429‒431 (1990).
- 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]
- 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]
- 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]
- 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]
- 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]
- J. S. Bell, "On the Einstein Podolsky Rosen paradox," Physics 1, 195‒200 (1964).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral phase contrast imaging in microscopy," Opt. Express 13, 689‒694 (2005). [CrossRef]
- S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral interferometry," Opt. Lett. 30, 1953‒1955 (2005). [CrossRef]
- M. Berry, J. Nye, and F. Wright, "The elliptic umbilic diffraction catastrophe," Phil. Trans. R. Soc. Lond. 291, 453‒484 (1979). [CrossRef]
- J. F. Nye and M. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165‒190 (1974). [CrossRef]
- M. V. Berry, "Coloured phase singularities," New J. Phys. 4, 66 (2002). [CrossRef]
- M. V. Berry, "Exploring the colours of dark light," New J. Phys. 4, 74 (2002). [CrossRef]
- 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]
- M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A 456, 2059‒2079 (2000). [CrossRef]
- R. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115‒125 (1936). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- E. Brasselet, N. Murazawa, and H. Misawa, "Optical vortices from liquid crystal droplets," Phys. Rev. Lett. 103, 103903 (2009). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- P. Coullet, G. Gil, and F. Rocca, "Optical vortices," Opt. Commun. 73, 403‒408 (1989). [CrossRef]
- 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]
- 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]
- J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- M. J. Padgett and J. Courtial, "Poincare-sphere equivalent for light beams containing orbital angular momentum," Opt. Lett. 24, 430‒432 (1999). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. D’Alessandro and G.-L. Oppo, "Gauss–Laguerre modes: a sensible basis for laser dynamics," Opt. Commun. 88, 130‒136 (1992). [CrossRef]
- 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]
- 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]
- W. Hossack, A. Darling, and A. Dahdouh, "Coordinate transformations with multiple computer-generated optical-elements," J. Mod. Opt. 34, 1235‒1250 (1987). [CrossRef]
- 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]
- W. Hossack, A. Darling, and A. Dahdouh, "Coordinate transformations with multiple computer-generated optical-elements," J. Mod. Opt. 34, 1235‒1250 (1987). [CrossRef]
- R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, "Topological stability of stored optical vortices," Phys. Rev. Lett. 98, 203601 (2007). [CrossRef]
- K. O’Holleran, M. Dennis, and M. Padgett, "Topology of light’s darkness," Phys. Rev. Lett. 102, 143902 (2009). [CrossRef]
- M. Dennis, K. O’Holleran, and M. Padgett, "Singular optics: optical vortices and polarization singularities," Prog. Opt. 53, 293‒363 (2009).
- 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]
- 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]
- K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, "Fractality of light’s darkness," Phys. Rev. Lett. 100, 053902 (2008). [CrossRef]
- J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005). [CrossRef]
- 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]
- M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A 456, 2059‒2079 (2000). [CrossRef]
- A. Desyatnikov, Y. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291‒391 (2005).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- P. Dirac, "Quantised singularities in the electromagnetic field," Proc. R. Soc. Lond. A 133, 60‒72 (1931). [CrossRef]
- 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]
- J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21‒27 (2001). [CrossRef]
- J. Durnin, J. J. Miceli Jr., and J. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499‒1501 (1987). [CrossRef]
- J. Durnin, J. J. Miceli Jr., and J. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499‒1501 (1987). [CrossRef]
- 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]
- 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]
- A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777‒780 (1935). [CrossRef]
- 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]
- 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]
- 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]
- R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, "Topological stability of stored optical vortices," Phys. Rev. Lett. 98, 203601 (2007). [CrossRef]
- 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]
- W. Firth and D. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450‒2453 (1997). [CrossRef]
- 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]
- K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, "Fractality of light’s darkness," Phys. Rev. Lett. 100, 053902 (2008). [CrossRef]
- 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]
- 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]
- G. Foo, D. M. Palacios, and G. A. Swartzlander, "Optical vortex coronagraph," Opt. Lett. 30, 3308‒3310 (2005). [CrossRef]
- G. Forbes and M. Alonso, "Measures of spread for periodic distributions and the associated uncertainty relations," Am. J. Phys. 69, 340‒347 (2001). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299‒315 (2008). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- M. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547‒549 (2001). [CrossRef]
- 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]
- 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]
- 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]
- B. Garetz, "Angular Dopper effect," J. Opt. Soc. Am. 71, 609‒611 (1981). [CrossRef]
- 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]
- G. Gbur, T. Visser, and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002). [CrossRef]
- R. W. Gerchberg and W. Saxton, "Practical algorithm for determination of phase from image and diffraction plane pictures," Optik 35, 237‒246 (1972).
- 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]
- R. Ghosh and L. Mandel, "Observation of nonclassical effects in the interference of two photons," Phys. Rev. Lett. 59, 1903‒1905 (1987). [CrossRef]
- P. Coullet, G. Gil, and F. Rocca, "Optical vortices," Opt. Commun. 73, 403‒408 (1989). [CrossRef]
- 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]
- 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]
- M. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547‒549 (2001). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- K. Ladavac and D. Grier, "Micro-optomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144‒1149 (2004). [CrossRef]
- D. Grier, "A revolution in optical manipulation," Nature 424, 810‒816 (2003). [CrossRef]
- J. W. Simmons and M. J. Guttmann, States, Waves, and Photons: a Modern Introduction to Light, Addison-Wesley, 1970.
- M. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547‒549 (2001). [CrossRef]
- 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]
- M. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547‒549 (2001). [CrossRef]
- M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, "Laser modes with helical wave-fronts," Phys. Rev. A 49, 3119‒3122 (1994). [CrossRef]
- M. Harwit, "Photon orbital angular momentum in astrophysics," Astrophys. J. 597, 1266‒1270 (2003). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. A. Swartzlander and R. I. Hernandez-Aranda, "Optical Rankine vortex and anomalous circulation of light," Phys. Rev. Lett. 99, 163901 (2007). [CrossRef]
- 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]
- 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]
- M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, "Laser modes with helical wave-fronts," Phys. Rev. A 49, 3119‒3122 (1994). [CrossRef]
- 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]
- 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]
- W. Hossack, A. Darling, and A. Dahdouh, "Coordinate transformations with multiple computer-generated optical-elements," J. Mod. Opt. 34, 1235‒1250 (1987). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- J. D. Jackson, Classical Electrodynamics, 3rd ed., Wiley, 1999.
- 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]
- 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]
- 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]
- S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral phase contrast imaging in microscopy," Opt. Express 13, 689‒694 (2005). [CrossRef]
- S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral interferometry," Opt. Lett. 30, 1953‒1955 (2005). [CrossRef]
- 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]
- 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]
- R. V. Jones, "Rotary ‘aether drag’," Proc. R. Soc. Lond. A 349, 423‒439 (1976). [CrossRef]
- R. V. Jones, "‘Fresnel aether drag’ in a transversely moving medium," Proc. R. Soc. Lond. A 328, 337‒352 (1972). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- S. Khonina, V. Kotlyar, and V. Soifer, "Diffraction optical elements matched to the Gauss–Laguerre modes," Opt. Spectrosc. 85, 636‒644 (1998).
- 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]
- 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]
- 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]
- A. Desyatnikov, Y. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291‒391 (2005).
- 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]
- 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]
- S. Khonina, V. Kotlyar, and V. Soifer, "Diffraction optical elements matched to the Gauss–Laguerre modes," Opt. Spectrosc. 85, 636‒644 (1998).
- 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]
- 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]
- 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]
- G. Nienhuis, J. P. Woerdman, and I. Kuscer, "Magnetic and mechanical Faraday effects," Phys. Rev. A 46, 7079‒7092 (1992). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503‒2506 (1992). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005). [CrossRef]
- 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]
- 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]
- J. Leach and M. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 154 (2003). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313‒316 (2001). [CrossRef]
- 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]
- R. Ghosh and L. Mandel, "Observation of nonclassical effects in the interference of two photons," Phys. Rev. Lett. 59, 1903‒1905 (1987). [CrossRef]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, 1995.
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21‒27 (2001). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- S. Sasaki and I. Mcnulty, "Proposal for generating brilliant x-ray beams carrying orbital angular momentum," Phys. Rev. Lett. 100, 124801 (2008). [CrossRef]
- J. Durnin, J. J. Miceli Jr., and J. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499‒1501 (1987). [CrossRef]
- E. Brasselet, N. Murazawa, and H. Misawa, "Optical vortices from liquid crystal droplets," Phys. Rev. Lett. 103, 103903 (2009). [CrossRef]
- G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305‒310 (2007). [CrossRef]
- 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]
- 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]
- 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]
- E. Brasselet, N. Murazawa, and H. Misawa, "Optical vortices from liquid crystal droplets," Phys. Rev. Lett. 103, 103903 (2009). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. Nienhuis, "Doppler effect induced by rotating lenses," Opt. Commun. 132, 8‒14 (1996). [CrossRef]
- G. Nienhuis, J. P. Woerdman, and I. Kuscer, "Magnetic and mechanical Faraday effects," Phys. Rev. A 46, 7079‒7092 (1992). [CrossRef]
- 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]
- M. Berry, J. Nye, and F. Wright, "The elliptic umbilic diffraction catastrophe," Phil. Trans. R. Soc. Lond. 291, 453‒484 (1979). [CrossRef]
- J. F. Nye and M. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165‒190 (1974). [CrossRef]
- J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, 1st ed., Taylor & Francis, 1999.
- 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]
- M. Dennis, K. O’Holleran, and M. Padgett, "Singular optics: optical vortices and polarization singularities," Prog. Opt. 53, 293‒363 (2009).
- K. O’Holleran, M. Dennis, and M. Padgett, "Topology of light’s darkness," Phys. Rev. Lett. 102, 143902 (2009). [CrossRef]
- K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, "Fractality of light’s darkness," Phys. Rev. Lett. 100, 053902 (2008). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. D’Alessandro and G.-L. Oppo, "Gauss–Laguerre modes: a sensible basis for laser dynamics," Opt. Commun. 88, 130‒136 (1992). [CrossRef]
- 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]
- 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]
- 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]
- K. O’Holleran, M. Dennis, and M. Padgett, "Topology of light’s darkness," Phys. Rev. Lett. 102, 143902 (2009). [CrossRef]
- M. Dennis, K. O’Holleran, and M. Padgett, "Singular optics: optical vortices and polarization singularities," Prog. Opt. 53, 293‒363 (2009).
- S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299‒315 (2008). [CrossRef]
- L. Allen and M. Padgett, "Equivalent geometric transformations for spin and orbital angular momentum of light," J. Mod. Opt. 54, 487‒491 (2007). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- J. Leach and M. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 154 (2003). [CrossRef]
- 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]
- 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]
- L. Allen, M. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291‒372 (1999).
- 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]
- 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]
- 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]
- 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]
- M. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World 10, 35‒38 (1997).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, "Fractality of light’s darkness," Phys. Rev. Lett. 100, 053902 (2008). [CrossRef]
- 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]
- 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]
- J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005). [CrossRef]
- 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]
- 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]
- M. J. Padgett and J. Courtial, "Poincare-sphere equivalent for light beams containing orbital angular momentum," Opt. Lett. 24, 430‒432 (1999). [CrossRef]
- 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]
- 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]
- 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]
- M. J. Padgett and L. Allen, "The Poynting vector in Laguerre–Gaussian laser modes," Opt. Commun. 121, 36‒40 (1995). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777‒780 (1935). [CrossRef]
- 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]
- M. Babiker, W. L. Power, and L. Allen, "Light-induced torque on moving atoms," Phys. Rev. Lett. 73, 1239‒1242 (1994). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, "Topological stability of stored optical vortices," Phys. Rev. Lett. 98, 203601 (2007). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral phase contrast imaging in microscopy," Opt. Express 13, 689‒694 (2005). [CrossRef]
- S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral interferometry," Opt. Lett. 30, 1953‒1955 (2005). [CrossRef]
- 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]
- 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]
- 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]
- P. Coullet, G. Gil, and F. Rocca, "Optical vortices," Opt. Commun. 73, 403‒408 (1989). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, "Topological stability of stored optical vortices," Phys. Rev. Lett. 98, 203601 (2007). [CrossRef]
- A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777‒780 (1935). [CrossRef]
- 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]
- 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]
- M. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547‒549 (2001). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- S. Sasaki and I. Mcnulty, "Proposal for generating brilliant x-ray beams carrying orbital angular momentum," Phys. Rev. Lett. 100, 124801 (2008). [CrossRef]
- R. W. Gerchberg and W. Saxton, "Practical algorithm for determination of phase from image and diffraction plane pictures," Optik 35, 237‒246 (1972).
- H. T. J. Verbeeck and P. Schattschneider, "Production and application of electron vortex beams," Nature 467, 301‒304 (2010). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, "Topological stability of stored optical vortices," Phys. Rev. Lett. 98, 203601 (2007). [CrossRef]
- 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]
- A. E. Siegman, Lasers, University Science Books, 1986.
- J. W. Simmons and M. J. Guttmann, States, Waves, and Photons: a Modern Introduction to Light, Addison-Wesley, 1970.
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- W. Firth and D. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450‒2453 (1997). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- S. Khonina, V. Kotlyar, and V. Soifer, "Diffraction optical elements matched to the Gauss–Laguerre modes," Opt. Spectrosc. 85, 636‒644 (1998).
- 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]
- 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]
- 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]
- V. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985‒990 (1992). [CrossRef]
- V. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser-beams with screw dislocations in their wave-fronts," JETP. Lett. 52, 429‒431 (1990).
- 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]
- 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]
- 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]
- 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]
- G. A. Swartzlander and R. I. Hernandez-Aranda, "Optical Rankine vortex and anomalous circulation of light," Phys. Rev. Lett. 99, 163901 (2007). [CrossRef]
- 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]
- G. Foo, D. M. Palacios, and G. A. Swartzlander, "Optical vortex coronagraph," Opt. Lett. 30, 3308‒3310 (2005). [CrossRef]
- G. A. Swartzlander, "Peering into darkness with a vortex spatial filter," Opt. Lett. 26, 497‒499 (2001). [CrossRef]
- K. Gahagan and G. A. Swartzlander, "Optical vortex trapping of particles," Opt. Lett. 21, 827‒829 (1996). [CrossRef]
- G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503‒2506 (1992). [CrossRef]
- H. Sztul and R. Alfano, "Double-slit interference with Laguerre–Gaussian beams," Opt. Lett. 31, 999‒1001 (2006). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- C. Tamm, "Frequency locking of 2 transverse optical modes of a laser," Phys. Rev. A 38, 5960‒5963 (1988). [CrossRef]
- 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]
- M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, "Laser modes with helical wave-fronts," Phys. Rev. A 49, 3119‒3122 (1994). [CrossRef]
- 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]
- 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]
- 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]
- M. Uchida and A. Tonomura, "Generation of electron beams carrying orbital angular momentum," Nature 464, 737‒739 (2010). [CrossRef]
- 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]
- G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305‒310 (2007). [CrossRef]
- L. Torner, J. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873‒881 (2005). [CrossRef]
- A. Desyatnikov, Y. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291‒391 (2005).
- 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]
- 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]
- L. Torner, J. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873‒881 (2005). [CrossRef]
- 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]
- G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305‒310 (2007). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- M. Uchida and A. Tonomura, "Generation of electron beams carrying orbital angular momentum," Nature 464, 737‒739 (2010). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- V. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985‒990 (1992). [CrossRef]
- V. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser-beams with screw dislocations in their wave-fronts," JETP. Lett. 52, 429‒431 (1990).
- M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, "Laser modes with helical wave-fronts," Phys. Rev. A 49, 3119‒3122 (1994). [CrossRef]
- J. M. Vaughan and D. Willetts, "Interference properties of a light-beam having a helical wave surface," Opt. Commun. 30, 263‒267 (1979). [CrossRef]
- 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]
- 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]
- A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 240401 (2002). [CrossRef]
- A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313‒316 (2001). [CrossRef]
- H. T. J. Verbeeck and P. Schattschneider, "Production and application of electron vortex beams," Nature 467, 301‒304 (2010). [CrossRef]
- 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]
- 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]
- 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]
- G. Gbur, T. Visser, and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 240401 (2002). [CrossRef]
- A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313‒316 (2001). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- J. M. Vaughan and D. Willetts, "Interference properties of a light-beam having a helical wave surface," Opt. Commun. 30, 263‒267 (1979). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. Nienhuis, J. P. Woerdman, and I. Kuscer, "Magnetic and mechanical Faraday effects," Phys. Rev. A 46, 7079‒7092 (1992). [CrossRef]
- 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]
- G. Gbur, T. Visser, and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002). [CrossRef]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, 1995.
- 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]
- M. Berry, J. Nye, and F. Wright, "The elliptic umbilic diffraction catastrophe," Phil. Trans. R. Soc. Lond. 291, 453‒484 (1979). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 240401 (2002). [CrossRef]
- A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313‒316 (2001). [CrossRef]
- 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]
Am. J. Phys.
- G. Forbes and M. Alonso, "Measures of spread for periodic distributions and the associated uncertainty relations," Am. J. Phys. 69, 340‒347 (2001). [CrossRef]
Appl. Optics
- 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]
Appl. Phys. B: Lasers and Optics
- 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]
Appl. Phys. Lett.
- 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]
- M. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547‒549 (2001). [CrossRef]
Astrophys. J.
- M. Harwit, "Photon orbital angular momentum in astrophysics," Astrophys. J. 597, 1266‒1270 (2003). [CrossRef]
J. Mod. Opt.
- W. Hossack, A. Darling, and A. Dahdouh, "Coordinate transformations with multiple computer-generated optical-elements," J. Mod. Opt. 34, 1235‒1250 (1987). [CrossRef]
- J. Arlt, "Handedness and azimuthal energy flow of optical vortex beams," J. Mod. Opt. 50, 1573‒1580 (2003).
- L. Allen and M. Padgett, "Equivalent geometric transformations for spin and orbital angular momentum of light," J. Mod. Opt. 54, 487‒491 (2007). [CrossRef]
- V. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985‒990 (1992). [CrossRef]
J. Opt. A. Pure Appl. Opt.
- 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]
J. Opt. B Quantum Semiclass. Opt.
- S. M. Barnett, "Optical angular-momentum flux," J. Opt. B Quantum Semiclass. Opt. 4, 7‒16 (2002). [CrossRef]
J. Opt. Soc. Am.
- J. Kirk and A. Jones, "Phase-only complex-valued spatial filter," J. Opt. Soc. Am. 61, 1023‒1028 (1971). [CrossRef]
- O. Bryngdahl, "Geometrical transformations in optics," J. Opt. Soc. Am. 64, 1092‒1099 (1974). [CrossRef]
- B. Garetz, "Angular Dopper effect," J. Opt. Soc. Am. 71, 609‒611 (1981). [CrossRef]
J. Opt. Soc. Am. B
- 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]
- 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]
- 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]
JETP. Lett.
- V. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser-beams with screw dislocations in their wave-fronts," JETP. Lett. 52, 429‒431 (1990).
Lab Chip
- 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]
Laser Photon. Rev.
- S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299‒315 (2008). [CrossRef]
Nat. Photonics
- 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]
Nat. Phys.
- 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]
- G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305‒310 (2007). [CrossRef]
- 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]
Nature
- 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]
- M. Uchida and A. Tonomura, "Generation of electron beams carrying orbital angular momentum," Nature 464, 737‒739 (2010). [CrossRef]
- H. T. J. Verbeeck and P. Schattschneider, "Production and application of electron vortex beams," Nature 467, 301‒304 (2010). [CrossRef]
- D. Grier, "A revolution in optical manipulation," Nature 424, 810‒816 (2003). [CrossRef]
- A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313‒316 (2001). [CrossRef]
New J. Phys.
- 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]
- 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]
- M. V. Berry, "Coloured phase singularities," New J. Phys. 4, 66 (2002). [CrossRef]
- M. V. Berry, "Exploring the colours of dark light," New J. Phys. 4, 74 (2002). [CrossRef]
- J. Leach and M. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 154 (2003). [CrossRef]
- J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005). [CrossRef]
Opt. Commun.
- 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]
- 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]
- 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]
- M. J. Padgett and L. Allen, "The Poynting vector in Laguerre–Gaussian laser modes," Opt. Commun. 121, 36‒40 (1995). [CrossRef]
- 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]
- 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]
- J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21‒27 (2001). [CrossRef]
- G. D’Alessandro and G.-L. Oppo, "Gauss–Laguerre modes: a sensible basis for laser dynamics," Opt. Commun. 88, 130‒136 (1992). [CrossRef]
- P. Coullet, G. Gil, and F. Rocca, "Optical vortices," Opt. Commun. 73, 403‒408 (1989). [CrossRef]
- J. M. Vaughan and D. Willetts, "Interference properties of a light-beam having a helical wave surface," Opt. Commun. 30, 263‒267 (1979). [CrossRef]
- S. Barnett and L. Allen, "Orbital angular momentum and non paraxial light beams," Opt. Commun. 110, 670‒678 (1994). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- G. Nienhuis, "Doppler effect induced by rotating lenses," Opt. Commun. 132, 8‒14 (1996). [CrossRef]
- 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]
Opt. Express
- K. Ladavac and D. Grier, "Micro-optomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144‒1149 (2004). [CrossRef]
- 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]
- 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]
- S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral phase contrast imaging in microscopy," Opt. Express 13, 689‒694 (2005). [CrossRef]
- L. Torner, J. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873‒881 (2005). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
Opt. Lasers Eng.
- 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]
Opt. Lett.
- S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral interferometry," Opt. Lett. 30, 1953‒1955 (2005). [CrossRef]
- G. Foo, D. M. Palacios, and G. A. Swartzlander, "Optical vortex coronagraph," Opt. Lett. 30, 3308‒3310 (2005). [CrossRef]
- H. Sztul and R. Alfano, "Double-slit interference with Laguerre–Gaussian beams," Opt. Lett. 31, 999‒1001 (2006). [CrossRef]
- 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]
- 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]
- M. J. Padgett and J. Courtial, "Poincare-sphere equivalent for light beams containing orbital angular momentum," Opt. Lett. 24, 430‒432 (1999). [CrossRef]
- K. Gahagan and G. A. Swartzlander, "Optical vortex trapping of particles," Opt. Lett. 21, 827‒829 (1996). [CrossRef]
- G. Calvo and A. Picón, "Spin-induced angular momentum switching," Opt. Lett. 32, 838‒840 (2007). [CrossRef]
- 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]
- G. A. Swartzlander, "Peering into darkness with a vortex spatial filter," Opt. Lett. 26, 497‒499 (2001). [CrossRef]
- 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]
- 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]
- 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]
Opt. Quantum. Electron
- 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]
Opt. Spectrosc.
- S. Khonina, V. Kotlyar, and V. Soifer, "Diffraction optical elements matched to the Gauss–Laguerre modes," Opt. Spectrosc. 85, 636‒644 (1998).
Optik
- R. W. Gerchberg and W. Saxton, "Practical algorithm for determination of phase from image and diffraction plane pictures," Optik 35, 237‒246 (1972).
Phil. Trans. R. Soc. Lond.
- M. Berry, J. Nye, and F. Wright, "The elliptic umbilic diffraction catastrophe," Phil. Trans. R. Soc. Lond. 291, 453‒484 (1979). [CrossRef]
Phys. Rev.
- R. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115‒125 (1936). [CrossRef]
- A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777‒780 (1935). [CrossRef]
Phys. Rev. A
- 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]
- 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]
- 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]
- G. Nienhuis, J. P. Woerdman, and I. Kuscer, "Magnetic and mechanical Faraday effects," Phys. Rev. A 46, 7079‒7092 (1992). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, "Laser modes with helical wave-fronts," Phys. Rev. A 49, 3119‒3122 (1994). [CrossRef]
- 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]
- 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]
- C. Tamm, "Frequency locking of 2 transverse optical modes of a laser," Phys. Rev. A 38, 5960‒5963 (1988). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
Phys. Rev. E
- 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]
- 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]
- 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]
Phys. Rev. Lett.
- R. Ghosh and L. Mandel, "Observation of nonclassical effects in the interference of two photons," Phys. Rev. Lett. 59, 1903‒1905 (1987). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 240401 (2002). [CrossRef]
- 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]
- 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]
- 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]
- G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503‒2506 (1992). [CrossRef]
- W. Firth and D. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450‒2453 (1997). [CrossRef]
- 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]
- 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]
- 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]
- E. Brasselet, N. Murazawa, and H. Misawa, "Optical vortices from liquid crystal droplets," Phys. Rev. Lett. 103, 103903 (2009). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, "Topological stability of stored optical vortices," Phys. Rev. Lett. 98, 203601 (2007). [CrossRef]
- G. A. Swartzlander and R. I. Hernandez-Aranda, "Optical Rankine vortex and anomalous circulation of light," Phys. Rev. Lett. 99, 163901 (2007). [CrossRef]
- M. Babiker, W. L. Power, and L. Allen, "Light-induced torque on moving atoms," Phys. Rev. Lett. 73, 1239‒1242 (1994). [CrossRef]
- 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]
- 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]
- S. Sasaki and I. Mcnulty, "Proposal for generating brilliant x-ray beams carrying orbital angular momentum," Phys. Rev. Lett. 100, 124801 (2008). [CrossRef]
- G. Gbur, T. Visser, and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002). [CrossRef]
- 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]
- 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]
- J. Durnin, J. J. Miceli Jr., and J. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499‒1501 (1987). [CrossRef]
- K. O’Holleran, M. Dennis, and M. Padgett, "Topology of light’s darkness," Phys. Rev. Lett. 102, 143902 (2009). [CrossRef]
- K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, "Fractality of light’s darkness," Phys. Rev. Lett. 100, 053902 (2008). [CrossRef]
- 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]
Phys. World
- M. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World 10, 35‒38 (1997).
Physics
- J. S. Bell, "On the Einstein Podolsky Rosen paradox," Physics 1, 195‒200 (1964).
Proc. R. Soc. Lond. A
- R. V. Jones, "Rotary ‘aether drag’," Proc. R. Soc. Lond. A 349, 423‒439 (1976). [CrossRef]
- 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]
- R. V. Jones, "‘Fresnel aether drag’ in a transversely moving medium," Proc. R. Soc. Lond. A 328, 337‒352 (1972). [CrossRef]
- P. Dirac, "Quantised singularities in the electromagnetic field," Proc. R. Soc. Lond. A 133, 60‒72 (1931). [CrossRef]
- J. F. Nye and M. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165‒190 (1974). [CrossRef]
- M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A 456, 2059‒2079 (2000). [CrossRef]
- 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]
Proc. R. Soc. Lond. A Ser. A
- 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]
Prog. Opt.
- L. Allen, M. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291‒372 (1999).
- M. Dennis, K. O’Holleran, and M. Padgett, "Singular optics: optical vortices and polarization singularities," Prog. Opt. 53, 293‒363 (2009).
- A. Desyatnikov, Y. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291‒391 (2005).
Science
- 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]
- 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]
- 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]
Other
- J. W. Simmons and M. J. Guttmann, States, Waves, and Photons: a Modern Introduction to Light, Addison-Wesley, 1970.
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, 1995.
- A. E. Siegman, Lasers, University Science Books, 1986.
- M. Kolobov, ed., Quantum Imaging, Springer, 2007.
- J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, 1st ed., Taylor & Francis, 1999.
- J. D. Jackson, Classical Electrodynamics, 3rd ed., Wiley, 1999.
2010, Dennis, Nat. Phys.
- 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]
- 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]
- M. Uchida and A. Tonomura, "Generation of electron beams carrying orbital angular momentum," Nature 464, 737‒739 (2010). [CrossRef]
- H. T. J. Verbeeck and P. Schattschneider, "Production and application of electron vortex beams," Nature 467, 301‒304 (2010). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- E. Brasselet, N. Murazawa, and H. Misawa, "Optical vortices from liquid crystal droplets," Phys. Rev. Lett. 103, 103903 (2009). [CrossRef]
- 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]
- 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]
- M. Dennis, K. O’Holleran, and M. Padgett, "Singular optics: optical vortices and polarization singularities," Prog. Opt. 53, 293‒363 (2009).
- K. O’Holleran, M. Dennis, and M. Padgett, "Topology of light’s darkness," Phys. Rev. Lett. 102, 143902 (2009). [CrossRef]
- S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299‒315 (2008). [CrossRef]
- K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, "Fractality of light’s darkness," Phys. Rev. Lett. 100, 053902 (2008). [CrossRef]
- 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]
- 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]
- 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]
- S. Sasaki and I. Mcnulty, "Proposal for generating brilliant x-ray beams carrying orbital angular momentum," Phys. Rev. Lett. 100, 124801 (2008). [CrossRef]
- 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]
- 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]
- 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]
- L. Allen and M. Padgett, "Equivalent geometric transformations for spin and orbital angular momentum of light," J. Mod. Opt. 54, 487‒491 (2007). [CrossRef]
- G. A. Swartzlander and R. I. Hernandez-Aranda, "Optical Rankine vortex and anomalous circulation of light," Phys. Rev. Lett. 99, 163901 (2007). [CrossRef]
- R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, "Topological stability of stored optical vortices," Phys. Rev. Lett. 98, 203601 (2007). [CrossRef]
- 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]
- 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]
- G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305‒310 (2007). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- A. Desyatnikov, Y. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291‒391 (2005).
- J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- M. Harwit, "Photon orbital angular momentum in astrophysics," Astrophys. J. 597, 1266‒1270 (2003). [CrossRef]
- J. Arlt, "Handedness and azimuthal energy flow of optical vortex beams," J. Mod. Opt. 50, 1573‒1580 (2003).
- 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]
- D. Grier, "A revolution in optical manipulation," Nature 424, 810‒816 (2003). [CrossRef]
- J. Leach and M. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 154 (2003). [CrossRef]
- G. Gbur, T. Visser, and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002). [CrossRef]
- M. V. Berry, "Coloured phase singularities," New J. Phys. 4, 66 (2002). [CrossRef]
- M. V. Berry, "Exploring the colours of dark light," New J. Phys. 4, 74 (2002). [CrossRef]
- 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]
- S. M. Barnett, "Optical angular-momentum flux," J. Opt. B Quantum Semiclass. Opt. 4, 7‒16 (2002). [CrossRef]
- A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 240401 (2002). [CrossRef]
- 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]
- 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]
- G. Forbes and M. Alonso, "Measures of spread for periodic distributions and the associated uncertainty relations," Am. J. Phys. 69, 340‒347 (2001). [CrossRef]
- 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]
- A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313‒316 (2001). [CrossRef]
- 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]
- 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]
- 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]
- J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21‒27 (2001). [CrossRef]
- 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]
- M. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547‒549 (2001). [CrossRef]
- 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]
- 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]
- M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A 456, 2059‒2079 (2000). [CrossRef]
- 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]
- 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]
- 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]
- L. Allen, M. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291‒372 (1999).
- 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]
- 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]
- 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]
- 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]
- S. Khonina, V. Kotlyar, and V. Soifer, "Diffraction optical elements matched to the Gauss–Laguerre modes," Opt. Spectrosc. 85, 636‒644 (1998).
- 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]
- 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]
- 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]
- W. Firth and D. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450‒2453 (1997). [CrossRef]
- M. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World 10, 35‒38 (1997).
- 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]
- 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]
- G. Nienhuis, "Doppler effect induced by rotating lenses," Opt. Commun. 132, 8‒14 (1996). [CrossRef]
- 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]
- M. J. Padgett and L. Allen, "The Poynting vector in Laguerre–Gaussian laser modes," Opt. Commun. 121, 36‒40 (1995). [CrossRef]
- 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]
- M. Babiker, W. L. Power, and L. Allen, "Light-induced torque on moving atoms," Phys. Rev. Lett. 73, 1239‒1242 (1994). [CrossRef]
- 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]
- 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]
- 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]
- S. Barnett and L. Allen, "Orbital angular momentum and non paraxial light beams," Opt. Commun. 110, 670‒678 (1994). [CrossRef]
- 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]
- 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]
- M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, "Laser modes with helical wave-fronts," Phys. Rev. A 49, 3119‒3122 (1994). [CrossRef]
- 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]
- 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]
- 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]
- V. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985‒990 (1992). [CrossRef]
- 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]
- G. D’Alessandro and G.-L. Oppo, "Gauss–Laguerre modes: a sensible basis for laser dynamics," Opt. Commun. 88, 130‒136 (1992). [CrossRef]
- 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]
- G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503‒2506 (1992). [CrossRef]
- 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]
- G. Nienhuis, J. P. Woerdman, and I. Kuscer, "Magnetic and mechanical Faraday effects," Phys. Rev. A 46, 7079‒7092 (1992). [CrossRef]
- 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]
- V. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser-beams with screw dislocations in their wave-fronts," JETP. Lett. 52, 429‒431 (1990).
- P. Coullet, G. Gil, and F. Rocca, "Optical vortices," Opt. Commun. 73, 403‒408 (1989). [CrossRef]
- 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]
- C. Tamm, "Frequency locking of 2 transverse optical modes of a laser," Phys. Rev. A 38, 5960‒5963 (1988). [CrossRef]
- J. Durnin, J. J. Miceli Jr., and J. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499‒1501 (1987). [CrossRef]
- W. Hossack, A. Darling, and A. Dahdouh, "Coordinate transformations with multiple computer-generated optical-elements," J. Mod. Opt. 34, 1235‒1250 (1987). [CrossRef]
- R. Ghosh and L. Mandel, "Observation of nonclassical effects in the interference of two photons," Phys. Rev. Lett. 59, 1903‒1905 (1987). [CrossRef]
- 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]
1979, Garetz, Opt. Commun.
- 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]
- M. Berry, J. Nye, and F. Wright, "The elliptic umbilic diffraction catastrophe," Phil. Trans. R. Soc. Lond. 291, 453‒484 (1979). [CrossRef]
- J. M. Vaughan and D. Willetts, "Interference properties of a light-beam having a helical wave surface," Opt. Commun. 30, 263‒267 (1979). [CrossRef]
- R. V. Jones, "Rotary ‘aether drag’," Proc. R. Soc. Lond. A 349, 423‒439 (1976). [CrossRef]
- 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]
- J. F. Nye and M. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165‒190 (1974). [CrossRef]
- R. W. Gerchberg and W. Saxton, "Practical algorithm for determination of phase from image and diffraction plane pictures," Optik 35, 237‒246 (1972).
- R. V. Jones, "‘Fresnel aether drag’ in a transversely moving medium," Proc. R. Soc. Lond. A 328, 337‒352 (1972). [CrossRef]
- J. S. Bell, "On the Einstein Podolsky Rosen paradox," Physics 1, 195‒200 (1964).
- R. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115‒125 (1936). [CrossRef]
- A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777‒780 (1935). [CrossRef]
- P. Dirac, "Quantised singularities in the electromagnetic field," Proc. R. Soc. Lond. A 133, 60‒72 (1931). [CrossRef]
- 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]
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