Abstract

Orbital angular momentum (OAM), a new dimension of photons, has potentials in lots of domains as high-dimensional data coding/decoding. Here we experimentally demonstrate a free-space data transmission system based on 8 bits multi-state OAM shift keying, where multiplexed optical vortices containing 8 various OAM states are employed to constitute 8 bits binary symbols. In the transmitter, the data coding of OAM shift keying is realized by switching a series of special-designed holograms. And in the receiver, the decoding is done by a single Dammann vortex grating along with image processing. We experimentally transmit data, including a gray-scale image, in free-space for 10 meters, showing zero bit-error-rate. The demonstrated results indicate a wide prospect for the future high-dimensional large data rate optical security communications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [Crossref]
  2. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
    [Crossref]
  3. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
    [Crossref]
  4. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit- scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
    [Crossref]
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    [Crossref]
  6. S. Yu, “Potentials and challenges of using orbital angular momentum communications in optical interconnects,” Opt. Express 23(3), 3075–3087 (2015).
    [Crossref]
  7. J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
    [Crossref]
  8. T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
    [Crossref]
  9. L. Zhu, G. Zhu, A. Wang, L. Wang, J. Ai, S. Chen, C. Du, J. Liu, S. Yu, and J. Wang, “18  km low-crosstalk OAM + WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation,” Opt. Lett. 43(8), 1890–1893 (2018).
    [Crossref]
  10. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pasko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
    [Crossref]
  11. A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
    [Crossref]
  12. S. Li and J. Wang, “Experimental demonstration of optical interconnects exploiting orbital angular momentum array,” Opt. Express 25(18), 21537–21547 (2017).
    [Crossref]
  13. S. Chen, S. Li, Y. Zhao, J. Liu, L. Zhu, A. Wang, J. Du, L. Shen, and J. Wang, “Demonstration of 20-Gbit/s high-speed Bessel beam encoding/decoding link with adaptive turbulence compensation,” Opt. Lett. 41(20), 4680–4683 (2016).
    [Crossref]
  14. S. Fu, Y. Zhai, C. Yin, H. Zhou, and C. Gao, “Mixed orbital angular momentum amplitude shift keying through a single hologram,” OSA Continuum 1(2), 295–308 (2018).
    [Crossref]
  15. S. Fu, Y. Zhai, H. Zhou, J. Zhang, T. Wang, C. Yin, and C. Gao, “Demonstration of free-space one-to-many multicasting link from orbital angular momentum encoding,” Opt. Lett. 44(19), 4753–4756 (2019).
    [Crossref]
  16. C. Kai, P. Huang, F. Shen, H. Zhou, and Z. Guo, “Orbital Angular Momentum Shift Keying Based Optical Communication System,” IEEE Photonics J. 9(2), 1–10 (2017).
    [Crossref]
  17. J. Li, M. Zhang, and D. Wang, “Adaptive Demodulator Using Machine Learning for Orbital Angular Momentum Shift Keying,” IEEE Photonics Technol. Lett. 29(17), 1455–1458 (2017).
    [Crossref]
  18. L. Zhu and J. Wang, “Simultaneous generation of multiple orbital angular momentum (OAM) modes using a single phase-only element,” Opt. Express 23(20), 26221–26233 (2015).
    [Crossref]
  19. N. Zhang, X. C. Yuan, and R. E. Burge, “Extending the detection range of optical vortices by Dammann vortex gratings,” Opt. Lett. 35(20), 3495–3497 (2010).
    [Crossref]
  20. S. Fu, T. Wang, S. Zhang, and C. Gao, “Integrating 5 × 5 Dammann gratings to detect orbital angular momentum states of beams with the range of −24 to + 24,” Appl. Opt. 55(7), 1514–1517 (2016).
    [Crossref]
  21. S. Fu, S. Zhang, T. Wang, and C. Gao, “Measurement of orbital angular momentum spectra of multiplexing optical vortices,” Opt. Express 24(6), 6240–6248 (2016).
    [Crossref]
  22. X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
    [Crossref]
  23. B. Guan, R. P. Scott, C. Qin, N. K. Fontaine, T. Su, C. Ferrari, M. Cappuzzo, F. Klemens, B. Keller, M. Earnshaw, and S. J. B. Yoo, “Free-space coherent optical communication with orbital angular, momentum multiplexing/demultiplexing using a hybrid 3D photonic integrated circuit,” Opt. Express 22(1), 145–156 (2014).
    [Crossref]
  24. J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
    [Crossref]
  25. Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
    [Crossref]
  26. G. C. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
    [Crossref]
  27. Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
    [Crossref]
  28. Y. D. Liu, C. Gao, X. Qi, and H. Weber, “Orbital angular momentum (OAM) spectrum correction in free space optical communication,” Opt. Express 16(10), 7091–7101 (2008).
    [Crossref]
  29. S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photonics Res. 4(5), B1–B4 (2016).
    [Crossref]
  30. Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013).
    [Crossref]
  31. S. Li and J. Wang, “Compensation of a distorted N-fold orbital angular momentum multicasting link using adaptive optics,” Opt. Lett. 41(7), 1482–1485 (2016).
    [Crossref]
  32. S. Fu, S. Zhang, T. Wang, and C. Gao, “Pre-turbulence compensation of orbital angular momentum beams based on a probe and the Gerchberg–Saxton algorithm,” Opt. Lett. 41(14), 3185–3188 (2016).
    [Crossref]
  33. J. Liu, P. Wang, X. Zhang, Y. He, X. Zhou, H. Ye, Y. Li, S. Xu, S. Chen, and D. Fan, “Deep learning based atmospheric turbulence compensation for orbital angular momentum beam distortion and communication,” Opt. Express 27(12), 16671–16688 (2019).
    [Crossref]

2019 (2)

2018 (4)

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

S. Fu, Y. Zhai, C. Yin, H. Zhou, and C. Gao, “Mixed orbital angular momentum amplitude shift keying through a single hologram,” OSA Continuum 1(2), 295–308 (2018).
[Crossref]

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
[Crossref]

L. Zhu, G. Zhu, A. Wang, L. Wang, J. Ai, S. Chen, C. Du, J. Liu, S. Yu, and J. Wang, “18  km low-crosstalk OAM + WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation,” Opt. Lett. 43(8), 1890–1893 (2018).
[Crossref]

2017 (3)

S. Li and J. Wang, “Experimental demonstration of optical interconnects exploiting orbital angular momentum array,” Opt. Express 25(18), 21537–21547 (2017).
[Crossref]

C. Kai, P. Huang, F. Shen, H. Zhou, and Z. Guo, “Orbital Angular Momentum Shift Keying Based Optical Communication System,” IEEE Photonics J. 9(2), 1–10 (2017).
[Crossref]

J. Li, M. Zhang, and D. Wang, “Adaptive Demodulator Using Machine Learning for Orbital Angular Momentum Shift Keying,” IEEE Photonics Technol. Lett. 29(17), 1455–1458 (2017).
[Crossref]

2016 (8)

S. Chen, S. Li, Y. Zhao, J. Liu, L. Zhu, A. Wang, J. Du, L. Shen, and J. Wang, “Demonstration of 20-Gbit/s high-speed Bessel beam encoding/decoding link with adaptive turbulence compensation,” Opt. Lett. 41(20), 4680–4683 (2016).
[Crossref]

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref]

S. Fu, T. Wang, S. Zhang, and C. Gao, “Integrating 5 × 5 Dammann gratings to detect orbital angular momentum states of beams with the range of −24 to + 24,” Appl. Opt. 55(7), 1514–1517 (2016).
[Crossref]

S. Fu, S. Zhang, T. Wang, and C. Gao, “Measurement of orbital angular momentum spectra of multiplexing optical vortices,” Opt. Express 24(6), 6240–6248 (2016).
[Crossref]

S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photonics Res. 4(5), B1–B4 (2016).
[Crossref]

S. Li and J. Wang, “Compensation of a distorted N-fold orbital angular momentum multicasting link using adaptive optics,” Opt. Lett. 41(7), 1482–1485 (2016).
[Crossref]

S. Fu, S. Zhang, T. Wang, and C. Gao, “Pre-turbulence compensation of orbital angular momentum beams based on a probe and the Gerchberg–Saxton algorithm,” Opt. Lett. 41(14), 3185–3188 (2016).
[Crossref]

2015 (4)

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

S. Yu, “Potentials and challenges of using orbital angular momentum communications in optical interconnects,” Opt. Express 23(3), 3075–3087 (2015).
[Crossref]

L. Zhu and J. Wang, “Simultaneous generation of multiple orbital angular momentum (OAM) modes using a single phase-only element,” Opt. Express 23(20), 26221–26233 (2015).
[Crossref]

2014 (1)

2013 (2)

2012 (2)

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

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

2011 (1)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

2010 (2)

N. Zhang, X. C. Yuan, and R. E. Burge, “Extending the detection range of optical vortices by Dammann vortex gratings,” Opt. Lett. 35(20), 3495–3497 (2010).
[Crossref]

G. C. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref]

2008 (2)

Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
[Crossref]

Y. D. Liu, C. Gao, X. Qi, and H. Weber, “Orbital angular momentum (OAM) spectrum correction in free space optical communication,” Opt. Express 16(10), 7091–7101 (2008).
[Crossref]

2004 (1)

1992 (1)

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

Ahmed, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013).
[Crossref]

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

Ai, J.

Allen, L.

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

Ashrafi, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Ashrafi, S.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Bao, C.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Barnett, S.

Beijersbergen, M. W.

G. C. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref]

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

Berkhout, G. C.

G. C. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref]

Boyd, R. W.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit- scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

Burge, R. E.

Cai, X.

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
[Crossref]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Cao, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Cappuzzo, M.

Chandrasekaran, N.

Chen, S.

Chen, Y.

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

Chremmos, I.

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

Courtial, J.

G. C. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pasko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[Crossref]

Dolinar, S.

Du, C.

Du, J.

Dudley, A.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref]

Earnshaw, M.

Erkmen, B. I.

Fan, D.

Fazal, I. M.

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

Ferrari, C.

Fontaine, N. K.

Forbes, A.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref]

Franke-Arnold, S.

Fu, S.

Gao, C.

S. Fu, Y. Zhai, H. Zhou, J. Zhang, T. Wang, C. Yin, and C. Gao, “Demonstration of free-space one-to-many multicasting link from orbital angular momentum encoding,” Opt. Lett. 44(19), 4753–4756 (2019).
[Crossref]

S. Fu, Y. Zhai, C. Yin, H. Zhou, and C. Gao, “Mixed orbital angular momentum amplitude shift keying through a single hologram,” OSA Continuum 1(2), 295–308 (2018).
[Crossref]

S. Fu, T. Wang, S. Zhang, and C. Gao, “Integrating 5 × 5 Dammann gratings to detect orbital angular momentum states of beams with the range of −24 to + 24,” Appl. Opt. 55(7), 1514–1517 (2016).
[Crossref]

S. Fu, S. Zhang, T. Wang, and C. Gao, “Measurement of orbital angular momentum spectra of multiplexing optical vortices,” Opt. Express 24(6), 6240–6248 (2016).
[Crossref]

S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photonics Res. 4(5), B1–B4 (2016).
[Crossref]

S. Fu, S. Zhang, T. Wang, and C. Gao, “Pre-turbulence compensation of orbital angular momentum beams based on a probe and the Gerchberg–Saxton algorithm,” Opt. Lett. 41(14), 3185–3188 (2016).
[Crossref]

Y. D. Liu, C. Gao, X. Qi, and H. Weber, “Orbital angular momentum (OAM) spectrum correction in free space optical communication,” Opt. Express 16(10), 7091–7101 (2008).
[Crossref]

Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
[Crossref]

Gao, M.

Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
[Crossref]

Gibson, G.

Guan, B.

Guo, Z.

C. Kai, P. Huang, F. Shen, H. Zhou, and Z. Guo, “Orbital Angular Momentum Shift Keying Based Optical Communication System,” IEEE Photonics J. 9(2), 1–10 (2017).
[Crossref]

Han, Y.

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
[Crossref]

Hao, Z.

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
[Crossref]

He, Y.

Huang, H.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit- scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013).
[Crossref]

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

Huang, P.

C. Kai, P. Huang, F. Shen, H. Zhou, and Z. Guo, “Orbital Angular Momentum Shift Keying Based Optical Communication System,” IEEE Photonics J. 9(2), 1–10 (2017).
[Crossref]

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T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Kai, C.

C. Kai, P. Huang, F. Shen, H. Zhou, and Z. Guo, “Orbital Angular Momentum Shift Keying Based Optical Communication System,” IEEE Photonics J. 9(2), 1–10 (2017).
[Crossref]

Keller, B.

Klemens, F.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit- scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

Lavery, M. P. J.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013).
[Crossref]

G. C. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref]

Lei, T.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

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Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
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Li, H.

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
[Crossref]

Li, J.

J. Li, M. Zhang, and D. Wang, “Adaptive Demodulator Using Machine Learning for Orbital Angular Momentum Shift Keying,” IEEE Photonics Technol. Lett. 29(17), 1455–1458 (2017).
[Crossref]

Li, L.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
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Li, Y.

J. Liu, P. Wang, X. Zhang, Y. He, X. Zhou, H. Ye, Y. Li, S. Xu, S. Chen, and D. Fan, “Deep learning based atmospheric turbulence compensation for orbital angular momentum beam distortion and communication,” Opt. Express 27(12), 16671–16688 (2019).
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T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Li, Z.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

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T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Liu, G. N.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
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Liu, Y. D.

Y. D. Liu, C. Gao, X. Qi, and H. Weber, “Orbital angular momentum (OAM) spectrum correction in free space optical communication,” Opt. Express 16(10), 7091–7101 (2008).
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Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
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J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
[Crossref]

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T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
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J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
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A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
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Niu, H.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
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Padgett, M. J.

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013).
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A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
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G. C. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref]

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Qi, X.

Qin, C.

Ramachandran, S.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit- scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit- scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013).
[Crossref]

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

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A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
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A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
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Shapiro, J. H.

Shen, F.

C. Kai, P. Huang, F. Shen, H. Zhou, and Z. Guo, “Orbital Angular Momentum Shift Keying Based Optical Communication System,” IEEE Photonics J. 9(2), 1–10 (2017).
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Sorel, M.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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Strain, M. J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
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Sun, C.

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
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J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
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A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit- scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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Wang, A.

Wang, D.

J. Li, M. Zhang, and D. Wang, “Adaptive Demodulator Using Machine Learning for Orbital Angular Momentum Shift Keying,” IEEE Photonics Technol. Lett. 29(17), 1455–1458 (2017).
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L. Zhu, G. Zhu, A. Wang, L. Wang, J. Ai, S. Chen, C. Du, J. Liu, S. Yu, and J. Wang, “18  km low-crosstalk OAM + WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation,” Opt. Lett. 43(8), 1890–1893 (2018).
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[Crossref]

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

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L. Zhu, G. Zhu, A. Wang, L. Wang, J. Ai, S. Chen, C. Du, J. Liu, S. Yu, and J. Wang, “18  km low-crosstalk OAM + WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation,” Opt. Lett. 43(8), 1890–1893 (2018).
[Crossref]

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
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Wang, T.

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Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit- scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013).
[Crossref]

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

Woerdman, J. P.

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

Xiao, Y.

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013).
[Crossref]

Xiong, B.

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
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Xu, S.

Xu, X.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Yan, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013).
[Crossref]

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

Yang, J. Y.

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

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Ye, H.

Yin, C.

Yoo, S. J. B.

Yu, C.

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
[Crossref]

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Yu, S.

L. Zhu, G. Zhu, A. Wang, L. Wang, J. Ai, S. Chen, C. Du, J. Liu, S. Yu, and J. Wang, “18  km low-crosstalk OAM + WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation,” Opt. Lett. 43(8), 1890–1893 (2018).
[Crossref]

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
[Crossref]

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

S. Yu, “Potentials and challenges of using orbital angular momentum communications in optical interconnects,” Opt. Express 23(3), 3075–3087 (2015).
[Crossref]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Yuan, X.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Yuan, X. C.

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit- scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

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

Zghal, M.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref]

Zhai, Y.

Zhang, J.

S. Fu, Y. Zhai, H. Zhou, J. Zhang, T. Wang, C. Yin, and C. Gao, “Demonstration of free-space one-to-many multicasting link from orbital angular momentum encoding,” Opt. Lett. 44(19), 4753–4756 (2019).
[Crossref]

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
[Crossref]

Zhang, M.

J. Li, M. Zhang, and D. Wang, “Adaptive Demodulator Using Machine Learning for Orbital Angular Momentum Shift Keying,” IEEE Photonics Technol. Lett. 29(17), 1455–1458 (2017).
[Crossref]

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Zhang, N.

Zhang, S.

Zhang, X.

Zhang, Y.

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

Zhao, Y.

Zhao, Z.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Zhou, H.

Zhou, X.

Zhu, G.

Zhu, J.

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Zhu, L.

Adv. Opt. Photonics (2)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Appl. Opt. (1)

IEEE Photonics J. (1)

C. Kai, P. Huang, F. Shen, H. Zhou, and Z. Guo, “Orbital Angular Momentum Shift Keying Based Optical Communication System,” IEEE Photonics J. 9(2), 1–10 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (1)

J. Li, M. Zhang, and D. Wang, “Adaptive Demodulator Using Machine Learning for Orbital Angular Momentum Shift Keying,” IEEE Photonics Technol. Lett. 29(17), 1455–1458 (2017).
[Crossref]

Light: Sci. Appl. (1)

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Nat. Commun. (1)

J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An InP-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 2652 (2018).
[Crossref]

Nat. Photonics (1)

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

Opt. Commun. (1)

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Opt. Express (8)

S. Fu, S. Zhang, T. Wang, and C. Gao, “Measurement of orbital angular momentum spectra of multiplexing optical vortices,” Opt. Express 24(6), 6240–6248 (2016).
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Y. D. Liu, C. Gao, X. Qi, and H. Weber, “Orbital angular momentum (OAM) spectrum correction in free space optical communication,” Opt. Express 16(10), 7091–7101 (2008).
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B. Guan, R. P. Scott, C. Qin, N. K. Fontaine, T. Su, C. Ferrari, M. Cappuzzo, F. Klemens, B. Keller, M. Earnshaw, and S. J. B. Yoo, “Free-space coherent optical communication with orbital angular, momentum multiplexing/demultiplexing using a hybrid 3D photonic integrated circuit,” Opt. Express 22(1), 145–156 (2014).
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J. Liu, P. Wang, X. Zhang, Y. He, X. Zhou, H. Ye, Y. Li, S. Xu, S. Chen, and D. Fan, “Deep learning based atmospheric turbulence compensation for orbital angular momentum beam distortion and communication,” Opt. Express 27(12), 16671–16688 (2019).
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S. Yu, “Potentials and challenges of using orbital angular momentum communications in optical interconnects,” Opt. Express 23(3), 3075–3087 (2015).
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G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pasko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
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L. Zhu and J. Wang, “Simultaneous generation of multiple orbital angular momentum (OAM) modes using a single phase-only element,” Opt. Express 23(20), 26221–26233 (2015).
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S. Li and J. Wang, “Experimental demonstration of optical interconnects exploiting orbital angular momentum array,” Opt. Express 25(18), 21537–21547 (2017).
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S. Chen, S. Li, Y. Zhao, J. Liu, L. Zhu, A. Wang, J. Du, L. Shen, and J. Wang, “Demonstration of 20-Gbit/s high-speed Bessel beam encoding/decoding link with adaptive turbulence compensation,” Opt. Lett. 41(20), 4680–4683 (2016).
[Crossref]

S. Fu, Y. Zhai, H. Zhou, J. Zhang, T. Wang, C. Yin, and C. Gao, “Demonstration of free-space one-to-many multicasting link from orbital angular momentum encoding,” Opt. Lett. 44(19), 4753–4756 (2019).
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N. Zhang, X. C. Yuan, and R. E. Burge, “Extending the detection range of optical vortices by Dammann vortex gratings,” Opt. Lett. 35(20), 3495–3497 (2010).
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L. Zhu, G. Zhu, A. Wang, L. Wang, J. Ai, S. Chen, C. Du, J. Liu, S. Yu, and J. Wang, “18  km low-crosstalk OAM + WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation,” Opt. Lett. 43(8), 1890–1893 (2018).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013).
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S. Li and J. Wang, “Compensation of a distorted N-fold orbital angular momentum multicasting link using adaptive optics,” Opt. Lett. 41(7), 1482–1485 (2016).
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Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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Phys. Rev. Lett. (2)

G. C. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref]

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

Sci. Rep. (1)

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref]

Science (2)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit- scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

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Figures (6)
Fig. 1.
Fig. 1. Concept of data transmission based on multi-state OAM shift keying.

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Fig. 2.
Fig. 2. Simulated examples of multiplexed vortices ({$|{{{l}_{k}}\rangle} $}={$|{{- 10}\rangle} $, $|{{- 7}\rangle} $, $|{{- 4}\rangle} $, $|{{- 1}\rangle} $, $|{1}\rangle $, $|{4}\rangle $, $|{7} \rangle$, $|{{10}\rangle} $}) passing through a DVG. (a) The case {ak}={1,1,1,1,1,1,1,1}; (b) The case {ak}={0,1,0,0,1,1,1,0}.

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Fig. 3.
Fig. 3. Experimental setup. LD, laser diode; SMF, single mode fiber; Col., collimator; PBS, polarized beam splitter; SLM1∼SLM3, liquid-crystal spatial light modulator; BS, beam splitter; R1∼R4, reflector; L1∼L8, lenses; CCD1 & CCD2, infrared CCD camera.

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Fig. 4.
Fig. 4. Some of the experimentally obtained 8 bits multi-state OAM shift keying symbols (20, 102, 249) and their corresponding decoding patterns. The 8 bits binary numbers of these three symbols are also marked in the decoding patterns.

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Fig. 5.
Fig. 5. The 64×64 gray image transmission through the 8 bits multi-state OAM shift keying. (a) The transmitted gray image; (b) The gray image recovered by the receiver.

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Fig. 6.
Fig. 6. Measured OAM spectra of three coded symbols in both the transmitter and receiver. (a)–(c) are the case of 256-ary numbers 74 (01001010), 99 (01100011) and 255 (11111111), respectively.

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Equations (2)

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| ψ ⟩ = ∑ k = 1 N a k | l k ⟩
exp ⁡ ( − i l m φ ) | ψ ⟩ = ∑ k = 1 N a k | l k − l m ⟩

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