Abstract

We have evaluated the channel capacity of OAM-based FSO link under a strong atmospheric turbulence regime when adaptive optics (AO) are employed to correct the wavefront phase distortions of OAM modes. The turbulence is emulated by the Monte-Carlo phase screen method, which is validated by comparison with the theoretical phase structure function. Based on that, a closed-loop AO system with the capability of real-time correction is designed and validated. The simulation results show that the phase distortions of OAM modes induced by turbulence can be significantly compensated by the real-time correction of the properly designed AO. Furthermore, the crosstalk across channels is reduced drastically, while a substantial enhancement of channel capacity can be obtained when AO is deployed.

© 2014 Optical Society of America

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2014 (5)

2013 (2)

L. Changyu, I. B. Djordjevic, and M. Cvijetic, “Quantum Few-Mode Fiber Communications Based on the Orbital Angular Momentum,” Photonics Technology Letters, IEEE 25(1), 3–6 (2013).
[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] [PubMed]

2012 (4)

2011 (2)

2008 (2)

2006 (2)

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum Key Distribution with Higher-Order Alphabets Using Spatially Encoded Qudits,” Phys. Rev. Lett. 96(9), 090501 (2006).
[Crossref] [PubMed]

G. Simon, J. Thomas, V. Alipasha, W. Gregor, and Z. Anton, “Experimental quantum cryptography with qutrits,” New J. Phys. 8(5), 75 (2006).
[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)

2003 (1)

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67(1), 012311 (2003).
[Crossref]

2002 (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

1993 (1)

L. C. Andrews, S. Vester, and C. E. Richardson, “Analytic Expressions for the Wave Structure Function Based on a Bump Spectral Model for Refractive Index Fluctuations,” J. Mod. Opt. 40(5), 931–938 (1993).
[Crossref]

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] [PubMed]

1983 (1)

Ahmed, N.

Alipasha, V.

G. Simon, J. Thomas, V. Alipasha, W. Gregor, and Z. Anton, “Experimental quantum cryptography with qutrits,” New J. Phys. 8(5), 75 (2006).
[Crossref]

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] [PubMed]

Almeida, M. P.

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum Key Distribution with Higher-Order Alphabets Using Spatially Encoded Qudits,” Phys. Rev. Lett. 96(9), 090501 (2006).
[Crossref] [PubMed]

Andrews, L. C.

L. C. Andrews, S. Vester, and C. E. Richardson, “Analytic Expressions for the Wave Structure Function Based on a Bump Spectral Model for Refractive Index Fluctuations,” J. Mod. Opt. 40(5), 931–938 (1993).
[Crossref]

R. L. Phillips and L. C. Andrews, “Spot size and divergence for Laguerre Gaussian beams of any order,” Appl. Opt. 22(5), 643–644 (1983).
[Crossref] [PubMed]

Anguita, J. A.

Anton, Z.

G. Simon, J. Thomas, V. Alipasha, W. Gregor, and Z. Anton, “Experimental quantum cryptography with qutrits,” New J. Phys. 8(5), 75 (2006).
[Crossref]

Bao, C.

Barnett, S.

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Beijersbergen, M. W.

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] [PubMed]

Birnbaum, K. M.

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] [PubMed]

Cerf, N. J.

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67(1), 012311 (2003).
[Crossref]

Chandrasekaran, N.

Changyu, L.

L. Changyu, I. B. Djordjevic, and M. Cvijetic, “Quantum Few-Mode Fiber Communications Based on the Orbital Angular Momentum,” Photonics Technology Letters, IEEE 25(1), 3–6 (2013).
[Crossref]

Courtial, J.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, 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] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Cui, Q.

Q. Cui, M. Li, and Z. Yu, “Influence of topological charges on random wandering of optical vortex propagating through turbulent atmosphere,” Opt. Commun. 329, 10–14 (2014).
[Crossref]

Cvijetic, M.

L. Changyu, I. B. Djordjevic, and M. Cvijetic, “Quantum Few-Mode Fiber Communications Based on the Orbital Angular Momentum,” Photonics Technology Letters, IEEE 25(1), 3–6 (2013).
[Crossref]

Ding, J.

Djordjevic, I. B.

L. Changyu, I. B. Djordjevic, and M. Cvijetic, “Quantum Few-Mode Fiber Communications Based on the Orbital Angular Momentum,” Photonics Technology Letters, IEEE 25(1), 3–6 (2013).
[Crossref]

Dolinar, S.

Dolinar, S. J.

Durt, T.

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67(1), 012311 (2003).
[Crossref]

Eliel, E. R.

Erkmen, B. I.

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]

Franke-Arnold, S.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, 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] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Gbur, G.

Gibson, G.

Gisin, N.

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67(1), 012311 (2003).
[Crossref]

Gong, L. Y.

Gregor, W.

G. Simon, J. Thomas, V. Alipasha, W. Gregor, and Z. Anton, “Experimental quantum cryptography with qutrits,” New J. Phys. 8(5), 75 (2006).
[Crossref]

Huang, H.

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] [PubMed]

Lavery, M. P. J.

Leach, J.

Lemelle, D. S.

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum Key Distribution with Higher-Order Alphabets Using Spatially Encoded Qudits,” Phys. Rev. Lett. 96(9), 090501 (2006).
[Crossref] [PubMed]

Li, M.

Q. Cui, M. Li, and Z. Yu, “Influence of topological charges on random wandering of optical vortex propagating through turbulent atmosphere,” Opt. Commun. 329, 10–14 (2014).
[Crossref]

Magaña-Loaiza, O. S.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16(3), 033020 (2014).
[Crossref]

Maher, L.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16(3), 033020 (2014).
[Crossref]

Malik, M.

Mirhosseini, M.

Monken, C. H.

Neifeld, M. A.

O’Sullivan, M.

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.

Pors, B.-J.

Ramachandran, S.

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] [PubMed]

Ren, Y.

Ribeiro, P. H. S.

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum Key Distribution with Higher-Order Alphabets Using Spatially Encoded Qudits,” Phys. Rev. Lett. 96(9), 090501 (2006).
[Crossref] [PubMed]

Richardson, C. E.

L. C. Andrews, S. Vester, and C. E. Richardson, “Analytic Expressions for the Wave Structure Function Based on a Bump Spectral Model for Refractive Index Fluctuations,” J. Mod. Opt. 40(5), 931–938 (1993).
[Crossref]

Robertson, D. J.

Rodenburg, B.

Rogawski, D.

Shapiro, J. H.

Simon, G.

G. Simon, J. Thomas, V. Alipasha, W. Gregor, and Z. Anton, “Experimental quantum cryptography with qutrits,” New J. Phys. 8(5), 75 (2006).
[Crossref]

Spreeuw, R. J. C.

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] [PubMed]

Steinhoff, N. K.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16(3), 033020 (2014).
[Crossref]

Thomas, J.

G. Simon, J. Thomas, V. Alipasha, W. Gregor, and Z. Anton, “Experimental quantum cryptography with qutrits,” New J. Phys. 8(5), 75 (2006).
[Crossref]

Tur, M.

Tyler, G. A.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16(3), 033020 (2014).
[Crossref]

Tyson, R. K.

Vasic, B. V.

Vasnetsov, M.

Vester, S.

L. C. Andrews, S. Vester, and C. E. Richardson, “Analytic Expressions for the Wave Structure Function Based on a Bump Spectral Model for Refractive Index Fluctuations,” J. Mod. Opt. 40(5), 931–938 (1993).
[Crossref]

Walborn, S. P.

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum Key Distribution with Higher-Order Alphabets Using Spatially Encoded Qudits,” Phys. Rev. Lett. 96(9), 090501 (2006).
[Crossref] [PubMed]

Wang, J.

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]

Willner, A. E.

Willner, M. J.

Woerdman, J. P.

B.-J. 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).
[PubMed]

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] [PubMed]

Xie, G.

Yan, Y.

Yanakas, M.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New J. Phys. 16(3), 033020 (2014).
[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.

Yu, Z.

Q. Cui, M. Li, and Z. Yu, “Influence of topological charges on random wandering of optical vortex propagating through turbulent atmosphere,” Opt. Commun. 329, 10–14 (2014).
[Crossref]

Yue, Y.

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

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] [PubMed]

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]

Zhao, S. M.

Zheng, B. Y.

Zukowski, M.

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67(1), 012311 (2003).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (2)

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

L. C. Andrews, S. Vester, and C. E. Richardson, “Analytic Expressions for the Wave Structure Function Based on a Bump Spectral Model for Refractive Index Fluctuations,” J. Mod. Opt. 40(5), 931–938 (1993).
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Figures (7)

Fig. 1
Fig. 1 Schematic of OAM-based FSO system with AO compensation.
Fig. 2
Fig. 2 (a) Phase screen generated by Monte Carlo phase screen method; (b) validation results.
Fig. 3
Fig. 3 Strehl ratio of OAM-based FSO with AO compensation.
Fig. 4
Fig. 4 Wavefront phase distortions resulting from atmospheric turbulence (a) without AO correction; (b) with AO correction.
Fig. 5
Fig. 5 Crosstalk (a) without AO correction; (b) with AO correction.
Fig. 6
Fig. 6 Channel capacities of OAM-based FSO.
Fig. 7
Fig. 7 Temporal properties of OAM-based FSO under dynamically evolving atmosphere: (a) Strehl ratio; (b) channel capacity.

Equations (16)

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Φ ϕ ( κ ) = 0.49 r 0 5 / 3 exp ( κ 2 / κ m 2 ) ( κ 2 + κ 0 2 ) 11 / 6 , for 0 κ < ,
D ϕ ( r ) = 8 π 0 κ 2 Φ ϕ ( κ ) ( 1 sin κ r κ r ) d κ ,
D ϕ ( r ) = 3.08 r 0 5 / 3 { Γ ( 5 6 ) κ m 5 / 3 [ 1 F 1 1 ( 5 6 ; 1 ; κ m 2 r 2 4 ) ] 9 5 κ 0 1 / 3 r 2 } ,
Δ = max { | D ϕ ( r ) theory D ϕ ( r ) fitting | max { D ϕ ( r ) theory } } ,
ϕ p = m = 1 N a m Z m ( x , y ) ,
[ Z 1 ( x , y ) x | ( x 1 , y 1 ) Z N ( x , y ) x | ( x 1 , y 1 ) Z 1 ( x , y ) x | ( x 277 , y 277 ) Z N ( x , y ) x | ( x 277 , y 277 ) Z 1 ( x , y ) y | ( x 1 , y 1 ) Z N ( x , y ) y | ( x 1 , y 1 ) Z 1 ( x , y ) y | ( x 277 , y 277 ) Z N ( x , y ) y | ( x 277 , y 277 ) ] [ a 1 a N ] = [ ϕ p x | ( x 1 , y 1 ) ϕ p x | ( x 277 , y 277 ) ϕ p y | ( x 1 , y 1 ) ϕ p y | ( x 277 , y 277 ) ] .
S = 1 π 2 | 0 1 0 2 π exp ( i k ϕ p ) ρ d ρ d φ | 2 ,
u ( r , θ , z ) = 2 π | | ! 1 ω ( z ) [ 2 r ω ( z ) ] | | exp [ r 2 ω 2 ( z ) ] exp [ i k r 2 z 2 ( z 2 + z R 2 ) ] × exp [ i ( | | + 1 ) tan 1 z z R ] exp ( i θ ) ,
r ( z ) = ω 0 2 + λ 2 z 2 / π 2 ω 0 2 | | + 1 .
u ( r , θ ) = C u ( r , θ ) ,
u 0 ( r , θ ) | u ( r , θ ) = { | u 0 ( r , θ ) | 2 r d r d θ , if = 0 0 , if 0 ,
P ( | 0 ) = | u ( r , θ ) | u ( r , θ ) I 0 | 2 = | C | 2 ,
I 0 = 0 D / 2 0 2 π | u 0 ( r , θ ) | 2 r d r d θ .
u ( r , θ ) = u 0 ( r , θ ) exp [ i ξ ( r , θ ) ] ,
ξ ( r , θ ) = 1500 1550 ξ 0 ( r , θ ) ,
C channel = max { p i } [ H ( Y ) H ( Y | X ) ] = max { P i } ( i j p i P j i log 2 i p i P j i P j i ) ,

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