Physical-layer security in fractional orbital angular momentum multiplexing under atmospheric turbulence channel

Yaqin Zhao; Jinjiang Li; Xin Zhong; Hongyan Shi; Hongyan Shi; Hongyan Shi

doi:10.1364/OE.27.023751

Optics Express
Vol. 27,
Issue 17,
pp. 23751-23762
(2019)
•https://doi.org/10.1364/OE.27.023751

Physical-layer security in fractional orbital angular momentum multiplexing under atmospheric turbulence channel

Yaqin Zhao, Jinjiang Li, Xin Zhong, and Hongyan Shi

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Yaqin Zhao, Jinjiang Li, Xin Zhong, and Hongyan Shi, "Physical-layer security in fractional orbital angular momentum multiplexing under atmospheric turbulence channel," Opt. Express 27, 23751-23762 (2019)

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Table of Contents Category
- Optical Communications and Interconnects
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: June 20, 2019
- Revised Manuscript: July 25, 2019
- Manuscript Accepted: July 26, 2019
- Published: August 5, 2019

Abstract

In this paper, the physical layer security (PLS) of fractional orbital angular momentum (OAM) multiplexing under atmospheric turbulence channels is studied. Based on the PLS theory, the secrecy capacities and the probabilities of positive secrecy capacities of fractional OAM (FrOAM) multiplexing systems with different topological charge intervals are analyzed. The influence of the eavesdropping ratio and the power allocation on secrecy capacities are compared. The simulation results show that, under the finite aperture limitation, the FrOAM multiplexing technique provides higher security over the integer OAM multiplexing in terms of the total secrecy capacities under weak and medium turbulence.

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References

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Year
Author
Publication

Z. Qu and I. B. Djordjevic, “High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing,” Opt. Express 25(7), 7919–7928 (2017).
[Crossref]
S. Li and J. Wang, “Adaptive free-space optical communications through turbulence using self-healing bessel beams,” Sci. Rep. 7(1), 43233 (2017).
[Crossref]
A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J. 54(8), 1355–1387 (1975).
[Crossref]
K. Shaneman and S. Gray, “Optical network security: technical analysis of fiber tapping mechanisms and methods for detection amp; prevention,” in IEEE MILCOM 2004. Military Communications Conference, 2004., vol. 2 (2004), 711–716.
J. Barros and M. R. D. Rodrigues, “Secrecy capacity of wireless channels,” in 2006 IEEE International Symposium on Information Theory, (2006) pp. 356–360.
M. Bloch, J. Barros, M. R. D. Rodrigues, and S. W. McLaughlin, “Wireless information-theoretic security,” IEEE Trans. Inf. Theory 54(6), 2515–2534 (2008).
[Crossref]
A. Mostafa and L. Lampe, “Physical-layer security for indoor visible light communications,” in 2014 IEEE International Conference on Communications (ICC), (2014) pp. 3342–3347.
V. G. Sidorovich, “Optical countermeasures and security of free-space optical communication links,” Proc. SPIE 5614, 97 (2004).
[Crossref]
M. Agaskar and V. W. S. Chan, “Nulling strategies for preventing interference and interception of free space optical communication,” in 2013 IEEE International Conference on Communications (ICC), (2013) pp. 3927–3932.
F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
[Crossref]
M. Obeed, A. M. Salhab, M. Alouini, and S. A. Zummo, “Survey on physical layer security in optical wireless communication systems,” in 2018 Seventh International Conference on Communications and Networking (ComNet), (2018), pp. 1–5.
J. Ji, X. Chen, and Q. Huang, “Performance analysis of fso/cdma system based on binary symmetric wiretap channel,” IET Commun. 13(1), 116–123 (2019).
[Crossref]
H. Lei, Z. Dai, I. S. Ansari, K. Park, G. Pan, and M. Alouini, “On secrecy performance of mixed rf-fso systems,” IEEE Photonics J. 9(4), 1–14 (2017).
[Crossref]
X. Sun and I. B. Djordjevic, “Physical-layer security in orbital angular momentum multiplexing free-space optical communications,” IEEE Photonics J. 8(1), 1–10 (2016).
[Crossref]
I. B. Djordjevic, S. Zhang, and T. Wang, “Oam-based physical-layer security enabled by hybrid free-space optical-terahertz technology,” in 2017 13th International Conference on Advanced Technologies, Systems and Services in Telecommunications (TELSIKS), (2017), pp. 317–320.
W. Zhang, S. Zheng, X. Hui, R. Dong, X. Jin, H. Chi, and X. Zhang, “Mode division multiplexing communication using microwave orbital angular momentum: An experimental study,” IEEE Trans. Wireless Commun. 16(2), 1308–1318 (2017).
[Crossref]
I. B. Djordjevic, “Oam-based hybrid free-space optical-terahertz multidimensional coded modulation and physical-layer security,” IEEE Photonics J. 9(4), 1–12 (2017).
[Crossref]
T. Wang and I. B. Djordjevic, “Physical-layer security in free-space optical communications using bessel-gaussian beams,” in 2018 IEEE Photonics Conference (IPC), (2018), pp. 1–2.
T. Wang, J. A. Gariano, and I. B. Djordjevic, “Employing bessel-gaussian beams to improve physical-layer security in free-space optical communications,” IEEE Photonics J. 10(5), 1–13 (2018).
[Crossref]
G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[Crossref]
I. B. Djordjevic, “Deep-space and near-earth optical communications by coded orbital angular momentum (oam) modulation,” Opt. Express 19(15), 14277–14289 (2011).
[Crossref]
J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]
M. Zhu, X. Zhang, W. Zhang, L. Xi, and X. Tang, “A new designed oam fiber enabling the integration of classical and quantum optical fiber communications,” Proc. SPIE 9619, 96190K (2015).
[Crossref]
D. Cozzolino, D. Bacco, B. D. Lio, K. Ingerslev, Y. Ding, K. Dalgaard, P. Kristensen, M. Galili, K. Rottwitt, S. Ramachandran, and L. K. Oxenlnwe, “Fiber-based high-dimensional quantum key distribution with twisted photons,” in CLEO Pacific Rim Conference 2018, (Optical Society of America, 2018), p. Th5A.1
D. Cozzolino, D. Bacco, B. Da Lio, K. Ingerslev, Y. Ding, K. Dalgaard, P. Kristensen, M. Galili, K. Rottwitt, S. Ramachandran, and L. K. Oxenløwe, “Orbital angular momentum states enabling fiber-based high-dimensional quantum communication,” Phys. Rev. Appl. 11(6), 064058 (2019).
[Crossref]
J. M. Kahn, G. Li, X. Li, and N. Zhao, “Capacity limits for free-space channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. W1B.3.
Y. Zhao, X. Zhong, G. Ren, S. He, and Z. Wu, “Capacity of arbitrary-order orbital angular momentum multiplexing system,” Opt. Commun. 387, 432–439 (2017).
[Crossref]
J. Zhou, Z. Xu, and J. Wang, “Performance evaluation of fractional orbital angular momentum (oam) based ldpc-coded free-space optical communications with atmospheric turbulence,” in Asia Communications and Photonics Conference 2014, (Optical Society of America, 2014), p. AF3D.2.
Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (oam) free-space optical communications with atmospheric turbulence assisted by mimo equalization,” in Advanced Photonics for Communications, (Optical Society of America, 2014), p. JT3A.1.
M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20(12), 13195–13200 (2012).
[Crossref]
I. B. Djordjevic and M. Arabaci, “Ldpc-coded orbital angular momentum (oam) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010).
[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, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
[Crossref]
X. Zhong, Y. Zhao, G. Ren, S. He, and Z. Wu, “Influence of finite apertures on orthogonality and completeness of laguerre-gaussian beams,” IEEE Access 6, 8742–8754 (2018).
[Crossref]
A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. 39(30), 5426–5445 (2000).
[Crossref]
J. Xiang, “Fast and accurate simulation of the turbulent phase screen using fast fourier transform,” Opt. Eng. 53(1), 016110 (2014).
[Crossref]
J. Sun, H. Xie, and D. Li, “Capacity in mimo channels based on different power allocation,” in 2010 Fifth International Conference on Internet Computing for Science and Engineering, (2010), pp. 93–96.
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]

2019 (2)

J. Ji, X. Chen, and Q. Huang, “Performance analysis of fso/cdma system based on binary symmetric wiretap channel,” IET Commun. 13(1), 116–123 (2019).
[Crossref]

D. Cozzolino, D. Bacco, B. Da Lio, K. Ingerslev, Y. Ding, K. Dalgaard, P. Kristensen, M. Galili, K. Rottwitt, S. Ramachandran, and L. K. Oxenløwe, “Orbital angular momentum states enabling fiber-based high-dimensional quantum communication,” Phys. Rev. Appl. 11(6), 064058 (2019).
[Crossref]

2018 (2)

T. Wang, J. A. Gariano, and I. B. Djordjevic, “Employing bessel-gaussian beams to improve physical-layer security in free-space optical communications,” IEEE Photonics J. 10(5), 1–13 (2018).
[Crossref]

X. Zhong, Y. Zhao, G. Ren, S. He, and Z. Wu, “Influence of finite apertures on orthogonality and completeness of laguerre-gaussian beams,” IEEE Access 6, 8742–8754 (2018).
[Crossref]

2017 (6)

Y. Zhao, X. Zhong, G. Ren, S. He, and Z. Wu, “Capacity of arbitrary-order orbital angular momentum multiplexing system,” Opt. Commun. 387, 432–439 (2017).
[Crossref]

H. Lei, Z. Dai, I. S. Ansari, K. Park, G. Pan, and M. Alouini, “On secrecy performance of mixed rf-fso systems,” IEEE Photonics J. 9(4), 1–14 (2017).
[Crossref]

W. Zhang, S. Zheng, X. Hui, R. Dong, X. Jin, H. Chi, and X. Zhang, “Mode division multiplexing communication using microwave orbital angular momentum: An experimental study,” IEEE Trans. Wireless Commun. 16(2), 1308–1318 (2017).
[Crossref]

I. B. Djordjevic, “Oam-based hybrid free-space optical-terahertz multidimensional coded modulation and physical-layer security,” IEEE Photonics J. 9(4), 1–12 (2017).
[Crossref]

Z. Qu and I. B. Djordjevic, “High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing,” Opt. Express 25(7), 7919–7928 (2017).
[Crossref]

S. Li and J. Wang, “Adaptive free-space optical communications through turbulence using self-healing bessel beams,” Sci. Rep. 7(1), 43233 (2017).
[Crossref]

2016 (1)

X. Sun and I. B. Djordjevic, “Physical-layer security in orbital angular momentum multiplexing free-space optical communications,” IEEE Photonics J. 8(1), 1–10 (2016).
[Crossref]

2015 (3)

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
[Crossref]

M. Zhu, X. Zhang, W. Zhang, L. Xi, and X. Tang, “A new designed oam fiber enabling the integration of classical and quantum optical fiber communications,” Proc. SPIE 9619, 96190K (2015).
[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]

2014 (2)

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, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
[Crossref]

J. Xiang, “Fast and accurate simulation of the turbulent phase screen using fast fourier transform,” Opt. Eng. 53(1), 016110 (2014).
[Crossref]

2012 (2)

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

M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20(12), 13195–13200 (2012).
[Crossref]

2011 (1)

I. B. Djordjevic, “Deep-space and near-earth optical communications by coded orbital angular momentum (oam) modulation,” Opt. Express 19(15), 14277–14289 (2011).
[Crossref]

2010 (1)

I. B. Djordjevic and M. Arabaci, “Ldpc-coded orbital angular momentum (oam) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010).
[Crossref]

2008 (1)

M. Bloch, J. Barros, M. R. D. Rodrigues, and S. W. McLaughlin, “Wireless information-theoretic security,” IEEE Trans. Inf. Theory 54(6), 2515–2534 (2008).
[Crossref]

2004 (2)

V. G. Sidorovich, “Optical countermeasures and security of free-space optical communication links,” Proc. SPIE 5614, 97 (2004).
[Crossref]

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

2000 (1)

A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. 39(30), 5426–5445 (2000).
[Crossref]

1975 (1)

A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J. 54(8), 1355–1387 (1975).
[Crossref]

Agaskar, M.

M. Agaskar and V. W. S. Chan, “Nulling strategies for preventing interference and interception of free space optical communication,” in 2013 IEEE International Conference on Communications (ICC), (2013) pp. 3927–3932.

Ahmed, N.

Alouini, M.

H. Lei, Z. Dai, I. S. Ansari, K. Park, G. Pan, and M. Alouini, “On secrecy performance of mixed rf-fso systems,” IEEE Photonics J. 9(4), 1–14 (2017).
[Crossref]

M. Obeed, A. M. Salhab, M. Alouini, and S. A. Zummo, “Survey on physical layer security in optical wireless communication systems,” in 2018 Seventh International Conference on Communications and Networking (ComNet), (2018), pp. 1–5.

Ansari, I. S.

H. Lei, Z. Dai, I. S. Ansari, K. Park, G. Pan, and M. Alouini, “On secrecy performance of mixed rf-fso systems,” IEEE Photonics J. 9(4), 1–14 (2017).
[Crossref]

Arabaci, M.

I. B. Djordjevic and M. Arabaci, “Ldpc-coded orbital angular momentum (oam) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010).
[Crossref]

Bacco, D.

D. Cozzolino, D. Bacco, B. D. Lio, K. Ingerslev, Y. Ding, K. Dalgaard, P. Kristensen, M. Galili, K. Rottwitt, S. Ramachandran, and L. K. Oxenlnwe, “Fiber-based high-dimensional quantum key distribution with twisted photons,” in CLEO Pacific Rim Conference 2018, (Optical Society of America, 2018), p. Th5A.1

Bao, C.

Barnett, S. M.

Barros, J.

M. Bloch, J. Barros, M. R. D. Rodrigues, and S. W. McLaughlin, “Wireless information-theoretic security,” IEEE Trans. Inf. Theory 54(6), 2515–2534 (2008).
[Crossref]

J. Barros and M. R. D. Rodrigues, “Secrecy capacity of wireless channels,” in 2006 IEEE International Symposium on Information Theory, (2006) pp. 356–360.

Belmonte, A.

A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. 39(30), 5426–5445 (2000).
[Crossref]

Bloch, M.

M. Bloch, J. Barros, M. R. D. Rodrigues, and S. W. McLaughlin, “Wireless information-theoretic security,” IEEE Trans. Inf. Theory 54(6), 2515–2534 (2008).
[Crossref]

Boyd, R. W.

Chan, V. W. S.

Chen, X.

J. Ji, X. Chen, and Q. Huang, “Performance analysis of fso/cdma system based on binary symmetric wiretap channel,” IET Commun. 13(1), 116–123 (2019).
[Crossref]

Chi, H.

Courtial, J.

Cozzolino, D.

Da Lio, B.

Dai, Z.

H. Lei, Z. Dai, I. S. Ansari, K. Park, G. Pan, and M. Alouini, “On secrecy performance of mixed rf-fso systems,” IEEE Photonics J. 9(4), 1–14 (2017).
[Crossref]

Dalgaard, K.

Ding, Y.

Djordjevic, I. B.

I. B. Djordjevic, “Oam-based hybrid free-space optical-terahertz multidimensional coded modulation and physical-layer security,” IEEE Photonics J. 9(4), 1–12 (2017).
[Crossref]

X. Sun and I. B. Djordjevic, “Physical-layer security in orbital angular momentum multiplexing free-space optical communications,” IEEE Photonics J. 8(1), 1–10 (2016).
[Crossref]

I. B. Djordjevic, “Deep-space and near-earth optical communications by coded orbital angular momentum (oam) modulation,” Opt. Express 19(15), 14277–14289 (2011).
[Crossref]

I. B. Djordjevic and M. Arabaci, “Ldpc-coded orbital angular momentum (oam) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010).
[Crossref]

I. B. Djordjevic, S. Zhang, and T. Wang, “Oam-based physical-layer security enabled by hybrid free-space optical-terahertz technology,” in 2017 13th International Conference on Advanced Technologies, Systems and Services in Telecommunications (TELSIKS), (2017), pp. 317–320.

T. Wang and I. B. Djordjevic, “Physical-layer security in free-space optical communications using bessel-gaussian beams,” in 2018 IEEE Photonics Conference (IPC), (2018), pp. 1–2.

Dolinar, S.

Dong, R.

Erkmen, B. I.

Fazal, I. M.

Franke-Arnold, S.

Galili, M.

Gariano, J. A.

Garrido-Balsells, J. M.

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
[Crossref]

Gibson, G.

Gomez, G.

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
[Crossref]

Gray, S.

K. Shaneman and S. Gray, “Optical network security: technical analysis of fiber tapping mechanisms and methods for detection amp; prevention,” in IEEE MILCOM 2004. Military Communications Conference, 2004., vol. 2 (2004), 711–716.

Gui, C.

Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (oam) free-space optical communications with atmospheric turbulence assisted by mimo equalization,” in Advanced Photonics for Communications, (Optical Society of America, 2014), p. JT3A.1.

He, S.

X. Zhong, Y. Zhao, G. Ren, S. He, and Z. Wu, “Influence of finite apertures on orthogonality and completeness of laguerre-gaussian beams,” IEEE Access 6, 8742–8754 (2018).
[Crossref]

Y. Zhao, X. Zhong, G. Ren, S. He, and Z. Wu, “Capacity of arbitrary-order orbital angular momentum multiplexing system,” Opt. Commun. 387, 432–439 (2017).
[Crossref]

Huang, H.

Huang, Q.

J. Ji, X. Chen, and Q. Huang, “Performance analysis of fso/cdma system based on binary symmetric wiretap channel,” IET Commun. 13(1), 116–123 (2019).
[Crossref]

Hui, X.

Ingerslev, K.

Ji, J.

J. Ji, X. Chen, and Q. Huang, “Performance analysis of fso/cdma system based on binary symmetric wiretap channel,” IET Commun. 13(1), 116–123 (2019).
[Crossref]

Jin, X.

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]

J. M. Kahn, G. Li, X. Li, and N. Zhao, “Capacity limits for free-space channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. W1B.3.

Kristensen, P.

Lampe, L.

A. Mostafa and L. Lampe, “Physical-layer security for indoor visible light communications,” in 2014 IEEE International Conference on Communications (ICC), (2014) pp. 3342–3347.

Lavery, M. P. J.

Leach, J.

Lei, H.

H. Lei, Z. Dai, I. S. Ansari, K. Park, G. Pan, and M. Alouini, “On secrecy performance of mixed rf-fso systems,” IEEE Photonics J. 9(4), 1–14 (2017).
[Crossref]

Li, D.

J. Sun, H. Xie, and D. Li, “Capacity in mimo channels based on different power allocation,” in 2010 Fifth International Conference on Internet Computing for Science and Engineering, (2010), pp. 93–96.

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]

J. M. Kahn, G. Li, X. Li, and N. Zhao, “Capacity limits for free-space channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. W1B.3.

Li, S.

S. Li and J. Wang, “Adaptive free-space optical communications through turbulence using self-healing bessel beams,” Sci. Rep. 7(1), 43233 (2017).
[Crossref]

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]

J. M. Kahn, G. Li, X. Li, and N. Zhao, “Capacity limits for free-space channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. W1B.3.

Lio, B. D.

Lopez-Martinez, F. J.

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
[Crossref]

Malik, M.

McLaughlin, S. W.

M. Bloch, J. Barros, M. R. D. Rodrigues, and S. W. McLaughlin, “Wireless information-theoretic security,” IEEE Trans. Inf. Theory 54(6), 2515–2534 (2008).
[Crossref]

Mirhosseini, M.

Mostafa, A.

A. Mostafa and L. Lampe, “Physical-layer security for indoor visible light communications,” in 2014 IEEE International Conference on Communications (ICC), (2014) pp. 3342–3347.

Neifeld, M. A.

O’Sullivan, M.

Obeed, M.

Oxenlnwe, L. K.

Oxenløwe, L. K.

Padgett, M. J.

Pan, G.

H. Lei, Z. Dai, I. S. Ansari, K. Park, G. Pan, and M. Alouini, “On secrecy performance of mixed rf-fso systems,” IEEE Photonics J. 9(4), 1–14 (2017).
[Crossref]

Park, K.

H. Lei, Z. Dai, I. S. Ansari, K. Park, G. Pan, and M. Alouini, “On secrecy performance of mixed rf-fso systems,” IEEE Photonics J. 9(4), 1–14 (2017).
[Crossref]

Pas’ko, V.

Qu, Z.

Ramachandran, S.

Ren, G.

X. Zhong, Y. Zhao, G. Ren, S. He, and Z. Wu, “Influence of finite apertures on orthogonality and completeness of laguerre-gaussian beams,” IEEE Access 6, 8742–8754 (2018).
[Crossref]

Y. Zhao, X. Zhong, G. Ren, S. He, and Z. Wu, “Capacity of arbitrary-order orbital angular momentum multiplexing system,” Opt. Commun. 387, 432–439 (2017).
[Crossref]

Ren, Y.

Rodenburg, B.

Rodrigues, M. R. D.

M. Bloch, J. Barros, M. R. D. Rodrigues, and S. W. McLaughlin, “Wireless information-theoretic security,” IEEE Trans. Inf. Theory 54(6), 2515–2534 (2008).
[Crossref]

J. Barros and M. R. D. Rodrigues, “Secrecy capacity of wireless channels,” in 2006 IEEE International Symposium on Information Theory, (2006) pp. 356–360.

Rottwitt, K.

Salhab, A. M.

Shaneman, K.

Shapiro, J. H.

Sidorovich, V. G.

V. G. Sidorovich, “Optical countermeasures and security of free-space optical communication links,” Proc. SPIE 5614, 97 (2004).
[Crossref]

Sun, J.

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Fig. 1. Schematic diagram of OAM multiplexing system under atmospheric turbulence channel. BS: beam splitter, M: mirror.

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Fig. 2. Simulation results of the atmospheric turbulence phase distribution with

$r_0=0.1$

m based on FFT compensation. (a) An example of the atmospheric turbulence phase distribution. (b) Comparison of the simulated and the theoretical phase structure functions.

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Fig. 3. Comparison of channel capacity between integer OAM multiplexing systems and FrOAM multiplexing systems with different power allocation schemes. ECP: equal channel power, FSP: fixed system power.

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Fig. 4. Aggregate secrecy capacities of different transmitted modes sets varies with turbulence intensity. ECP: equal channel power scheme. FSP:fixed system power.

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Fig. 5. Comparison of the aggregate secrecy capacities and the average secrecy capacities per channel of different systems under ECP scheme. The solid lines are the aggregate secrecy capacities and the dotted lines are the average secrecy capacities per channel.

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Fig. 6. Changes in secrecy capacities of the systems with different topological charge sets and different interception ratios. (a) System

$S$

. (b) System

$S1$

. (c) System

$S2$

. (d) System

$S3$

. ECP: equal channel power. FSP: fixed system power.

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Fig. 7. Relation between Eve’s interception ratio and the probabilities of positive secrecy capacity of OAM multiplexing systems with different topological charge sets under different turbulence intensities. (a)

$C_n^{2}=1\times 10^{-14}\textrm {m}^{-2/3}$

. (b)

$C_n^{2}=5\times 10^{-14}\textrm {m}^{-2/3}$

. (c)

$C_n^{2}=1\times 10^{-13}\textrm {m}^{-2/3}$

. (d)

$C_n^{2}=5\times 10^{-13}\textrm {m}^{-2/3}$

. ECP: equal channel power. FSP: fixed system power.

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Tables (1)

Table 1. Topological charge sets and key parameters of the simulated systems

View Table

Equations (15)

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

\begin{aligned} L G_{p}^{(ℓ)} (r, ϕ, z) & = \sqrt{\frac{2 p!}{π (p + | ℓ |)!}} \frac{1}{ω (z)} {[\frac{r \sqrt{2}}{ω (z)}]}^{| ℓ |} L_{p}^{(| ℓ |)} [\frac{2 r^{2}}{ω^{2} (z)}] \exp [- \frac{r^{2}}{ω^{2} (z)}] \times \\ \exp [- \frac{i k r z}{2 (z^{2} + z_{R}^{2})}] \exp [i (2 p + | ℓ | + 1) \tan^{- 1} (\frac{z}{z_{R}})] \exp (- i ℓ ϕ), \end{aligned}

{⟨ L G_{p_{1}}^{(ℓ_{1})}, L G_{p_{2}}^{(ℓ_{2})} ⟩ |}_{r_{a}} = C_{(p_{1}, p_{2})}^{(ℓ_{1}, ℓ_{2})} S (ℓ_{1} - ℓ_{2}) {T_{(p_{1}, p_{2})}^{(ℓ_{1}, ℓ_{2})} [g (x)] |}_{u},

\begin{aligned} C_{(p_{1}, p_{2})}^{(ℓ_{1}, ℓ_{2})} = \sqrt{\frac{p_{1}! p_{2}!}{Γ (p_{1} + | ℓ_{1} | + 1) Γ (p_{2} + | ℓ_{2} | + 1)}}, \end{aligned}

\begin{aligned} S (ℓ_{1} - ℓ_{2}) = \frac{\sin [π (ℓ_{1} - ℓ_{2})]}{π (ℓ_{1} - ℓ_{2})} \exp [j π (ℓ_{1} - ℓ_{2})], \end{aligned}

\begin{aligned} {T_{(p_{1}, p_{2})}^{(ℓ_{1}, ℓ_{2})} [g (x)] |}_{u} = {\begin{cases} \frac{1}{p_{1}!} \int_{0}^{u} x^{\frac{| ℓ_{2} | - | ℓ_{1} |}{2}} D^{p_{1}} [e^{- x} x^{p_{1} + | ℓ_{1} |}] L_{p_{2}}^{(| ℓ_{2} |)} (x) d x, \\ \frac{1}{p_{2}!} \int_{0}^{u} x^{\frac{| ℓ_{1} | - | ℓ_{2} |}{2}} D^{p_{2}} [e^{- x} x^{p_{2} + | ℓ_{2} |}] L_{p_{1}}^{(| ℓ_{1} |)} (x) d x, \end{cases} \end{aligned}

Φ_{n} (κ) = 0.033 C_{n}^{2} κ^{- \frac{11}{3}},

D_{theory} (r) = 6.88 {(\frac{r}{r_{0}})}^{\frac{5}{3}} .

H = [\begin{matrix} h_{1, 1} & h_{1, 2} & \dots & h_{1, N_{T}} \\ h_{2, 1} & h_{2, 2} & \dots & h_{2, N_{T}} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ h_{N_{R}, 1} & h_{N_{R}, 2} & \dots & h_{N_{R}, N_{T}} \end{matrix}],

y = \sqrt{\frac{P_{x}}{N_{T}}} H x + n,

C (H) = \log_{2} [det (I_{N_{R}} + \frac{P_{x}}{N_{T} N_{0}} {H H}^{H})],

\bar{C} = E {C (H)},

C_{AB} = \log_{2} {det [I_{N_{R}} + \frac{(1 - r_{e}) P_{R}}{N_{R} N_{0}} H_{B} H_{B}^{H}]},

C_{AE} = \log_{2} [det (I_{N_{R}} + \frac{r_{e} P_{R}}{N_{R} N_{0}} H_{E} H_{E}^{H})],

C_{S} = C_{AB} - C_{AE} .

P_{S}^{+} = Pr (C_{S} > 0)

System index	Topological charge interval	Topological charge set	Mode number $M$
$S$	1	${- 2, - 1, 0, 1, 2}$	5
$S 1$	0.8	${- 1.6, - 0.8, 0, 0.8, 1.6}$	5
$S 2$	0.6	${- 1.8, - 1.2, - 0.6, 0, 0.6, 1.2, 1.8}$	7
$S 3$	0.4	${- 2, - 1.6, - 1.2, - 0.8, - 0.4,$	11
		$0, 0.4, 0.8, 1.2, 1.6, 2}$