Abstract

Vector vortex beams are structured states of light that are nonseparable in their polarisation and spatial mode, they are eigenmodes of free-space and many fiber systems, and have the capacity to be used as information carriers for both classical and quantum communication. Here, we outline recent progress in our understanding of these modes, from their creation to their characterization and detection. We then use these tools to study their propagation behavior in free-space and optical fiber and show that modal cross-talk results in a decay of vector states into separable scalar modes, with a concomitant loss of information. We present a comparison between probabilistic and deterministic detection schemes showing that the former, while ubiquitous, negates the very benefit of increased dimensionality in quantum communication while reducing signal in classical communication links. This work provides a useful introduction to the field as well as presenting new findings and perspectives to advance it further.

© 2017 OAPA

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. E. Willneret al., “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon., vol. 7, no. 1, pp. 66–106, 2015.
  2. A. E. Willneret al., “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Philos. Trans. Roy. Soc. A, Math., Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .
  3. H. Rubinsztein-Dunlopet al., “Roadmap on structured light,” J. Opt., vol. 19,  2017, Art. no. .
  4. C. Rosales-Guzmán and A. Forbes, How to Shape Light With Spatial Light Modulators, vol. SL30. Bellingham, WA, USA: SPIE Press, 2017.
  5. A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon., vol. 8, pp. 200–227,  2016.
  6. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon., vol. 7, pp. 354–362,  2013.
  7. S. Berdagué and P. Facq, “Mode division multiplexing in optical fibers.,” Appl. Opt., vol. 21, no. 11, pp. 1950–1955, 1982.
  8. G. Gibsonet al., “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express, vol. 12, no. 22, pp. 5448–5456, 2004.
  9. G. Keiser, Optical Fiber Communications. (McGraw-Hill Series in Electrical and Computer Engineering: Communications and Signal Processing), 3rd ed. New York, NY, USA: McGraw-Hill, 2000.
  10. J. Wanget al., “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon., vol. 6, no. 7, pp. 488–496, 2012.
  11. V. Sleifferet al., “737 Tb/s ($\text{96} \times \text{3} \times$ 256-Gb/s) mode-division-multiplexed DP-16QAM transmission with inline MM-EDFA,” Opt. Express, vol. 20, pp. B428–B438,  2012.
  12. H. Huanget al., “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett., vol. 39, pp. 197–200,  2014.
  13. Y. Yanet al., “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nature Commun., vol. 5,  2014, Art. no. .
  14. M. Krennet al., “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys., vol. 16, no. 11, 2014, Art. no. .
  15. A. Wang, L. Zhu, J. Liu, C. Du, Q. Mo, and J. Wang, “Demonstration of hybrid orbital angular momentum multiplexing and time-division multiplexing passive optical network,” Opt. Express, vol. 23, pp. 29457–29466,  2015.
  16. Y. Renet al., “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett., vol. 41, pp. 622–625,  2016.
  17. G. Xieet al., “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre–Gaussian beams with different radial indices,” Opt. Lett., vol. 41, pp. 3447–3450,  2016.
  18. J. Wang, “Advances in communications using optical vortices,” Photon. Res., vol. 4, pp. B14–B28,  2016.
  19. N. Bozinovicet al., “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science, vol. 340, no. 6140, pp. 1545–1548, 2013.
  20. H. Hübelet al., “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express, vol. 15, no. 12, pp. 7853–7862, 2007.
  21. R. Ursinet al., “Entanglement-based quantum communication over 144 km,” Nature Phys., vol. 3, pp. 481–486,  2007.
  22. X.-S. Maet al., “Quantum teleportation over 143 kilometres using active feed-forward,” Nature, vol. 489, no. 7415, pp. 269–273, 2012.
  23. T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B. Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of entanglement over 143 km,” Proc. Nat. Acad. Sci. USA, vol. 112, no. 46, pp. 14202–14205, 2015.
  24. T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett., vol. 84, no. 20, pp. 4729–4732, 2000.
  25. A. Poppeet al., “Practical quantum key distribution with polarization entangled photons,” Opt. Express, vol. 12, no. 16, pp. 3865–3871, 2004.
  26. C.-Z. Penget al., “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett., vol. 98,  2007, Art. no. .
  27. J. Yinet al., “Satellite-based entanglement distribution over 1200 kilometers,” Science, vol. 356, no. 6343, pp. 1140–1144, 2017.
  28. H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A, vol. 61,  2000, Art. no. .
  29. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett., vol. 88,  2002, Art. no. .
  30. L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A, vol. 82,  2010, Art. no. .
  31. S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys., vol. 8, pp. 75–83,  2006.
  32. M. Mafuet al., “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A, vol. 88,  2013, Art. no. .
  33. M. Mirhosseiniet al., “High-dimensional quantum cryptography with twisted light,” New J. Phys., vol. 17,  2015, Art. no. .
  34. B. Ndaganoet al., “Characterizing quantum channels with non-separable states of classical light,” Nature Phys., vol. 13, pp. 397–402,  2017.
  35. M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes,” Philos. Trans. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .
  36. B. Ndaganoet al., “A deterministic detector for vector vortex states,” Sci. Rep., vol. 7, 2017, Art. no. .
  37. A. Sitet al., “High-dimensional intracity quantum cryptography with structured photons,” Optica, vol. 4, pp. 1006–1010,  2017.
  38. M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A, vol. 92, no. 2, 2015, Art. no. .
  39. Q. Zhan, “Cylindrical vector beams: From mathematical concepts to applications,” Adv. Opt. Photon., vol. 1, pp. 1–57,  2009.
  40. M. P. J. Laveryet al., “Space division multiplexing in a basis of vector modes,” in Proc. Eur. Conf. Opt. Commun.,  2014, pp. 1–3.
  41. J. Zhang, F. Li, J. Li, Y. Feng, and Z. Li, “120 Gbit/s 2 $\times$ 2 vector-modes-division- multiplexing DD-OFDM-32QAM free-space transmission,” IEEE Photon. J., vol. 8, no. 6,  2016, Art. no. .
  42. Y. Zhao and J. Wang, “High-base vector beam encoding/decoding for visible-light communications,” Opt. Lett., vol. 40, pp. 4843–4846,  2015.
  43. G. Milioneet al., “4 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett., vol. 40, no. 9, pp. 1980–1983, 2015.
  44. G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett., vol. 40, pp. 4887–4890,  2015.
  45. P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Lett., vol. 24, pp. 15143–15159,  2016.
  46. B. Ndagano, R. Brüning, M. McLaren, M. Duparré, and A. Forbes, “Fiber propagation of vector modes,” Opt. Express, vol. 23, pp. 17330–17336,  2015.
  47. P. Gregget al., “Q-plates as higher order polarization controllers for orbital angular momentum modes of fiber,” Opt. Lett., vol. 40, pp. 1729–1732,  2015.
  48. C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A, vol. 77,  2008, Art. no. .
  49. G. Valloneet al., “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett., vol. 113,  2014, Art. no. .
  50. G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett., vol. 107,  2011, Art. no. .
  51. M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett., vol. 24, pp. 430–432,  1999.
  52. A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett., vol. 38, pp. 3429–3432,  2013.
  53. R. Brüninget al., “Data transmission with twisted light through a free-space to fiber optical communication link,” J. Opt., vol. 18, no. 3, 2016, Art. no. .
  54. B. Sephton, A. Dudley, and A. Forbes, “Revealing the radial modes in vortex beams,” Appl. Opt., vol. 55, no. 28, pp. 7830–7835, 2016.
  55. R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys., vol. 28, pp. 361–374, 1998.
  56. L. J. Pereira, A. Z. Khoury, and K. Dechoum, “Quantum and classical separability of spin-orbit laser modes,” Phys. Rev. A, vol. 90,  2014, Art. no. .
  57. F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys., vol. 16,  2014, Art. no. .
  58. D. Guzman-Silvaet al., “Demonstration of local teleportation using classical entanglement,” Laser Photon. Rev., vol. 10, no. 2, pp. 317–321,  2016.
  59. E. Karimi and R. W. Boyd, “Classical entanglement?” Science, vol. 350, pp. 1172–1173,  2015.
  60. E. Karimiet al., “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A, vol. 82,  2010, Art. no. .
  61. V. D’Ambrosioet al., “Photonic polarization gears for ultra-sensitive angular measurements,” Nature Commun., vol. 4,  2013, Art. no. .
  62. Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide Lattices,” Phys. Rev. Lett., vol. 102,  2009, Art. no. .
  63. R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A, vol. 81,  2010, Art. no. .
  64. R. Keil, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, and A. Szameit, “Classical characterization of biphoton correlation in waveguide lattices,” Phys. Rev. A, vol. 83,  2011, Art. no. .
  65. G. M. Lerman, L. Stern, and U. Levy, “Generation and tight focusing of hybridly polarized vector beams,” Opt. Express, vol. 18, no. 26, pp. 27650–27657, 2010.
  66. M. Michihata, T. Hayashi, and Y. Takaya, “Measurement of axial and transverse trapping stiffness of optical tweezers in air using a radially polarized beam,” Appl. Opt., vol. 48, no. 32, pp. 6143–6151, 2009.
  67. S. Berg-Johansenet al., “Classically entangled optical beams for high-speed kinematic sensing,” Optica, vol. 2, no. 10, pp. 1–5, 2015.
  68. A. Forbes, “Controlling light's helicity at the source: Orbital angular momentum states from lasers,” Philos. Trans. Roy. Soc. A, vol. 375, no. 2087, 2017, Art. no. .
  69. D. Naidooet al., “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nature Photon., vol. 10, pp. 327–332,  2016.
  70. S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express, vol. 19, no. 13, pp. 119163–119168, 2011.
  71. X. Caiet al., “Integrated compact optical vortex beam emitters,” Science, vol. 338, pp. 363–366,  2012.
  72. K. A.-A. Darryl Naidoo, M. Fromager, and A. Forbes, “Radially polarized cylindrical vector beams from a monolithic microchip laser,” Opt. Eng., vol. 54, 2015, Art. no. .
  73. W. Shuet al., “Propagation model for vector beams generated by metasurfaces,” Opt. Express, vol. 24, no. 18, pp. 21177–21189, 2016.
  74. P. Miaoet al., “Orbital angular momentum microlaser,” Science, vol. 353, pp. 464–467,  2016.
  75. L. Gonget al., “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys., vol. 116, no. 18, 2014, Art. no. .
  76. Y.-X. Ren, Z.-X. Fang, L. Gong, K. Huang, Y. Chen, and R.-D. Lu, “Digital generation and control of Hermite–Gaussian modes with an amplitude digital micromirror device,” J. Opt., vol. 17,  2015, Art. no. .
  77. M. A. A. Neil, F. Massoumian, R. Juskaitis, and T. Wilson, “Method for the generation of arbitrary complex vector wave fronts,” Opt. Lett., vol. 27, no. 21, pp. 1929–1931, 2002.
  78. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys., vol. 9, 2007, Art. no. .
  79. I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express, vol. 20, no. 1, pp. 364–376, 2012.
  80. S. Pancharatnam, “Generalized theory of interference and its applications. Partially coherent pencils,” Proc. Indian Acad. Sci., Sect. A, vol. 44, pp. 247–262, 1956.
  81. M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 392, no. 1802, pp. 45–57, 1984.
  82. E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett., vol. 90,  2003, Art. no. .
  83. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett., vol. 96,  2006, Art. no. .
  84. L. Marrucciet al., “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt., vol. 13,  2011, Art. no. .
  85. Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett., vol. 26, no. 18, pp. 1424–1426, 2001.
  86. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam–Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett., vol. 27, no. 13, pp. 1141–1143, 2002.
  87. G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam–Berry phase optical elements,” Opt. Lett., vol. 27, pp. 1875–1857,  2002.
  88. E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett., vol. 82, no. 3, pp. 328–330, 2003.
  89. A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun., vol. 251, pp. 306–314,  2005.
  90. R. C. Devlinet al., “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express, vol. 25, no. 1, pp. 377–393, 2017.
  91. Z. Zhao, J. Wang, S. Li, and A. E. Willner, “Metamaterials-based broadband generation of orbital angular momentum carrying vector beams,” Opt. Lett., vol. 38, pp. 932–934,  2013.
  92. X. Yiet al., “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express, vol. 22, pp. 17207–17215,  2014.
  93. F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon., vol. 3, pp. 1558–1563,  2016.
  94. B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett., vol. 41, pp. 3407–3410,  2016.
  95. T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express, vol. 17, pp. 9347–9356,  2009.
  96. C. Schulze, S. Ngcobo, M. Duparré, and A. Forbes, “Modal decomposition without a priori scale information,” Opt. Express, vol. 20, no. 25, pp. 27866–27873, 2012.
  97. I. a. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express, vol. 20, no. 10, pp. 10996–11004, 2012.
  98. C. Schulze, D. Flamm, A. Dudley, A. Forbes, and M. Duparré, “Modal decomposition for measuring the orbital angular momentum density of light,” Proc. SPIE, vol. 8637,  2013, Art. no. .
  99. Y. Li, J. Kim, and M. J. Escuti, “Orbital angular momentum generation and mode transformation with high efficiency using forked polarization gratings,” Appl. Opt., vol. 51, no. 34, pp. 8236–8245, 2012.
  100. 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., vol. 105,  2010, Art. no. .
  101. R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nature Commun., vol. 5,  2014, Art. no. .
  102. M. P. J. Laveryet al., “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys., vol. 15,  2013, Art. no. .
  103. A. Ferenczi and N. Lütkenhaus, “Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning,” Phys. Rev. A, vol. 85,  2012, Art. no. .
  104. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett., vol. 94, no. 15, 2005, Art. no. .
  105. M. Maliket al., “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express, vol. 20, no. 12, pp. 13195–13200, 2012.
  106. B. Rodenburget al., “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett., vol. 37, no. 17, pp. 3735–3737, 2012.
  107. S. K. Goyal, A. H. Ibrahim, F. S. Roux, T. Konrad, and A. Forbes, “The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum,” J. Opt., vol. 18, no. 6, 2016, Art. no. .
  108. C. Chen, H. Yang, S. Tong, and Y. Lou, “Changes in orbital-angular-momentum modes of a propagated vortex Gaussian beam through weak-to-strong atmospheric turbulence,” Opt. Express, vol. 24, no. 7, pp. 6959–6975, 2016.
  109. W. Wootters, “Entanglement of formation and concurrence,” Quantum Inf. Comput., vol. 1, no. 1, pp. 27–44, 2001.
  110. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, vol. 1, 2nd ed. Bellingham, WA, USA: SPIE,  2005.
  111. M. A. Cox, C. Rosales-Guzmán, M. P. J. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express, vol. 24, no. 16, pp. 18105–18113, 2016.

2017 (9)

A. E. Willneret al., “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Philos. Trans. Roy. Soc. A, Math., Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .

H. Rubinsztein-Dunlopet al., “Roadmap on structured light,” J. Opt., vol. 19,  2017, Art. no. .

J. Yinet al., “Satellite-based entanglement distribution over 1200 kilometers,” Science, vol. 356, no. 6343, pp. 1140–1144, 2017.

B. Ndaganoet al., “Characterizing quantum channels with non-separable states of classical light,” Nature Phys., vol. 13, pp. 397–402,  2017.

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes,” Philos. Trans. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .

B. Ndaganoet al., “A deterministic detector for vector vortex states,” Sci. Rep., vol. 7, 2017, Art. no. .

A. Sitet al., “High-dimensional intracity quantum cryptography with structured photons,” Optica, vol. 4, pp. 1006–1010,  2017.

A. Forbes, “Controlling light's helicity at the source: Orbital angular momentum states from lasers,” Philos. Trans. Roy. Soc. A, vol. 375, no. 2087, 2017, Art. no. .

R. C. Devlinet al., “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express, vol. 25, no. 1, pp. 377–393, 2017.

2016 (17)

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon., vol. 3, pp. 1558–1563,  2016.

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett., vol. 41, pp. 3407–3410,  2016.

S. K. Goyal, A. H. Ibrahim, F. S. Roux, T. Konrad, and A. Forbes, “The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum,” J. Opt., vol. 18, no. 6, 2016, Art. no. .

C. Chen, H. Yang, S. Tong, and Y. Lou, “Changes in orbital-angular-momentum modes of a propagated vortex Gaussian beam through weak-to-strong atmospheric turbulence,” Opt. Express, vol. 24, no. 7, pp. 6959–6975, 2016.

M. A. Cox, C. Rosales-Guzmán, M. P. J. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express, vol. 24, no. 16, pp. 18105–18113, 2016.

D. Naidooet al., “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nature Photon., vol. 10, pp. 327–332,  2016.

W. Shuet al., “Propagation model for vector beams generated by metasurfaces,” Opt. Express, vol. 24, no. 18, pp. 21177–21189, 2016.

P. Miaoet al., “Orbital angular momentum microlaser,” Science, vol. 353, pp. 464–467,  2016.

P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Lett., vol. 24, pp. 15143–15159,  2016.

R. Brüninget al., “Data transmission with twisted light through a free-space to fiber optical communication link,” J. Opt., vol. 18, no. 3, 2016, Art. no. .

B. Sephton, A. Dudley, and A. Forbes, “Revealing the radial modes in vortex beams,” Appl. Opt., vol. 55, no. 28, pp. 7830–7835, 2016.

D. Guzman-Silvaet al., “Demonstration of local teleportation using classical entanglement,” Laser Photon. Rev., vol. 10, no. 2, pp. 317–321,  2016.

J. Zhang, F. Li, J. Li, Y. Feng, and Z. Li, “120 Gbit/s 2 $\times$ 2 vector-modes-division- multiplexing DD-OFDM-32QAM free-space transmission,” IEEE Photon. J., vol. 8, no. 6,  2016, Art. no. .

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon., vol. 8, pp. 200–227,  2016.

Y. Renet al., “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett., vol. 41, pp. 622–625,  2016.

G. Xieet al., “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre–Gaussian beams with different radial indices,” Opt. Lett., vol. 41, pp. 3447–3450,  2016.

J. Wang, “Advances in communications using optical vortices,” Photon. Res., vol. 4, pp. B14–B28,  2016.

2015 (14)

A. Wang, L. Zhu, J. Liu, C. Du, Q. Mo, and J. Wang, “Demonstration of hybrid orbital angular momentum multiplexing and time-division multiplexing passive optical network,” Opt. Express, vol. 23, pp. 29457–29466,  2015.

A. E. Willneret al., “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon., vol. 7, no. 1, pp. 66–106, 2015.

Y. Zhao and J. Wang, “High-base vector beam encoding/decoding for visible-light communications,” Opt. Lett., vol. 40, pp. 4843–4846,  2015.

G. Milioneet al., “4 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett., vol. 40, no. 9, pp. 1980–1983, 2015.

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett., vol. 40, pp. 4887–4890,  2015.

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A, vol. 92, no. 2, 2015, Art. no. .

T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B. Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of entanglement over 143 km,” Proc. Nat. Acad. Sci. USA, vol. 112, no. 46, pp. 14202–14205, 2015.

E. Karimi and R. W. Boyd, “Classical entanglement?” Science, vol. 350, pp. 1172–1173,  2015.

M. Mirhosseiniet al., “High-dimensional quantum cryptography with twisted light,” New J. Phys., vol. 17,  2015, Art. no. .

B. Ndagano, R. Brüning, M. McLaren, M. Duparré, and A. Forbes, “Fiber propagation of vector modes,” Opt. Express, vol. 23, pp. 17330–17336,  2015.

P. Gregget al., “Q-plates as higher order polarization controllers for orbital angular momentum modes of fiber,” Opt. Lett., vol. 40, pp. 1729–1732,  2015.

K. A.-A. Darryl Naidoo, M. Fromager, and A. Forbes, “Radially polarized cylindrical vector beams from a monolithic microchip laser,” Opt. Eng., vol. 54, 2015, Art. no. .

Y.-X. Ren, Z.-X. Fang, L. Gong, K. Huang, Y. Chen, and R.-D. Lu, “Digital generation and control of Hermite–Gaussian modes with an amplitude digital micromirror device,” J. Opt., vol. 17,  2015, Art. no. .

S. Berg-Johansenet al., “Classically entangled optical beams for high-speed kinematic sensing,” Optica, vol. 2, no. 10, pp. 1–5, 2015.

2014 (9)

L. Gonget al., “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys., vol. 116, no. 18, 2014, Art. no. .

G. Valloneet al., “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett., vol. 113,  2014, Art. no. .

L. J. Pereira, A. Z. Khoury, and K. Dechoum, “Quantum and classical separability of spin-orbit laser modes,” Phys. Rev. A, vol. 90,  2014, Art. no. .

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys., vol. 16,  2014, Art. no. .

H. Huanget al., “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett., vol. 39, pp. 197–200,  2014.

Y. Yanet al., “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nature Commun., vol. 5,  2014, Art. no. .

M. Krennet al., “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys., vol. 16, no. 11, 2014, Art. no. .

X. Yiet al., “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express, vol. 22, pp. 17207–17215,  2014.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nature Commun., vol. 5,  2014, Art. no. .

2013 (8)

M. P. J. Laveryet al., “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys., vol. 15,  2013, Art. no. .

C. Schulze, D. Flamm, A. Dudley, A. Forbes, and M. Duparré, “Modal decomposition for measuring the orbital angular momentum density of light,” Proc. SPIE, vol. 8637,  2013, Art. no. .

Z. Zhao, J. Wang, S. Li, and A. E. Willner, “Metamaterials-based broadband generation of orbital angular momentum carrying vector beams,” Opt. Lett., vol. 38, pp. 932–934,  2013.

N. Bozinovicet al., “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science, vol. 340, no. 6140, pp. 1545–1548, 2013.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon., vol. 7, pp. 354–362,  2013.

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett., vol. 38, pp. 3429–3432,  2013.

M. Mafuet al., “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A, vol. 88,  2013, Art. no. .

V. D’Ambrosioet al., “Photonic polarization gears for ultra-sensitive angular measurements,” Nature Commun., vol. 4,  2013, Art. no. .

2012 (11)

X. Caiet al., “Integrated compact optical vortex beam emitters,” Science, vol. 338, pp. 363–366,  2012.

I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express, vol. 20, no. 1, pp. 364–376, 2012.

J. Wanget al., “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon., vol. 6, no. 7, pp. 488–496, 2012.

V. Sleifferet al., “737 Tb/s ($\text{96} \times \text{3} \times$ 256-Gb/s) mode-division-multiplexed DP-16QAM transmission with inline MM-EDFA,” Opt. Express, vol. 20, pp. B428–B438,  2012.

X.-S. Maet al., “Quantum teleportation over 143 kilometres using active feed-forward,” Nature, vol. 489, no. 7415, pp. 269–273, 2012.

C. Schulze, S. Ngcobo, M. Duparré, and A. Forbes, “Modal decomposition without a priori scale information,” Opt. Express, vol. 20, no. 25, pp. 27866–27873, 2012.

I. a. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express, vol. 20, no. 10, pp. 10996–11004, 2012.

Y. Li, J. Kim, and M. J. Escuti, “Orbital angular momentum generation and mode transformation with high efficiency using forked polarization gratings,” Appl. Opt., vol. 51, no. 34, pp. 8236–8245, 2012.

M. Maliket al., “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express, vol. 20, no. 12, pp. 13195–13200, 2012.

B. Rodenburget al., “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett., vol. 37, no. 17, pp. 3735–3737, 2012.

A. Ferenczi and N. Lütkenhaus, “Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning,” Phys. Rev. A, vol. 85,  2012, Art. no. .

2011 (4)

L. Marrucciet al., “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt., vol. 13,  2011, Art. no. .

R. Keil, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, and A. Szameit, “Classical characterization of biphoton correlation in waveguide lattices,” Phys. Rev. A, vol. 83,  2011, Art. no. .

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express, vol. 19, no. 13, pp. 119163–119168, 2011.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett., vol. 107,  2011, Art. no. .

2010 (5)

E. Karimiet al., “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A, vol. 82,  2010, Art. no. .

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A, vol. 81,  2010, Art. no. .

G. M. Lerman, L. Stern, and U. Levy, “Generation and tight focusing of hybridly polarized vector beams,” Opt. Express, vol. 18, no. 26, pp. 27650–27657, 2010.

L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A, vol. 82,  2010, Art. no. .

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., vol. 105,  2010, Art. no. .

2009 (4)

2008 (1)

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A, vol. 77,  2008, Art. no. .

2007 (4)

C.-Z. Penget al., “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett., vol. 98,  2007, Art. no. .

H. Hübelet al., “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express, vol. 15, no. 12, pp. 7853–7862, 2007.

R. Ursinet al., “Entanglement-based quantum communication over 144 km,” Nature Phys., vol. 3, pp. 481–486,  2007.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys., vol. 9, 2007, Art. no. .

2006 (2)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett., vol. 96,  2006, Art. no. .

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys., vol. 8, pp. 75–83,  2006.

2005 (2)

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun., vol. 251, pp. 306–314,  2005.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett., vol. 94, no. 15, 2005, Art. no. .

2004 (2)

2003 (2)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett., vol. 82, no. 3, pp. 328–330, 2003.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett., vol. 90,  2003, Art. no. .

2002 (4)

2001 (2)

2000 (2)

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett., vol. 84, no. 20, pp. 4729–4732, 2000.

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A, vol. 61,  2000, Art. no. .

1999 (1)

1998 (1)

R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys., vol. 28, pp. 361–374, 1998.

1984 (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 392, no. 1802, pp. 45–57, 1984.

1982 (1)

1956 (1)

S. Pancharatnam, “Generalized theory of interference and its applications. Partially coherent pencils,” Proc. Indian Acad. Sci., Sect. A, vol. 44, pp. 247–262, 1956.

Aiello, A.

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys., vol. 16,  2014, Art. no. .

Alfano, R. R.

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett., vol. 40, pp. 4887–4890,  2015.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett., vol. 107,  2011, Art. no. .

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, vol. 1, 2nd ed. Bellingham, WA, USA: SPIE,  2005.

Aolita, L.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A, vol. 77,  2008, Art. no. .

Bechmann-Pasquinucci, H.

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A, vol. 61,  2000, Art. no. .

Beijersbergen, M. W.

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., vol. 105,  2010, Art. no. .

Berdagué, S.

Berg-Johansen, S.

Berkhout, G. C. G.

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., vol. 105,  2010, Art. no. .

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys., vol. 9, 2007, Art. no. .

Berry, M. V.

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 392, no. 1802, pp. 45–57, 1984.

Biener, G.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun., vol. 251, pp. 306–314,  2005.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett., vol. 82, no. 3, pp. 328–330, 2003.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam–Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett., vol. 27, no. 13, pp. 1141–1143, 2002.

G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam–Berry phase optical elements,” Opt. Lett., vol. 27, pp. 1875–1857,  2002.

Bomzon, Z.

Borges, C. V. S.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A, vol. 77,  2008, Art. no. .

Bourennane, M.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett., vol. 88,  2002, Art. no. .

Boyd, R. W.

E. Karimi and R. W. Boyd, “Classical entanglement?” Science, vol. 350, pp. 1172–1173,  2015.

Bozinovic, N.

N. Bozinovicet al., “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science, vol. 340, no. 6140, pp. 1545–1548, 2013.

Bromberg, Y.

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide Lattices,” Phys. Rev. Lett., vol. 102,  2009, Art. no. .

Brüning, R.

R. Brüninget al., “Data transmission with twisted light through a free-space to fiber optical communication link,” J. Opt., vol. 18, no. 3, 2016, Art. no. .

B. Ndagano, R. Brüning, M. McLaren, M. Duparré, and A. Forbes, “Fiber propagation of vector modes,” Opt. Express, vol. 23, pp. 17330–17336,  2015.

Cai, X.

X. Caiet al., “Integrated compact optical vortex beam emitters,” Science, vol. 338, pp. 363–366,  2012.

Cerf, N. J.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett., vol. 88,  2002, Art. no. .

Chen, C.

Chen, X.

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon., vol. 3, pp. 1558–1563,  2016.

Chen, Y.

Y.-X. Ren, Z.-X. Fang, L. Gong, K. Huang, Y. Chen, and R.-D. Lu, “Digital generation and control of Hermite–Gaussian modes with an amplitude digital micromirror device,” J. Opt., vol. 17,  2015, Art. no. .

Cottrell, D. M.

Courtial, J.

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., vol. 105,  2010, Art. no. .

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett., vol. 24, pp. 430–432,  1999.

Cox, M. A.

Crawford, P. R.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett., vol. 90,  2003, Art. no. .

D’Ambrosio, V.

V. D’Ambrosioet al., “Photonic polarization gears for ultra-sensitive angular measurements,” Nature Commun., vol. 4,  2013, Art. no. .

Davis, J. A.

Dechoum, K.

L. J. Pereira, A. Z. Khoury, and K. Dechoum, “Quantum and classical separability of spin-orbit laser modes,” Phys. Rev. A, vol. 90,  2014, Art. no. .

Devlin, R. C.

Dreisow, F.

R. Keil, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, and A. Szameit, “Classical characterization of biphoton correlation in waveguide lattices,” Phys. Rev. A, vol. 83,  2011, Art. no. .

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A, vol. 81,  2010, Art. no. .

Du, C.

Dudley, A.

Duparré, M.

Erhard, M.

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes,” Philos. Trans. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .

Escuti, M.

Escuti, M. J.

Facq, P.

Fang, Z.-X.

Y.-X. Ren, Z.-X. Fang, L. Gong, K. Huang, Y. Chen, and R.-D. Lu, “Digital generation and control of Hermite–Gaussian modes with an amplitude digital micromirror device,” J. Opt., vol. 17,  2015, Art. no. .

Feng, Y.

J. Zhang, F. Li, J. Li, Y. Feng, and Z. Li, “120 Gbit/s 2 $\times$ 2 vector-modes-division- multiplexing DD-OFDM-32QAM free-space transmission,” IEEE Photon. J., vol. 8, no. 6,  2016, Art. no. .

Ferenczi, A.

A. Ferenczi and N. Lütkenhaus, “Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning,” Phys. Rev. A, vol. 85,  2012, Art. no. .

Fickler, R.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nature Commun., vol. 5,  2014, Art. no. .

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon., vol. 7, pp. 354–362,  2013.

Fink, M.

T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B. Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of entanglement over 143 km,” Proc. Nat. Acad. Sci. USA, vol. 112, no. 46, pp. 14202–14205, 2015.

Flamm, D.

C. Schulze, D. Flamm, A. Dudley, A. Forbes, and M. Duparré, “Modal decomposition for measuring the orbital angular momentum density of light,” Proc. SPIE, vol. 8637,  2013, Art. no. .

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express, vol. 17, pp. 9347–9356,  2009.

Forbes, A.

A. Forbes, “Controlling light's helicity at the source: Orbital angular momentum states from lasers,” Philos. Trans. Roy. Soc. A, vol. 375, no. 2087, 2017, Art. no. .

S. K. Goyal, A. H. Ibrahim, F. S. Roux, T. Konrad, and A. Forbes, “The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum,” J. Opt., vol. 18, no. 6, 2016, Art. no. .

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon., vol. 8, pp. 200–227,  2016.

B. Sephton, A. Dudley, and A. Forbes, “Revealing the radial modes in vortex beams,” Appl. Opt., vol. 55, no. 28, pp. 7830–7835, 2016.

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett., vol. 41, pp. 3407–3410,  2016.

M. A. Cox, C. Rosales-Guzmán, M. P. J. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express, vol. 24, no. 16, pp. 18105–18113, 2016.

B. Ndagano, R. Brüning, M. McLaren, M. Duparré, and A. Forbes, “Fiber propagation of vector modes,” Opt. Express, vol. 23, pp. 17330–17336,  2015.

K. A.-A. Darryl Naidoo, M. Fromager, and A. Forbes, “Radially polarized cylindrical vector beams from a monolithic microchip laser,” Opt. Eng., vol. 54, 2015, Art. no. .

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A, vol. 92, no. 2, 2015, Art. no. .

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett., vol. 38, pp. 3429–3432,  2013.

C. Schulze, D. Flamm, A. Dudley, A. Forbes, and M. Duparré, “Modal decomposition for measuring the orbital angular momentum density of light,” Proc. SPIE, vol. 8637,  2013, Art. no. .

C. Schulze, S. Ngcobo, M. Duparré, and A. Forbes, “Modal decomposition without a priori scale information,” Opt. Express, vol. 20, no. 25, pp. 27866–27873, 2012.

I. a. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express, vol. 20, no. 10, pp. 10996–11004, 2012.

C. Rosales-Guzmán and A. Forbes, How to Shape Light With Spatial Light Modulators, vol. SL30. Bellingham, WA, USA: SPIE Press, 2017.

Fromager, M.

K. A.-A. Darryl Naidoo, M. Fromager, and A. Forbes, “Radially polarized cylindrical vector beams from a monolithic microchip laser,” Opt. Eng., vol. 54, 2015, Art. no. .

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys., vol. 9, 2007, Art. no. .

Galvez, E. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett., vol. 90,  2003, Art. no. .

Gerardot, B. D.

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon., vol. 3, pp. 1558–1563,  2016.

Giacobino, E.

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys., vol. 16,  2014, Art. no. .

Gibson, G.

Gisin, N.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett., vol. 88,  2002, Art. no. .

Gong, L.

Y.-X. Ren, Z.-X. Fang, L. Gong, K. Huang, Y. Chen, and R.-D. Lu, “Digital generation and control of Hermite–Gaussian modes with an amplitude digital micromirror device,” J. Opt., vol. 17,  2015, Art. no. .

L. Gonget al., “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys., vol. 116, no. 18, 2014, Art. no. .

Goyal, S. K.

S. K. Goyal, A. H. Ibrahim, F. S. Roux, T. Konrad, and A. Forbes, “The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum,” J. Opt., vol. 18, no. 6, 2016, Art. no. .

Gregg, P.

Gröblacher, S.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys., vol. 8, pp. 75–83,  2006.

Guzman-Silva, D.

D. Guzman-Silvaet al., “Demonstration of local teleportation using classical entanglement,” Laser Photon. Rev., vol. 10, no. 2, pp. 317–321,  2016.

Haglin, P. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett., vol. 90,  2003, Art. no. .

Handsteiner, J.

T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B. Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of entanglement over 143 km,” Proc. Nat. Acad. Sci. USA, vol. 112, no. 46, pp. 14202–14205, 2015.

Hasman, E.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun., vol. 251, pp. 306–314,  2005.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett., vol. 82, no. 3, pp. 328–330, 2003.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam–Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett., vol. 27, no. 13, pp. 1141–1143, 2002.

G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam–Berry phase optical elements,” Opt. Lett., vol. 27, pp. 1875–1857,  2002.

Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett., vol. 26, no. 18, pp. 1424–1426, 2001.

Hayashi, T.

Heinrich, M.

R. Keil, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, and A. Szameit, “Classical characterization of biphoton correlation in waveguide lattices,” Phys. Rev. A, vol. 83,  2011, Art. no. .

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A, vol. 81,  2010, Art. no. .

Herbst, T.

T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B. Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of entanglement over 143 km,” Proc. Nat. Acad. Sci. USA, vol. 112, no. 46, pp. 14202–14205, 2015.

Hernandez, T. M.

Huang, H.

Huang, K.

Y.-X. Ren, Z.-X. Fang, L. Gong, K. Huang, Y. Chen, and R.-D. Lu, “Digital generation and control of Hermite–Gaussian modes with an amplitude digital micromirror device,” J. Opt., vol. 17,  2015, Art. no. .

Hübel, H.

Huber, M.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nature Commun., vol. 5,  2014, Art. no. .

Huguenin, J. A. O.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A, vol. 77,  2008, Art. no. .

Ibrahim, A. H.

S. K. Goyal, A. H. Ibrahim, F. S. Roux, T. Konrad, and A. Forbes, “The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum,” J. Opt., vol. 18, no. 6, 2016, Art. no. .

Iwahashi, S.

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express, vol. 19, no. 13, pp. 119163–119168, 2011.

Jennewein, T.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys., vol. 8, pp. 75–83,  2006.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett., vol. 84, no. 20, pp. 4729–4732, 2000.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys., vol. 9, 2007, Art. no. .

Juskaitis, R.

Kaiser, T.

Karimi, E.

E. Karimi and R. W. Boyd, “Classical entanglement?” Science, vol. 350, pp. 1172–1173,  2015.

E. Karimiet al., “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A, vol. 82,  2010, Art. no. .

Karlsson, A.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett., vol. 88,  2002, Art. no. .

Keil, R.

R. Keil, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, and A. Szameit, “Classical characterization of biphoton correlation in waveguide lattices,” Phys. Rev. A, vol. 83,  2011, Art. no. .

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A, vol. 81,  2010, Art. no. .

Keiser, G.

G. Keiser, Optical Fiber Communications. (McGraw-Hill Series in Electrical and Computer Engineering: Communications and Signal Processing), 3rd ed. New York, NY, USA: McGraw-Hill, 2000.

Khoury, A. Z.

L. J. Pereira, A. Z. Khoury, and K. Dechoum, “Quantum and classical separability of spin-orbit laser modes,” Phys. Rev. A, vol. 90,  2014, Art. no. .

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A, vol. 77,  2008, Art. no. .

Kim, J.

Kitamura, K.

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express, vol. 19, no. 13, pp. 119163–119168, 2011.

Kleiner, V.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun., vol. 251, pp. 306–314,  2005.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett., vol. 82, no. 3, pp. 328–330, 2003.

G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam–Berry phase optical elements,” Opt. Lett., vol. 27, pp. 1875–1857,  2002.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam–Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett., vol. 27, no. 13, pp. 1141–1143, 2002.

Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett., vol. 26, no. 18, pp. 1424–1426, 2001.

Konrad, T.

S. K. Goyal, A. H. Ibrahim, F. S. Roux, T. Konrad, and A. Forbes, “The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum,” J. Opt., vol. 18, no. 6, 2016, Art. no. .

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A, vol. 92, no. 2, 2015, Art. no. .

Krenn, M.

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes,” Philos. Trans. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .

M. Krennet al., “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys., vol. 16, no. 11, 2014, Art. no. .

Kurosaka, Y.

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express, vol. 19, no. 13, pp. 119163–119168, 2011.

Lahini, Y.

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide Lattices,” Phys. Rev. Lett., vol. 102,  2009, Art. no. .

Lapkiewicz, R.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nature Commun., vol. 5,  2014, Art. no. .

Lavery, M. P.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nature Commun., vol. 5,  2014, Art. no. .

Lavery, M. P. J.

M. A. Cox, C. Rosales-Guzmán, M. P. J. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express, vol. 24, no. 16, pp. 18105–18113, 2016.

M. P. J. Laveryet al., “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys., vol. 15,  2013, Art. no. .

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., vol. 105,  2010, Art. no. .

M. P. J. Laveryet al., “Space division multiplexing in a basis of vector modes,” in Proc. Eur. Conf. Opt. Commun.,  2014, pp. 1–3.

Leach, J.

Lerman, G. M.

Leuchs, G.

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys., vol. 16,  2014, Art. no. .

Levy, U.

Li, F.

J. Zhang, F. Li, J. Li, Y. Feng, and Z. Li, “120 Gbit/s 2 $\times$ 2 vector-modes-division- multiplexing DD-OFDM-32QAM free-space transmission,” IEEE Photon. J., vol. 8, no. 6,  2016, Art. no. .

Li, J.

J. Zhang, F. Li, J. Li, Y. Feng, and Z. Li, “120 Gbit/s 2 $\times$ 2 vector-modes-division- multiplexing DD-OFDM-32QAM free-space transmission,” IEEE Photon. J., vol. 8, no. 6,  2016, Art. no. .

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon., vol. 3, pp. 1558–1563,  2016.

Li, P.

P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Lett., vol. 24, pp. 15143–15159,  2016.

Li, S.

Li, Y.

Li, Z.

J. Zhang, F. Li, J. Li, Y. Feng, and Z. Li, “120 Gbit/s 2 $\times$ 2 vector-modes-division- multiplexing DD-OFDM-32QAM free-space transmission,” IEEE Photon. J., vol. 8, no. 6,  2016, Art. no. .

Litvin, I. a.

Liu, J.

Lou, Y.

Lu, R.-D.

Y.-X. Ren, Z.-X. Fang, L. Gong, K. Huang, Y. Chen, and R.-D. Lu, “Digital generation and control of Hermite–Gaussian modes with an amplitude digital micromirror device,” J. Opt., vol. 17,  2015, Art. no. .

Lütkenhaus, N.

A. Ferenczi and N. Lütkenhaus, “Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning,” Phys. Rev. A, vol. 85,  2012, Art. no. .

Ma, X.-S.

X.-S. Maet al., “Quantum teleportation over 143 kilometres using active feed-forward,” Nature, vol. 489, no. 7415, pp. 269–273, 2012.

Mafu, M.

M. Mafuet al., “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A, vol. 88,  2013, Art. no. .

Malik, M.

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes,” Philos. Trans. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .

M. Maliket al., “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express, vol. 20, no. 12, pp. 13195–13200, 2012.

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett., vol. 96,  2006, Art. no. .

Marquardt, C.

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys., vol. 16,  2014, Art. no. .

Marrucci, L.

L. Marrucciet al., “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt., vol. 13,  2011, Art. no. .

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett., vol. 96,  2006, Art. no. .

Massoumian, F.

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys., vol. 9, 2007, Art. no. .

McLaren, M.

Mhlanga, T.

Miao, P.

P. Miaoet al., “Orbital angular momentum microlaser,” Science, vol. 353, pp. 464–467,  2016.

Michihata, M.

Milione, G.

Mirhosseini, M.

M. Mirhosseiniet al., “High-dimensional quantum cryptography with twisted light,” New J. Phys., vol. 17,  2015, Art. no. .

Mo, Q.

Morandotti, R.

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide Lattices,” Phys. Rev. Lett., vol. 102,  2009, Art. no. .

Moreno, I.

Naidoo, D.

D. Naidooet al., “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nature Photon., vol. 10, pp. 327–332,  2016.

Naidoo, K. A.-A. Darryl

K. A.-A. Darryl Naidoo, M. Fromager, and A. Forbes, “Radially polarized cylindrical vector beams from a monolithic microchip laser,” Opt. Eng., vol. 54, 2015, Art. no. .

Ndagano, B.

B. Ndaganoet al., “Characterizing quantum channels with non-separable states of classical light,” Nature Phys., vol. 13, pp. 397–402,  2017.

B. Ndaganoet al., “A deterministic detector for vector vortex states,” Sci. Rep., vol. 7, 2017, Art. no. .

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett., vol. 41, pp. 3407–3410,  2016.

B. Ndagano, R. Brüning, M. McLaren, M. Duparré, and A. Forbes, “Fiber propagation of vector modes,” Opt. Express, vol. 23, pp. 17330–17336,  2015.

Neil, M. A. A.

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon., vol. 7, pp. 354–362,  2013.

Ngcobo, S.

Nguyen, T. A.

Niv, A.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun., vol. 251, pp. 306–314,  2005.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett., vol. 82, no. 3, pp. 328–330, 2003.

G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam–Berry phase optical elements,” Opt. Lett., vol. 27, pp. 1875–1857,  2002.

Noda, S.

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express, vol. 19, no. 13, pp. 119163–119168, 2011.

Nolan, D. A.

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett., vol. 40, pp. 4887–4890,  2015.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett., vol. 107,  2011, Art. no. .

Nolte, S.

R. Keil, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, and A. Szameit, “Classical characterization of biphoton correlation in waveguide lattices,” Phys. Rev. A, vol. 83,  2011, Art. no. .

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A, vol. 81,  2010, Art. no. .

Padgett, M. J.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nature Commun., vol. 5,  2014, Art. no. .

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., vol. 105,  2010, Art. no. .

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett., vol. 24, pp. 430–432,  1999.

Pancharatnam, S.

S. Pancharatnam, “Generalized theory of interference and its applications. Partially coherent pencils,” Proc. Indian Acad. Sci., Sect. A, vol. 44, pp. 247–262, 1956.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett., vol. 96,  2006, Art. no. .

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett., vol. 94, no. 15, 2005, Art. no. .

Peng, C.-Z.

C.-Z. Penget al., “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett., vol. 98,  2007, Art. no. .

Pereira, L. J.

L. J. Pereira, A. Z. Khoury, and K. Dechoum, “Quantum and classical separability of spin-orbit laser modes,” Phys. Rev. A, vol. 90,  2014, Art. no. .

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, vol. 1, 2nd ed. Bellingham, WA, USA: SPIE,  2005.

Poppe, A.

Pysher, M. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett., vol. 90,  2003, Art. no. .

Ren, Y.

Ren, Y.-X.

Y.-X. Ren, Z.-X. Fang, L. Gong, K. Huang, Y. Chen, and R.-D. Lu, “Digital generation and control of Hermite–Gaussian modes with an amplitude digital micromirror device,” J. Opt., vol. 17,  2015, Art. no. .

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon., vol. 7, pp. 354–362,  2013.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys., vol. 9, 2007, Art. no. .

Rodenburg, B.

Rosales-Guzmán, C.

Roux, F. S.

S. K. Goyal, A. H. Ibrahim, F. S. Roux, T. Konrad, and A. Forbes, “The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum,” J. Opt., vol. 18, no. 6, 2016, Art. no. .

I. a. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express, vol. 20, no. 10, pp. 10996–11004, 2012.

Rubinsztein-Dunlop, H.

H. Rubinsztein-Dunlopet al., “Roadmap on structured light,” J. Opt., vol. 19,  2017, Art. no. .

Sakai, K.

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express, vol. 19, no. 13, pp. 119163–119168, 2011.

Sand, D.

Scarani, V.

L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A, vol. 82,  2010, Art. no. .

Scheidl, T.

T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B. Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of entanglement over 143 km,” Proc. Nat. Acad. Sci. USA, vol. 112, no. 46, pp. 14202–14205, 2015.

Schröter, S.

Schulze, C.

C. Schulze, D. Flamm, A. Dudley, A. Forbes, and M. Duparré, “Modal decomposition for measuring the orbital angular momentum density of light,” Proc. SPIE, vol. 8637,  2013, Art. no. .

C. Schulze, S. Ngcobo, M. Duparré, and A. Forbes, “Modal decomposition without a priori scale information,” Opt. Express, vol. 20, no. 25, pp. 27866–27873, 2012.

Sephton, B.

Sheridan, L.

L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A, vol. 82,  2010, Art. no. .

Shu, W.

Silberberg, Y.

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide Lattices,” Phys. Rev. Lett., vol. 102,  2009, Art. no. .

Simon, C.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett., vol. 84, no. 20, pp. 4729–4732, 2000.

Sit, A.

Sleiffer, V.

Souza, C. E. R.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A, vol. 77,  2008, Art. no. .

Spreeuw, R. J. C.

R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys., vol. 28, pp. 361–374, 1998.

Sroor, H.

Stern, L.

Szameit, A.

R. Keil, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, and A. Szameit, “Classical characterization of biphoton correlation in waveguide lattices,” Phys. Rev. A, vol. 83,  2011, Art. no. .

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A, vol. 81,  2010, Art. no. .

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett., vol. 107,  2011, Art. no. .

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett., vol. 90,  2003, Art. no. .

Takaya, Y.

Takayama, N.

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express, vol. 19, no. 13, pp. 119163–119168, 2011.

Tittel, W.

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A, vol. 61,  2000, Art. no. .

Tong, S.

Töppel, F.

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys., vol. 16,  2014, Art. no. .

Tünnermann, A.

R. Keil, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, and A. Szameit, “Classical characterization of biphoton correlation in waveguide lattices,” Phys. Rev. A, vol. 83,  2011, Art. no. .

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A, vol. 81,  2010, Art. no. .

Ursin, R.

T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B. Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of entanglement over 143 km,” Proc. Nat. Acad. Sci. USA, vol. 112, no. 46, pp. 14202–14205, 2015.

R. Ursinet al., “Entanglement-based quantum communication over 144 km,” Nature Phys., vol. 3, pp. 481–486,  2007.

Vallone, G.

G. Valloneet al., “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett., vol. 113,  2014, Art. no. .

Vaziri, A.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys., vol. 8, pp. 75–83,  2006.

Versfeld, D. J.

Walborn, S. P.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A, vol. 77,  2008, Art. no. .

Wang, A.

Wang, B.

P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Lett., vol. 24, pp. 15143–15159,  2016.

Wang, J.

Weihs, G.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys., vol. 8, pp. 75–83,  2006.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett., vol. 84, no. 20, pp. 4729–4732, 2000.

Weinfurter, H.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett., vol. 84, no. 20, pp. 4729–4732, 2000.

Wen, D.

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon., vol. 3, pp. 1558–1563,  2016.

Williams, R. E.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett., vol. 90,  2003, Art. no. .

Willner, A. E.

A. E. Willneret al., “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Philos. Trans. Roy. Soc. A, Math., Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .

A. E. Willneret al., “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon., vol. 7, no. 1, pp. 66–106, 2015.

Z. Zhao, J. Wang, S. Li, and A. E. Willner, “Metamaterials-based broadband generation of orbital angular momentum carrying vector beams,” Opt. Lett., vol. 38, pp. 932–934,  2013.

Wilson, T.

Wittmann, B.

T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B. Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of entanglement over 143 km,” Proc. Nat. Acad. Sci. USA, vol. 112, no. 46, pp. 14202–14205, 2015.

Wootters, W.

W. Wootters, “Entanglement of formation and concurrence,” Quantum Inf. Comput., vol. 1, no. 1, pp. 27–44, 2001.

Xie, G.

Xin, J.

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon., vol. 3, pp. 1558–1563,  2016.

Yan, Y.

Y. Yanet al., “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nature Commun., vol. 5,  2014, Art. no. .

Yang, H.

Yi, X.

Yin, J.

J. Yinet al., “Satellite-based entanglement distribution over 1200 kilometers,” Science, vol. 356, no. 6343, pp. 1140–1144, 2017.

Yue, F.

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon., vol. 3, pp. 1558–1563,  2016.

Zeilinger, A.

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes,” Philos. Trans. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .

T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B. Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of entanglement over 143 km,” Proc. Nat. Acad. Sci. USA, vol. 112, no. 46, pp. 14202–14205, 2015.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nature Commun., vol. 5,  2014, Art. no. .

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys., vol. 8, pp. 75–83,  2006.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett., vol. 84, no. 20, pp. 4729–4732, 2000.

Zhan, Q.

Zhang, J.

J. Zhang, F. Li, J. Li, Y. Feng, and Z. Li, “120 Gbit/s 2 $\times$ 2 vector-modes-division- multiplexing DD-OFDM-32QAM free-space transmission,” IEEE Photon. J., vol. 8, no. 6,  2016, Art. no. .

Zhang, X.

P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Lett., vol. 24, pp. 15143–15159,  2016.

Zhao, Y.

Zhao, Z.

Zhu, L.

ACS Photon. (1)

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon., vol. 3, pp. 1558–1563,  2016.

Adv. Opt. Photon. (3)

Appl. Opt. (4)

Appl. Phys. Lett. (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett., vol. 82, no. 3, pp. 328–330, 2003.

Found. Phys. (1)

R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys., vol. 28, pp. 361–374, 1998.

IEEE Photon. J. (1)

J. Zhang, F. Li, J. Li, Y. Feng, and Z. Li, “120 Gbit/s 2 $\times$ 2 vector-modes-division- multiplexing DD-OFDM-32QAM free-space transmission,” IEEE Photon. J., vol. 8, no. 6,  2016, Art. no. .

J. Appl. Phys. (1)

L. Gonget al., “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys., vol. 116, no. 18, 2014, Art. no. .

J. Opt. (5)

Y.-X. Ren, Z.-X. Fang, L. Gong, K. Huang, Y. Chen, and R.-D. Lu, “Digital generation and control of Hermite–Gaussian modes with an amplitude digital micromirror device,” J. Opt., vol. 17,  2015, Art. no. .

L. Marrucciet al., “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt., vol. 13,  2011, Art. no. .

S. K. Goyal, A. H. Ibrahim, F. S. Roux, T. Konrad, and A. Forbes, “The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum,” J. Opt., vol. 18, no. 6, 2016, Art. no. .

R. Brüninget al., “Data transmission with twisted light through a free-space to fiber optical communication link,” J. Opt., vol. 18, no. 3, 2016, Art. no. .

H. Rubinsztein-Dunlopet al., “Roadmap on structured light,” J. Opt., vol. 19,  2017, Art. no. .

Laser Photon. Rev. (1)

D. Guzman-Silvaet al., “Demonstration of local teleportation using classical entanglement,” Laser Photon. Rev., vol. 10, no. 2, pp. 317–321,  2016.

Nature (1)

X.-S. Maet al., “Quantum teleportation over 143 kilometres using active feed-forward,” Nature, vol. 489, no. 7415, pp. 269–273, 2012.

Nature Commun. (3)

Y. Yanet al., “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nature Commun., vol. 5,  2014, Art. no. .

V. D’Ambrosioet al., “Photonic polarization gears for ultra-sensitive angular measurements,” Nature Commun., vol. 4,  2013, Art. no. .

R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nature Commun., vol. 5,  2014, Art. no. .

Nature Photon. (3)

D. Naidooet al., “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nature Photon., vol. 10, pp. 327–332,  2016.

J. Wanget al., “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon., vol. 6, no. 7, pp. 488–496, 2012.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon., vol. 7, pp. 354–362,  2013.

Nature Phys. (2)

R. Ursinet al., “Entanglement-based quantum communication over 144 km,” Nature Phys., vol. 3, pp. 481–486,  2007.

B. Ndaganoet al., “Characterizing quantum channels with non-separable states of classical light,” Nature Phys., vol. 13, pp. 397–402,  2017.

New J. Phys. (6)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys., vol. 8, pp. 75–83,  2006.

M. Krennet al., “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys., vol. 16, no. 11, 2014, Art. no. .

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys., vol. 9, 2007, Art. no. .

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys., vol. 16,  2014, Art. no. .

M. Mirhosseiniet al., “High-dimensional quantum cryptography with twisted light,” New J. Phys., vol. 17,  2015, Art. no. .

M. P. J. Laveryet al., “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys., vol. 15,  2013, Art. no. .

Opt. Commun. (1)

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun., vol. 251, pp. 306–314,  2005.

Opt. Eng. (1)

K. A.-A. Darryl Naidoo, M. Fromager, and A. Forbes, “Radially polarized cylindrical vector beams from a monolithic microchip laser,” Opt. Eng., vol. 54, 2015, Art. no. .

Opt. Express (18)

W. Shuet al., “Propagation model for vector beams generated by metasurfaces,” Opt. Express, vol. 24, no. 18, pp. 21177–21189, 2016.

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express, vol. 19, no. 13, pp. 119163–119168, 2011.

I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express, vol. 20, no. 1, pp. 364–376, 2012.

B. Ndagano, R. Brüning, M. McLaren, M. Duparré, and A. Forbes, “Fiber propagation of vector modes,” Opt. Express, vol. 23, pp. 17330–17336,  2015.

A. Wang, L. Zhu, J. Liu, C. Du, Q. Mo, and J. Wang, “Demonstration of hybrid orbital angular momentum multiplexing and time-division multiplexing passive optical network,” Opt. Express, vol. 23, pp. 29457–29466,  2015.

H. Hübelet al., “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express, vol. 15, no. 12, pp. 7853–7862, 2007.

V. Sleifferet al., “737 Tb/s ($\text{96} \times \text{3} \times$ 256-Gb/s) mode-division-multiplexed DP-16QAM transmission with inline MM-EDFA,” Opt. Express, vol. 20, pp. B428–B438,  2012.

G. Gibsonet al., “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express, vol. 12, no. 22, pp. 5448–5456, 2004.

A. Poppeet al., “Practical quantum key distribution with polarization entangled photons,” Opt. Express, vol. 12, no. 16, pp. 3865–3871, 2004.

R. C. Devlinet al., “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express, vol. 25, no. 1, pp. 377–393, 2017.

G. M. Lerman, L. Stern, and U. Levy, “Generation and tight focusing of hybridly polarized vector beams,” Opt. Express, vol. 18, no. 26, pp. 27650–27657, 2010.

X. Yiet al., “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express, vol. 22, pp. 17207–17215,  2014.

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express, vol. 17, pp. 9347–9356,  2009.

C. Schulze, S. Ngcobo, M. Duparré, and A. Forbes, “Modal decomposition without a priori scale information,” Opt. Express, vol. 20, no. 25, pp. 27866–27873, 2012.

I. a. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express, vol. 20, no. 10, pp. 10996–11004, 2012.

C. Chen, H. Yang, S. Tong, and Y. Lou, “Changes in orbital-angular-momentum modes of a propagated vortex Gaussian beam through weak-to-strong atmospheric turbulence,” Opt. Express, vol. 24, no. 7, pp. 6959–6975, 2016.

M. Maliket al., “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express, vol. 20, no. 12, pp. 13195–13200, 2012.

M. A. Cox, C. Rosales-Guzmán, M. P. J. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express, vol. 24, no. 16, pp. 18105–18113, 2016.

Opt. Lett. (17)

B. Rodenburget al., “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett., vol. 37, no. 17, pp. 3735–3737, 2012.

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett., vol. 41, pp. 3407–3410,  2016.

Z. Zhao, J. Wang, S. Li, and A. E. Willner, “Metamaterials-based broadband generation of orbital angular momentum carrying vector beams,” Opt. Lett., vol. 38, pp. 932–934,  2013.

Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett., vol. 26, no. 18, pp. 1424–1426, 2001.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam–Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett., vol. 27, no. 13, pp. 1141–1143, 2002.

G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam–Berry phase optical elements,” Opt. Lett., vol. 27, pp. 1875–1857,  2002.

M. A. A. Neil, F. Massoumian, R. Juskaitis, and T. Wilson, “Method for the generation of arbitrary complex vector wave fronts,” Opt. Lett., vol. 27, no. 21, pp. 1929–1931, 2002.

H. Huanget al., “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett., vol. 39, pp. 197–200,  2014.

Y. Renet al., “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett., vol. 41, pp. 622–625,  2016.

G. Xieet al., “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre–Gaussian beams with different radial indices,” Opt. Lett., vol. 41, pp. 3447–3450,  2016.

P. Gregget al., “Q-plates as higher order polarization controllers for orbital angular momentum modes of fiber,” Opt. Lett., vol. 40, pp. 1729–1732,  2015.

Y. Zhao and J. Wang, “High-base vector beam encoding/decoding for visible-light communications,” Opt. Lett., vol. 40, pp. 4843–4846,  2015.

G. Milioneet al., “4 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett., vol. 40, no. 9, pp. 1980–1983, 2015.

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett., vol. 40, pp. 4887–4890,  2015.

P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Lett., vol. 24, pp. 15143–15159,  2016.

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett., vol. 24, pp. 430–432,  1999.

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett., vol. 38, pp. 3429–3432,  2013.

Optica (2)

Philos. Trans. Roy. Soc. A (1)

A. Forbes, “Controlling light's helicity at the source: Orbital angular momentum states from lasers,” Philos. Trans. Roy. Soc. A, vol. 375, no. 2087, 2017, Art. no. .

Philos. Trans. Roy. Soc. A, Math., Phys. Eng. Sci. (1)

A. E. Willneret al., “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Philos. Trans. Roy. Soc. A, Math., Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .

Philos. Trans. Roy. Soc. Lond. A, Math. Phys. Eng. Sci. (1)

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes,” Philos. Trans. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 375, no. 2087, 2017, Art. no. .

Photon. Res. (1)

Phys. Rev. A (10)

M. Mafuet al., “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A, vol. 88,  2013, Art. no. .

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A, vol. 92, no. 2, 2015, Art. no. .

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A, vol. 61,  2000, Art. no. .

L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A, vol. 82,  2010, Art. no. .

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A, vol. 81,  2010, Art. no. .

R. Keil, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, and A. Szameit, “Classical characterization of biphoton correlation in waveguide lattices,” Phys. Rev. A, vol. 83,  2011, Art. no. .

E. Karimiet al., “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A, vol. 82,  2010, Art. no. .

L. J. Pereira, A. Z. Khoury, and K. Dechoum, “Quantum and classical separability of spin-orbit laser modes,” Phys. Rev. A, vol. 90,  2014, Art. no. .

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A, vol. 77,  2008, Art. no. .

A. Ferenczi and N. Lütkenhaus, “Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning,” Phys. Rev. A, vol. 85,  2012, Art. no. .

Phys. Rev. Lett. (10)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett., vol. 94, no. 15, 2005, Art. no. .

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., vol. 105,  2010, Art. no. .

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett., vol. 90,  2003, Art. no. .

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett., vol. 96,  2006, Art. no. .

G. Valloneet al., “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett., vol. 113,  2014, Art. no. .

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett., vol. 107,  2011, Art. no. .

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide Lattices,” Phys. Rev. Lett., vol. 102,  2009, Art. no. .

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett., vol. 84, no. 20, pp. 4729–4732, 2000.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett., vol. 88,  2002, Art. no. .

C.-Z. Penget al., “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett., vol. 98,  2007, Art. no. .

Proc. Indian Acad. Sci., Sect. A (1)

S. Pancharatnam, “Generalized theory of interference and its applications. Partially coherent pencils,” Proc. Indian Acad. Sci., Sect. A, vol. 44, pp. 247–262, 1956.

Proc. Nat. Acad. Sci. USA (1)

T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B. Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of entanglement over 143 km,” Proc. Nat. Acad. Sci. USA, vol. 112, no. 46, pp. 14202–14205, 2015.

Proc. Roy. Soc. Lond. A, Math. Phys. Eng. Sci. (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Roy. Soc. Lond. A, Math. Phys. Eng. Sci., vol. 392, no. 1802, pp. 45–57, 1984.

Proc. SPIE (1)

C. Schulze, D. Flamm, A. Dudley, A. Forbes, and M. Duparré, “Modal decomposition for measuring the orbital angular momentum density of light,” Proc. SPIE, vol. 8637,  2013, Art. no. .

Quantum Inf. Comput. (1)

W. Wootters, “Entanglement of formation and concurrence,” Quantum Inf. Comput., vol. 1, no. 1, pp. 27–44, 2001.

Sci. Rep. (1)

B. Ndaganoet al., “A deterministic detector for vector vortex states,” Sci. Rep., vol. 7, 2017, Art. no. .

Science (5)

J. Yinet al., “Satellite-based entanglement distribution over 1200 kilometers,” Science, vol. 356, no. 6343, pp. 1140–1144, 2017.

N. Bozinovicet al., “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science, vol. 340, no. 6140, pp. 1545–1548, 2013.

X. Caiet al., “Integrated compact optical vortex beam emitters,” Science, vol. 338, pp. 363–366,  2012.

P. Miaoet al., “Orbital angular momentum microlaser,” Science, vol. 353, pp. 464–467,  2016.

E. Karimi and R. W. Boyd, “Classical entanglement?” Science, vol. 350, pp. 1172–1173,  2015.

Other (4)

C. Rosales-Guzmán and A. Forbes, How to Shape Light With Spatial Light Modulators, vol. SL30. Bellingham, WA, USA: SPIE Press, 2017.

G. Keiser, Optical Fiber Communications. (McGraw-Hill Series in Electrical and Computer Engineering: Communications and Signal Processing), 3rd ed. New York, NY, USA: McGraw-Hill, 2000.

M. P. J. Laveryet al., “Space division multiplexing in a basis of vector modes,” in Proc. Eur. Conf. Opt. Commun.,  2014, pp. 1–3.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, vol. 1, 2nd ed. Bellingham, WA, USA: SPIE,  2005.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.