Abstract

Turbulent fluctuations of the energy density of broadband pulsed Laguerre–Gaussian beams are studied based on numerical solution of the parabolic wave equation for the complex spectral amplitude of the wave field by the split-step method. It is shown that in the regime of strong scintillations, the relative variance of energy density of the pulsed beams can take values smaller than unity, in contrast to the strong scintillation index of the continuous-wave beams, which tends to unity with increasing the turbulence strength. The level of residual spatial correlation of the energy density of pulsed beams exceeds that for the continuous-wave beams. It increases with shortening of the pulse duration and increasing of the refractive turbulence strength.

© 2016 Optical Society of America

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References

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    [Crossref]
  5. 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]
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2015 (3)

A. V. Falits, “Wandering and intensity fluctuations of focused Laguerre–Gaussian beam in the turbulent atmosphere,” Opt. Atmos. Okeana 28(9), 763–771 (2015).

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, 66–106 (2015).

V. A. Banakh, L. O. Gerasimova, and I. N. Smalikho, “Numerical investigation of short-pulse laser radiation propagation in a turbulent atmosphere,” Quantum Electron. 45(3), 258–264 (2015).
[Crossref]

2014 (5)

2012 (2)

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]

V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
[Crossref]

2011 (1)

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

2008 (1)

2004 (1)

2000 (1)

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)

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54(6), 626–629 (1983).

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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

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] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014).
[Crossref]

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]

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]

Anguita, J. A.

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, 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, 66–106 (2015).

Banakh, V. A.

V. A. Banakh, L. O. Gerasimova, and I. N. Smalikho, “Numerical investigation of short-pulse laser radiation propagation in a turbulent atmosphere,” Quantum Electron. 45(3), 258–264 (2015).
[Crossref]

V. A. Banakh and A. V. Falits, “Turbulent broadening of Laguerre–Gaussian beam in the atmosphere,” Opt. Spectrosc. 117(6), 942–948 (2014).
[Crossref]

V. A. Banakh and I. N. Smalikho, “Fluctuations of energy density of short-pulse optical radiation in the turbulent atmosphere,” Opt. Express 22(19), 22285–22297 (2014).
[Crossref] [PubMed]

V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
[Crossref]

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54(6), 626–629 (1983).

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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

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] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014).
[Crossref]

Barnett, S.

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]

Boyd, R. W.

Buldakov, V. M.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54(6), 626–629 (1983).

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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

Courtial, J.

Dolinar, S.

Erkmen, B. I.

Falits, A. V.

A. V. Falits, “Wandering and intensity fluctuations of focused Laguerre–Gaussian beam in the turbulent atmosphere,” Opt. Atmos. Okeana 28(9), 763–771 (2015).

V. A. Banakh and A. V. Falits, “Turbulent broadening of Laguerre–Gaussian beam in the atmosphere,” Opt. Spectrosc. 117(6), 942–948 (2014).
[Crossref]

V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
[Crossref]

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.

Frehlich, R.

Gerasimova, L. O.

V. A. Banakh, L. O. Gerasimova, and I. N. Smalikho, “Numerical investigation of short-pulse laser radiation propagation in a turbulent atmosphere,” Quantum Electron. 45(3), 258–264 (2015).
[Crossref]

Gibson, G.

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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

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] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014).
[Crossref]

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]

Lavery, M. P. 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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014).
[Crossref]

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, 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] [PubMed]

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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014).
[Crossref]

Mironov, V. L.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54(6), 626–629 (1983).

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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

Neifeld, M. A.

Padgett, M.

Padgett, M. J.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

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] [PubMed]

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

Pas’ko, V.

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, 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, 66–106 (2015).

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] [PubMed]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014).
[Crossref]

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]

Shapiro, J. H.

Smalikho, I. N.

V. A. Banakh, L. O. Gerasimova, and I. N. Smalikho, “Numerical investigation of short-pulse laser radiation propagation in a turbulent atmosphere,” Quantum Electron. 45(3), 258–264 (2015).
[Crossref]

V. A. Banakh and I. N. Smalikho, “Fluctuations of energy density of short-pulse optical radiation in the turbulent atmosphere,” Opt. Express 22(19), 22285–22297 (2014).
[Crossref] [PubMed]

V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
[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]

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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

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] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014).
[Crossref]

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]

Vasic, B. V.

Vasnetsov, M.

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, 66–106 (2015).

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.

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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014).
[Crossref]

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, 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] [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]

Woerdman, J. P.

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.

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, 66–106 (2015).

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] [PubMed]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014).
[Crossref]

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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

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] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014).
[Crossref]

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]

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.

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.-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, 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, 66–106 (2015).

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

Adv. Opt. Photonics (2)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[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, 66–106 (2015).

Appl. Opt. (2)

Atmos. Oceanic Opt. (1)

V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
[Crossref]

Nat. Commun. (1)

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

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

Opt. Atmos. Okeana (1)

A. V. Falits, “Wandering and intensity fluctuations of focused Laguerre–Gaussian beam in the turbulent atmosphere,” Opt. Atmos. Okeana 28(9), 763–771 (2015).

Opt. Express (2)

Opt. Lett. (1)

Opt. Spectrosc. (2)

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54(6), 626–629 (1983).

V. A. Banakh and A. V. Falits, “Turbulent broadening of Laguerre–Gaussian beam in the atmosphere,” Opt. Spectrosc. 117(6), 942–948 (2014).
[Crossref]

Optica (1)

Phys. Rev. A (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]

Quantum Electron. (1)

V. A. Banakh, L. O. Gerasimova, and I. N. Smalikho, “Numerical investigation of short-pulse laser radiation propagation in a turbulent atmosphere,” Quantum Electron. 45(3), 258–264 (2015).
[Crossref]

Other (7)

Yu. A. Anan’ev, Optical Cavities and Laser Beams. (Nauka, 1990) [in Russian].

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (Nauka, 1988) [in Russian]

V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

V. A. Banakh and I. N. Smalikho, Coherent Doppler wind lidars in a turbulent atmosphere (Artech House, 2013)

M. V. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Wave Theory (Nauka, 1979) [in Russian].

V. E. Zuev, V. A. Banakh, and V. V. Pokasov, Current Problems of Atmospheric Optics Vol.5 Optics of the Turbulent Atmosphere (Gidrometeoizdat, 1988) [in Russian].

A. E. Siegman, "How to (Maybe) Measure Laser Beam Quality," in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.

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Figures (9)

Fig. 1
Fig. 1 Two-dimensional (a, b, e, f) and one-dimensional (c, d, g, h) distributions of the normalized intensity I N of cw radiation (a, c, e, g) and normalized energy density W N of pulsed τ P (0) = 3 fs (b, d, f, h) Gaussian beam with а = 5 cm at C n 2 = 10−13 m-2/3 (a)–(d) and C n 2 = 10−12 m-2/3 (e)–(h).
Fig. 2
Fig. 2 Two-dimensional (a, b, e, f) and one-dimensional (c, d, g, h) distributions of the normalized intensity I N of cw radiation (a, c, e, g) and normalized energy density W N of pulsed τ P (0) = 3 fs (b, d, f, h) Gaussian beam with а = 2 cm at C n 2 = 10−13 m-2/3 (a)–(d) and C n 2 = 10−12 m-2/3 (e)–(h).
Fig. 3
Fig. 3 Two-dimensional (a, b, e, f) and one-dimensional (c, d, g, h) distributions of the normalized intensity I N of cw radiation (a, c, e, g) and normalized energy density W N of pulsed τ P (0) = 3 fs (b, d, f, h) Laguerre beam E 08 0 , а = 5 cm at C n 2 = 10−13 m-2/3 (a)–(d) and C n 2 = 10−12 m-2/3 (e)–(h).
Fig. 4
Fig. 4 Two-dimensional (a, b, e, f) and one-dimensional (c, d, g, h) distributions of normalized intensity I N of cw radiation (a, c, e, g) and normalized energy density W N of pulsed τ P (0) = 3 fs (b, d, f, h) Laguerre beam E 08 0 , а = 2 cm at C n 2 = 10−13 m-2/3 (a)–(d) and C n 2 = 10−12 m-2/3 (e)–(h).
Fig. 5
Fig. 5 Standard deviation of relative fluctuations of the energy density of pulsed (curves 1'–3′, 1”–3”) and cw (curves 1–3) Laguerre–Gaussian modes E 00 0 (curves 1, 1', 1”), E 02 0 (curves 2, 2', 2”), E 08 0 (curves 3, 3′, 3”) as a function of the parameter β 0 . Pulse duration τ P (0) = 5 fs (curves 1', 2', 3′) and 3 fs (curves 1”, 2”, 3”).
Fig. 6
Fig. 6 Standard deviation of relative energy density fluctuations of pulsed ( τ P (0) = 5 fs, curves 1'–3′) and cw (curves 1–3) Laguerre–Gaussian modes E 00 0 (curves 1, 1'), E 02 0 (curves 2, 2'), E 08 0 (curves 3, 3”) as a function of the parameter β 0 .
Fig. 7
Fig. 7 Coefficient of spatial correlation of energy density fluctuations of pulsed (curves 1'–3′, 1”–3”) and cw (curves 1–3) Laguerre–Gaussian modes E 00 0 (curves 1, 1', 1”), E 02 0 (curves 2, 2', 2”), E 08 0 (curves 3, 3′, 3”) at β 0 2 124 and τ P (0) = 5 fs (curves 1'–3′), 3 fs (curves 1”–3”).
Fig. 8
Fig. 8 Coefficient of spatial correlation of energy density fluctuations of pulsed (curves 1'–3′, 1”–3”) and cw (curves 1–3) Laguerre–Gaussian modes E 00 0 (curves 1, 1', 1”), E 02 0 (curves 2, 2', 2”), E 08 0 (curves 3, 3′, 3”) at β 0 2 185 , τ P (0) = 5 fs (curves 1'– 3′), 3 fs (curves 1”– 3”).
Fig. 9
Fig. 9 Coefficient of spatial correlation of energy density fluctuations of pulsed τ P (0) = 5 fs (curves 1'–6') and cw (curves 1–6) Laguerre–Gaussian modes E 00 0 (curves 1, 1', 4, 4'), E 02 0 (curves 2, 2', 5, 5′), E 08 0 (curves 3, 3′, 6, 6') at β 0 2 124 (curves 1–3, 1'–3′) and β 0 2 185 (curves 4–6, 4'–6').

Equations (12)

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E(0,ρ,t)= E nm 0 (ρ)exp( t 2 2 τ 0 2 2πj f 0 t ),
E nm 0 (ρ)= E nm 0 (0) (j) m 1 2 ( ρ a ) m exp[ ρ 2 2 a 2 +j ψ 0 +jmθ ] L n m ( ρ 2 a 2 ).
E 00 0 (ρ)= E 0 (0)exp( ρ 2 2 a 2 +j Ψ 0 ),
E ˜ (x,ρ,f)= + dtE(x,ρ,t)exp(2πjft)=U(x,ρ,f)exp( 2πjf n(f) x c ) ,
j4πf c U(x,ρ,f) x + Δ U(x,ρ,f)+2 ( 2πf c ) 2 n (x,ρ)U(x,ρ,f)=0,
E ˜ (0,ρ,f)= 2π τ 0 E nm 0 (ρ)exp[ (f f 0 ) 2 (2π τ 0 ) 2 2 ].
D Ψ (r,f)=< [ Ψ i (ρ+r,f) Ψ i (ρ,f)] 2 >=2 + d 2 κ S Ψ (κ,f)[1 e 2πjκρ ] ,
S Ψ (κ,f)=0.382 C n 2 Δx (f/c) 2 |κ | 11/3 ,
W(x,ρ)= + df S 1 (x,ρ,f)= + df | U(x,ρ,f) | 2
σ W 2 (x,ρ)= W 2 (x,ρ) / W(x,ρ) 2 1,
C W (x, ρ 1 , ρ 2 )= W(x, ρ 1 )W(x, ρ 2 ) W(x, ρ 1 ) W(x, ρ 2 ) ( ( W 2 (x, ρ 1 ) W(x, ρ 1 ) 2 )( W 2 (x, ρ 2 ) W(x, ρ 2 ) 2 ) ) 1/2
β 0 2 =1.23 C n 2 ( 2π/ λ 0 ) 7 6 x 11 6 ,

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