Abstract

In this work, a 1550 nm fiber-to-free-space optical communication link is successfully demonstrated employing the superposition of two coherently coupled orbital angular momentum (CCOAM) states. Information is encoded onto both the amplitude and phase of the CCOAM beams and is mapped to a three-dimensional (3D) constellation space using quadrature amplitude modulation (QAM) equivalent architecture. The 3D QAM constellation is based on a higher-order Poincare sphere equivalent for OAM states, and multiple spherical constellations are demonstrated for 64- and 128-QAM, providing a 6X and 7X increase in spectral efficiency by fully exploiting the available 3D space. The experimental results are presented showing a bit error rate (BER) below the forward error correction (FEC) limit. Multiple experimental parameters which could contribute to constellation distortions are also discussed.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (4)

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

R. B. Rodrigues, J. Gonzales, B. P. da Silva, J. A. O. Huguenin, M. Martinelli, R. M. de Araújo, C. E. R. Souza, and A. Z. Khoury, “Orbital angular momentum symmetry in a driven optical parametric oscillator,” Opt. Lett. 43(11), 2486–2489 (2018).
[Crossref] [PubMed]

L. A. Rusch, M. Rad, K. Allahverdyan, I. Fazal, and E. Bernier, “Carrying data on the orbital angular momentum of light,” IEEE Commun. Mag. 56(2), 219–224 (2018).
[Crossref]

K. Morgan, Y. Li, W. Li, J. K. Miller, R. J. Watkins, and E. G. Johnson, “Multilevel quadrature amplitude multiplexing using coherently coupled orbital angular momentum modes,” Opt. Express 26(9), 12180–12190 (2018).
[Crossref] [PubMed]

2017 (3)

2016 (5)

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

J. Baghdady, K. Miller, K. Morgan, M. Byrd, S. Osler, R. Ragusa, W. Li, B. M. Cochenour, and E. G. Johnson, “Multi-gigabit/s underwater optical communication link using orbital angular momentum multiplexing,” Opt. Express 24(9), 9794–9805 (2016).
[Crossref] [PubMed]

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

J. Liu and J. Wang, “Polarization-insensitive PAM-4-carrying free-space orbital angular momentum (OAM) communications,” Opt. Express 24(4), 4258–4269 (2016).
[Crossref] [PubMed]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

2015 (1)

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

2012 (1)

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

2011 (2)

S. G. Kang, Z. Chen, J. Y. Kim, J. S. Bae, and J. S. Lim, “Construction of higher-level 3-D signal constellations and their accurate symbol error probabilities in AWGN,” IEEE Trans. Signal Process. 59(12), 6267–6272 (2011).
[Crossref]

I. B. Djordjevic, M. Arabaci, L. Xu, and T. Wang, “Spatial-domain-based multidimensional modulation for multi-Tb/s serial optical transmission,” Opt. Express 19(7), 6845–6857 (2011).
[Crossref] [PubMed]

2010 (1)

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81(4), 043844 (2010).
[Crossref]

1999 (1)

1992 (1)

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

Abaza, M.

A. Mansour, R. Mesleh, and M. Abaza, “New challenges in wireless and free space optical communications,” Opt. Lasers Eng. 89, 95–108 (2017).
[Crossref]

Ahmed, N.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

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

Allahverdyan, K.

L. A. Rusch, M. Rad, K. Allahverdyan, I. Fazal, and E. Bernier, “Carrying data on the orbital angular momentum of light,” IEEE Commun. Mag. 56(2), 219–224 (2018).
[Crossref]

Allen, L.

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

Arabaci, M.

Arbabi, A.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Arbabi, E.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Ashrafi, S.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Bae, J. S.

S. G. Kang, Z. Chen, J. Y. Kim, J. S. Bae, and J. S. Lim, “Construction of higher-level 3-D signal constellations and their accurate symbol error probabilities in AWGN,” IEEE Trans. Signal Process. 59(12), 6267–6272 (2011).
[Crossref]

Baghdady, J.

Barnett, S. M.

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81(4), 043844 (2010).
[Crossref]

Beijersbergen, M. W.

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

Bernier, E.

L. A. Rusch, M. Rad, K. Allahverdyan, I. Fazal, and E. Bernier, “Carrying data on the orbital angular momentum of light,” IEEE Commun. Mag. 56(2), 219–224 (2018).
[Crossref]

Byrd, M.

Cao, Y.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Chen, Z.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

S. G. Kang, Z. Chen, J. Y. Kim, J. S. Bae, and J. S. Lim, “Construction of higher-level 3-D signal constellations and their accurate symbol error probabilities in AWGN,” IEEE Trans. Signal Process. 59(12), 6267–6272 (2011).
[Crossref]

Cochenour, B. M.

Courtial, J.

da Silva, B. P.

de Araújo, R. M.

Djordjevic, I. B.

Dolinar, S.

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

Dudley, A.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

Fan, D.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Faraon, A.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Fazal, I.

L. A. Rusch, M. Rad, K. Allahverdyan, I. Fazal, and E. Bernier, “Carrying data on the orbital angular momentum of light,” IEEE Commun. Mag. 56(2), 219–224 (2018).
[Crossref]

Fazal, I. M.

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

Forbes, A.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

Franke-Arnold, S.

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81(4), 043844 (2010).
[Crossref]

Gonzales, J.

Huang, H.

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

Huguenin, J. A. O.

Ireland, D. G.

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81(4), 043844 (2010).
[Crossref]

Jack, B.

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81(4), 043844 (2010).
[Crossref]

Jiang, L.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

Johnson, E. G.

Kamali, S. M.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Kang, S. G.

S. G. Kang, Z. Chen, J. Y. Kim, J. S. Bae, and J. S. Lim, “Construction of higher-level 3-D signal constellations and their accurate symbol error probabilities in AWGN,” IEEE Trans. Signal Process. 59(12), 6267–6272 (2011).
[Crossref]

Ke, Y.

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photon. Res. 5(1), 15–21 (2017).
[Crossref]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Khoury, A. Z.

Kim, J. Y.

S. G. Kang, Z. Chen, J. Y. Kim, J. S. Bae, and J. S. Lim, “Construction of higher-level 3-D signal constellations and their accurate symbol error probabilities in AWGN,” IEEE Trans. Signal Process. 59(12), 6267–6272 (2011).
[Crossref]

Leach, J.

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81(4), 043844 (2010).
[Crossref]

Li, L.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Li, W.

Li, Y.

Lim, J. S.

S. G. Kang, Z. Chen, J. Y. Kim, J. S. Bae, and J. S. Lim, “Construction of higher-level 3-D signal constellations and their accurate symbol error probabilities in AWGN,” IEEE Trans. Signal Process. 59(12), 6267–6272 (2011).
[Crossref]

Ling, X.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Litvin, I.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Liu, C.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Liu, J.

Liu, Y.

Liu, Z.

Luo, B.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

Luo, H.

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photon. Res. 5(1), 15–21 (2017).
[Crossref]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Mansour, A.

A. Mansour, R. Mesleh, and M. Abaza, “New challenges in wireless and free space optical communications,” Opt. Lasers Eng. 89, 95–108 (2017).
[Crossref]

Marrucci, L.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Martinelli, M.

McLaren, M.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

Mesleh, R.

A. Mansour, R. Mesleh, and M. Abaza, “New challenges in wireless and free space optical communications,” Opt. Lasers Eng. 89, 95–108 (2017).
[Crossref]

Miller, J. K.

Miller, K.

Morgan, K.

Naidoo, D.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Osler, S.

Padgett, M. J.

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81(4), 043844 (2010).
[Crossref]

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24(7), 430–432 (1999).
[Crossref] [PubMed]

Pan, W.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

Pan, Y.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

Piccirillo, B.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Rad, M.

L. A. Rusch, M. Rad, K. Allahverdyan, I. Fazal, and E. Bernier, “Carrying data on the orbital angular momentum of light,” IEEE Commun. Mag. 56(2), 219–224 (2018).
[Crossref]

Ragusa, R.

Ren, Y.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

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

Rodrigues, R. B.

Romero, J.

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81(4), 043844 (2010).
[Crossref]

Roux, F. S.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Rusch, L. A.

L. A. Rusch, M. Rad, K. Allahverdyan, I. Fazal, and E. Bernier, “Carrying data on the orbital angular momentum of light,” IEEE Commun. Mag. 56(2), 219–224 (2018).
[Crossref]

Shu, W.

Souza, C. E. R.

Spreeuw, R. J.

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

Tur, M.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

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

Wang, J.

Wang, T.

Wang, Z.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Watkins, R. J.

Wen, S.

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photon. Res. 5(1), 15–21 (2017).
[Crossref]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Willner, A. E.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

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

Willner, A. J.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Woerdman, J. P.

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

Xie, D.

Xie, G.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Xu, L.

Yan, L.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

Yan, Y.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

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

Yang, C.

Yang, J.

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

Yao, A. M.

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81(4), 043844 (2010).
[Crossref]

Yi, A.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

Yi, X.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Yue, Y.

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

Zhao, Z.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Zhou, X.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Zhu, L.

Adv. Opt. Photonics (1)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

IEEE Commun. Mag. (1)

L. A. Rusch, M. Rad, K. Allahverdyan, I. Fazal, and E. Bernier, “Carrying data on the orbital angular momentum of light,” IEEE Commun. Mag. 56(2), 219–224 (2018).
[Crossref]

IEEE Trans. Signal Process. (1)

S. G. Kang, Z. Chen, J. Y. Kim, J. S. Bae, and J. S. Lim, “Construction of higher-level 3-D signal constellations and their accurate symbol error probabilities in AWGN,” IEEE Trans. Signal Process. 59(12), 6267–6272 (2011).
[Crossref]

Nat. Photonics (2)

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

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Opt. Commun. (1)

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (1)

A. Mansour, R. Mesleh, and M. Abaza, “New challenges in wireless and free space optical communications,” Opt. Lasers Eng. 89, 95–108 (2017).
[Crossref]

Opt. Lett. (3)

Photon. Res. (1)

Phys. Rev. A (3)

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81(4), 043844 (2010).
[Crossref]

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

Sci. Rep. (1)

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Other (1)

J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz spectral efficiency using OFDM/OQAM 64-QAM signals over pol-muxed 22 orbital angular momentum (OAM) modes,” In Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, 2014), pp. 1–3.

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Figures (6)

Fig. 1
Fig. 1 (a), the concept of the interference of OAM beams with opposite spiral phase with both amplitude and phase modulation; (b), the experimental setup of the OAM beams intereference; and (c), the OAM equivalent high order Poincaré sphere (HOPS).
Fig. 2
Fig. 2 Example 16-QAM constellation with 2-sphere (K = 2), 2-latitude (N = 2) and 4-phase(L = 4) and the corresponding symbol map. The two spheres are separated by radius r, or the total power.
Fig. 3
Fig. 3 Block diagram of receiver setup sampled at t = Tb .
Fig. 4
Fig. 4 The experiment setup of the CCOAM communication system and the actual receiver picture.
Fig. 5
Fig. 5 The measured double sphere 64-QAM and triple-sphere 128-QAM 3D star constellations plotted in a normalized optical power scale. For 128-QAM constellation, individual spheres are also shown in different scales.
Fig. 6
Fig. 6 The measured BER plotted against measured SNR for 64- and 128- QAM constellations with simulated results.

Equations (14)

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S KNL ( r K , α N , φ L ,t)= U 1 ( r K , α N , φ L ,t)+ U 2 ( r K , α N , φ L ,t) = r K g(t) α N 2 exp(imψ)exp( i φ L 2 g(t)) + r K g(t)(1 α N 2 ) exp(imψ)exp( i φ L 2 g(t)).
p(t)= n S KNL ( r K , α N , φ L ,t) δ(tnT).
Φ I (ψ)=cos( mψ ),
Φ Q (ψ)=cos[ m( ψπ/4m ) ].
Φ m (ψ)=exp( imψ ),
Φ +m (ψ)=exp( +imψ ).
P I (t)= n P I g(tnT)= n P RX [1+sin(θ)cos(φ)] g(tnT),
P Q (t)= n P Q g(tnT)= n P RX [1+sin(θ)sin(φ)]g(tnT) ,
P +m (t)= n P +m g(tnT)= n 1 2 P RX (1+cos(θ))g(tnT) ,
P m (t)= n P m g(tnT)= n 1 2 P RX (1cos(θ))g(tnT) .
I= n P RX sin(θ)cos(φ) g(tnT),
Q= n P RX sin(θ)sin(φ)g(tnT) .
Z= n P RX cos(θ)g(tnT) .
SNR=10 log 10 j ( I ¯ j 2 + Q ¯ j 2 + Z ¯ j 2 ) j [ ( I j I ¯ j ) 2 + ( Q j Q ¯ j ) 2 + ( Z j Z ¯ j ) 2 ] ,

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