Abstract

Orbital angular momentum (OAM), which describes the “phase twist” (helical phase pattern) of light beams, has recently gained interest due to its potential applications in many diverse areas. Particularly promising is the use of OAM for optical communications since: (i) coaxially propagating OAM beams with different azimuthal OAM states are mutually orthogonal, (ii) inter-beam crosstalk can be minimized, and (iii) the beams can be efficiently multiplexed and demultiplexed. As a result, multiple OAM states could be used as different carriers for multiplexing and transmitting multiple data streams, thereby potentially increasing the system capacity. In this paper, we review recent progress in OAM beam generation/detection, multiplexing/demultiplexing, and its potential applications in different scenarios including free-space optical communications, fiber-optic communications, and RF communications. Technical challenges and perspectives of OAM beams are also discussed.

© 2015 Optical Society of America

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2014 (17)

B. Ung, P. Vaity, L. Wang, Y. Messaddeq, L. A. Rusch, and S. LaRochelle, “Few-mode fiber with inverse-parabolic graded-index profile for transmission of OAM-carrying modes,” Opt. Express 22, 18044–18055 (2014).
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S. Li and J. Wang, “A compact trench-assisted multi-orbital-angular-momentum multi-ring fiber for ultrahigh-density space-division multiplexing (19 rings × 22 modes),” Sci. Rep. 4, 3853 (2014).

N. Ahmed, H. Huang, Y. Ren, Y. Yan, G. Xie, M. Tur, and A. E. Willner, “Reconfigurable 2 × 2 orbital angular momentum based optical switching of 50-Gbaud QPSK channels,” Opt. Express 22, 756–761 (2014).
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H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8, 595–604 (2014).
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G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (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).
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E. Karimi, S. A. Schulz, I. D. Leon, V. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3, e167 (2014).
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P. J. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8, 345–348 (2014).
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A. J. Lee, C. Zhang, T. Omatsu, and H. M. Pask, “An intracavity, frequency-doubled self-Raman vortex laser,” Opt. Express 22, 5400–5409 (2014).
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M. J. Strain, X. Cai, J. Wang, J. Zhu, D. B. Phillips, L. Chen, M. Lopez-Garcia, J. L. O’Brien, M. G. Thompson, M. Sorel, and S. Yu, “Fast electrical switching of orbital angular momentum modes using ultra-compact integrated vortex emitters,” Nat. Commun. 5, 4856 (2014).
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H. Huang, Y. Ren, G. Xie, Y. Yan, Y. Yue, N. Ahmed, M. P. J. Lavery, M. J. Padgett, S. Dolinar, M. Tur, and A. E. Willner, “Tunable orbital angular momentum mode filter based on optical geometric transformation,” Opt. Lett. 39, 1689–1692 (2014).
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B. Guan, R. P. Scott, C. Qin, N. K. Fontaine, T. Su, C. Ferrari, M. Cappuzzo, F. Klemens, B. Keller, M. Earnshaw, and S. J. B. Yoo, “Free-space coherent optical communication with orbital angular, momentum multiplexing/demultiplexing using a hybrid 3D photonic integrated circuit,” Opt. Express 22, 145–156 (2014).
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H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100  Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39, 197–200 (2014).
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M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Twisted light communication through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
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N. Chandrasekaran and J. H. Shapiro, “Photon information efficient communication through atmospheric turbulence–Part I: channel model and propagation statistics,” J. Lightwave Technol. 32, 1075–1087 (2014).
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Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39, 2845–2848 (2014).
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H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4 × 4 MIMO equalization,” Opt. Lett. 39, 4360–4363 (2014).
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2013 (13)

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062–4065 (2013).
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D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (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, 1545–1548 (2013).
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Z. Zhao, J. Wang, S. Li, and A. E. Willner, “Metamaterials-based broadband generation of orbital angular momentum carrying vector beams,” Opt. Lett. 38, 932–934 (2013).
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J. Zeng, X. Wang, J. Sun, A. Pandey, A. N. Cartwright, and N. M. Litchinitser, “Manipulating complex light with metamaterials,” Sci. Rep. 3, 2826 (2013).

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, 30196–30203 (2013).
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Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15, 044005 (2013).
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M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
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A. Hamadou Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88, 012312 (2013).
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M. J. Willner, H. Huang, N. Ahmed, G. Xie, Y. Ren, Y. Yan, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “Reconfigurable orbital angular momentum and polarization manipulation of 100  Gbit/s QPSK data channels,” Opt. Lett. 38, 5240–5243 (2013).
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Y. Yue, H. Huang, N. Ahmed, Y. Yan, Y. Ren, G. Xie, D. Rogawski, M. Tur, and A. E. Willner, “Reconfigurable switching of orbital-angular-momentum-based free-space data channels,” Opt. Lett. 38, 5118–5121 (2013).
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H. Huang, Y. Yue, Y. Yan, N. Ahmed, Y. Ren, M. Tur, and A. E. Willner, “Liquid-crystal-on-silicon-based optical add/drop multiplexer for orbital-angular-momentum multiplexed optical links,” Opt. Lett. 38, 5142–5145 (2013).
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Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38, 3930–3933 (2013).
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2012 (16)

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Dolinar, M. Tur, and A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).
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J. Leach, E. Bolduc, D. J. Gauthier, and R. W. Boyd, “Secure information capacity of photons entangled in many dimensions,” Phys. Rev. A 85, 060304 (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, 033001 (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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N. Bozinovic, S. Golowich, P. Kristensen, and S. Ramachandran, “Control of orbital angular momentum of light with optical fibers,” Opt. Lett. 37, 2451–2453 (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, 488–496 (2012).
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S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, and M. Kosihba, “12-core fiber with one ring structure for extremely large capacity transmission,” Opt. Express 20, 28398–28408 (2012).
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A. E. Willner, J. Wang, and H. Huang, “Applied physics. A different angle on light communications,” Science 337, 655–656 (2012).
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M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195–13200 (2012).
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D. Zhang, X. Feng, and Y. Huang, “Encoding and decoding of orbital angular momentum for wireless optical interconnects on chip,” Opt. Express 20, 26986–26995 (2012).
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M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20, 2110–2115 (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, 3735–3737 (2012).
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T. Su, R. P. Scott, S. S. Djordjevic, N. K. Fontaine, D. J. Geisler, X. Cai, and S. J. B. Yoo, “Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices,” Opt. Express 20, 9396–9402 (2012).
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K. Kano, Y. Kozawa, and S. Sato, “Generation of purely single transverse mode vortex beam from a He-Ne laser cavity with a spot-defect mirror,” Int. J. Opt. 2012, 359141 (2012).

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X. Cai, J. Wang, M. J. Strain, B. J. Morris, J. Zhu, M. Sorel, J. L. O’ Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
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2011 (11)

C. R. Doerr and L. L. Buhl, “Circular grating coupler for creating focused azimuthally and radially polarized beams,” Opt. Lett. 36, 1209–1211 (2011).
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P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett. 47, 972–973 (2011).
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P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express 19, 16680–16696 (2011).
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I. B. Djordjevic, “Deep-space and near-Earth optical communications by coded orbital angular momentum (OAM) modulation,” Opt. Express 19, 14277–14289 (2011).
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D. S. Millar and S. J. Savory, “Blind adaptive equalization of polarization-switched QPSK modulation,” Opt. Express 19, 8533–8538 (2011).
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B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112-Tb/s space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,” Opt. Express 19, 16665–16671 (2011).
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S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle, “6 × 56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6 × 6 MIMO equalization,” Opt. Express 19, 16697–16707 (2011).
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A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).

Y. Yan, J. Wang, L. Zhang, J.-Y. Yang, I. M. Fazal, N. Ahmed, B. Shamee, A. E. Willner, K. Birnbaum, and S. J. Dolinar, “Fiber coupler for generating orbital angular momentum modes,” Opt. Lett. 36, 4269–4271 (2011).
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L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (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, 333–337 (2011).
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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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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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2009 (3)

2008 (2)

J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. 47, 2414–2429 (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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2007 (7)

B. Thidé, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. 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. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
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A. Farid and S. Hranilovic, “Outage capacity optimization for free space optical links with pointing errors,” J. Lightwave Technol. 25, 1702–1710 (2007).
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M. Okida, T. Omatsu, M. Itoh, and T. Yatagai, “Direct generation of high power Laguerre-Gaussian output from a diode-pumped Nd:YVO4 1.3-μm bounce laser,” Opt. Express 15, 7616–7622 (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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J. H. Shapiro, S. Guha, and B. I. Erkmen, “Ultimate channel capacity of free-space optical communications,” J. Opt. Netw. 4, 501–516 (2005).
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J. Leach, M. Padgett, S. 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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M. Bourennane, A. Karlsson, G. Bjork, N. Gisin, and N. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A 35, 10065–10076 (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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2001 (2)

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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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 phase plate,” Opt. Commun. 127, 183–188 (1996).
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G. Xie, L. Li, Y. Ren, H. Huang, Y. Yan, N. Ahmed, Z. Zhao, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Performance metrics and design considerations for a free-space optical orbital-angular-momentum multiplexed communication link,” Optica (to be published).

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Figures (24)

Figure 1
Figure 1

Two cases of angular momenta: (a) a spinning object carrying SAM and (b) an orbiting object carrying OAM. (c) A circularly polarized light beam carrying SAM, and (d) the phase structure of an OAM-carrying light beam.

Figure 2
Figure 2

Conceptual schematic of a communication system employing OAM multiplexing.

Figure 3
Figure 3

Three approaches to convert a Gaussian beam into an OAM beam: (a) a spiral phase plate, (b) a phase hologram with a spiral phase pattern, or (c) a phase hologram with a “fork” pattern. In this example, the conversion to an OAM beam with = + 3 is depicted.

Figure 4
Figure 4

Mid-infrared metasurface phase plate that can generate OAM beams. (a) The fabricated metasurface phase plate. (b) Magnified structure of the designed metasurface. (c) Interferogram of the generated OAM beam with = + 1 . Reprinted from Yu et al., Science 334, 333–337 (2011) [24] by permission from AAAS.

Figure 5
Figure 5

Q-plate (QP) can convert a left circularly polarized beam into a helically phased beam with right circular polarization, or vice versa. Reprinted from Marrucci et al., J. Opt. 13, 064001 (2011) [30] © IOP Publishing. Reproduced with permission. All rights reserved.

Figure 6
Figure 6

Vortex beam generator using a ring resonator embedded with circularly distributed gratings [42]. (a) structure of the device. (b) distributed gratings in a linear waveguide producing a tilted plane wave by diffraction. (c) schematic view of the on-chip OAM generator. (d1)  three OAM emitters fabricated on a single chip. (d2) OAM beams generated by using the emitter array and (d3) their interferograms. Reprinted from Cai et al., Science 338, 363–366 (2012) [42] by permission from AAAS.

Figure 7
Figure 7

Schematic depiction of spatial multiplexing and demultiplexing: (a) spatial multiplexing using cascaded beam splitters (BS) and (b) demultiplexing using cascaded beam splitters and conjugate SPPs (or phase holograms).

Figure 8
Figure 8

Concept of an OAM mode sorter. The log-polar geometrical-transformation-based mode sorter can be used as an OAM multiplexer (when light propagates from right to left) and a demultiplexer (when light propagates from left to right).

Figure 9
Figure 9

OAM multiplexing/demultiplexing using photonic integrated circuit: (a) concept and principle, and (b) simulated and experimentally generated OAM beams ( = + 2 , + 3 , and + 4 ) using the photonic integrated circuit shown in (a). Reprinted with permission from [48]. Copyright 2012 Optical Society of America. (c) Conceptual schematic of the 3D integrated device for OAM multiplexing and demultiplexing. Reprinted with permission from [54]. Copyright 2014 Optical Society of America.

Figure 10
Figure 10

Experimental results of a free-space optical data link multiplexed with four OAM beams. (a) Intensity profile of the four OAM beams generated ( = 8 , + 10 , + 12 , and 14 ) and their superposition. (b) The optical spectrum of each channel after demultiplexing. (c) The recovered constellations of the 16-QAM signals carried on each OAM beam. Reprinted with permission from [56]. Copyright 2011 Optical Society of America.

Figure 11
Figure 11

(a) Three steps to produce 24 multiplexed OAM beams using two SLMs, mirrors, beam splitters, a half-wave plate and a PBS. (b) The optical spectrum of the WDM signal carried on an OAM beam with = + 10 . Reprinted with permission from [58]. Copyright 2014 Optical Society of America.

Figure 12
Figure 12

(a) A rotating phase plate is used as an atmospheric turbulence emulator. An ideal OAM beam emerges as a distorted OAM after passing through the phase plate. (b) Measured power distribution of an OAM beam after passing through the turbulence emulator with different strengths. Reprinted with permission from [70]. Copyright 2013 Optical Society of America.

Figure 13
Figure 13

A feedback loop including a wavefront sensor and a wavefront corrector can be used to partially compensate the turbulence-induced distortions. (a) Concept of feedback loop of the wavefront compensator. (b) Experimental results of the wavefront compensation. (b1)–(b3) Distorted OAM beams with = + 1 , + 5 , and + 9 . (b4)–(b6) Distortion mitigation using adaptive optics. Reprinted with permission from [73]. Copyright 2014 Optical Society of America.

Figure 14
Figure 14

Schematic diagram of the modeled free-space optical data link employing OAM multiplexing.

Figure 15
Figure 15

Simulation results. (a) Simulated spot size (diameter) of different orders of OAM beams as a function of transmission distance when the spot size of the transmitted beam is 3 cm. (b) Simulated spot size of different orders of OAM beams as a function of the transmitted beam size for a 100 m link. (c) Simulated power loss as a function of aperture size when only = + 3 beam is transmitted; D t , transmitted beam size. © 2014 IEEE. Reprinted, with permission, from Xie et al., IEEE Globecom 2014, Optical Wireless Communication Workshop (2014) [78].

Figure 16
Figure 16

Three different cases of alignment between the transmitter and receiver: (a) a perfectly aligned system, (b) a system with lateral displacement, and (c) a system with receiver angular error. Tx, transmitter; Rx, receiver; z , transmission distance; d , displacement; φ , angular error. © 2014 IEEE. Reprinted, with permission, from Xie et al., IEEE Globecom 2014, Optical Wireless Communication Workshop (2014) [78].

Figure 17
Figure 17

(a),(b) Simulated power distribution among different OAM modes as a function of lateral displacement/receiver angular error over a 100-m link for which only the OAM + 3 is transmitted. The transmitted beam size is 3 cm and the receiver aperture size is 4.5 cm. (c),(d) XT-1 as functions of lateral displacement/receiver angular error for different transmission distances with different transmitted beam sizes. The receiver size is 1.5 times the transmitted beam size. XT-1, the ratio of the received power on OAM+4 to the received power on OAM+3; Dt, transmitted beam size; z, transmission distance.

Figure 18
Figure 18

Experimental demonstration of the free-space propagation of OAM beams across the city of Vienna. ZAMG: transmitter building (Zentralanstalt für Meteorologie und Geodynamik, Central Institute for Meteorology and Geodynamics). IQOQI: receiver building. Top: picture of an alignment laser from IQOQI to ZAMG, captured at ZAMG. Left: the sender modulates a 532 nm laser with an SLM. The different phase holograms that modulate the beam are shown; they correspond to superpositions of OAM modes (from top to bottom) with = ± 1 , = ± 1 rotated, = ± 4 , and = ± 15 . Right: the observed modes at the receiver recorded with a CCD camera. The images correspond to the modulated phases on the left. Reprinted from Krenn et al., New J. Phys. 16, 1367 (2014) [60] © IOP Publishing. Reproduced by permission. All rights reserved.

Figure 19
Figure 19

Data transmission experiment using OAM multiplexing over a 5 km FMF. MIMO DSP was used to mitigate the mode coupling effects. (a) Schematic setup of the data transmission experiment. (b1)–(b8) Recovered constellations of a 20 Gbit / s QPSK signal carried on each OAM beam (top, without MIMO DSP; bottom, with MIMO DSP). (c) Measured BER curves. Reprinted with permission from [53]. Copyright 2014 Optical Society of America.

Figure 20
Figure 20

Vortex fiber was demonstrated to be able to maintain the OAM modes after propagating over a length of 1.1 km. (a) Cross-sectional view of the vortex fiber. (b) Refractive profile of the vortex fiber. (c) The intensity and interferograms of modes at the vortex fiber output. Modified from Bozinovic et al., Science 340, 1545–1548 (2013) [7] by permission from AAAS.

Figure 21
Figure 21

Concept of data exchanging between two channels carried on different OAM states. Reprinted with permission from [94]. Copyright 2013 Optical Society of America.

Figure 22
Figure 22

(a) Concept of a ROADM for data channels carried on multiplexed OAM beams. (b1)–(b6) Experimental results: observed intensity profiles of beams at each step of add/drop operation. Reprinted with permission from [97]. Copyright 2013 Optical Society of America.

Figure 23
Figure 23

Experimental demonstration of seven-dimensional QKD system using OAM modes and the corresponding mutually unbiased basis of angular position (ANG). (a) Conceptual experimental setup. A highly attenuated He–Ne laser modulated by an AOM was used as the source. The laser output was then encoded with spatial mode information using a DMD. Bob’s mode sorter and fan-out elements map the OAM modes and the ANG modes into separated spots. AOM, acousto-optic modulator; DMD, digital micro-mirror device; SLM, spatial light modulator; NPBS, non-polarization beam splitter. (b) CCD images of produced light field profiles in two complementary spatial bases of seven-dimensional OAM and ANG modes. Reprinted with permission from [111].

Figure 24
Figure 24

Experiment demonstrating 32 Gbit / s data transmission using eight multiplexed OAM beams at 28 GHz frequency range. (a) Measured intensity profiles of generated OAM beams and their interferograms. (b) Measured crosstalk of each channel after demultiplexing. (c) Recovered constellations of 4 Gbit / s 16-QAM signal carried on each of the two polarizations of the = + 3 beam. (d1)–(d4) Measured BER curves of the data channels carried on each OAM beam. Reprinted by permission from Macmillan Publishers Ltd.: Yan et al., Nat. Commun. 5, 4876 (2014) [121]. Copyright 2014.

Tables (1)

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Table 1. Measured Crosstalk of Each OAM Beam after Demultiplexing [dB]

Equations (3)

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U 1 = ( r , θ , z ) = A 1 ( r , z ) exp ( i 1 θ ) ,
U 2 = ( r , θ , z ) = A 2 ( r , z ) exp ( i 2 θ ) ,
0 2 π U 1 U 2 * d θ = { 0 if 1 2 A 1 A 2 * if 1 = 2 .

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