Abstract

The radial average-power distribution and normalized average power of orbital-angular-momentum (OAM) modes in a vortex Gaussian beam after passing through weak-to-strong atmospheric turbulence are theoretically formulated. Based on numerical calculations, the role of the intrinsic mode index, initial beam radius and turbulence strength in OAM-mode variations of a propagated vortex Gaussian beam is explored, and the validity of the pure-phase-perturbation approximation employed in existing theoretical studies is examined. Comparison between turbulence-induced OAM-mode scrambling of vortex Gaussian beams and that of either Laguerre-Gaussian (LG) beams or pure vortex beams has been made. Analysis shows that the normalized average power of OAM modes changes with increasing receiver-aperture size until it approaches a nearly stable value. For a receiver-aperture size of practical interest, OAM-mode scrambling is severer with a larger mode index or smaller initial beam radius besides stronger turbulence. Under moderate-to-strong turbulence condition, for two symmetrically-neighboring extrinsic OAM modes, the normalized average power of the one with an index closer to zero may be greater than that of the other one. The validity of the pure-phase-perturbation approximation is determined by the intrinsic mode index, initial beam radius and turbulence strength. It makes sense to jointly control the amplitude and phase of a fundamental Gaussian beam for producing an OAM-carrying beam.

© 2016 Optical Society of America

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References

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2015 (4)

2014 (3)

2013 (1)

2012 (2)

Y. Zhang, I. B. Djordjevic, and X. Gao, “On the quantum-channel capacity for orbital angular momentum-based free-space optical communications,” Opt. Lett. 37(15), 3267–3269 (2012).
[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. Photon. 6(7), 488–496 (2012).
[Crossref]

2011 (1)

2010 (2)

V. P. Aksenov, F. Y. Kanev, and C. E. Pogutsa, “Spatial coherence, mean wave tilt, and mean local wave-propagation vector of a Laguerre-Gaussian beam passing through a random phase screen,” Atm. Ocean. Opt. 23(5), 344–352 (2010).
[Crossref]

Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. 283(7), 1209–1212 (2010).
[Crossref]

2009 (2)

2008 (2)

2007 (1)

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

2005 (2)

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

J. H. Shapiro, S. Guha, and B. I. Erkmen, “Ultimate channel capacity of free-space optical communications,” J. Opt. Netw. 4(8), 501–516 (2005).
[Crossref]

2004 (1)

Ahmed, N.

G. Xie, Y. Ren, H. Huang, M. P. J. Lavery, N. Ahmed, Y. Yan, C. Bao, L. Li, Z. Zhao, Y. Cao, M. Willner, M. Tur, S. J. Dolinar, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Phase correction for a distorted orbital angular momentum beam using a Zernike polynomials-based stochastic-parallel-gradient-descent algorithm,” Opt. Lett. 40(7), 1197–1200 (2015).
[Crossref] [PubMed]

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. Photon. 7(1), 66–106 (2015).

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, 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. Photon. 6(7), 488–496 (2012).
[Crossref]

Aksenov, V. P.

V. P. Aksenov, F. Y. Kanev, and C. E. Pogutsa, “Spatial coherence, mean wave tilt, and mean local wave-propagation vector of a Laguerre-Gaussian beam passing through a random phase screen,” Atm. Ocean. Opt. 23(5), 344–352 (2010).
[Crossref]

Andrews, L. C.

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

Andrews, R.

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

Anguita, J. A.

Ashrafi, N.

Ashrafi, S.

Bao, C.

Barnett, S. M.

Boyd, R. W.

Cai, Y.

Cao, Y.

Chandrasekaran, N.

Charnotskii, M.

Courtial, J.

Djordjevic, I. B.

Dolinar, S.

Dolinar, S. J.

Erkmen, B. I.

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. Photon. 6(7), 488–496 (2012).
[Crossref]

Fickler, R.

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

Fink, M.

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

Franke-Arnold, S.

Gao, J.

Gao, X.

Gbur, G.

Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. 283(7), 1209–1212 (2010).
[Crossref]

G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A 25(1), 225–230 (2008).
[Crossref]

Gibson, G.

Gopaul, C.

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

Gu, Y.

Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. 283(7), 1209–1212 (2010).
[Crossref]

Guha, S.

Handsteiner, J.

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

Huang, H.

G. Xie, Y. Ren, H. Huang, M. P. J. Lavery, N. Ahmed, Y. Yan, C. Bao, L. Li, Z. Zhao, Y. Cao, M. Willner, M. Tur, S. J. Dolinar, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Phase correction for a distorted orbital angular momentum beam using a Zernike polynomials-based stochastic-parallel-gradient-descent algorithm,” Opt. Lett. 40(7), 1197–1200 (2015).
[Crossref] [PubMed]

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. Photon. 7(1), 66–106 (2015).

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, 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. Photon. 6(7), 488–496 (2012).
[Crossref]

Kanev, F. Y.

V. P. Aksenov, F. Y. Kanev, and C. E. Pogutsa, “Spatial coherence, mean wave tilt, and mean local wave-propagation vector of a Laguerre-Gaussian beam passing through a random phase screen,” Atm. Ocean. Opt. 23(5), 344–352 (2010).
[Crossref]

Korotkova, O.

Krenn, M.

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

Lavery, M. P. J.

Li, L.

Liu, X.

Malik, M.

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

Molisch, A. F.

Neifeld, M.

Neifeld, M. A.

Padgett, M. J.

Pas’ko, V.

Paterson, C.

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

Phillips, R. L.

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

Pogutsa, C. E.

V. P. Aksenov, F. Y. Kanev, and C. E. Pogutsa, “Spatial coherence, mean wave tilt, and mean local wave-propagation vector of a Laguerre-Gaussian beam passing through a random phase screen,” Atm. Ocean. Opt. 23(5), 344–352 (2010).
[Crossref]

Ramachandran, S.

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. Photon. 7(1), 66–106 (2015).

G. Xie, Y. Ren, H. Huang, M. P. J. Lavery, N. Ahmed, Y. Yan, C. Bao, L. Li, Z. Zhao, Y. Cao, M. Willner, M. Tur, S. J. Dolinar, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Phase correction for a distorted orbital angular momentum beam using a Zernike polynomials-based stochastic-parallel-gradient-descent algorithm,” Opt. Lett. 40(7), 1197–1200 (2015).
[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, 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. Photon. 6(7), 488–496 (2012).
[Crossref]

Roux, F. S.

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

Scheidl, T.

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

Shapiro, J. H.

Steinhoff, N. K.

Tur, M.

G. Xie, Y. Ren, H. Huang, M. P. J. Lavery, N. Ahmed, Y. Yan, C. Bao, L. Li, Z. Zhao, Y. Cao, M. Willner, M. Tur, S. J. Dolinar, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Phase correction for a distorted orbital angular momentum beam using a Zernike polynomials-based stochastic-parallel-gradient-descent algorithm,” Opt. Lett. 40(7), 1197–1200 (2015).
[Crossref] [PubMed]

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. Photon. 7(1), 66–106 (2015).

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, 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. Photon. 6(7), 488–496 (2012).
[Crossref]

Tyler, G. A.

Tyson, R. K.

Ursin, R.

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

Vasic, B. V.

Vasnetsov, M.

Wang, F.

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. Photon. 7(1), 66–106 (2015).

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 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. Photon. 7(1), 66–106 (2015).

G. Xie, Y. Ren, H. Huang, M. P. J. Lavery, N. Ahmed, Y. Yan, C. Bao, L. Li, Z. Zhao, Y. Cao, M. Willner, M. Tur, S. J. Dolinar, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Phase correction for a distorted orbital angular momentum beam using a Zernike polynomials-based stochastic-parallel-gradient-descent algorithm,” Opt. Lett. 40(7), 1197–1200 (2015).
[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, 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. Photon. 6(7), 488–496 (2012).
[Crossref]

Willner, M.

Xie, G.

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. Photon. 7(1), 66–106 (2015).

G. Xie, Y. Ren, H. Huang, M. P. J. Lavery, N. Ahmed, Y. Yan, C. Bao, L. Li, Z. Zhao, Y. Cao, M. Willner, M. Tur, S. J. Dolinar, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Phase correction for a distorted orbital angular momentum beam using a Zernike polynomials-based stochastic-parallel-gradient-descent algorithm,” Opt. Lett. 40(7), 1197–1200 (2015).
[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, 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. Photon. 6(7), 488–496 (2012).
[Crossref]

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. Photon. 6(7), 488–496 (2012).
[Crossref]

Yao, A. M.

Yue, Y.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 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 spatial modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Zhang, Y.

Zhao, F.

Zhao, Z.

Zhu, Y.

Adv. Opt. Photon. (2)

Appl. Opt. (1)

Atm. Ocean. Opt. (1)

V. P. Aksenov, F. Y. Kanev, and C. E. Pogutsa, “Spatial coherence, mean wave tilt, and mean local wave-propagation vector of a Laguerre-Gaussian beam passing through a random phase screen,” Atm. Ocean. Opt. 23(5), 344–352 (2010).
[Crossref]

J. Opt. Netw. (1)

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

Nat. Photon. (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. Photon. 6(7), 488–496 (2012).
[Crossref]

New J. Phys. (2)

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

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[Crossref]

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Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. 283(7), 1209–1212 (2010).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Optica (1)

Phys. Rev. A (1)

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

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

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Figures (11)

Fig. 1
Fig. 1

Scaled radial power distribution of the intrinsic OAM mode of a propagated vortex Gaussian beam in the absence of atmospheric turbulence. I m ( m ) ( r ) is not a random quantity.

Fig. 2
Fig. 2

Scaled radial average-power distribution of OAM modes of a propagated vortex Gaussian beam through atmospheric turbulence with qc = 6.5 fixed.

Fig. 3
Fig. 3

Scaled radial average-power distribution of OAM modes of a propagated vortex Gaussian beam through atmospheric turbulence with qc = 1.5 fixed.

Fig. 4
Fig. 4

Normalized average power of OAM modes in a propagated vortex Gaussian beam through atmospheric turbulence in terms of the scaled receiver-aperture radius with qc = 6.5 fixed. The curves associated with l = m correspond to intrinsic OAM modes and the other ones to extrinsic OAM modes.

Fig. 5
Fig. 5

Normalized average power of OAM modes in a propagated vortex Gaussian beam through atmospheric turbulence in terms of the scaled receiver-aperture radius with qc = 1.5 fixed. The curves associated with l = m correspond to intrinsic OAM modes and the other ones to extrinsic OAM modes.

Fig. 6
Fig. 6

Normalized average power of both intrinsic and extrinsic OAM modes in a propagated vortex Gaussian beam through atmospheric turbulence with qw = 1 fixed. The shaded circles with red color represent intrinsic modes and those with blue color denote extrinsic modes. The receiver-aperture radius R is specified as the root-mean-square radius of a propagated vortex Gaussian beam with intrinsic mode index m at the receiver plane in the absence of atmospheric turbulence.

Fig. 7
Fig. 7

Average density of both intrinsic and extrinsic OAM modes in a propagated vortex Gaussian beam through atmospheric turbulence with qw = 1 fixed. The shaded circles with red color represent intrinsic modes and those with blue color denote extrinsic modes. The receiver-aperture radius R is specified as the root-mean-square radius of a propagated vortex Gaussian beam with intrinsic mode index m at the receiver plane in the absence of atmospheric turbulence.

Fig. 8
Fig. 8

Scaled radial average-power distribution of OAM modes of a propagated vortex Gaussian beam through atmospheric turbulence with qc = 6.5 fixed. The curves annotated with “Numerical” in the legend represent the results calculated according to Eqs. (13)(19), and those with “PPP approx.” in the legend denote the results obtained based on the pure-phase-perturbation approximation.

Fig. 9
Fig. 9

Scaled radial average-power distribution of OAM modes of a propagated vortex Gaussian beam through atmospheric turbulence with qw = 1 fixed. The curves annotated with “Numerical” in the legend represent the results calculated according to Eqs. (13)(19), and those with “PPP approx.” in the legend denote the results obtained based on the pure-phase-perturbation approximation.

Fig. 10
Fig. 10

Changes in Θ(r,m − l) with varying scaled radial distance. The curves annotated with “Quad.” in the legend represent the results calculated with H (r,θd) given by Eq. (22), and those with “Accu.” denote the results obtained with H (r,θd) = exp{−6.88 × 22/3[r/(2.1ρ0)]5/3|sin(θd/2)|5/3}. ρ0 = 6.5qF.

Fig. 11
Fig. 11

Changes in ω(m) (r,L) with varying scaled radial distance when R = ∞. (a) vortex Gaussian beams; (b) pure vortex beams; (c) LG0m beams. The parameter w0 associated with LG0m beams is the radius of the Gaussian term included in the expression used to describe LG0m beams at the transmitter plane [18]. ρ0 = 6.5qF.

Equations (27)

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U 0 ( m ) ( s , 0 ) = a 0 exp ( s 2 w 0 2 ) exp ( i m φ ) ,
U 0 ( m ) ( r , L ) = a 0 C 0 ( m ) A ( m ) ( r ) exp ( i m θ )
C 0 ( m ) = π k 2 8 L 2 ( i ) m + 1 exp ( i k L ) [ i k 2 L ( 1 + i α 0 L ) ] 3 / 2 ,
A ( m ) ( r ) = r exp [ i k r 2 2 L i k r 2 4 L ( 1 + i α 0 L ) ] × [ I m / 2 1 / 2 ( i k r 2 4 L ( 1 + i α 0 L ) ) I m / 2 + 1 / 2 ( i k r 2 4 L ( 1 + i α 0 L ) ) ] ,
U ( m ) ( r , L ) = a 0 C 0 ( m ) A ( m ) ( r ) exp ( i m θ ) exp [ ψ ( m ) ( r ) ] ,
exp [ ψ ( m ) ( r , θ ) ] = n = c n ( m ) ( r ) exp ( i n θ )
c n ( m ) ( r ) = 1 2 π 0 2 π d θ exp [ ψ ( m ) ( r , θ ) ] exp ( i n θ ) ,
U ( m ) ( r , θ , L ) = l = u l ( m ) ( r ) exp ( i l θ )
u l ( m ) ( r ) = 1 2 π 0 2 π d θ U ( m ) ( r , θ , L ) exp ( i l θ )
u l ( m ) ( r ) = a 0 C 0 ( m ) A ( m ) ( r ) c l m ( m ) ( r ) .
P ^ l ( m ) ( R ) = P l ( m ) ( R ) P ¯ ( m ) ( R )
P l ( m ) ( R ) = 2 π 0 R d r r I l ( m ) ( r ) ,
I l ( m ) ( r ) = 1 2 π 0 2 π d θ d Γ 2 ( m ) ( r , θ d , L ) exp ( i l θ d ) ,
Γ 2 ( m ) ( r , θ d , L ) = U ( m ) ( r , θ 1 , L ) U ( m ) * ( r , θ 1 θ d , L ) .
Γ 2 ( m ) ( r , θ d , L ) = a 0 2 ( k 2 π L ) 2 exp [ 3 r 2 2 ρ 0 2 ( 1 cos θ d ) ] π ρ 0 2 × V 1 ( m ) ( T r 0 , K ) V 1 ( m ) * ( r 0 , K ) μ ( κ ) d 2 K
T = [ cos θ d sin θ d sin θ d cos θ d ] , r 0 = [ r 0 ] ,
V 1 ( m ) ( r , K ) = V ˜ 0 ( m ) ( k r 2 π L K ) exp ( i π K r )
V ˜ 0 ( m ) ( K ) = ( i ) m π 5 / 2 2 κ W 0 3 exp ( π 2 κ 2 W 0 2 2 ) exp ( i m θ κ ) × [ I m / 2 1 / 2 ( π 2 κ 2 W 0 2 2 ) I m / 2 + 1 / 2 ( π 2 κ 2 W 0 2 2 ) ] ,
μ ( κ ) = exp ( π 2 ρ 0 2 κ 2 ) ,
Γ 2 ( m ) ( r , θ d , L ) = I ^ ( m ) ( r , L ) exp ( i m θ d ) H ( r , θ d )
I ^ ( m ) ( r , L ) = a 0 2 C 0 ( m ) C 0 ( m ) * A ( m ) ( r ) A ( m ) * ( r ) ,
H ( r , θ d ) = exp [ 4 r 2 sin 2 ( θ d / 2 ) ρ 0 2 ] .
p ¯ l ( m ) ( R ) = P l ( m ) ( R ) l = P l ( m ) ( R ) .
P ^ l ( m ) ( R ) = 0 R ω ( m ) ( r , L ) Θ ( r , m l ) d r
ω ( m ) ( r , L ) = 2 π I ^ ( m ) ( r , L ) r / C t ( R ) ,
Θ ( r , m l ) = 1 2 π 0 2 π d θ d H ( r , θ d ) exp [ i ( l m ) θ d ] ,
C t ( R ) = 2 π 0 R d r r I ^ ( m ) ( r , L ) ,

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