Abstract

We derive the probabilities of the signal OAM state and crosstalk OAM state for a Laguerre-Gaussian (LG) beam propagating through Kolmogorov and Non-Kolmogorov turbulence, and derive the accurate analytical function of the probability for the received OAM state modulated by an arbitrary receiver aperture. The probability of the detected OAM state with a receiver aperture for different values of the radius is demonstrated numerically. Our numerical results show that the probability of the signal OAM state remains almost invariant when the radius of the receiver aperture varies. The probability of the crosstalk OAM state decreases with the decrease of the radius of the receiver aperture, thus it can be optimized by choosing a suitable value of the radius of the receiver aperture. Our results will be useful in free-space optical communications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (4)

N. Li, X. Chu, P. Zhang, X. Feng, C. Fan, and C. Qiao, “Compensation for the orbital angular momentum of a vortex beam in turbulent atmosphere by adaptive optics,” Opt. Laser Technol. 98, 7–11 (2018).
[Crossref]

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital-angular-momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

K. Zhang, Y. Yuan, D. Zhang, X. Ding, B. Ratni, S. N. Burokur, M. Lu, K. Tang, and Q. Wu, “Phase-engineered metalenses to generate converging and non-diffractive vortex beam carrying orbital angular momentum in microwave region,” Opt. Express 26(2), 1351–1360 (2018).
[Crossref] [PubMed]

M. Charnotskii, “Turbulence effects on fluctuations of the aperture-averaged orbital angular momentum,” J. Opt. Soc. Am. A 35(5), 702–711 (2018).
[Crossref] [PubMed]

2017 (2)

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams,” Sci. Rep. 7(1), 42276 (2017).
[Crossref] [PubMed]

Y. Yuan, T. Lei, S. Gao, X. Weng, L. Du, and X. Yuan, “The Orbital Angular Momentum Spreading for Cylindrical Vector Beams in Turbulent Atmosphere,” IEEE Photonics J. 9(2), 6100610 (2017).
[Crossref]

2016 (2)

2015 (3)

2014 (3)

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

M. Nairat and D. Voelz, “Propagation of rotational field correlation through atmospheric turbulence,” Opt. Lett. 39(7), 1838–1840 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (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]

B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37(17), 3735–3737 (2012).
[Crossref] [PubMed]

2011 (1)

X. Chu, C. Qiao, and X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43(7), 1150–1154 (2011).
[Crossref]

2010 (2)

2009 (1)

2008 (1)

2007 (1)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[Crossref]

2006 (1)

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)

1999 (1)

1980 (1)

1967 (1)

D. L. Fried, “Aperture Averaging of Scintillation,” J. Opt. Soc. Am. A 57(2), 169–175 (1967).
[Crossref]

Ahmed, N.

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[Crossref]

Anguita, J. A.

Barnett, S.

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]

Burokur, S. N.

Cai, Y.

Carter, W. H.

Chandrasekaran, N.

Charnotskii, M.

Chi, H.

Chu, X.

N. Li, X. Chu, P. Zhang, X. Feng, C. Fan, and C. Qiao, “Compensation for the orbital angular momentum of a vortex beam in turbulent atmosphere by adaptive optics,” Opt. Laser Technol. 98, 7–11 (2018).
[Crossref]

X. Chu, C. Qiao, and X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43(7), 1150–1154 (2011).
[Crossref]

Courtial, J.

Ding, D.

Ding, X.

Dolinar, S.

Du, L.

Y. Yuan, T. Lei, S. Gao, X. Weng, L. Du, and X. Yuan, “The Orbital Angular Momentum Spreading for Cylindrical Vector Beams in Turbulent Atmosphere,” IEEE Photonics J. 9(2), 6100610 (2017).
[Crossref]

Erkmen, B. I.

Fan, C.

N. Li, X. Chu, P. Zhang, X. Feng, C. Fan, and C. Qiao, “Compensation for the orbital angular momentum of a vortex beam in turbulent atmosphere by adaptive optics,” Opt. Laser Technol. 98, 7–11 (2018).
[Crossref]

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]

Feng, X.

N. Li, X. Chu, P. Zhang, X. Feng, C. Fan, and C. Qiao, “Compensation for the orbital angular momentum of a vortex beam in turbulent atmosphere by adaptive optics,” Opt. Laser Technol. 98, 7–11 (2018).
[Crossref]

X. Chu, C. Qiao, and X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43(7), 1150–1154 (2011).
[Crossref]

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[Crossref]

Fickler, R.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Fink, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Franke-Arnold, S.

Fried, D. L.

D. L. Fried, “Aperture Averaging of Scintillation,” J. Opt. Soc. Am. A 57(2), 169–175 (1967).
[Crossref]

Gao, S.

Y. Yuan, T. Lei, S. Gao, X. Weng, L. Du, and X. Yuan, “The Orbital Angular Momentum Spreading for Cylindrical Vector Beams in Turbulent Atmosphere,” IEEE Photonics J. 9(2), 6100610 (2017).
[Crossref]

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams,” Sci. Rep. 7(1), 42276 (2017).
[Crossref] [PubMed]

Gibson, G.

Handsteiner, J.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

He, Y.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Hu, L.

Hu, Z.

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital-angular-momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

Y. Zhu, L. Zhang, Z. Hu, and Y. Zhang, “Effects of non-Kolmogorov turbulence on the spiral spectrum of Hypergeometric-Gaussian laser beams,” Opt. Express 23(7), 9137–9146 (2015).
[Crossref] [PubMed]

Huang, H.

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]

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. 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]

Hui, X.

Jia, P.

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

Jiang, Y.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Jin, X.

Korotkova, O.

Krenn, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

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.

Lei, T.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams,” Sci. Rep. 7(1), 42276 (2017).
[Crossref] [PubMed]

Y. Yuan, T. Lei, S. Gao, X. Weng, L. Du, and X. Yuan, “The Orbital Angular Momentum Spreading for Cylindrical Vector Beams in Turbulent Atmosphere,” IEEE Photonics J. 9(2), 6100610 (2017).
[Crossref]

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

Li, N.

N. Li, X. Chu, P. Zhang, X. Feng, C. Fan, and C. Qiao, “Compensation for the orbital angular momentum of a vortex beam in turbulent atmosphere by adaptive optics,” Opt. Laser Technol. 98, 7–11 (2018).
[Crossref]

Li, Y.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams,” Sci. Rep. 7(1), 42276 (2017).
[Crossref] [PubMed]

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

Li, Z.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams,” Sci. Rep. 7(1), 42276 (2017).
[Crossref] [PubMed]

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

Liao, J.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Lin, J.

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

Liu, G. N.

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

Liu, X.

Lu, M.

Lukin, V. P.

Malik, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37(17), 3735–3737 (2012).
[Crossref] [PubMed]

Min, C.

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

Mirhosseini, M.

Nairat, M.

Neifeld, M.

Neifeld, M. A.

Niu, H.

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

Nosov, E. V.

Nosov, V. V.

O’Sullivan, M. N.

Ou, J.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

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.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[Crossref]

Qiao, C.

N. Li, X. Chu, P. Zhang, X. Feng, C. Fan, and C. Qiao, “Compensation for the orbital angular momentum of a vortex beam in turbulent atmosphere by adaptive optics,” Opt. Laser Technol. 98, 7–11 (2018).
[Crossref]

X. Chu, C. Qiao, and X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43(7), 1150–1154 (2011).
[Crossref]

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]

Ratni, B.

Ren, Y.

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]

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. 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.

Scheidl, T.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Shapiro, J. H.

Shchepakina, E.

Steinhoff, N. K.

Tang, H.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Tang, K.

Torgaev, A. V.

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[Crossref]

Tur, M.

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]

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.

Ursin, R.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Vasic, B. V.

Vasnetsov, M.

Voelz, D.

Wang, F.

Wang, J.

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital-angular-momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

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

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]

Wang, S.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Wei, M.

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital-angular-momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

Weng, X.

Y. Yuan, T. Lei, S. Gao, X. Weng, L. Du, and X. Yuan, “The Orbital Angular Momentum Spreading for Cylindrical Vector Beams in Turbulent Atmosphere,” IEEE Photonics J. 9(2), 6100610 (2017).
[Crossref]

Willner, A. E.

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]

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]

Wu, Q.

Xie, G.

Xie, Z.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams,” Sci. Rep. 7(1), 42276 (2017).
[Crossref] [PubMed]

Xu, X.

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

Yan, Y.

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]

Yu, C.

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

Yu, S.

Yuan, X.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams,” Sci. Rep. 7(1), 42276 (2017).
[Crossref] [PubMed]

Y. Yuan, T. Lei, S. Gao, X. Weng, L. Du, and X. Yuan, “The Orbital Angular Momentum Spreading for Cylindrical Vector Beams in Turbulent Atmosphere,” IEEE Photonics J. 9(2), 6100610 (2017).
[Crossref]

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

Yuan, Y.

K. Zhang, Y. Yuan, D. Zhang, X. Ding, B. Ratni, S. N. Burokur, M. Lu, K. Tang, and Q. Wu, “Phase-engineered metalenses to generate converging and non-diffractive vortex beam carrying orbital angular momentum in microwave region,” Opt. Express 26(2), 1351–1360 (2018).
[Crossref] [PubMed]

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams,” Sci. Rep. 7(1), 42276 (2017).
[Crossref] [PubMed]

Y. Yuan, T. Lei, S. Gao, X. Weng, L. Du, and X. Yuan, “The Orbital Angular Momentum Spreading for Cylindrical Vector Beams in Turbulent Atmosphere,” IEEE Photonics J. 9(2), 6100610 (2017).
[Crossref]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [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]

Zeilinger, A.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Zhang, D.

Zhang, J.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Zhang, K.

Zhang, L.

Zhang, M.

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

Zhang, P.

N. Li, X. Chu, P. Zhang, X. Feng, C. Fan, and C. Qiao, “Compensation for the orbital angular momentum of a vortex beam in turbulent atmosphere by adaptive optics,” Opt. Laser Technol. 98, 7–11 (2018).
[Crossref]

Zhang, X.

Zhang, Y.

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital-angular-momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

Y. Zhu, L. Zhang, Z. Hu, and Y. Zhang, “Effects of non-Kolmogorov turbulence on the spiral spectrum of Hypergeometric-Gaussian laser beams,” Opt. Express 23(7), 9137–9146 (2015).
[Crossref] [PubMed]

Zheng, S.

Zhu, J.

Zhu, Y.

Appl. Opt. (3)

IEEE Photonics J. (1)

Y. Yuan, T. Lei, S. Gao, X. Weng, L. Du, and X. Yuan, “The Orbital Angular Momentum Spreading for Cylindrical Vector Beams in Turbulent Atmosphere,” IEEE Photonics J. 9(2), 6100610 (2017).
[Crossref]

J. Opt. Soc. Am. A (3)

Light Sci. (1)

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

Nat. Photonics (1)

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]

New J. Phys. (1)

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Opt. Commun. (2)

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital-angular-momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

Opt. Express (6)

Opt. Laser Technol. (2)

X. Chu, C. Qiao, and X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43(7), 1150–1154 (2011).
[Crossref]

N. Li, X. Chu, P. Zhang, X. Feng, C. Fan, and C. Qiao, “Compensation for the orbital angular momentum of a vortex beam in turbulent atmosphere by adaptive optics,” Opt. Laser Technol. 98, 7–11 (2018).
[Crossref]

Opt. Lett. (5)

Photon. Res. (1)

Phys. Rev. Lett. (1)

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

Proc. SPIE (1)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[Crossref]

Sci. Rep. (1)

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams,” Sci. Rep. 7(1), 42276 (2017).
[Crossref] [PubMed]

Science (1)

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]

Other (2)

S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Elsevier Academic Press Burlington, 2000).

L. C. Andrews and R. L. Phillips, Laser beam propagation in the turbulent atmosphere, (2nd edition, SPIE press, Bellington, 2005).

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Figures (6)

Fig. 1
Fig. 1 Schematic of the OAM state disturbed by a circular receiver aperture and turbulent atmosphere.
Fig. 2
Fig. 2 Probability of the OAM state of a LG beam propagating through Kolmogorov turbulence optimized by a receiver aperture for different values of the radius a (a) 25mm (b) 50mm (c) 75mm and (d) infinity.
Fig. 3
Fig. 3 Probability of the OAM state of a LG beam propagating through Non-Kolmogorov turbulence optimized by a receiver aperture for different values of the radius a (a) 25mm (b) 50mm (c) 75mm and (d) infinity.
Fig. 4
Fig. 4 3D-probability of the OAM states of a LG beam propagating through Kolmogorov turbulence versus the propagation distance and the radius of a receiver aperture for different values of the topological charge difference (a) Δl = 0 (b) Δl = 1 (c) Δl = 2 (d) Δl = 3.
Fig. 5
Fig. 5 3D-probability of the OAM states of a LG beam propagating through Non-Kolmogorov turbulence of an arbitrary parameter α = 3.1 versus the propagation distance and the radius of a receiver aperture for different values of the topological charge difference (a) Δl = 0 (b) Δl = 1 (c) Δl = 2 (d) Δl = 3.
Fig. 6
Fig. 6 3D-probability of a LG beam propagating through Non-Kolmogorov turbulence versus an arbitrary parameter and the radius of a receiver aperture for different values of the topological charge difference (a) Δl = 0 (b) Δl = 1 (c) Δl = 2 (d) Δl = 3.

Equations (15)

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

ρ 0 2 = π 2 k 2 z 3 κ 3 Φ n ( κ ) d κ .
Φ n N T ( κ ) = A ( α ) C ˜ n 2 exp ( κ 2 / κ m 2 ) ( κ 2 + κ 0 2 ) α / 2 , 0 κ < , 3 < α < 4.
A ( α ) = 1 4 π 2 Γ ( α 1 ) cos ( α π 2 ) .
ρ 0 N T = { 1 3 π 2 k 2 z A ( α ) 2 ( α 2 ) C ˜ n 2 [ κ m 2 α β exp ( κ 0 2 κ m 2 ) Γ ( 2 α 2 , κ 0 2 κ m 2 ) 2 κ 0 4 α ] } 1 2
ρ 0 T = ( 0.545 C n 2 k 2 z ) 3 / 5
ψ ( r , θ , z ) = R l 0 ( r , z ) exp ( i l 0 θ ) 2 π exp [ i ϕ ( r , θ ) ] .
ψ ( r , θ , z ) = l a l ( z ) R l ( r , z ) exp ( i l θ ) 2 π .
a l ( z ) = R l ( r , z ) exp ( i l θ ) 2 π | ψ ( r , θ , z ) .
P ( l ) = P ( l | ψ ) = | a l ( z ) | 2 = ψ * ( r , θ , z ) ψ ( r , θ , z ) r d r exp [ i l ( θ θ ) ] 2 π d θ d θ .
H ( r ) = t = 1 10 A t exp ( B t a 2 r 2 ) .
P ( l ) = ψ * ( r , θ , z ) ψ ( r , θ , z ) H ( r ) H * ( r ) r d r exp [ i l ( θ θ ) ] 2 π d θ d θ .
P ( l ) = 1 4 π 2 t = 1 10 t = 1 10 A t A t * | R l 0 ( r , z ) | 2 exp [ B t + B t * a 2 r 2 ] × exp { 2 r 2 ρ 0 j 2 [ 1 cos ( Δ θ ) ] } exp ( i Δ l Δ θ ) r d r d Δ θ .
R l 0 ( r , z ) = 2 π | l 0 | ! exp ( i k z ) r l 0 ( k w 0 2 2 i z + k w 0 2 ) l + 0 1 exp ( k r 2 2 i z + k w 0 2 ) .
P ( l ) = t = 1 10 t = 1 10 A t A t * ( 2 π | l 0 | ! ) ( k 2 w 0 4 k 2 w 0 4 + 4 z 2 ) l + 0 1 q = 0 1 q ! Γ ( q + Δ l + 1 ) ( 1 ρ 0 j 2 ) 2 q + Δ l × ( l + 0 2 q + Δ l ) ! 2 ( B t + B t * a 2 + 2 ρ 0 j 2 + 2 k 2 w 0 2 k 2 w 0 4 + 4 z 2 ) l + 0 2 q + Δ l + 1
I p ( z ) = i p J p ( i z ) = k = 0 1 k ! Γ ( k + p + 1 ) ( z 2 ) 2 k + p 0 2 π exp [ i n ϕ 1 + ξ cos ( ϕ 1 ϕ 2 ) ] d ϕ 1 = 2 π exp ( i n ϕ 2 ) I n ( ξ ) 0 x 2 n + 1 exp ( q x 2 ) d x = n ! 2 q n + 1

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