Abstract

A novel scheme is proposed to mitigate the atmospheric turbulence effect in free space optical (FSO) communication employing orbital angular momentum (OAM) multiplexing. In this scheme, the Gaussian beam is used as an auxiliary light with a common-path to obtain the distortion information caused by atmospheric turbulence. After turbulence, the heterodyne coherent detection technology is demonstrated to realize the turbulence mitigation. With the same turbulence distortion, the OAM beams and the Gaussian beam are respectively utilized as the signal light and the local oscillation light. Then the turbulence distortion is counteracted to a large extent. Meanwhile, a phase matching method is proposed to select the specific OAM mode. The discrimination between the neighboring OAM modes is obviously improved by detecting the output photocurrent. Moreover, two methods of beam size adjustment have been analyzed to achieve better performance for turbulence mitigation. Numerical results show that the system bit error rate (BER) can reach 10−5 under strong turbulence in simulation situation.

© 2017 Optical Society of America

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References

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2017 (1)

2016 (12)

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).
[PubMed]

A. Forbes, A. Dudley, and M. Mclaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).

S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photonics Res. 4(5), B1–B4 (2016).

C. Rickenstorff, J. A. Rodrigo, and T. Alieva, “Programmable simulator for beam propagation in turbulent atmosphere,” Opt. Express 24(9), 10000–10012 (2016).
[PubMed]

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).

A. E. Willner, “Communication with a twist,” IEEE Spectr. 53(8), 34–39 (2016).

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Comm. Surv. and Tutor. 19(1), 57–96 (2016).

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(5), 054013 (2016).

J. Li, W. Wang, M. Duan, and J. Wei, “Influence of non-Kolmogorov atmospheric turbulence on the beam quality of vortex beams,” Opt. Express 24(18), 20413–20423 (2016).
[PubMed]

S. Li and J. Wang, “Compensation of a distorted N-fold orbital angular momentum multicasting link using adaptive optics,” Opt. Lett. 41(7), 1482–1485 (2016).
[PubMed]

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).

R. Neo, M. Goodwin, J. Zheng, J. Lawrence, S. Leon-Saval, J. Bland-Hawthorn, and G. Molina-Terriza, “Measurement and limitations of optical orbital angular momentum through corrected atmospheric turbulence,” Opt. Express 24(3), 2919–2930 (2016).
[PubMed]

2015 (2)

2014 (4)

2013 (4)

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).
[PubMed]

H. Huang, Y. Yue, N. Ahmed, S. J. Dolinar, and A. E. Willner, “Performance analysis of spectrally efficient free-space data link using spatially multiplexed orbital angular momentum beams,” Proc. SPIE 8647, 846706 (2013).

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre–Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15(4), 044007 (2013).

B. Rodenburg, M. Mirhosseini, M. Malik, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating real-world turbulence in the lab: orbital angular momentum communication through 1 km of atmosphere,” New J. Phys. 16, 033020 (2013).

2012 (3)

2006 (2)

S. H. Eng, D. M. Cai, Z. Wang, and K. Alameh, “Optimization of liquid-crystal spatial light modulator for precise phase generation,” Optoelectron. Microelectronic Mater. Devices 6(1), 105–108 (2006).

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2(3), 209–224 (2006).

1995 (1)

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1–3), 36–40 (1995).

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[PubMed]

Ahmed, N.

G. Xie, C. Liu, L. Li, Y. Ren, Z. Zhao, Y. Yan, N. Ahmed, Z. Wang, A. J. Willner, C. Bao, Y. Cao, P. Liao, M. Ziyadi, A. Almaiman, S. Ashrafi, M. Tur, and A. E. Willner, “Spatial light structuring using a combination of multiple orthogonal orbital angular momentum beams with complex coefficients,” Opt. Lett. 42(5), 991–994 (2017).
[PubMed]

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).
[PubMed]

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
[PubMed]

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[PubMed]

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).
[PubMed]

H. Huang, Y. Yue, N. Ahmed, S. J. Dolinar, and A. E. Willner, “Performance analysis of spectrally efficient free-space data link using spatially multiplexed orbital angular momentum beams,” Proc. SPIE 8647, 846706 (2013).

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

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(5), 054013 (2016).

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre–Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15(4), 044007 (2013).

Alameh, K.

S. H. Eng, D. M. Cai, Z. Wang, and K. Alameh, “Optimization of liquid-crystal spatial light modulator for precise phase generation,” Optoelectron. Microelectronic Mater. Devices 6(1), 105–108 (2006).

Alieva, T.

Allen, L.

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1–3), 36–40 (1995).

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[PubMed]

Almaiman, A.

Anguita, J. A.

J. A. Anguita, H. Rodriguez, and C. Quezada, “Experimental propagation of optical Laguerre-Gauss beams in turbulence,” in Proceedings of Aerospace Conference (IEEE, 2014), pp. 1–6.

Ashrafi, S.

Bao, C.

Beghi, A.

A. Beghi, A. Cenedese, and A. Masiero, “Efficient algorithms for the reconstruction and prediction of atmospheric turbulence in AO systems,” in Proceedings of Control Conference (IEEE, 2014), pp. 2430–2435.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[PubMed]

Bian, L. A.

L. A. Bian, L. Mingtuan, and L. Peiguo, “Capacity analysis of OAM multiplexing system for radio communications,” in Proceedings of IEEE Conference on Microwave, Antenna, Propagation, and EMC Technologies (MAPE) (IEEE, 2015), pp. 267–271.

Birnbaum, K. M.

Bland-Hawthorn, J.

Boyd, R. W.

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).
[PubMed]

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
[PubMed]

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17, 023011 (2014).

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).
[PubMed]

B. Rodenburg, M. Mirhosseini, M. Malik, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating real-world turbulence in the lab: orbital angular momentum communication through 1 km of atmosphere,” New J. Phys. 16, 033020 (2013).

B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37(17), 3735–3737 (2012).
[PubMed]

Cai, D. M.

S. H. Eng, D. M. Cai, Z. Wang, and K. Alameh, “Optimization of liquid-crystal spatial light modulator for precise phase generation,” Optoelectron. Microelectronic Mater. Devices 6(1), 105–108 (2006).

Cao, Y.

Cenedese, A.

A. Beghi, A. Cenedese, and A. Masiero, “Efficient algorithms for the reconstruction and prediction of atmospheric turbulence in AO systems,” in Proceedings of Control Conference (IEEE, 2014), pp. 2430–2435.

Chandrasekaran, N.

Chen, C.

Chen, H.

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).

Cheng, W.

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).

Dainty, J. C.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2(3), 209–224 (2006).

Ding, J.

Djordjevic, I. B.

Z. Qu and I. B. Djordjevic, “Experimental evaluation of LDPC-coded OAM based FSO communication in the presence of atmospheric turbulence,” in Proceedings of IEEE Conference on Telecommunication in Modern Satellite, Cable and Broadcasting Services (TELSIKS) (IEEE, 2015), pp. 117–122.

Dolinar, S.

Dolinar, S. J.

Duan, M.

Dudley, A.

A. Forbes, A. Dudley, and M. Mclaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).

Eng, S. H.

S. H. Eng, D. M. Cai, Z. Wang, and K. Alameh, “Optimization of liquid-crystal spatial light modulator for precise phase generation,” Optoelectron. Microelectronic Mater. Devices 6(1), 105–108 (2006).

Erkmen, B. I.

Fazal, I. M.

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

Feng, F.

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(5), 054013 (2016).

Forbes, A.

A. Forbes, A. Dudley, and M. Mclaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).

Fu, S.

S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photonics Res. 4(5), B1–B4 (2016).

Gao, C.

S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photonics Res. 4(5), B1–B4 (2016).

Glindemann, A.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2(3), 209–224 (2006).

Gong, L.

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).

Gong, L. Y.

Goodwin, M.

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).
[PubMed]

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
[PubMed]

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram of the proposed turbulence mitigation in OAMs multiplexing link. BS, beam splitter; PBS, polarization beam splitter; SLM, spatial light modulator; AT, atmospheric turbulence; PD, photo detector.
Fig. 2
Fig. 2 Schematic diagram of two-beam distortion counteraction in LG02 mode transmission.
Fig. 3
Fig. 3 (a) Normalized power spectrum of the initial OAM, where the single LG02 mode is transmitted through the strong turbulence ( C n 2 =1× 10 13 m 2/3 ) in a distance of 1 km. (b) Normalized power spectrum of LG modes after turbulence. (c) Normalized power spectrum of the detected LG modes.
Fig. 4
Fig. 4 (a) Normalized power spectrum of the initial state of two OAM multiplexed modes (LG02 and LG04) is transmitted through the moderate turbulence ( C n 2 =1× 10 14 m 2/3 ) for a distance of 1 km. (b) Normalized power spectrum of LG modes after turbulence. (c) Normalized power spectrum of the detected LG modes.
Fig. 5
Fig. 5 (a) Normalized power spectrum of the initial state of three OAM multiplexed modes (LG02, LG0-3 and LG04) is transmitted through the moderate turbulence ( C n 2 =1× 10 14 m 2/3 ) for a distance of 1 km. (b) Normalized power spectrum of LG modes after turbulence. (c) Normalized power spectrum of the detected LG modes.
Fig. 6
Fig. 6 BER of four multiplexed OAM channels carrying the QPSK signal. (a) The BER and the constellation diagram of different OAM channels. Here, the absolute value | l |=2,3,5,8correspond to l=2,3,5,8, respectively. (b) The BER of four multiplexed OAM channels under different atmospheric turbulence strength.
Fig. 7
Fig. 7 The constellation diagram of four multiplexed OAM channels carrying the QPSK signal. Both the proposed method and the direct detection are presented.
Fig. 8
Fig. 8 Schematic diagram of three situations. (a) without adjustment; (b) adjust the Gaussian beam size to fit for the highest order OAM beam; (c) adjust the OAM beam waists to fit for the Gaussian beam. wOAM, rOAM are respectively the beam waists, beam sizes of the OAM beams, and wG, rG are respectively the beam waist, beam size of the Gaussian beam.
Fig. 9
Fig. 9 The constellation diagram of four multiplexed OAM channels based on the proposed method (a) without adjustment, (b) adjust the Gaussian beam size to fit for the highest order OAM beam and (c) adjust the OAM beam waists to fit for the Gaussian beam.
Fig. 10
Fig. 10 The BER of four multiplexed OAM channels under the turbulence strength C n 2 =5× 10 14 m 2/3 . The situations of without adjustment, with Gaussian beam size adjustment, and with OAM beam waists adjustment are presented.

Tables (1)

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Table 1 Power weight of LG02 mode in four simulations

Equations (16)

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U(r,θ)=A(r)exp(ilθ)
U MUX (r,θ,t)= s=1 N m s (t) A s ( r )exp(i l s θ)
m s (t)=αexp(ωt+i ψ s ) , ψ s { π 4 , 3π 4 , 5π 4 , 7π 4 }
Φ(κ)=0.033 C n 2 κ 113 , κ[ 2π/ L 0 ,2π/ l 0 ]
r 0 = [ 2.91 6.88 k 2 0 L C n 2 (z) dz] 3/5
σ R 2 =1.23 k 7/6 C n 2 L 11/6
D ϕ (r)=6.88 (r/ r 0 ) 5/3
U MUX ' (r,θ,t)= s=1 N m s (t) A s ' (r)exp(i l s θ)exp(iϕ)
U(r,t)= A ' (r)exp(iϕ)
U ' = A ' (r)exp(iϕ)exp(i l p θ)
I 0 + 0 2π ( | U MUX ' + U ' | 2 )rdrdθ
I=βRe( 0 + 0 2π U MUX ' U '* rdrdθ) =βRe{ 0 + 0 2π [ s=1 N m s (t) A s ' (r)exp(i l s θ)exp(iϕ) ] A ' * (r) ×exp(iϕ)exp(i l p θ)rdrdθ }
I={ βRe [ 0 + 0 2π m p (t) A p ' (r) A ' (r)rdrd θ ] i f s=p; 0 otherwise
I= c p cos(Δωt+ ψ p )
U(r,θ,z)= 2p! π(p+| l |)! 1 w(z) [ r 2 w(z) ] | l | L p l [ 2 r 2 w 2 (z) ] ×exp[ r 2 w 2 (z) ] exp[ ik r 2 z 2( z 2 + z R 2 ) ] ×exp[ i(2p+| l |+1) tan 1 z z R ] exp(ilθ)
I direct = 0 + 0 2π { | U MUX ' +[ U G exp(i l p θ) ] | 2 } rdrdθ .

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