Abstract

Free-space optical communication with spatial modes of light has become topical due to the possibility of dramatically increasing communication bandwidth via Mode Division Multiplexing (MDM). While both scalar and vector vortex modes have been used as transmission bases, it has been suggested that the latter is more robust in turbulence. Using orbital angular momentum as an example, we demonstrate theoretically and experimentally that the crosstalk due to turbulence is the same in the scalar and vector basis sets of such modes. This work brings new insights about the behaviour of vector and scalar modes in turbulence, but more importantly it demonstrates that when considering optimal modes for MDM, the choice should not necessarily be based on their vectorial nature.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (7)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200 (2016).
[Crossref]

R. Brüning, B. Ndagano, and M. Mclaren, “Data transmission with twisted light through a free-space to fiber optical communication link,” J. Opt. 18, 03LT01 (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, 6959 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41, 622 (2016).
[Crossref] [PubMed]

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photon. 10, 327 (2016).
[Crossref]

M. Charnotskii, “Propagation of polarized waves in inhomogeneous media,” J. Opt. Soc. Am. A 33, 1385 (2016).
[Crossref]

V. P. Aksenov, V V Kolosov, G. A. Filimonov, and C. E. Pogutsa, “Orbital angular momentum of a laser beam in a turbulent medium: preservation of the average value and variance of fluctuations,” J. Opt. 18, 054013 (2016).
[Crossref]

2015 (7)

J. Liu and J. Wang, “Demonstration of polarization-insensitive spatial light modulation using a single polarization-sensitive spatial light modulator,” Sci. Rep. 5, 9959 (2015).
[Crossref] [PubMed]

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett. 40, 4887 (2015).
[Crossref] [PubMed]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, and R. R. Alfano, and Others, “4× 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de) multiplexer,” Opt. Lett. 40, 1980 (2015).
[Crossref] [PubMed]

M. Andersson, E. Berglind, and G. Björk, “Orbital angular momentum modes do not increase the channel capacity in communication links,” New J. Phys. 17, 043040 (2015).
[Crossref]

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photon. 9, 822 (2015).
[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. Photon. 7, 66 (2015).

G. Funes, M. Vial, and J. A. Anguita, “Orbital-angular-momentum crosstalk and temporal fading in a terrestrial laser link using single-mode fiber coupling,” Opt. Express 23, 23133–42 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (2)

2012 (5)

2011 (1)

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 53601 (2011).
[Crossref]

2010 (3)

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

D. J. Richardson, “Filling the Light Pipe,” Science 330, 327 (2010).
[Crossref] [PubMed]

L. H.-C. Pu Ji-Xiong, Wang Tao, and L. Cheng-Liang, “Propagation of cylindrical vector beams in a turbulent atmosphere,” Chin. Phys. B 19, 89201 (2010).
[Crossref]

2009 (3)

2008 (1)

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

2004 (1)

1992 (2)

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulations of a Kolmogorov phase screen,” Waves in Random Media 2, 209 (1992).
[Crossref]

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, 8185 (1992).
[Crossref] [PubMed]

1982 (1)

Ahmed, N.

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41, 622 (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. Photon. 7, 66 (2015).

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39, 4360 (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, 376 (2014).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, and M. Tur, and Others, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062 (2013).
[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. Photon. 6, 488 (2012).
[Crossref]

Aksenov, V. P.

V. P. Aksenov, V V Kolosov, G. A. Filimonov, and C. E. Pogutsa, “Orbital angular momentum of a laser beam in a turbulent medium: preservation of the average value and variance of fluctuations,” J. Opt. 18, 054013 (2016).
[Crossref]

Alfano, R. R.

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, 8185 (1992).
[Crossref] [PubMed]

Andersson, M.

M. Andersson, E. Berglind, and G. Björk, “Orbital angular momentum modes do not increase the channel capacity in communication links,” New J. Phys. 17, 043040 (2015).
[Crossref]

Anguita, J. A.

Ashrafi, N.

Ashrafi, S.

Bao, C.

Barnett, S. M.

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

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, 8185 (1992).
[Crossref] [PubMed]

Berdagué, S.

Berglind, E.

M. Andersson, E. Berglind, and G. Björk, “Orbital angular momentum modes do not increase the channel capacity in communication links,” New J. Phys. 17, 043040 (2015).
[Crossref]

Berkhout, G. C. G.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Björk, G.

M. Andersson, E. Berglind, and G. Björk, “Orbital angular momentum modes do not increase the channel capacity in communication links,” New J. Phys. 17, 043040 (2015).
[Crossref]

Bock, R.

Boyd, R. W.

Brüning, R.

R. Brüning, B. Ndagano, and M. Mclaren, “Data transmission with twisted light through a free-space to fiber optical communication link,” J. Opt. 18, 03LT01 (2016).
[Crossref]

Cai, Y.

R. Chen, Y. Dong, F. Wang, and Y. Cai, “Statistical properties of a cylindrical vector partially coherent beam in turbulent atmosphere,” Appl. Phys. B 112, 247–259 (2013).
[Crossref]

Cao, Y.

Chandrasekaran, N.

Charnotskii, M.

Chen, C.

Chen, R.

R. Chen, Y. Dong, F. Wang, and Y. Cai, “Statistical properties of a cylindrical vector partially coherent beam in turbulent atmosphere,” Appl. Phys. B 112, 247–259 (2013).
[Crossref]

Cheng, W.

Cheng-Liang, L.

L. H.-C. Pu Ji-Xiong, Wang Tao, and L. Cheng-Liang, “Propagation of cylindrical vector beams in a turbulent atmosphere,” Chin. Phys. B 19, 89201 (2010).
[Crossref]

Courtial, J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448 (2004).
[Crossref] [PubMed]

Dainty, J. C.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulations of a Kolmogorov phase screen,” Waves in Random Media 2, 209 (1992).
[Crossref]

Ding, J.

Djordjevic, I. B.

Dolinar, S.

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. Photon. 6, 488 (2012).
[Crossref]

Dolinar, S. J.

Dong, Y.

R. Chen, Y. Dong, F. Wang, and Y. Cai, “Statistical properties of a cylindrical vector partially coherent beam in turbulent atmosphere,” Appl. Phys. B 112, 247–259 (2013).
[Crossref]

Dudley, A.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200 (2016).
[Crossref]

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photon. 10, 327 (2016).
[Crossref]

Duparré, M.

Erkmen, B. I.

Facq, P.

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. Photon. 6, 488 (2012).
[Crossref]

Fickler, R.

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

Filimonov, G. A.

V. P. Aksenov, V V Kolosov, G. A. Filimonov, and C. E. Pogutsa, “Orbital angular momentum of a laser beam in a turbulent medium: preservation of the average value and variance of fluctuations,” J. Opt. 18, 054013 (2016).
[Crossref]

Fink, M.

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

Flamm, D.

Forbes, A.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photon. 10, 327 (2016).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200 (2016).
[Crossref]

Franke-Arnold, S.

Funes, G.

Gbur, G.

Gibson, G.

Glindemann, A.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulations of a Kolmogorov phase screen,” Waves in Random Media 2, 209 (1992).
[Crossref]

Gong, L. Y.

Gu, Y.

Handsteiner, J.

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

Haus, J. W.

Huang, H.

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41, 622 (2016).
[Crossref] [PubMed]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, and R. R. Alfano, and Others, “4× 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de) multiplexer,” Opt. Lett. 40, 1980 (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, 66 (2015).

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H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39, 4360 (2014).
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Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, and M. Tur, and Others, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062 (2013).
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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. Photon. 6, 488 (2012).
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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, 376 (2014).
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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. Photon. 6, 488 (2012).
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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, 8185 (1992).
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[Crossref] [PubMed]

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[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, 66 (2015).

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39, 4360 (2014).
[Crossref] [PubMed]

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[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, and M. Tur, and Others, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062 (2013).
[Crossref] [PubMed]

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[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, 66 (2015).

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39, 4360 (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, 376 (2014).
[Crossref]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, and M. Tur, and Others, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38, 4062 (2013).
[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. Photon. 6, 488 (2012).
[Crossref]

Yang, H.

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. Photon. 6, 488 (2012).
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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. Photon. 6, 488 (2012).
[Crossref]

Zeilinger, A.

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

Zhao, N.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photon. 9, 822 (2015).
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Zhao, S. M.

Zhao, Z.

Zheng, B. Y.

Adv. Opt. Photon. (2)

Appl. Opt. (2)

Appl. Phys. B (1)

R. Chen, Y. Dong, F. Wang, and Y. Cai, “Statistical properties of a cylindrical vector partially coherent beam in turbulent atmosphere,” Appl. Phys. B 112, 247–259 (2013).
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Chin. Phys. B (1)

L. H.-C. Pu Ji-Xiong, Wang Tao, and L. Cheng-Liang, “Propagation of cylindrical vector beams in a turbulent atmosphere,” Chin. Phys. B 19, 89201 (2010).
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J. Opt. (2)

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Figures (4)

Fig. 1
Fig. 1 Illustration of the scalar (top) and CVV (bottom) modes described in Eq. (1) and Eq. (2) respectively, with arrows indicating polarisation distribution which is constant for scalar and variable for CVV modes, for = ±1. The phase of the four scalar modes in the transverse plane increases from −π (red) to π (blue) for positive ’s and decreases in the opposite direction for negative ’s whereas the phase for CVV modes is a superposition of both.
Fig. 2
Fig. 2 Simplified schematic diagram of the experimental setup showing the three main parts. The configuration of the half- and quarter-wave plates (HWP and QWP) and polarisers for different modes is summarised in the Appendix. The polarisation invariant SLM is made up by a polarising beam splitter (PBS), mirror and half wave plate rotated to 45° so that arbitrarily polarised scalar and vector beams can be modulated by the SLM, which is encoded with random Kolmogorov turbulence screens. The perturbed beams which return along the same path as the incoming beams are directed by a beam splitter (BS) to the detection part of the setup which performs modal decomposition.
Fig. 3
Fig. 3 Comparison of vector and scalar crosstalk for SR = 1.0 (top) for experimental setup validation and SR = 0.6 (middle) and SR = 0.2 (bottom).
Fig. 4
Fig. 4 Percentage of the signal in the crosstalk of scalar and vector cases showing insets of the beam with increasing turbulence. Both mode sets have the same crosstalk performance. Error bars are the standard error of the mean.

Tables (1)

Tables Icon

Table 1 Configuration of the various components of the experimental setup, depending on the required mode to be generated or decomposed.

Equations (21)

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| R + = | | R ,
| L + = | | L ,
| R = | | R ,
| L = | | L ,
| TM = 2 1 / 2 ( | | R + | | L ) ,
| TE = 2 1 / 2 ( | | R | | L ) ,
| HE e = 2 1 / 2 ( | | L + | | R ) ,
| HE o = 2 1 / 2 ( | | L | | R ) .
| turb . p | ,
| R + turb . p 0 | | R + p 2 | | R = | R turb . +
| TM turb . p 0 | | R + p 0 | | L + p 2 | | L + p 2 | | R = | T M turb .
R + | R turb + 2 = | R | ( p 0 | | R + p 2 | | R ) 2 = p 0 2 .
TM | TM turb 2 = ( 1 2 ( | R | + | L | ) ( p 0 | | R p 0 | | L + p 2 | | L + p 2 | | R ) 2 = p 0 2
M scalar = ( p 0 2 0 p 2 2 0 0 p 0 2 0 p 2 2 p 2 2 0 p 0 2 0 0 p 2 2 0 p 0 2 ) ,
M vector = ( p 0 2 p 2 + p 2 2 4 0 p 2 p 2 2 4 p 2 + p 2 2 4 p 0 2 p 2 p 2 2 4 0 0 p 2 P 2 2 4 p 0 2 p 2 + P 2 2 4 p 2 p 2 2 4 0 p 2 + p 2 2 4 p 0 2 ) .
N vector = i j M vector = ( p 2 + p 2 2 + p 2 p 2 2 ) = 2 ( p 2 2 + p 2 2 )
N scalar = i j M scalar = 2 ( p 2 2 + p 2 2 )
N scalar = N vector = 2 ( p 2 2 + p 2 2 )
C = 1 4 × i j M × 100 % ,
Q ^ [ | R | L ] = [ | + 2 q | L | 2 q | R ] ,
Q ^ [ | H | V ] = [ | + 2 q | R + | 2 q | L | + 2 q | R | 2 q | L ] ,

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