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.

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2010 (9)

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).
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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).
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M. Uchida and A. Tonomura, "Generation of electron beams carrying orbital angular momentum," Nature 464, 737‒739 (2010).
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H. T. J. Verbeeck and P. Schattschneider, "Production and application of electron vortex beams," Nature 467, 301‒304 (2010).
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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).
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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).
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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).
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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).
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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).
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2009 (8)

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).
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D. Ghai, P. Senthilkumaran, and R. Sirohi, "Single-slit diffraction of an optical beam with phase singularity," Opt. Lasers Eng. 47, 123‒126 (2009).
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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).
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E. Brasselet, N. Murazawa, and H. Misawa, "Optical vortices from liquid crystal droplets," Phys. Rev. Lett. 103, 103903 (2009).
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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).
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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).
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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).
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2008 (11)

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299‒315 (2008).
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K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, "Fractality of light’s darkness," Phys. Rev. Lett. 100, 053902 (2008).
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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).
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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).
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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).
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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).
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S. Sasaki and I. Mcnulty, "Proposal for generating brilliant x-ray beams carrying orbital angular momentum," Phys. Rev. Lett. 100, 124801 (2008).
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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).
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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).
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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).
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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).
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2007 (9)

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).
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R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, "Topological stability of stored optical vortices," Phys. Rev. Lett. 98, 203601 (2007).
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L. Allen and M. Padgett, "Equivalent geometric transformations for spin and orbital angular momentum of light," J. Mod. Opt. 54, 487‒491 (2007).
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G. Calvo and A. Picón, "Spin-induced angular momentum switching," Opt. Lett. 32, 838‒840 (2007).
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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).
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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).
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G. A. Swartzlander and R. I. Hernandez-Aranda, "Optical Rankine vortex and anomalous circulation of light," Phys. Rev. Lett. 99, 163901 (2007).
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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).
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G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305‒310 (2007).
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2006 (11)

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).
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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).
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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).
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L. Marrucci, C. Manzo, and D. Paparo, "Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media," Phys. Rev. Lett. 96, 163905 (2006).
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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).
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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).
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J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, "An optically driven pump for microfluidics," Lab Chip 6, 735‒739 (2006).
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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).
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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).
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H. Sztul and R. Alfano, "Double-slit interference with Laguerre–Gaussian beams," Opt. Lett. 31, 999‒1001 (2006).
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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).
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2005 (9)

L. Torner, J. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873‒881 (2005).
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S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral phase contrast imaging in microscopy," Opt. Express 13, 689‒694 (2005).
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S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral interferometry," Opt. Lett. 30, 1953‒1955 (2005).
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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).
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A. Desyatnikov, Y. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291‒391 (2005).

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).
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J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
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J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005).
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G. Foo, D. M. Palacios, and G. A. Swartzlander, "Optical vortex coronagraph," Opt. Lett. 30, 3308‒3310 (2005).
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2004 (9)

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).
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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).
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G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, "Triggered qutrits for quantum communication protocols," Phys. Rev. Lett. 92, 167903 (2004).
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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).
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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).
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K. Ladavac and D. Grier, "Micro-optomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144‒1149 (2004).
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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).
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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).
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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).
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2003 (6)

J. Arlt, "Handedness and azimuthal energy flow of optical vortex beams," J. Mod. Opt. 50, 1573‒1580 (2003).

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).
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M. Harwit, "Photon orbital angular momentum in astrophysics," Astrophys. J. 597, 1266‒1270 (2003).
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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).
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J. Leach and M. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 154 (2003).
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D. Grier, "A revolution in optical manipulation," Nature 424, 810‒816 (2003).
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2002 (9)

G. Gbur, T. Visser, and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002).
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M. V. Berry, "Coloured phase singularities," New J. Phys. 4, 66 (2002).
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S. M. Barnett, "Optical angular-momentum flux," J. Opt. B Quantum Semiclass. Opt. 4, 7‒16 (2002).
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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).
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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).
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A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 240401 (2002).
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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).
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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).
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2001 (10)

G. Forbes and M. Alonso, "Measures of spread for periodic distributions and the associated uncertainty relations," Am. J. Phys. 69, 340‒347 (2001).
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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).
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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313‒316 (2001).
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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).
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L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912 (2001).
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M. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547‒549 (2001).
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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).
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J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21‒27 (2001).
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M. V. Berry and M. R. Dennis, "Knotted and linked phase singularities in monochromatic waves," Proc. R. Soc. Lond. A 457, 2251‒2263 (2001).
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G. A. Swartzlander, "Peering into darkness with a vortex spatial filter," Opt. Lett. 26, 497‒499 (2001).
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2000 (5)

J. Gutiérrez-Vega, M. Iturbe-Castillo, and S. Chávez-Cerda, "Alternative formulation for invariant optical fields: Mathieu beams," Opt. Lett. 25, 1493‒1495 (2000).
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M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A 456, 2059‒2079 (2000).
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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).
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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).
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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).
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1999 (4)

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).
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M. J. Padgett and J. Courtial, "Poincare-sphere equivalent for light beams containing orbital angular momentum," Opt. Lett. 24, 430‒432 (1999).
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L. Allen, M. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291‒372 (1999).

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]

1998 (5)

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).
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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).
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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).
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S. Khonina, V. Kotlyar, and V. Soifer, "Diffraction optical elements matched to the Gauss–Laguerre modes," Opt. Spectrosc. 85, 636‒644 (1998).

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).
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1997 (7)

W. Firth and D. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450‒2453 (1997).
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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).
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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).
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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).
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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).
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M. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World 10, 35‒38 (1997).

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).
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1996 (4)

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).
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K. Gahagan and G. A. Swartzlander, "Optical vortex trapping of particles," Opt. Lett. 21, 827‒829 (1996).
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G. Nienhuis, "Doppler effect induced by rotating lenses," Opt. Commun. 132, 8‒14 (1996).
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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).
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1995 (2)

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).
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M. J. Padgett and L. Allen, "The Poynting vector in Laguerre–Gaussian laser modes," Opt. Commun. 121, 36‒40 (1995).
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1994 (8)

S. Barnett and L. Allen, "Orbital angular momentum and non paraxial light beams," Opt. Commun. 110, 670‒678 (1994).
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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).
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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).
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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).
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M. Babiker, W. L. Power, and L. Allen, "Light-induced torque on moving atoms," Phys. Rev. Lett. 73, 1239‒1242 (1994).
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L. Allen, M. Babiker, and W. L. Power, "Azimuthal Dopper-shift in light-beams with orbital angular momentum," Opt. Commun. 112, 141‒144 (1994).
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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).
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M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, "Laser modes with helical wave-fronts," Phys. Rev. A 49, 3119‒3122 (1994).
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1993 (3)

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).
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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).
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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).
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1992 (8)

V. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985‒990 (1992).
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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).
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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).
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G. D’Alessandro and G.-L. Oppo, "Gauss–Laguerre modes: a sensible basis for laser dynamics," Opt. Commun. 88, 130‒136 (1992).
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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).
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G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503‒2506 (1992).
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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).
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G. Nienhuis, J. P. Woerdman, and I. Kuscer, "Magnetic and mechanical Faraday effects," Phys. Rev. A 46, 7079‒7092 (1992).
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1991 (1)

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).
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1990 (3)

1989 (2)

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).
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P. Coullet, G. Gil, and F. Rocca, "Optical vortices," Opt. Commun. 73, 403‒408 (1989).
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1988 (1)

C. Tamm, "Frequency locking of 2 transverse optical modes of a laser," Phys. Rev. A 38, 5960‒5963 (1988).
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1987 (3)

J. Durnin, J. J. Miceli Jr., and J. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499‒1501 (1987).
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W. Hossack, A. Darling, and A. Dahdouh, "Coordinate transformations with multiple computer-generated optical-elements," J. Mod. Opt. 34, 1235‒1250 (1987).
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1982 (1)

A. Aspect, J. Dalibard, and G. Roger, "Experimental test of Bell’s inequalities using time-varying analyzers," Phys. Rev. Lett. 49, 1804‒1807 (1982).
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1981 (1)

1979 (3)

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).
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J. M. Vaughan and D. Willetts, "Interference properties of a light-beam having a helical wave surface," Opt. Commun. 30, 263‒267 (1979).
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1976 (2)

R. V. Jones, "Rotary ‘aether drag’," Proc. R. Soc. Lond. A 349, 423‒439 (1976).
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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).
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1974 (2)

J. F. Nye and M. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165‒190 (1974).
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O. Bryngdahl, "Geometrical transformations in optics," J. Opt. Soc. Am. 64, 1092‒1099 (1974).
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1972 (2)

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).
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1971 (1)

1964 (1)

J. S. Bell, "On the Einstein Podolsky Rosen paradox," Physics 1, 195‒200 (1964).

1936 (1)

R. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115‒125 (1936).
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1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777‒780 (1935).
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1931 (1)

P. Dirac, "Quantised singularities in the electromagnetic field," Proc. R. Soc. Lond. A 133, 60‒72 (1931).
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1909 (1)

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).
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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).
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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).
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Abdul-Malik, R.

Abo-Shaeer, J. R.

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).
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Aiello, A.

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).
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Alfano, R.

Allen, L.

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).
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S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299‒315 (2008).
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L. Allen and M. Padgett, "Equivalent geometric transformations for spin and orbital angular momentum of light," J. Mod. Opt. 54, 487‒491 (2007).
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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).
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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).
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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).
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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).
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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, 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]

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. 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).
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S. Barnett and L. Allen, "Orbital angular momentum and non paraxial light beams," Opt. Commun. 110, 670‒678 (1994).
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M. Babiker, W. L. Power, and L. Allen, "Light-induced torque on moving atoms," Phys. Rev. Lett. 73, 1239‒1242 (1994).
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L. Allen, M. Babiker, and W. L. Power, "Azimuthal Dopper-shift in light-beams with orbital angular momentum," Opt. Commun. 112, 141‒144 (1994).
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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).
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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).
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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).
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G. Forbes and M. Alonso, "Measures of spread for periodic distributions and the associated uncertainty relations," Am. J. Phys. 69, 340‒347 (2001).
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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).
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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).
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Arlt, J.

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).
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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).
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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).
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Arnold, S.

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).
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Aspect, A.

A. Aspect, J. Dalibard, and G. Roger, "Experimental test of Bell’s inequalities using time-varying analyzers," Phys. Rev. Lett. 49, 1804‒1807 (1982).
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Babiker, M.

L. Allen, M. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291‒372 (1999).

L. Allen, M. Babiker, and W. L. Power, "Azimuthal Dopper-shift in light-beams with orbital angular momentum," Opt. Commun. 112, 141‒144 (1994).
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M. Babiker, W. L. Power, and L. Allen, "Light-induced torque on moving atoms," Phys. Rev. Lett. 73, 1239‒1242 (1994).
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Barnett, S. M.

Barnett, S.

Barnett, S. M.

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).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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S. M. Barnett, "Optical angular-momentum flux," J. Opt. B Quantum Semiclass. Opt. 4, 7‒16 (2002).
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J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
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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).
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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).
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Battipiede, F.

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).
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Baudisch, M.

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).
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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).
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Figures (24)

Figure 1
Figure 1

The spin angular momentum (SAM) of light is connected to the polarization of the electric field. Light with linear polarization (left) carries no SAM, whereas right or left circularly polarized light (right) carries a SAM of ± ħ per photon.

Figure 2
Figure 2

Helical phase fronts for (a) = 0 , (b) = 1 , (c) = 2 , and (d) = 3 .

Figure 3
Figure 3

Combination of Hermite–Gaussian modes H G 01 and H G 10 to produce a helically phased Laguerre–Gaussian mode ( L G 01 ). Top, normalized intensity plots; bottom, corresponding phase profiles.

Figure 4
Figure 4

Complex paths of vortex lines form complicated topological features. These can be unbounded (red) or loops (white).

Figure 5
Figure 5

A spiral phase plate can generate a helically phased beam from a Gaussian. In this case = 0 = 2 .

Figure 6
Figure 6

Normalized intensity (top) and phase (bottom) plots of Laguerre–Gaussian modes: L G 01 , L G 11 , and L G 21 (left to right) showing the p + 1 concentric rings and the effect on the phase pattern.

Figure 7
Figure 7

Normalized intensity (top) and phase (bottom) profiles of some superpositions of Laguerre–Gaussian modes: L G 01 + L G 05 , L G 0 5 + L G 05 , and L G 10 + L G 05 (left to right).

Figure 8
Figure 8

A helical phase profile exp ( i ϕ ) converts a Gaussian laser beam into a helical mode whose wave fronts resemble an -fold corkscrew. In this case = 3 .

Figure 9
Figure 9

A combination of the phase distribution of the desired optical component (left) plus a linear phase ramp (middle) creates a forked diffraction grating (right), which can produce a helically phased beam. In this case = 3 .

Figure 10
Figure 10

Combining Hermite–Gaussian modes to produce Laguerre–Gaussian modes. An HG mode at 45 ° can be decomposed into a set of HG modes, and this same set of HG modes, when rephased, can combine to form a particular LG mode: 1 2 H G 02 + i 2 H G 11 + 1 2 H G 20 = L G 02 .

Figure 11
Figure 11

π / 2 and π-converters.

Figure 12
Figure 12

An extended incoherent light source illuminating a spiral phase plate produces a vortex beam with a nonzero on-axis intensity.

Figure 13
Figure 13

Illumination of a forked diffraction grating with a source with a broad spectral bandwidth results in a white-light vortex.

Figure 14
Figure 14

Transfer of angular momentum in optical tweezers. A trapped object can be rotated either by the transfer of SAM from a circularly polarized beam (left) or by the transfer of OAM from a high-order Laguerre–Gaussian beam.

Figure 15
Figure 15

Bloch sphere for OAM states. The pure state | a is defined by its latitude ( 0 θ a π ) and longitude ( 0 ϕ a < 2 π ) on the sphere. The poles ( θ a = 0 , π ) represent the states | , | respectively, while around the equator ( θ a = π / 2 ) are the equally weighted superpositions of | and | with no net OAM.

Figure 16
Figure 16

The mechanically induced ether drag associated with a spinning cylinder rotates both the polarization and the image through the same angle.

Figure 17
Figure 17

Behavior of spiral waves in lasers [110]. Spatial distribution of field in the presence of (a) three and (b) five spiral defects; yellow corresponds to low intensity, and blue to high intensity. Each phase singularity rotates around its core, while the whole pattern rotates around the center. (c) Spatial distribution of field with a total topological charge of 8. Seven defects rotate around a central defect.

Figure 18
Figure 18

Conservation of energy and momentum in spontaneous parametric downconversion.

Figure 19
Figure 19

Optical sprinklers: signals with a number of domain walls that rotate in time. (a)–(c) are for = 1 ; (d) is for = 2 .

Figure 20
Figure 20

Spontaneous parametric downconversion produces entangled photons.

Figure 21
Figure 21

A diffractive optical element comprising a diffraction grating with fork dislocation centered on the beam axis can convert a helically phased mode into the fundamental Gaussian mode, which can then be coupled to single-mode fiber.

Figure 22
Figure 22

The uncertainty relationship for angle-angular momentum, analogous to that for position and momentum.

Figure 23
Figure 23

Phase profiles of (a) the transforming and (b) the phase-correcting optical element; d is the length of the transformed beam. In (b) only that part of the phase-correcting element is shown that is illuminated by the transformed beam. In the experiment, the phase profiles are displayed on the SLMs with 2% phase modulation. (c) Schematic overview of the setup. SLMs are used both to generate Laguerre–Gaussian beams (SLM1) and to create the desired phase profiles for the transforming and phase-correcting optical elements (SLM2 and SLM3, respectively). L1 is the Fourier-transforming lens, and lens L2 focuses the transformed beams. Beam splitters ensure perpendicular incidence on the SLMs.

Figure 24
Figure 24

Ghost imaging: coincidence measurements of two beams of entangled photons—one of which interacts with an object and one of which doesn’t—can be used to reconstruct a “ghost” image of the object.

Equations (3)

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L G p = 2 p ! π p + | | ! 1 w ( z ) r 2 w ( z ) | | exp r 2 w 2 ( z ) L p | | 2 r 2 w 2 ( z ) exp [ i ϕ ] exp i k 0 r 2 z 2 ( z 2 + z R 2 ) exp i ( 2 p + | | + 1 ) tan 1 z z R
L p | | ( x ) = ( 1 ) | | d | | d x | | L p + | | ( x ) ,
| a = cos θ a 2 | + e i ϕ a sin θ a 2 | ,

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