Abstract

Orbital angular momentum (OAM) mode crosstalk induced by atmospheric turbulence is a challenging phenomenon commonly occurring in OAM-based free-space optical (FSO) communication. Recent advances have facilitated new practicable methods using abruptly autofocusing light beams for weakening the turbulence effect on the FSO link. In this work, we show that a circular phase-locked Airy vortex beam array (AVBA) with sufficient elements has the inherent ability to form an abruptly autofocusing light beam carrying OAM, and its focusing properties can be controlled on demand by adjusting the topological charge values and locations of these vortices embedded in the array elements. The performance of a tailored Airy vortex beam array (TAVBA) through atmospheric turbulence is numerically studied. In a comparison with the ring Airy vortex beam (RAVB), the results indicate that TAVBA can be a superior light source for effectively reducing the intermodal crosstalk and vortex splitting, thus leading to improvement in the FSO system performance.

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

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2017 (4)

H. Kaushal and G. Kaddoum, “Optical Communication in Space: Challenges and Mitigation Techniques,” IEEE Trans. Vehicular Technol. 19(1), 57–96 (2017).

Y. Zhang, P. Wang, L. Guo, W. Wang, and H. Tian, “Performance analysis of an OAM multiplexing-based MIMO FSO system over atmospheric turbulence using space-time coding with channel estimation,” Opt. Express 25(17), 19995–20011 (2017).
[Crossref] [PubMed]

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

X. Yan, L. Guo, M. Cheng, J. Li, Q. Huang, and R. Sun, “Probability density of orbital angular momentum mode of autofocusing Airy beam carrying power-exponent-phase vortex through weak anisotropic atmosphere turbulence,” Opt. Express 25(13), 15286–15298 (2017).
[Crossref] [PubMed]

2016 (5)

2015 (4)

2014 (6)

2013 (1)

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3(1), 1406 (2013).
[Crossref] [PubMed]

2012 (2)

2011 (1)

2010 (3)

2008 (3)

2007 (1)

J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46(8), 086002 (2007).
[Crossref]

2005 (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

2003 (1)

F. Zhang, “Non-adaptive transformation to calculate the propagation of the focused laser beams,” Chin. J. Quantum Elect. 20(6), 656–660 (2003).

2000 (1)

1997 (1)

A. Mamaev, M. Saffman, and A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[Crossref]

1993 (1)

1980 (1)

M. Nazarathy and J. Shamir, “Fourier optics described by operator algebra,” J. Opt. Soc. Am. A 70(2), 150–159 (1980).
[Crossref]

Ahmed, N.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[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]

Y. Yan, G. Xie, M. P. 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. 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]

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

Andrews, L. C.

J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46(8), 086002 (2007).
[Crossref]

Ashrafi, N.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[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]

Ashrafi, S.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[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]

Banzer, P.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

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]

Y. Yan, G. Xie, M. P. 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. 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]

Bock, R.

Bos, J. P.

Boyd, R. W.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. 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]

Cao, Y.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[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]

Y. Yan, G. Xie, M. P. 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]

Cao, Z.

Chen, C.

C. Chen, H. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
[Crossref]

Chen, R. P.

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3(1), 1406 (2013).
[Crossref] [PubMed]

Cheng, M.

Chew, K. H.

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3(1), 1406 (2013).
[Crossref] [PubMed]

Christodoulides, D. N.

Cottrell, D. M.

Dai, H. T.

Davis, J. A.

Desyatnikov, A. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

Ding, J.

Efremidis, N. K.

Elser, D.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Flatté, S. M.

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

Fu, S.

Gan, X.

Gao, C.

Gao, J.

Gbur, G.

Ge, X. L.

Gerber, J. S.

Ghassemlooy, Z.

Gong, L. Y.

Gu, Y.

Günthner, K.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Guo, C. S.

Guo, L.

He, S.

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3(1), 1406 (2013).
[Crossref] [PubMed]

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. Yan, G. Xie, M. P. 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. 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]

Huang, Q.

Hulea, M.

Jiang, Y.

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Optical Communication in Space: Challenges and Mitigation Techniques,” IEEE Trans. Vehicular Technol. 19(1), 57–96 (2017).

Kaushal, H.

H. Kaushal and G. Kaddoum, “Optical Communication in Space: Challenges and Mitigation Techniques,” IEEE Trans. Vehicular Technol. 19(1), 57–96 (2017).

Kavehrad, M.

C. Chen, H. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
[Crossref]

Kivshar, Y. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

Lavery, M. P.

Y. Yan, G. Xie, M. P. 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. 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]

Lavery, M. P. J.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[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]

Leach, J.

Leuchs, G.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Li, J.

Li, L.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[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]

Y. Yan, G. Xie, M. P. 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. 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]

Li, P.

Liu, S.

Liu, X.

Liu, Y. J.

Lu, X.

Luo, D.

Mamaev, A.

A. Mamaev, M. Saffman, and A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[Crossref]

Marquardt, C.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Martin, J.

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(1), 66–106 (2015).
[Crossref]

Y. Yan, G. Xie, M. P. 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]

Nazarathy, M.

M. Nazarathy and J. Shamir, “Fourier optics described by operator algebra,” J. Opt. Soc. Am. A 70(2), 150–159 (1980).
[Crossref]

Neifeld, M. A.

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

Padgett, M. J.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Y. Yan, G. Xie, M. P. 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]

Peng, T.

Peuntinger, C.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Phillips, R. L.

J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46(8), 086002 (2007).
[Crossref]

Rajbhandari, S.

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(1), 66–106 (2015).
[Crossref]

Rao, R.

Rao Gudimetla, V. S.

Recolons, J.

J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46(8), 086002 (2007).
[Crossref]

Ren, Y.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[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]

Y. Yan, G. Xie, M. P. 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. 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]

Roggemann, M. C.

Saffman, M.

A. Mamaev, M. Saffman, and A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[Crossref]

Sand, D.

Semenov, A. A.

D. Vasylyev, A. A. Semenov, and W. Vogel, “Atmospheric Quantum Channels with Weak and Strong Turbulence,” Phys. Rev. Lett. 117(9), 090501 (2016).
[Crossref] [PubMed]

Shamir, J.

M. Nazarathy and J. Shamir, “Fourier optics described by operator algebra,” J. Opt. Soc. Am. A 70(2), 150–159 (1980).
[Crossref]

Shao, H.

Shapiro, J. H.

Sun, R.

Sun, X. W.

Tang, X.

Tian, H.

Torner, L.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

Tur, M.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[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]

Y. Yan, G. Xie, M. P. 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. 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]

Tyson, R. K.

Vasylyev, D.

D. Vasylyev, A. A. Semenov, and W. Vogel, “Atmospheric Quantum Channels with Weak and Strong Turbulence,” Phys. Rev. Lett. 117(9), 090501 (2016).
[Crossref] [PubMed]

Vogel, W.

D. Vasylyev, A. A. Semenov, and W. Vogel, “Atmospheric Quantum Channels with Weak and Strong Turbulence,” Phys. Rev. Lett. 117(9), 090501 (2016).
[Crossref] [PubMed]

Wang, B. Y.

Wang, G.-Y.

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(1), 66–106 (2015).
[Crossref]

Wang, P.

Wang, W.

Wang, Z.

Willner, A. E.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[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]

Y. Yan, G. Xie, M. P. 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. 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]

Willner, A. J.

Xie, G.

Yan, X.

Yan, Y.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[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]

Y. Yan, G. Xie, M. P. 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. 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]

Yang, H.

C. Chen, H. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
[Crossref]

Yu, W.

Zeng, B.

Zhang, F.

F. Zhang, “Non-adaptive transformation to calculate the propagation of the focused laser beams,” Chin. J. Quantum Elect. 20(6), 656–660 (2003).

Zhang, Y.

Zhao, F.

Zhao, J.

Zhao, S. M.

Zhao, Z.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[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]

Y. Yan, G. Xie, M. P. 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]

Zheng, B. Y.

Zheng, W.

Zhou, Z.

C. Chen, H. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
[Crossref]

Zhu, X.

Zhu, Y.

Zozulya, A.

A. Mamaev, M. Saffman, and A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[Crossref]

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]

Appl. Opt. (2)

Chin. J. Quantum Elect. (1)

F. Zhang, “Non-adaptive transformation to calculate the propagation of the focused laser beams,” Chin. J. Quantum Elect. 20(6), 656–660 (2003).

IEEE Trans. Vehicular Technol. (1)

H. Kaushal and G. Kaddoum, “Optical Communication in Space: Challenges and Mitigation Techniques,” IEEE Trans. Vehicular Technol. 19(1), 57–96 (2017).

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (5)

Laser Photonics Rev. (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

Nat. Commun. (1)

Y. Yan, G. Xie, M. P. 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]

Opt. Eng. (1)

J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46(8), 086002 (2007).
[Crossref]

Opt. Express (9)

J. A. Davis, D. M. Cottrell, and D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20(12), 13302–13310 (2012).
[Crossref] [PubMed]

Y. Jiang, Z. Cao, H. Shao, W. Zheng, B. Zeng, and X. Lu, “Trapping two types of particles by modified circular Airy beams,” Opt. Express 24(16), 18072–18081 (2016).
[Crossref] [PubMed]

Y. Jiang, X. Zhu, W. Yu, H. Shao, W. Zheng, and X. Lu, “Propagation characteristics of the modified circular Airy beam,” Opt. Express 23(23), 29834–29841 (2015).
[Crossref] [PubMed]

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).
[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]

X. Yan, L. Guo, M. Cheng, J. Li, Q. Huang, and R. Sun, “Probability density of orbital angular momentum mode of autofocusing Airy beam carrying power-exponent-phase vortex through weak anisotropic atmosphere turbulence,” Opt. Express 25(13), 15286–15298 (2017).
[Crossref] [PubMed]

Y. Zhang, P. Wang, L. Guo, W. Wang, and H. Tian, “Performance analysis of an OAM multiplexing-based MIMO FSO system over atmospheric turbulence using space-time coding with channel estimation,” Opt. Express 25(17), 19995–20011 (2017).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

S. M. Zhao, J. Leach, L. Y. Gong, J. Ding, and B. Y. Zheng, “Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states,” Opt. Express 20(1), 452–461 (2012).
[Crossref] [PubMed]

Opt. Lasers Eng. (1)

C. Chen, H. Yang, M. Kavehrad, and Z. Zhou, “Propagation of radial Airy array beams through atmospheric turbulence,” Opt. Lasers Eng. 52, 106–114 (2014).
[Crossref]

Opt. Lett. (5)

Optica (1)

Photon. Res. (1)

Phys. Rev. Lett. (2)

D. Vasylyev, A. A. Semenov, and W. Vogel, “Atmospheric Quantum Channels with Weak and Strong Turbulence,” Phys. Rev. Lett. 117(9), 090501 (2016).
[Crossref] [PubMed]

A. Mamaev, M. Saffman, and A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[Crossref]

Prog. Opt. (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

Sci. Adv. (1)

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Sci. Rep. (1)

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3(1), 1406 (2013).
[Crossref] [PubMed]

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L. C. Andrews and R. L. Phillips, Laser beam propagation through random media (SPIE, 2005).

Y. Hu, Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airy Beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds, (Springer, 2012).

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation With Examples in MATLAB (SPIE, 2010).

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Figures (8)

Fig. 1
Fig. 1 Multiple random phase screen model.
Fig. 2
Fig. 2 Intensity patterns of a four-beamlet Airy beam array propagating in both free space and turbulent atmosphere: (a) C n 2 =0, z = 3km; (b) C n 2 =0, z = 8 km; (c) C n 2 =1.0× 10 14 m 2/3 , z = 3km; (d) C n 2 =1.0× 10 14 m 2/3 , z = 8 km. Each beam profile is normalized to its own maximum.
Fig. 3
Fig. 3 Normalized intensity profiles of the different optical vortices placed at different points ( x c , y c ) in the Airy background beams. (a) l=0, x c = y c =0; (b) l=2, x c =0.10m, y c =0; (c) l=2, x c =0, y c =0.10m; (d) l=2 x c = y c =0.10m; (e) l=4, x c = y c =0.10m; (f) one-dimensional normalized intensity plots of (d) and (e) in black and red colors, respectively. The projections of the central dark hollow areas of the vortices in the cross-sectional profile are shown by the white dotted circles whose radii strongly depends on the value of topological charge.
Fig. 4
Fig. 4 Gallery of intensity and phase distributions of the radial phased-locked Airy array vortex beams. The first to fourth columns correspond to the number of beamlets with n=2m1, n=2m, n=2m+10, and n=60, respectively. The first and third rows correspond to the intensity distributions while the second and fourth rows correspond to the spiral phase patterns with m = 3 and 5, respectively.
Fig. 5
Fig. 5 Intensity and phase distributions of the vortex beams with m = 3: (a) RAVB; (b) AVBA; (c) TAVBA. The first and second columns correspond to the input plane, while the third and fourth columns correspond to the focal plane. (d) Intensity images of TAVBA at different locations along the propagation direction.
Fig. 6
Fig. 6 Intensity distributions of TAVBAs with different values of l and x c at the focal plane. (a)–(c) Keeping x c =0.03m and varying l = 1, 2, and 4; (b)–(f) keeping l = 4, and varying x c =0.05, 0.09, and 0.11m; (g) and (h) normalized intensity cross sections of TAVBAs corresponding to (a)–(c) and (d)–(f), respectively.
Fig. 7
Fig. 7 Intensity distributions and spiral phase maps for m = 3 and m = 5 after propagation through atmospheric turbulence. (a) C n 2 =5× 10 16 m 2/3 ; (b) C n 2 =5× 10 15 m 2/3 . A linear gray-scale pallet is used in this case, where black (white) corresponds to a phase of 0 ( 2π).
Fig. 8
Fig. 8 Crosstalk from the transmitted OAM channels to neighboring channels: (a) m = 3; (b) m = 5.

Tables (1)

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Table 1 Parameters values used in the simulations

Equations (14)

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E j (x,y,z=0)= [ (x x c )+isign(l)(y y c ) ] | l | Ai( X x 0 )Ai( Y y 0 )exp[ a( X x 0 + Y y 0 ) ],
[ X Y ]=[ cos( j1 n 2π+π) sin( j1 n 2π+π) sin j1 n 2π+π) cos( j1 n 2π+π) ][ x y ]+[ d d ],
E(x,y,z=0)= j=1 n [ (x x c )+isign(l)(y y c ) ] | l | Ai( X x 0 )Ai( Y y 0 )exp[ a( X x 0 + Y y 0 ) ] exp(i ϕ j ),
E(x,y,z=0)=Ai( r 0 x 2 + y 2 ω )exp[ a r 0 x 2 + y 2 ω ]exp[ imarctan( y x ) ],
{ b;x,y }E(x,y)=exp[ i k 2 b( x 2 + y 2 ) ]E(x,y),
FFT{ x,y; f x , f y }E(x,y)= E(x,y)exp[ i2π( f x x+ f y y ) ]dxdy ,
IFFT{ f x , f y ;x,y }E(x,y)= E(x,y)exp[ i2π( f x x+ f y y ) ]dxdy ,
2 { b;x,y }={ 4 π 2 k b;x,y }.
E(x,y,z)=Bexp[ iC( x,y,z ) ][ m ˜ n1 1 m ˜ n1 z n1 ; x n , y n ]× j=1 N l 1 { S( x j+1 , y j+1 )IFFT[ f x j , f y j ; x j+1 m ˜ j , y j+1 m ˜ j ] × 2 [ Δ z j m ˜ j ; f x j , f y j ]FFT[ x j+1 , y j+1 ; f x j , f y j ] 1 m ˜ j }×{ [ 1 m ˜ 1 z 1 ; x 1 , y 1 ]E( x 1 , y 1 ) } ,
C= k( 1B ) 2zB ( x 2 + y 2 ),
E(x,y,z)=Bexp[ iC( x,y,z ) ][ m ˜ n1 1 m ˜ n1 z n1 ; x n , y n ]× j=1 n1 { S( x j , y j )exp[ i φ j ( x j , y j ) ] ×IFFT[ f x j , f y j ; x j+1 m ˜ j , y j+1 m ˜ j ] 2 [ Δ z j m ˜ j ; f x j , f y j ]FFT[ x j+1 , y j+1 ; f x j , f y j ] 1 m ˜ j }, ×{ [ 1 m ˜ 1 z 1 ; x 1 , y 1 ]exp[ i φ 1 ( x 1 , y 1 ) ]E( x 1 , y 1 ) }
φ j ( x,y )= n = m = c n , m j exp[ i2π( f x n x+ f y m y ) ]+ p=1 N p n =1 1 m =1 1 c n , m ,p j exp[ i2π( f x n x+ f y m y ) ],
c n , m j =h( n , m ) 1 L x L y 0.023 r 0 j 5/6 exp ( f x n 2 + f y m 2 f m 2 ) 1/2 ( f x n 2 + f y m 2 + f 0 2 ) 11/ 12 ,
c n , m ,p j =h( n , m ) 3 p L x L y 0.023 r 0 j 5/6 exp ( f x n 2 + f y m 2 f m 2 ) 1/2 ( f x n 2 + f y m 2 + f 0 2 ) 11/ 12 ,

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