Abstract

Twenty-five years ago Allen, Beijersbergen, Spreeuw, and Woerdman published their seminal paper establishing that light beams with helical phase-fronts carried an orbital angular momentum. Previously orbital angular momentum had been associated only with high-order atomic/molecular transitions and hence considered to be a rare occurrence. The realization that every photon in a laser beam could carry an orbital angular momentum that was in excess of the angular momentum associated with photon spin has led both to new understandings of optical effects and various applications. These applications range from optical manipulation, imaging and quantum optics, to optical communications. This brief review will examine some of the research in the field to date and consider what future directions might hold.

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Corrections

15 May 2017: A correction was made to the title.


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2016 (8)

N. Radwell, R. D. Hawley, J. B. Götte, and S. Franke-Arnold, “Achromatic vector vortex beams from a glass cone,” Nat. Commun. 7, 10564 (2016).
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K. J. Mitchell, S. Turtaev, M. J. Padgett, T. Čižmár, and D. B. Phillips, “High-speed spatial control of the intensity, phase and polarisation of vector beams using a digital micro-mirror device,” Opt. Express 24(25), 29269–29282 (2016).
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M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nat. Photonics 10(4), 248–252 (2016).
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S. Restuccia, D. Giovannini, G. Gibson, and M. Padgett, “Comparing the information capacity of Laguerre-Gaussian and Hermite-Gaussian modal sets in a finite-aperture system,” Opt. Express 24(24), 27127–27136 (2016).
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A. Trichili, A. B. Salem, A. Dudley, M. Zghal, and A. Forbes, “Encoding information using Laguerre Gaussian modes over free space turbulence media,” Opt. Lett. 41(13), 3086–3089 (2016).
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A. Wang, L. Zhu, S. Chen, C. Du, Q. Mo, and J. Wang, “Characterization of LDPC-coded orbital angular momentum modes transmission and multiplexing over a 50-km fiber,” Opt. Express 24(11), 11716–11726 (2016).
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G. Xie, Y. Ren, Y. Yan, H. Huang, N. Ahmed, L. Li, Z. Zhao, C. Bao, M. Tur, S. Ashrafi, and A. E. Willner, “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre-Gaussian beams with different radial indices,” Opt. Lett. 41(15), 3447–3450 (2016).
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M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. U.S.A. 113(48), 13648–13653 (2016).
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2015 (8)

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
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M. Krenn, J. Handsteiner, M. Fink, R. Fickler, and A. Zeilinger, “Twisted photon entanglement through turbulent air across Vienna,” Proc. Natl. Acad. Sci. U.S.A. 112(46), 14197–14201 (2015).
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N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9(12), 822–826 (2015).
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M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
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A. Jesacher, M. Ritsch-Marte, and R. Piestun, “Three-dimensional information from two-dimensional scans: a scanning microscope with post acquisition refocusing capability,” Optica 2(3), 210–214 (2015).
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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66 (2015).
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X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
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J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11(8), 629–634 (2015).
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2014 (3)

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
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M. Padgett, “Light’s twist,” Proc. Math. Phys. Eng. Sci. 470(2172), 20140633 (2014).
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Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

2013 (7)

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lutkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88(3), 032305 (2013).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
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Z. Yan and N. F. Scherer, “Optical vortex induced rotation of silver nanowires,” J. Phys. Chem. Lett. 4(17), 2937–2942 (2013).
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M. P. Lee, G. M. Gibson, R. Bowman, S. Bernet, M. Ritsch-Marte, D. B. Phillips, and M. J. Padgett, “A multi-modal stereo microscope based on a spatial light modulator,” Opt. Express 21(14), 16541–16551 (2013).
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M. Mirhosseini, O. S. Magaña-Loaiza, C. Chen, B. Rodenburg, M. Malik, and R. W. Boyd, “Rapid generation of light beams carrying orbital angular momentum,” Opt. Express 21(25), 30196–30203 (2013).
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S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
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Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4, 2374 (2013).
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2012 (12)

C. Greenshields, R. L. Stamps, and S. Franke-Arnold, “Vacuum Faraday effect for electrons,” New J. Phys. 14(10), 103040 (2012).
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C. E. Demore, Z. Yang, A. Volovick, S. Cochran, M. P. MacDonald, and G. C. Spalding, “Mechanical evidence of the orbital angular momentum to energy ratio of vortex beams,” Phys. Rev. Lett. 108(19), 194301 (2012).
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R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
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P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3, 1278 (2012).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
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N. M. Litchinitser, “Applied physics. Structured light meets structured matter,” Science 337(6098), 1054–1055 (2012).
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M. Tamagnone, C. Craeye, and J. Perruisseau-Carrier, “Comment on 'Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(11), 118001 (2012).
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F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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R. Steiger, S. Bernet, and M. Ritsch-Marte, “SLM-based off-axis Fourier filtering in microscopy with white light illumination,” Opt. Express 20(14), 15377–15384 (2012).
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V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
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B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37(17), 3735–3737 (2012).
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2011 (4)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
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A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
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2010 (5)

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464(7289), 737–739 (2010).
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J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (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(5992), 662–665 (2010).
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G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Measuring orbital angular momentum superpositions of light by mode transformation,” Phys. Rev. Lett. 105, 153601 (2010).
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C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2010).
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2009 (2)

2008 (6)

M. R. Dennis, A. C. Hamilton, and J. Courtial, “Superoscillation in speckle patterns,” Opt. Lett. 33(24), 2976–2978 (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(5), 053902 (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(2), 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(1), 013018 (2008).
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G. A. Swartzlander, E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, “Astronomical demonstration of an optical vortex coronagraph,” Opt. Express 16(14), 10200–10207 (2008).
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S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16(26), 22048–22057 (2008).
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2007 (2)

2006 (4)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
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H. I. Sztul, V. Kartazayev, and R. R. Alfano, “Laguerre-Gaussian supercontinuum,” Opt. Lett. 31(18), 2725–2727 (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(6), 735–739 (2006).
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K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14(7), 3039–3044 (2006).
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2005 (5)

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
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S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral interferometry,” Opt. Lett. 30(15), 1953–1955 (2005).
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S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13(3), 689–694 (2005).
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L. Torner, J. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13(3), 873–881 (2005).
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C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
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2004 (5)

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(22), 5448–5456 (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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S. Gspan, A. Meyer, S. Bernet, and M. Ritsch-Marte, “Optoacoustic generation of a helicoidal ultrasonic beam,” J. Acoust. Soc. Am. 115(3), 1142–1146 (2004).
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K. Ladavac and D. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Opt. Express 12(6), 1144–1149 (2004).
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K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
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2003 (3)

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
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J. Leach and M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 154 (2003).
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A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
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2002 (3)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
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A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (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(21), 1875–1877 (2002).
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2001 (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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G. A. Swartzlander, “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26(8), 497–499 (2001).
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1998 (2)

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
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M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
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1997 (3)

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
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J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144(4-6), 210–213 (1997).
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I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78(13), 2539–2542 (1997).
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1996 (1)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
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1995 (2)

H. He, M. E. J. 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(5), 826–829 (1995).
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M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
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1994 (3)

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994).
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M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 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(9), 1239–1242 (1994).
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1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
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1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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1990 (1)

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocations in their wave-fronts,” JETP Lett. 52, 429–431 (1990).

1989 (1)

P. Coullet, G. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
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1988 (1)

C. Tamm, “Frequency locking of two transverse optical modes of a laser,” Phys. Rev. A Gen. Phys. 38(11), 5960–5963 (1988).
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1986 (1)

1981 (1)

1979 (1)

M. V. Berry, J. F. Nye, and F. Wright, “The elliptic umbilic diffraction catastrophe,” Philos. Trans. R. Soc. Lond. A 291(1382), 453–484 (1979).
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1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
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1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
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1932 (1)

C. G. Darwin, “Notes on the theory of radiation,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 136(829), 36–52 (1932).
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1931 (1)

P. A. M. Dirac, “Quantised singularities in the electromagnetic field,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 133(821), 60–72 (1931).
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1909 (1)

J. H. 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 Contain. Pap. Math. Phys. Character 82(557), 560–567 (1909).
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’t Hooft, G. W.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
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Abdul-Malik, R. S.

Agrawal, A.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Ahmed, N.

G. Xie, Y. Ren, Y. Yan, H. Huang, N. Ahmed, L. Li, Z. Zhao, C. Bao, M. Tur, S. Ashrafi, and A. E. Willner, “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre-Gaussian beams with different radial indices,” Opt. Lett. 41(15), 3447–3450 (2016).
[Crossref] [PubMed]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66 (2015).
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Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Aiello, A.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
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Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Alfano, R. R.

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref] [PubMed]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144(4-6), 210–213 (1997).
[Crossref]

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