Abstract

As a recently explored property of light, orbital angular momentum (OAM) has potential in enabling multiplexing of multiple data-carrying beams, to increase the transmission capacity and spectral efficiency of a communication system. For the use of OAM multiplexing in free-space optical (FSO) communications, atmospheric turbulence presents a critical challenge. In this paper, we experimentally demonstrate simultaneous pre- and post-turbulence compensation of multiple OAM beams, in a bidirectional free-space optical communications link, using a single adaptive optics (AO) system. Each beam carries a 100  Gbit/s signal, and propagates through an emulated atmospheric turbulence. A specifically designed AO system, which utilizes a Gaussian beam for wavefront sensing and correction, is built at one end of the bidirectional link. We show that this AO system can be used to not only post-compensate the received OAM beams, but also pre-compensate the outgoing OAM beams emitted from the same link end. Experimental results show that this compensation technique helps reduce the crosstalk onto adjacent modes by more than 12 dB, achieving bit error rates below the forward error correction limit of 1×103, for both directions of the link. The results of work might be helpful to future implementation of OAM multiplexing, in a high-capacity FSO bidirectional link affected by atmospheric turbulence.

© 2014 Optical Society of America

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References

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N. Chandrasekaran, J. H. Shapiro, “Photon information efficient communication through atmospheric turbulence—part I: channel model and propagation statistics,” IEEE J. Lightwave Technol. 32, 1075–1087 (2014).

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39, 2845–2848 (2014).
[Crossref]

2013 (3)

2012 (8)

J. Leach, E. Bolduc, D. J. Gauthier, R. W. Boyd, “Secure information capacity of photons entangled in many dimensions,” Phys. Rev. A 85, 060304(R) (2012).
[Crossref]

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

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightwave Technol. 30, 521–531 (2012).
[Crossref]

T. Su, R. P. Scott, S. S. Djordjevic, N. K. Fontaine, D. J. Geisler, X. Cai, S. J. B. Yoo, “Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices,” Opt. Express 20, 9396–9402 (2012).
[Crossref]

B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37, 3735–3737 (2012).
[Crossref]

R. R. Parenti, J. M. Roth, J. H. Shapiro, F. G. Walther, J. A. Greco, “Experimental observations of channel reciprocity in single-mode free-space optical links,” Opt. Express 20, 21635–21644 (2012).
[Crossref]

C. Huang, H. Huang, H. Toyoda, T. Inoue, H. Liu, “Correlation matching method for high-precision position detection of optical vortex using Shack–Hartmann wavefront sensor,” Opt. Express 20, 26099–26109 (2012).
[Crossref]

J. H. Shapiro, A. L. Puryear, “Reciprocity-enhanced optical communication through atmospheric turbulence—part I: reciprocity proofs and far-field power transfer optimization,” J. Opt. Commun. Netw. 4, 947–954 (2012).
[Crossref]

2011 (2)

2010 (2)

2009 (1)

2008 (1)

2005 (2)

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 1–11 (2005).
[Crossref]

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

2004 (1)

2002 (2)

J. D. Barchers, D. L. Fried, “Optimal control of laser beams for propagation through a turbulent medium,” J. Opt. Soc. Am. A 19, 1779–1793 (2002).
[Crossref]

X. Zhu, J. Kahn, “Free space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[Crossref]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
[Crossref]

1972 (1)

1971 (1)

Ahmed, N.

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39, 2845–2848 (2014).
[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, A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062–4065 (2013).
[Crossref]

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

Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
[Crossref]

Andrews, L.

L. Andrews, R. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Anguita, J. A.

Arabaci, M.

Bao, C.

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39, 2845–2848 (2014).
[Crossref]

Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

Barchers, J. D.

Barnett, S.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
[Crossref]

Biérent, R.

Bolduc, E.

J. Leach, E. Bolduc, D. J. Gauthier, R. W. Boyd, “Secure information capacity of photons entangled in many dimensions,” Phys. Rev. A 85, 060304(R) (2012).
[Crossref]

Bolle, C.

Boyd, R. W.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39, 2845–2848 (2014).
[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, A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062–4065 (2013).
[Crossref]

J. Leach, E. Bolduc, D. J. Gauthier, R. W. Boyd, “Secure information capacity of photons entangled in many dimensions,” Phys. Rev. A 85, 060304(R) (2012).
[Crossref]

B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37, 3735–3737 (2012).
[Crossref]

G. A. Tyler, R. W. Boyd, “Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum,” Opt. Lett. 34, 142–144 (2009).
[Crossref]

Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

Bozinovic, N.

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

Burke, D.

Burrows, E. C.

Cai, X.

Chandrasekaran, N.

Courtial, J.

Dainty, C.

Dennis, M. R.

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 1–11 (2005).
[Crossref]

Devaney, N.

Djordjevic, I. B.

Djordjevic, S. S.

Dolinar, S.

Dolinar, S. J.

Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

Erkmen, B. I.

Esmaeelpour, M.

Essiambre, R.-J.

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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Fontaine, N. K.

Foschini, G. J.

Franke-Arnold, S.

Fried, D. L.

Gauthier, D. J.

J. Leach, E. Bolduc, D. J. Gauthier, R. W. Boyd, “Secure information capacity of photons entangled in many dimensions,” Phys. Rev. A 85, 060304(R) (2012).
[Crossref]

Geisler, D. J.

Gibson, G.

Gnauck, A. H.

Greco, J. A.

Huang, C.

Huang, H.

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39, 2845–2848 (2014).
[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, A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062–4065 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

C. Huang, H. Huang, H. Toyoda, T. Inoue, H. Liu, “Correlation matching method for high-precision position detection of optical vortex using Shack–Hartmann wavefront sensor,” Opt. Express 20, 26099–26109 (2012).
[Crossref]

Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

Inoue, T.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media, 2nd ed. (Academic, 1978).

Kahn, J.

X. Zhu, J. Kahn, “Free space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[Crossref]

Kristensen, P.

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

Lavery, M. P. J.

Leach, J.

J. Leach, E. Bolduc, D. J. Gauthier, R. W. Boyd, “Secure information capacity of photons entangled in many dimensions,” Phys. Rev. A 85, 060304(R) (2012).
[Crossref]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 1–11 (2005).
[Crossref]

Li, L.

Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

Lingle, R.

Liu, H.

Magaña-Loaiza, O. S.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

Maher, L.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
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A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
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B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
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B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37, 3735–3737 (2012).
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McCurdy, A. H.

Michau, V.

Mirhosseini, M.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
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B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37, 3735–3737 (2012).
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Mumtaz, S.

Murphy, K.

Neifeld, M.

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, A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062–4065 (2013).
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Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

Neifeld, M. A.

O’Sullivan, M. N.

Padgett, M.

Padgett, M. J.

Parenti, R. R.

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C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Randel, S.

Ren, Y.

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39, 2845–2848 (2014).
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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, A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062–4065 (2013).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
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Rodenburg, B.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
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B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37, 3735–3737 (2012).
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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, A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062–4065 (2013).
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B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
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Su, T.

Toyoda, H.

Tur, M.

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39, 2845–2848 (2014).
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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, A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062–4065 (2013).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

Tyler, G.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
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Vasnetsov, M.

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A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
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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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
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Willner, A. E.

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39, 2845–2848 (2014).
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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, A. E. Willner, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062–4065 (2013).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

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Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

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Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
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Yan, Y.

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39, 2845–2848 (2014).
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B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
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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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
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Adv. Opt. Photon. (1)

Appl. Opt. (1)

IEEE J. Lightwave Technol. (1)

N. Chandrasekaran, J. H. Shapiro, “Photon information efficient communication through atmospheric turbulence—part I: channel model and propagation statistics,” IEEE J. Lightwave Technol. 32, 1075–1087 (2014).

IEEE Trans. Commun. (1)

X. Zhu, J. Kahn, “Free space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Commun. Netw. (1)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

New J. Phys. (2)

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 1–11 (2005).
[Crossref]

Opt. Express (7)

Opt. Lett. (5)

Phys. Rev. A (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
[Crossref]

J. Leach, E. Bolduc, D. J. Gauthier, R. W. Boyd, “Secure information capacity of photons entangled in many dimensions,” Phys. Rev. A 85, 060304(R) (2012).
[Crossref]

Phys. Rev. Lett. (1)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

Science (1)

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

Other (3)

L. Andrews, R. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

A. Ishimaru, Wave Propagation and Scattering in Random Media, 2nd ed. (Academic, 1978).

Y. Ren, H. Huang, G. Xie, C. Bao, L. Li, N. Ahmed, Y. Yan, M. Willner, M. P. J. Lavery, M. Tur, M. Neifeld, S. J. Dolinar, M. J. Padgett, R. W. Boyd, J. H. Shapiro, A. E. Willner, “Simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum 100-Gbit/s data channels in a bidirectional link using a single adaptive-optics system,” in OSA Frontiers in Optics (Optical Society of America, 2013), paper FW6B.6.

Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. Propagation geometry of a bidirectional OAM multiplexed optical communication link through atmospheric turbulence; Comp., compensation; Gen., generation; RX, receiver; TX, transmitter.
Fig. 2.
Fig. 2. Concept diagram. One group of multiplexed data-carrying OAM beams from TX-1 is first distorted by atmospheric turbulence, and then compensated by the AO system (post-compensation). Another group of OAM beams from TX-2 first experiences pre-compensation by the AO system, and then propagates through the same turbulence (pre-compensation). RX, receiver; TX, transmitter.
Fig. 3.
Fig. 3. Experimental setup; AO, adaptive optics; BS, beam-splitter; Col, Collimator; DeMUX, Demultiplexer; FM, flip mirror; HWP. half wave plate; MUX, multiplexer; OC, optical coupler; PBS, polarizing beam splitter; PC, polarization controller; QPSK, quadrature phase-shift keying; RX, receiver; SLM, spatial light modulator; TX, Transmitter; WFS, Shack–Hartmann wavefront sensor.
Fig. 4.
Fig. 4. OAM beams = 3 , 5, before and after compensation of the TX-1/RX-1 link (post-compensation) and TX-2/RX-2 link (pre-compensation), respectively; (a1), (a2), (a5), (a6), (b1), (b2), (b5), and (b6) far-field intensity profiles; (a3), (a4), (a7), (a8), (b3), (b4), (b7), and (b8) interferograms; (c1) and (c2) interferograms of the OAM beams = 3 , 5 without turbulence.
Fig. 5.
Fig. 5. (a) Received power of the OAM beam = 5 , under different turbulence realizations; (b) crosstalk from the OAM = 5 channel to neighboring channels, under a random turbulence realization, with and without pre- or post-compensation.
Fig. 6.
Fig. 6. (a1)–(a8) Recovered QPSK constellations of OAM channel = 5 , for TX-1/RX-1 and TX-2/RX-2 links; (b) BER for OAM channel = 5 , when transmitting three multiplexed channels ( = 3 , 5, and 7, with Δ = 2 , or = 1 , 5, and 9, with Δ = 4 ) under a random turbulence realization, with and without post-and pre-compensation; XT, crosstalk.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

A 1 d r 1 | ε ( r 1 ) | 2 = 1 .
A 1 d r 1 ε * ( r 1 ) ε ( r 1 ) = 0 , for .
A 1 d r 1 ε ( r 1 ) h ( r 1 , r 2 , t ) ,
A 1 d r 1 ε ( r 1 ) h ( r 1 , r 2 ) e i φ ( r 2 ) ,
P 1 = P T | A 2 d r 2 ε * ( r 2 ) A 1 d r 1 ε ( r 1 ) h ( r 1 , r 2 ) e i φ ( r 2 ) | 2 .
P 2 = P T | A 1 d r 1 ε ( r 1 ) A 2 dr 2 ε * ( r 2 ) h ( r 2 , r 1 ) e i φ ( r 2 ) | 2 ,
P 1 = P 2 .

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