Abstract

The changes in the radial content of orbital-angular-momentum (OAM) photonic states described by Laguerre-Gaussian (LG) modes with a radial index of zero, suffering from turbulence-induced distortions, are explored by numerical simulations. For a single-photon field with a given LG mode propagating through weak-to-strong atmospheric turbulence, both the average LG and OAM mode densities are dependent only on two nondimensional parameters, i.e., the Fresnel ratio and coherence-width-to-beam-radius (CWBR) ratio. It is found that atmospheric turbulence causes the radially-adjacent-mode mixing, besides the azimuthally-adjacent-mode mixing, in the propagated photonic states; the former is relatively slighter than the latter. With the same Fresnel ratio, the probabilities that a photon can be found in the zero-index radial mode of intended OAM states in terms of the relative turbulence strength behave very similarly; a smaller Fresnel ratio leads to a slower decrease in the probabilities as the relative turbulence strength increases. A photon can be found in various radial modes with approximately equal probability when the relative turbulence strength turns great enough. The use of a single-mode fiber in OAM measurements can result in photon loss and hence alter the observed transition probability between various OAM states. The bit error probability in OAM-based free-space optical communication systems that transmit photonic modes belonging to the same orthogonal LG basis may depend on what digit is sent.

© 2016 Optical Society of America

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References

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2016 (2)

2015 (6)

G. Funes, M. Vial, and J. A. Anguita, “Orbital-angular-momentum crosstalk and temporal fading in a terrestrial laser link using single-mode fiber coupling,” Opt. Express 23(18), 23133–23142 (2015).
[Crossref] [PubMed]

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[Crossref] [PubMed]

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9(12), 822–826 (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).

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
[Crossref]

F. S. Roux, “Entanglement evolution of twisted photons in strong atmospheric turbulence,” Phys. Rev. A 92(1), 012326 (2015).
[Crossref]

2014 (1)

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

2013 (3)

J. R. G. Alonso and T. A. Brun, “Protecting orbital-angular-momentum-photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88(2), 022326 (2013).
[Crossref]

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88(1), 012312 (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] [PubMed]

2012 (4)

2011 (2)

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

B. Pors, C. H. Monken, E. R. Eliel, and J. P. Woerdman, “Transport of orbital-angular-momentum entanglement through a turbulent atmosphere,” Opt. Express 19(7), 6671–6683 (2011).
[Crossref] [PubMed]

2009 (1)

2008 (2)

2007 (1)

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94 (2007).
[Crossref]

2005 (1)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

2004 (1)

1998 (1)

1988 (1)

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).

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] [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]

Alonso, J. R. G.

J. R. G. Alonso and T. A. Brun, “Protecting orbital-angular-momentum-photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88(2), 022326 (2013).
[Crossref]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[Crossref]

Andrews, R.

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94 (2007).
[Crossref]

Anguita, J. A.

Aolita, L.

O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref] [PubMed]

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).

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).

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).

Barnett, S. M.

Bisesto, F.

O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref] [PubMed]

Boyd, R. W.

Brun, T. A.

J. R. G. Alonso and T. A. Brun, “Protecting orbital-angular-momentum-photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88(2), 022326 (2013).
[Crossref]

Buchleitner, A.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
[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).

Chandrasekaran, N.

Charnotskii, M.

Chen, C.

Chen, M.

M. Chen, K. Dholakia, and M. Mazilu, “Is there an optimal basis to maximise optical information transfer?” Sci. Rep. 6, 22821 (2016).
[Crossref] [PubMed]

Courtial, J.

D’Ambrosio, V.

O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Dholakia, K.

M. Chen, K. Dholakia, and M. Mazilu, “Is there an optimal basis to maximise optical information transfer?” Sci. Rep. 6, 22821 (2016).
[Crossref] [PubMed]

Djordjevic, I. B.

Dolinar, S.

Eliel, E. R.

Erkmen, B. I.

Farías, O. J.

O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref] [PubMed]

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]

Flatté, S. M.

Forbes, A.

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88(1), 012312 (2013).
[Crossref]

Franke-Arnold, S.

Funes, G.

Gao, X.

Gbur, G.

Gibson, G.

Gopaul, C.

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94 (2007).
[Crossref]

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).

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] [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]

Ibrahim, A. H.

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88(1), 012312 (2013).
[Crossref]

Kahn, J. M.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9(12), 822–826 (2015).
[Crossref]

Konrad, T.

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88(1), 012312 (2013).
[Crossref]

Lavery, M. P. J.

Leeb, W. R.

Leonhard, N. D.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
[Crossref]

Li, G.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9(12), 822–826 (2015).
[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).

Li, X.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9(12), 822–826 (2015).
[Crossref]

Lou, Y.

Malik, M.

Marrucci, L.

O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Martin, J. M.

Mazilu, M.

M. Chen, K. Dholakia, and M. Mazilu, “Is there an optimal basis to maximise optical information transfer?” Sci. Rep. 6, 22821 (2016).
[Crossref] [PubMed]

McLaren, M.

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88(1), 012312 (2013).
[Crossref]

Mirhosseini, M.

Molisch, A. F.

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).

Monken, C. H.

Neifeld, M.

Neifeld, M. A.

O’Sullivan, M. N.

Padgett, M.

Padgett, M. J.

Pas’ko, V.

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[Crossref]

Pors, B.

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).

Ren, 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).

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] [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]

Robertson, D. J.

Rodenburg, B.

Roux, F. S.

F. S. Roux, “Entanglement evolution of twisted photons in strong atmospheric turbulence,” Phys. Rev. A 92(1), 012326 (2015).
[Crossref]

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88(1), 012312 (2013).
[Crossref]

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in Matlab (SPIE, 2010).

Sciarrino, F.

O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Shapiro, J. H.

Shatokhin, V. N.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
[Crossref]

Slussarenko, S.

O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Sponselli, A.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Steinhoff, N. K.

Taballione, C.

O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref] [PubMed]

Tong, S.

Tur, M.

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).

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] [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]

Tyler, G. A.

Tyson, R. K.

Vallone, G.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Vasic, B. V.

Vasnetsov, M.

Vial, M.

Villoresi, P.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Walborn, S. P.

O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref] [PubMed]

Wang, 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).

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. E.

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).

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] [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]

Winzer, P. J.

Woerdman, J. P.

Xie, G.

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).

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] [PubMed]

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).

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] [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, H.

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.

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

Zhang, Y.

Zhao, N.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9(12), 822–826 (2015).
[Crossref]

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).

Adv. Opt. Photonics (2)

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).

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

Appl. Opt. (2)

J. Opt. Soc. Am. A (2)

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]

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9(12), 822–826 (2015).
[Crossref]

New J. Phys. (1)

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94 (2007).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. A (4)

J. R. G. Alonso and T. A. Brun, “Protecting orbital-angular-momentum-photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88(2), 022326 (2013).
[Crossref]

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
[Crossref]

F. S. Roux, “Entanglement evolution of twisted photons in strong atmospheric turbulence,” Phys. Rev. A 92(1), 012326 (2015).
[Crossref]

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88(1), 012312 (2013).
[Crossref]

Phys. Rev. Lett. (2)

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

Sci. Rep. (2)

M. Chen, K. Dholakia, and M. Mazilu, “Is there an optimal basis to maximise optical information transfer?” Sci. Rep. 6, 22821 (2016).
[Crossref] [PubMed]

O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref] [PubMed]

Other (2)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[Crossref]

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in Matlab (SPIE, 2010).

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Figures (8)

Fig. 1
Fig. 1 Average irradiance distribution of LG 0 l beams propagating through atmospheric turbulence with l = 2 and Λ0 = 1, where Ω = 5.62 for both (a) and (d), Ω = 3.16 for both (b) and (e), Ω = 1.78 for both (c) and (f). The subplots (a) – (c) are average irradiance patterns obtained by numerical simulations; the subplots (d) – (f) are cross-sectional profiles of the average irradiance patterns scaled by the maximum average irradiance obtained according to the analytical solution given by Eq. (14). 600 simulated field realizations are used to compute the average irradiance distribution.
Fig. 2
Fig. 2 Azimuthally-adjacent-mode spread in terms of Ω−1 for an LG 0 l -mode field propagating through atmospheric turbulence with l ≡ 4. The curves are smoothing-spline-based fitted results obtained according to the simulation ones denoted by the circles and asterisks. (a) Λ0 = 0.1; (b) Λ0 = 1.
Fig. 3
Fig. 3 Probability of finding a photon in various radial modes of an intended OAM photonic state in terms of the relative turbulence strength | l | + 1 Ω 1 . The photonic field is due to a single photon with an LG 0 l mode propagating from the source to observation planes in atmospheric turbulence. The curves are smoothing-spline-based fitted results obtained according to the simulation ones denoted by the circles, asterisks and triangles. Indeed, the results for l = l′ = 0 or 4 are also obtained, which show similar features and are omitted to make the displayed curves distinguishable. (a) Λ0 = 0.1; (b) Λ0 = 1; (c) Λ0 = 10.
Fig. 4
Fig. 4 Probability of finding a photon in various radial modes of extrinsic OAM states in terms of the relative turbulence strength | l | + 1 Ω 1 with Λ0 = 0.1 being fixed. The photonic field is due to a single photon with an LG 0 l mode propagating from the source to observation planes in atmospheric turbulence. The curves are smoothing-spline-based fitted results obtained according to the simulation ones denoted by the circles and asterisks. (a) l = 1; (b) l = 2; (c) l = 3; (d) l = 4. The results with Λ0 = 1 or 10 actually show similar features and are omitted for saving space.
Fig. 5
Fig. 5 Probability of finding a photon in various LG q l modes belonging to the same orthonormal LG basis. The photonic field is due to a single photon with an LG 0 l mode propagating from the source to observation planes in atmospheric turbulence. (a) Λ0 = 1, Ω = 5.62, l = 0; (b) Λ0 = 1, Ω = 5.62, l = 2; (c) Λ0 = 1, Ω = 5.62, l = 4; (d) Λ0 = 1, Ω = 1, l = 0; (e) Λ0 = 1, Ω = 1, l = 2; (f) Λ0 = 1, Ω = 1, l = 4.
Fig. 6
Fig. 6 Probability of finding a photon in different radial modes of various intended OAM photonic states impaired by atmospheric turbulence. All the transmitted photonic states in each subplot are LG 0 l modes that belong to the same orthonormal LG basis. The LG 0 l modes with different Λ0 belong to different orthonormal LG bases. The absolute turbulence strengths for (a) – (c) are identical with r0 = 7.1 cm, and those for (d) – (f) are identical with r0 = 22.6 cm. (a) Λ0 = 0.1, Ω = 1; (b) Λ0 = 1, Ω = 3.2; (c) Λ0 = 10, Ω = 10; (d) Λ0 = 0.1, Ω = 3.2; (e) Λ0 = 1, Ω = 10; (f) Λ0 = 10, Ω = 31.6.
Fig. 7
Fig. 7 Fiber-coupling efficiency ξ (q, l) in terms of q and l. The value of the parameter a that can maximize ξ (0, l) for a given intended OAM state l is used to calculate ξ (q ≠ 0, l).
Fig. 8
Fig. 8 Probability of detecting a photon in different radial modes of various intended OAM states impaired by atmospheric turbulence with the use of a single-mode fiber. Each subplot is obtained under the same conditions as its counterpart in Fig. 6, except for the use of a single-mode fiber. 0,l (q′, l′)=p0,l (q′, l′) ξ(q′, l′). (a) Λ0 = 0.1, Ω = 1; (b) Λ0 = 1, Ω = 3.2; (c) Λ0 = 10, Ω = 10; (d) Λ0 = 0.1, Ω = 3.2; (e) Λ0 = 1, Ω = 10; (f) Λ0 = 10, Ω = 31.6.

Equations (16)

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U q , l ( r , z = L ) = i k 2 π L exp ( i k L ) d 2 s U q , l ( 0 ) ( s ) exp [ i k | s r | 2 2 L + ψ ( r , s ) ] ,
U q , l ( 0 ) ( s , θ ) = 1 2 π N q , l w 0 ( s 2 w 0 ) | l | exp ( i l θ ) exp ( s 2 w 0 2 ) L q | l | ( 2 s 2 w 0 2 )
Γ q , l ( r , r , z = L ) = ( k 2 π L ) 2 d 2 s d 2 s Γ q , l ( 0 ) ( s , s ) × exp [ i k | s r | 2 2 L i k | s r | 2 2 L ] × exp ( r d 2 + r d s d + s d 2 ρ 0 2 ) ,
Γ q , l ( 0 ) ( s , s ) = U q , l ( 0 ) ( s , θ ) U q , l ( 0 ) * ( s , θ )
Γ q , l ( r , r , z = L ) = N q , l 2 π 3 Λ 0 k 4 L Γ ˜ q , l ( r ^ , r ^ , z = L )
Γ ˜ q , l ( r ^ , r ^ , z = L ) = exp ( 2.1 2 | r ^ r ^ | 2 Ω 2 ) d 2 s ^ d 2 s ^ × F ( s ^ , s ^ , r ^ , r ^ , Λ 0 , Ω , q , l ) ,
F ( s ^ , s ^ , r ^ , r ^ , Λ 0 , Ω , q , l ) = ( s ^ 2 ) | l | exp ( i l θ ) exp ( s ^ 2 ) L q | l | ( 2 s ^ 2 ) × ( s ^ 2 ) | l | exp ( i l θ ) exp ( s ^ 2 ) L q | l | ( 2 s ^ 2 ) × exp [ i | s ^ r ^ | 2 Λ 0 i | s ^ r ^ | 2 Λ 0 2.1 2 | s ^ s ^ | 2 Ω 2 ] × exp [ 2.1 2 ( r ^ r ^ ) ( s ^ s ^ ) Ω 2 ] ,
U q , l ( r , ϕ , z = L ) = q = 0 l = a q , l ( q , l ) U q , l ( 0 ) ( r , ϕ , z = L ) ,
a q , l ( q , l ) = 0 2 π 0 U q , l ( r , ϕ , z = L ) U q , l ( 0 ) * ( r , ϕ , z = L ) r d r d ϕ ,
U q , l ( 0 ) ( r , ϕ , z = L ) = 1 2 π ρ q , l ( r , L ) exp ( i l ϕ )
p q , l ( q , l ) = | a q , l ( q , l ) | 2 ,
p q , l ( q , l ) = N q , l 2 N q , l 2 4 π 6 Λ 0 4 d 2 r ^ d 2 r ^ × Γ ˜ q , l ( r ^ , r ^ , z L ) Γ ˜ q , l ( 0 ) ( r ^ , r ^ , z = L ) ,
P q , l ( l ) = q = 0 p q , l ( q , l ) .
I 0 , l ( r , z = L ) = 1 { { I 0 , l ( 0 ) ( r , z = L ) } { η ( r , z = L ) } } ,
{ η ( r , z = L ) } = exp [ 1 2 D s p ( κ L k ) ] ,
ξ ( q , l ) = | 𝒜 d 2 r U q , l ( 0 ) ( r , z = L ) Θ ( r ) U m * ( r ) | 2 𝒜 d 2 r | U q , l ( 0 ) ( r , z = L ) | 2 ,

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