Abstract

The probability densities of orbital angular momentum (OAM) modes of the autofocusing Airy beam (AAB) carrying power-exponent-phase vortex (PEPV) after passing through the weak anisotropic non-Kolmogorov turbulent atmosphere are theoretically formulated. It is found that the AAB carrying PEPV is the result of the weighted superposition of multiple OAM modes at differing positions within the beam cross-section, and the mutual crosstalk among different OAM modes will compensate the distortion of each OAM mode and be helpful for boosting the anti-jamming performance of the communication link. Based on numerical calculations, the role of the wavelength, waist width, topological charge and power order of PEPV in the probability density distribution variations of OAM modes of the AAB carrying PEPV is explored. Analysis shows that a relatively small beam waist and longer wavelength are good for separating the detection regions between signal OAM mode and crosstalk OAM modes. The probability density distribution of the signal OAM mode does not change obviously with the topological charge variation; but it will be greatly enhanced with the increase of power order. Furthermore, it is found that the detection region center position of crosstalk OAM mode is an emergent property resulting from power order and topological charge. Therefore, the power order can be introduced as an extra steering parameter to modulate the probability density distributions of OAM modes. These results provide guidelines for the design of an optimal detector, which has potential application in optical vortex communication systems.

© 2017 Optical Society of America

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References

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2017 (1)

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

2016 (10)

J. Gao, Y. Zhu, D. Wang, Y. Zhang, Z. Hu, and M. Cheng, “Bessel–Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30 (2016).
[Crossref]

Y. Zhu, L. Zhang, and Y. Zhang, “Spiral spectrum of Airy–Schell beams through non-Kolmogorov turbulence,” Chin. Opt. Lett. 14(4), 042101 (2016).
[Crossref]

C. Chen, H. Yang, S. Tong, and Y. Lou, “Changes in orbital-angular-momentum modes of a propagated vortex Gaussian beam through weak-to-strong atmospheric turbulence,” Opt. Express 24(7), 6959–6975 (2016).
[Crossref] [PubMed]

Y. Zhu, Y. Zhang, and Z. Hu, “Spiral spectrum of Airy beams propagation through moderate-to-strong turbulence of maritime atmosphere,” Opt. Express 24(10), 10847–10857 (2016).
[Crossref] [PubMed]

J. Wang, S. Zhu, H. Wang, Y. Cai, and Z. Li, “Second-order statistics of a radially polarized cosine-Gaussian correlated Schell-model beam in anisotropic turbulence,” Opt. Express 24(11), 11626–11639 (2016).
[Crossref] [PubMed]

M. Cheng, L. Guo, J. Li, and Q. Huang, “Propagation properties of an optical vortex carried by a Bessel-Gaussian beam in anisotropic turbulence,” J. Opt. Soc. Am. A 33(8), 1442–1450 (2016).
[Crossref] [PubMed]

G. Lao, Z. Zhang, and D. Zhao, “Propagation of the power-exponent-phase vortex beam in paraxial ABCD system,” Opt. Express 24(16), 18082–18094 (2016).
[Crossref] [PubMed]

M. A. Cox, C. Rosales-Guzmán, M. P. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express 24(16), 18105–18113 (2016).
[Crossref] [PubMed]

F. Wang and O. Korotkova, “Random optical beam propagation in anisotropic turbulence along horizontal links,” Opt. Express 24(21), 24422–24434 (2016).
[Crossref] [PubMed]

Y. Zhang, Q. Zhang, X. Ma, Z. Jiang, T. Xu, S. Wu, and X. Wu, “Measurement of Airy-vortex beam topological charges based on a pixelated micropolarizer array,” Appl. Opt. 55(32), 9299–9304 (2016).
[Crossref] [PubMed]

2015 (5)

2014 (7)

2013 (2)

2012 (1)

2011 (1)

2010 (1)

2009 (2)

T. Wang, J. Pu, and Z. Chen, “Beam-spreading and topological charge of vortex beams propagating in a turbulent atmosphere,” Opt. Commun. 282(7), 1255–1259 (2009).
[Crossref]

L. G. Wang, W. W. Zheng, and L. Q. Wang, “The effect of atmospheric turbulence on the propagation properties of optical vortices formed by using coherent laser beam arrays,” J. Opt. A, Pure Appl. Opt. 11(6), 065703 (2009).
[Crossref]

2008 (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)

2003 (2)

G.-H. Kim, H. J. Lee, J.-U. Kim, and H. Suk, “Propagation dynamics of optical vortices with anisotropic phase profiles,” J. Opt. Soc. Am. B 20(2), 351–359 (2003).
[Crossref]

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53(7), 537–578 (2003).
[Crossref]

2001 (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

G. Molina-Terriza, E. M. Wright, and L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26(3), 163–165 (2001).
[Crossref] [PubMed]

1992 (1)

G. Grechko, A. Gurvich, V. Kan, S. Kireev, and S. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Ahmed, N.

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(1), 66–106 (2015).
[Crossref]

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
[Crossref] [PubMed]

Ashrafi, S.

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (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. Photonics 7(1), 66–106 (2015).
[Crossref]

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(1), 66–106 (2015).
[Crossref]

Barnett, S.

Bock, R.

Bouchal, Z.

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53(7), 537–578 (2003).
[Crossref]

Boyd, R. W.

Cai, Y.

Cao, Y.

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (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. Photonics 7(1), 66–106 (2015).
[Crossref]

Chandrasekaran, N.

Chao, L.

Chávez-Cerda, S.

J. Rogel-Salazar, H. A. Jiménez-Romero, and S. Chávez-Cerda, “Full characterization of Airy beams under physical principles,” Phys. Rev. A 89(2), 204–208 (2014).
[Crossref]

Chen, B.

Chen, C.

Chen, Z.

Cheng, M.

M. Cheng, L. Guo, J. Li, and Q. Huang, “Propagation properties of an optical vortex carried by a Bessel-Gaussian beam in anisotropic turbulence,” J. Opt. Soc. Am. A 33(8), 1442–1450 (2016).
[Crossref] [PubMed]

J. Gao, Y. Zhu, D. Wang, Y. Zhang, Z. Hu, and M. Cheng, “Bessel–Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30 (2016).
[Crossref]

Christodoulides, D. N.

Chu, X.

Conan, J.-M.

Courtial, J.

Cox, M. A.

Dagang, J.

Dalaudier, F.

Dan, W.

Deng, D.

Dolinar, S.

Efremidis, N. K.

Erkmen, B. I.

Eyyuboglu, H. T.

H. T. Eyyuboğlu and E. Sermutlu, “Partially coherent Airy beam and its propagation in turbulent media,” Appl. Phys. B 110(4), 451–457 (2013).
[Crossref]

Forbes, A.

Franke-Arnold, S.

Gan, X.

Gao, J.

Gibson, G.

Grechko, G.

G. Grechko, A. Gurvich, V. Kan, S. Kireev, and S. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Guo, L.

Gurvich, A.

G. Grechko, A. Gurvich, V. Kan, S. Kireev, and S. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Hu, Y.

Hu, Z.

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(1), 66–106 (2015).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. 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]

Huang, Q.

Huang, S.

Jian, H.

Jiang, Z.

Jiménez-Romero, H. A.

J. Rogel-Salazar, H. A. Jiménez-Romero, and S. Chávez-Cerda, “Full characterization of Airy beams under physical principles,” Phys. Rev. A 89(2), 204–208 (2014).
[Crossref]

Kan, V.

G. Grechko, A. Gurvich, V. Kan, S. Kireev, and S. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Ke, D.

Kim, G.-H.

Kim, J.-U.

Kireev, S.

G. Grechko, A. Gurvich, V. Kan, S. Kireev, and S. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Korotkova, O.

Lao, G.

Lavery, M. P.

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(1), 66–106 (2015).
[Crossref]

Leach, J.

Lee, H. J.

Li, J.

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(1), 66–106 (2015).
[Crossref]

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
[Crossref] [PubMed]

Li, P.

Li, Z.

Liao, P.

Linquist, R. D.

Liu, C.

Liu, S.

Liu, X.

Lou, C.

Lou, Y.

Ma, X.

Ma, Y.

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

Malik, M.

Michau, V.

Mills, M. S.

Mirhosseini, M.

Molina-Terriza, G.

G. Molina-Terriza, E. M. Wright, and L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26(3), 163–165 (2001).
[Crossref] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

Molisch, A. F.

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
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L. G. Wang, W. W. Zheng, and L. Q. Wang, “The effect of atmospheric turbulence on the propagation properties of optical vortices formed by using coherent laser beam arrays,” J. Opt. A, Pure Appl. Opt. 11(6), 065703 (2009).
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D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
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D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
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Zhu, S.

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Adv. Opt. Photonics (1)

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(1), 66–106 (2015).
[Crossref]

Adv. Space Res. (1)

G. Grechko, A. Gurvich, V. Kan, S. Kireev, and S. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

H. T. Eyyuboğlu and E. Sermutlu, “Partially coherent Airy beam and its propagation in turbulent media,” Appl. Phys. B 110(4), 451–457 (2013).
[Crossref]

Chin. Opt. Lett. (1)

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J. Opt. A, Pure Appl. Opt. (1)

L. G. Wang, W. W. Zheng, and L. Q. Wang, “The effect of atmospheric turbulence on the propagation properties of optical vortices formed by using coherent laser beam arrays,” J. Opt. A, Pure Appl. Opt. 11(6), 065703 (2009).
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J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

T. Wang, J. Pu, and Z. Chen, “Beam-spreading and topological charge of vortex beams propagating in a turbulent atmosphere,” Opt. Commun. 282(7), 1255–1259 (2009).
[Crossref]

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

Opt. Express (15)

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).
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P. Li, S. Liu, T. Peng, G. Xie, X. Gan, and J. Zhao, “Spiral autofocusing Airy beams carrying power-exponent-phase vortices,” Opt. Express 22(7), 7598–7606 (2014).
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Y. Zhu, X. Liu, J. Gao, Y. Zhang, and F. Zhao, “Probability density of the orbital angular momentum mode of Hankel-Bessel beams in an atmospheric turbulence,” Opt. Express 22(7), 7765–7772 (2014).
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H. Jian, D. Ke, L. Chao, Z. Peng, J. Dagang, and Y. Zhoushi, “Effectiveness of adaptive optics system in satellite-to-ground coherent optical communication,” Opt. Express 22(13), 16000–16007 (2014).
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M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. 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] [PubMed]

M. Yao, I. Toselli, and O. Korotkova, “Propagation of electromagnetic stochastic beams in anisotropic turbulence,” Opt. Express 22(26), 31608–31619 (2014).
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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).
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J. Gao, Y. Zhang, W. Dan, and Z. Hu, “Turbulent effects of strong irradiance fluctuations on the orbital angular momentum mode of fractional Bessel Gauss beams,” Opt. Express 23(13), 17024–17034 (2015).
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B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, and D. Deng, “Propagation of sharply autofocused ring Airy Gaussian vortex beams,” Opt. Express 23(15), 19288–19298 (2015).
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C. Chen, H. Yang, S. Tong, and Y. Lou, “Changes in orbital-angular-momentum modes of a propagated vortex Gaussian beam through weak-to-strong atmospheric turbulence,” Opt. Express 24(7), 6959–6975 (2016).
[Crossref] [PubMed]

Y. Zhu, Y. Zhang, and Z. Hu, “Spiral spectrum of Airy beams propagation through moderate-to-strong turbulence of maritime atmosphere,” Opt. Express 24(10), 10847–10857 (2016).
[Crossref] [PubMed]

J. Wang, S. Zhu, H. Wang, Y. Cai, and Z. Li, “Second-order statistics of a radially polarized cosine-Gaussian correlated Schell-model beam in anisotropic turbulence,” Opt. Express 24(11), 11626–11639 (2016).
[Crossref] [PubMed]

G. Lao, Z. Zhang, and D. Zhao, “Propagation of the power-exponent-phase vortex beam in paraxial ABCD system,” Opt. Express 24(16), 18082–18094 (2016).
[Crossref] [PubMed]

M. A. Cox, C. Rosales-Guzmán, M. P. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express 24(16), 18105–18113 (2016).
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F. Wang and O. Korotkova, “Random optical beam propagation in anisotropic turbulence along horizontal links,” Opt. Express 24(21), 24422–24434 (2016).
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Opt. Lett. (5)

Photonics Res. (1)

J. Gao, Y. Zhu, D. Wang, Y. Zhang, Z. Hu, and M. Cheng, “Bessel–Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30 (2016).
[Crossref]

Phys. Rev. A (1)

J. Rogel-Salazar, H. A. Jiménez-Romero, and S. Chávez-Cerda, “Full characterization of Airy beams under physical principles,” Phys. Rev. A 89(2), 204–208 (2014).
[Crossref]

Phys. Rev. Lett. (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

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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L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, 2005)

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Figures (9)

Fig. 1
Fig. 1 Schematic diagram of the effects of atmospheric turbulence on an OAM beam. An ideal OAM mode can be break down into multiple OAM modes.
Fig. 2
Fig. 2 Spiral phase patterns of the PEPV beam at the initial plane with different topological charges and power orders. (a) v = 3, n = 1; (b) v = 3, n = 2;(c) v = 3, n = 5;(d) v = 6, n = 2.
Fig. 3
Fig. 3 Concept of turbulent atmosphere communication link using PEPV. (a) The turbulence resistance of the beam carrying PEPV. (b) OAM modes weight mapping. The beam carrying PEPV is the result of the weighted superposition of multiple propagating OAM beams at differing positions within the beam cross-section. And the mutual crosstalk among different OAM modes will compensate the distortion of each signal OAM mode and be helpful to let the distributive characteristics of these components get close to the initial state.
Fig. 4
Fig. 4 The probability density distribution curves of the OAM modes of the AAB carrying PEPV in the anisotropic atmospheric turbulence:(a) signal OAM modes; (b) crosstalk OAM modes.
Fig. 5
Fig. 5 The normalized probability density curves of the OAM modes against ρforω: (a) signal OAM modes; (b) crosstalk OAM modes with Δm=1 .
Fig. 6
Fig. 6 The normalized probability density curves of the OAM modes against ρ forλ: (a) signal OAM modes; (b) crosstalk OAM modes with Δm=1 .
Fig. 7
Fig. 7 The normalized probability density curves of the OAM modes plotted against ρ for several values of n = 2, 2.5, 3, 3.5, 4, and 5: (a) signal OAM modes; (b) crosstalk OAM modes with Δm=1 .
Fig. 8
Fig. 8 The normalized probability density curves of the OAM modes plotted against ρ for several values of v = 1, 2, 3, 4, and 5: (a) signal OAM modes; (b) crosstalk OAM modes with Δm=1 .
Fig. 9
Fig. 9 The changes of the detection region center of crosstalk OAM modes with Δm=1 against topological charge v and power order n.

Equations (13)

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E (0) (r,φ,z=0)=Ai( r 0 r ω )exp( a r 0 r ω )exp[ i2vπ ( φ 2π ) n ],
E( ρ,θ,z )= ik 2πz exp(ikz) drdφ E (0) (r,φ,z=0) ×exp{ ik[ ρ 2 + r 2 2ρrcos(θφ) ] 2z +ψ(ρ,θ,z) },
A 0 ωexp( a 3 3 )(1 ω a 2 r 0 ).
exp( z 2 (t 1 t ))= l= J l (z) t l , J l (z)= (1) l J l (z) ,
E( ρ,θ,z )= ik 2πz exp(ikz)w( r 0 w a 2 )exp( ik ρ 2 +ik r 0 2 2z + a 3 3 ) ×[ l= (i) l exp(ilθ) M l J l ( k r 0 ρ z ) ]exp[ ψ(ρ,θ,z) ],
M l = 0 2π exp[ i(2vπ ( φ 2π ) n +lφ) ] dφ={ j=0 h=0 i j+h v j l h ( 2π ) j+h+1 j!h!(nj+h+1) ,l0 j=0 i j v j ( 2π ) j+1 j!(nj+1) ,l=0.
E( ρ,θ,z )= 1 2π m β m (ρ,z)exp(imθ) ,
β m (ρ,z)= 1 2π 0 2π E( ρ,θ,z )exp(imθ) dθ.
| β m (ρ,z) | 2 = 1 2π 0 2π 0 2π E( ρ,θ,z ) E ( ρ, θ ,z )exp[ im(θ θ ) ] × exp[ ψ(ρ,θ,z)+ψ( ρ , θ ,z ) ] dθd θ ,
exp[ ψ( ρ,θ,z )+ψ( ρ , θ ,z ) ] =exp( D(ρ,θ, ρ , θ ) 2 ) exp( ρ 2 + ρ 2 2ρ ρ cos(θ θ ) ρ 0 2 ),
ρ 0 = { ξ x 2 + ξ y 2 2 ξ x 2 ξ y 2 π 2 k 2 zA(α) C ˜ n 2 /[6(α2)]×[ κ 2α γexp( κ 0 2 κ 2 )Γ(2 α 2 , κ 0 2 κ 2 )2 κ 0 4α ] } 1 /2 ,
0 2π exp[ im(θ θ ) ] exp[ ηcos(θ θ ) ]dθ=2πexp[ im θ ] I m (η),
| β m (ρ,z) | 2 =2π[ ( kw 2πz ) 2 ( r 0 w a 2 ) 2 exp( 2 a 3 3 2 ρ 2 ρ 0 2 ) ] ×{ l=1 [ ( l =1 ( M l + M l )( M l + M l ) + M 0 ( M l + M l ) ) J l ( k r 0 ρ z ) 2 I lm ( 2 ρ 2 ρ 0 2 ) ] +[ M 0 l =1 ( M l + M l )+ M 0 M 0 ] J 0 ( k r 0 ρ z ) 2 I m ( 2 ρ 2 ρ 0 2 ) }.

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