Abstract

The fiber coupling efficiency between the turbulent ocean to fiber of a partially coherent Gaussian beam propagating through the weak to strong anisotropic oceanic turbulence is studied. We derive the expression of new model of the fiber coupling efficiency for the partially coherent Gaussian beam. The numerical analyses reveal that larger inner scale and anisotropic factor, weaker oceanic turbulence strength, and smaller temperature-salinity contribution ratio will lead to a higher coupling efficiency; a longer wavelength, an suitable aperture diameter of the coupling lens, an optimum focal length and beam size, and a higher coherent degree will improve the fiber coupling efficiency. Our fiber coupling efficiency is higher than the previous fiber coupling efficiency.

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

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References

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    [Crossref] [PubMed]
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    [Crossref]
  6. L. Tan, M. Li, Q. Yang, and J. Ma, “Fiber-coupling efficiency of Gaussian Schell model for optical communication through atmospheric turbulence,” Appl. Opt. 54, 2318–2325 (2015).
    [Crossref] [PubMed]
  7. J. Ma, L. Ma, Q. Yang, and Q. Ran, “Statistical model of the efficiency for spatial light coupling into a single-mode fiber in the presence of atmospheric turbulence,” Appl. Opt. 54, 9287–9293 (2015).
    [Crossref] [PubMed]
  8. B. Hu, H. Shi, and Y. Zhang, “Fiber-coupling efficiency of Gaussian-Schell model beams through an ocean to fiber optical communication link,” Opt. Commun. 417, 14–18 (2018).
    [Crossref]
  9. F. Hanson and M. Lasher, “Effects of underwater turbulence on laser beam propagation and coupling into single-mode optical fiber,” Appl. Opt. 49, 3224–3230 (2010).
    [Crossref] [PubMed]
  10. M. Cheng, L. Guo, J. Li, and Y. Zhang, “Channel capacity of the OAM-based free-space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8, 1–11 (2016).
  11. M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55, 4642–4648 (2016).
    [Crossref] [PubMed]
  12. M. Cheng, L. Guo, and Y. Zhang, “Changes of propagation properties of orbital angular momentum for Laguerre-Gaussian beams in weak turbulent ocean,” Chin. J. Radio Sci 31, 737–742 (2016).
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    [Crossref]
  14. M. Chen and Y. Zhang, “Effects of anisotropic oceanic turbulence on the propagation of the OAM mode of a partially coherent modified Bessel correlated vortex beam,” Waves Random Complex Media, 1–12 (2018).
    [Crossref]
  15. B. Hu, L. Yu, and Y. Zhang, “Fiber coupling efficiency of Gaussian-Schell model beams in an ocean to fiber link with a Zernike tilt correction,” Appl. Opt. 57, 5831–5836 (2018).
    [Crossref]
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    [Crossref]
  17. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
    [Crossref]
  18. L. Yu and Y. Zhang, “Analysis of modal crosstalk for communication in turbulent ocean using Lommel-Gaussian beam,” Opt. Express 25, 22565–22574 (2017).
    [Crossref] [PubMed]
  19. Y. Yang, L. Yu, Q. Wang, and Y. Zhang, “Wander of the short-term spreading filter for partially coherent Gaussian beams through the anisotropic turbulent ocean,” Appl. Opt. 56, 7046–7052 (2017).
    [Crossref] [PubMed]
  20. A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53, 49–55 (2015).
    [Crossref]
  21. Y. Ata and Y. Baykal, “Anisotropic non-Kolmogorov turbulence effect on transmittance of multi-Gaussian beam,” Waves Random Complex Media, 1–12 (2018).
    [Crossref]

2018 (2)

B. Hu, H. Shi, and Y. Zhang, “Fiber-coupling efficiency of Gaussian-Schell model beams through an ocean to fiber optical communication link,” Opt. Commun. 417, 14–18 (2018).
[Crossref]

B. Hu, L. Yu, and Y. Zhang, “Fiber coupling efficiency of Gaussian-Schell model beams in an ocean to fiber link with a Zernike tilt correction,” Appl. Opt. 57, 5831–5836 (2018).
[Crossref]

2017 (2)

2016 (4)

M. Cheng, L. Guo, J. Li, and Y. Zhang, “Channel capacity of the OAM-based free-space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8, 1–11 (2016).

M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55, 4642–4648 (2016).
[Crossref] [PubMed]

M. Cheng, L. Guo, and Y. Zhang, “Changes of propagation properties of orbital angular momentum for Laguerre-Gaussian beams in weak turbulent ocean,” Chin. J. Radio Sci 31, 737–742 (2016).

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

2015 (3)

2010 (1)

2006 (1)

2005 (2)

2002 (2)

1998 (1)

Andrews, L. C.

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

Ata, Y.

Y. Ata and Y. Baykal, “Anisotropic non-Kolmogorov turbulence effect on transmittance of multi-Gaussian beam,” Waves Random Complex Media, 1–12 (2018).
[Crossref]

Baykal, Y.

Y. Ata and Y. Baykal, “Anisotropic non-Kolmogorov turbulence effect on transmittance of multi-Gaussian beam,” Waves Random Complex Media, 1–12 (2018).
[Crossref]

Chen, M.

M. Chen and Y. Zhang, “Effects of anisotropic oceanic turbulence on the propagation of the OAM mode of a partially coherent modified Bessel correlated vortex beam,” Waves Random Complex Media, 1–12 (2018).
[Crossref]

Cheng, M.

M. Cheng, L. Guo, J. Li, and Y. Zhang, “Channel capacity of the OAM-based free-space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8, 1–11 (2016).

M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55, 4642–4648 (2016).
[Crossref] [PubMed]

M. Cheng, L. Guo, and Y. Zhang, “Changes of propagation properties of orbital angular momentum for Laguerre-Gaussian beams in weak turbulent ocean,” Chin. J. Radio Sci 31, 737–742 (2016).

Cheng, Q.

Davidson, F. M.

Dikmelik, Y.

Fletcher, A. S.

A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53, 49–55 (2015).
[Crossref]

Guo, L.

M. Cheng, L. Guo, and Y. Zhang, “Changes of propagation properties of orbital angular momentum for Laguerre-Gaussian beams in weak turbulent ocean,” Chin. J. Radio Sci 31, 737–742 (2016).

M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55, 4642–4648 (2016).
[Crossref] [PubMed]

M. Cheng, L. Guo, J. Li, and Y. Zhang, “Channel capacity of the OAM-based free-space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8, 1–11 (2016).

Hamilton, S. A.

A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53, 49–55 (2015).
[Crossref]

Hanson, F.

Hu, B.

B. Hu, H. Shi, and Y. Zhang, “Fiber-coupling efficiency of Gaussian-Schell model beams through an ocean to fiber optical communication link,” Opt. Commun. 417, 14–18 (2018).
[Crossref]

B. Hu, L. Yu, and Y. Zhang, “Fiber coupling efficiency of Gaussian-Schell model beams in an ocean to fiber link with a Zernike tilt correction,” Appl. Opt. 57, 5831–5836 (2018).
[Crossref]

Hu, Z.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Huang, Q.

Lasher, M.

Leeb, W. R.

Li, J.

M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55, 4642–4648 (2016).
[Crossref] [PubMed]

M. Cheng, L. Guo, J. Li, and Y. Zhang, “Channel capacity of the OAM-based free-space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8, 1–11 (2016).

Li, M.

Li, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Liu, Q.

Ma, J.

Ma, L.

Mitchell, G.

Moores, J. D.

A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53, 49–55 (2015).
[Crossref]

Phillips, R. L.

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

Qiao, C.

Ran, Q.

Ricklin, J. C.

Shi, H.

B. Hu, H. Shi, and Y. Zhang, “Fiber-coupling efficiency of Gaussian-Schell model beams through an ocean to fiber optical communication link,” Opt. Commun. 417, 14–18 (2018).
[Crossref]

Stanton, S.

Tan, L.

Toyoshima, M.

Wallner, O.

Wang, Q.

Winzer, P. J.

Wu, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Yang, Q.

Yang, Y.

Yu, L.

Zhang, D.

Zhang, Y.

B. Hu, H. Shi, and Y. Zhang, “Fiber-coupling efficiency of Gaussian-Schell model beams through an ocean to fiber optical communication link,” Opt. Commun. 417, 14–18 (2018).
[Crossref]

B. Hu, L. Yu, and Y. Zhang, “Fiber coupling efficiency of Gaussian-Schell model beams in an ocean to fiber link with a Zernike tilt correction,” Appl. Opt. 57, 5831–5836 (2018).
[Crossref]

L. Yu and Y. Zhang, “Analysis of modal crosstalk for communication in turbulent ocean using Lommel-Gaussian beam,” Opt. Express 25, 22565–22574 (2017).
[Crossref] [PubMed]

Y. Yang, L. Yu, Q. Wang, and Y. Zhang, “Wander of the short-term spreading filter for partially coherent Gaussian beams through the anisotropic turbulent ocean,” Appl. Opt. 56, 7046–7052 (2017).
[Crossref] [PubMed]

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

M. Cheng, L. Guo, J. Li, and Y. Zhang, “Channel capacity of the OAM-based free-space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8, 1–11 (2016).

M. Cheng, L. Guo, and Y. Zhang, “Changes of propagation properties of orbital angular momentum for Laguerre-Gaussian beams in weak turbulent ocean,” Chin. J. Radio Sci 31, 737–742 (2016).

M. Chen and Y. Zhang, “Effects of anisotropic oceanic turbulence on the propagation of the OAM mode of a partially coherent modified Bessel correlated vortex beam,” Waves Random Complex Media, 1–12 (2018).
[Crossref]

Appl. Opt. (8)

O. Wallner, P. J. Winzer, and W. R. Leeb, “Alignment tolerances for plane-wave to single-mode fiber coupling and their mitigation by use of pigtailed collimators,” Appl. Opt. 41, 637–643 (2002).
[Crossref] [PubMed]

Y. Yang, L. Yu, Q. Wang, and Y. Zhang, “Wander of the short-term spreading filter for partially coherent Gaussian beams through the anisotropic turbulent ocean,” Appl. Opt. 56, 7046–7052 (2017).
[Crossref] [PubMed]

L. Tan, M. Li, Q. Yang, and J. Ma, “Fiber-coupling efficiency of Gaussian Schell model for optical communication through atmospheric turbulence,” Appl. Opt. 54, 2318–2325 (2015).
[Crossref] [PubMed]

M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55, 4642–4648 (2016).
[Crossref] [PubMed]

F. Hanson and M. Lasher, “Effects of underwater turbulence on laser beam propagation and coupling into single-mode optical fiber,” Appl. Opt. 49, 3224–3230 (2010).
[Crossref] [PubMed]

B. Hu, L. Yu, and Y. Zhang, “Fiber coupling efficiency of Gaussian-Schell model beams in an ocean to fiber link with a Zernike tilt correction,” Appl. Opt. 57, 5831–5836 (2018).
[Crossref]

Y. Dikmelik and F. M. Davidson, “Fiber-coupling efficiency for free-space optical communication through atmospheric turbulence,” Appl. Opt. 44, 4946–4952 (2005).
[Crossref] [PubMed]

J. Ma, L. Ma, Q. Yang, and Q. Ran, “Statistical model of the efficiency for spatial light coupling into a single-mode fiber in the presence of atmospheric turbulence,” Appl. Opt. 54, 9287–9293 (2015).
[Crossref] [PubMed]

Chin. J. Radio Sci (1)

M. Cheng, L. Guo, and Y. Zhang, “Changes of propagation properties of orbital angular momentum for Laguerre-Gaussian beams in weak turbulent ocean,” Chin. J. Radio Sci 31, 737–742 (2016).

IEEE Commun. Mag. (1)

A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53, 49–55 (2015).
[Crossref]

IEEE Photonics J. (1)

M. Cheng, L. Guo, J. Li, and Y. Zhang, “Channel capacity of the OAM-based free-space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8, 1–11 (2016).

J. Opt. Netw. (1)

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

Opt. Commun. (2)

B. Hu, H. Shi, and Y. Zhang, “Fiber-coupling efficiency of Gaussian-Schell model beams through an ocean to fiber optical communication link,” Opt. Commun. 417, 14–18 (2018).
[Crossref]

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Other (3)

M. Chen and Y. Zhang, “Effects of anisotropic oceanic turbulence on the propagation of the OAM mode of a partially coherent modified Bessel correlated vortex beam,” Waves Random Complex Media, 1–12 (2018).
[Crossref]

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

Y. Ata and Y. Baykal, “Anisotropic non-Kolmogorov turbulence effect on transmittance of multi-Gaussian beam,” Waves Random Complex Media, 1–12 (2018).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 The fiber coupling efficiency η of two models as a function of focal length f with different wavelength λ.
Fig. 2
Fig. 2 The fiber coupling efficiency η of two models as a function of the propagation distance z with different coherent length σ0.
Fig. 3
Fig. 3 The fiber coupling efficiency η of two models as a function of beam size w0 with different anisotropic factor ζ.
Fig. 4
Fig. 4 The fiber coupling efficiency η of two models as a function of the receiver lens diameter D with different temperature structure constant C m 2 .
Fig. 5
Fig. 5 The fiber coupling efficiency η of two models as a function of relative strength of temperature and salinity fluctuations ϖ with different inner scale l0.

Equations (23)

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η = P c P a = | A E A ( r ) F A * ( r ) | 2 d r | A E A ( r ) | 2 d r = A F A * ( r 1 ) F A ( r 2 ) W ( r 1 , r 2 , z ) d r 1 d r 2 | A E A ( r ) | 2 d r ,
F A ( r ) = 2 π ω 0 λ f exp [ ( π ω 0 r λ f ) 2 ] ,
u ( ρ , 0 ) = exp [ ( 1 w 0 2 + i k 2 R 0 ) ρ 2 ] ,
u ( r , z ) = i k 2 π z d 2 ρ u ( ρ , 0 ) exp [ i k z + i k | r ρ | 2 2 z + ψ ( ρ , r ) ] ,
W ( r 1 , r 2 , z ) = ( k 2 π z ) 2 d 2 ρ 1 d 2 ρ 2 W ( ρ 1 , ρ 2 , 0 ) exp [ ψ * ( ρ 1 , r 1 , z ) + ψ ( ρ 2 , r 2 , z ) ] o × exp [ i k ( r 1 ρ 1 ) 2 ( r 2 ρ 2 ) 2 2 z ] 2 ,
W ( ρ 1 , ρ 2 , 0 ) = u ( ρ 1 , 0 ) u * ( ρ 2 , 0 ) exp [ ( ρ 1 ρ 2 ) 2 2 σ 0 2 ] .
r s = 1 2 ( r 1 + r 2 ) , r d = r 1 r 2 , ρ s = 1 2 ( ρ 1 + ρ 2 ) , ρ d = ρ 1 ρ 2 ,
W ( ρ d , ρ s , 0 ) = exp { 1 w 0 2 [ 1 2 ( ρ d 2 + 4 ρ s 2 ) ] } i k ρ d ρ s R 0 ρ d 2 2 σ 0 2 ,
exp { i k 2 z [ ( r 1 ρ 1 ) 2 ( r 2 ρ 2 ) 2 ] } = exp [ i k z ( ρ s r s ) ( ρ d r d ) ] .
exp [ ψ * ( ρ 1 , r 1 , z ) + ψ ( ρ 2 , r 2 , z ) ] o exp ( r d 2 + ρ d 2 + r d ρ d ρ 0 2 ) ,
ρ 0 = [ π 2 k 2 z 3 0 κ 3 Φ n ( κ ζ , ζ ) d κ ] 1 / 2 ,
Φ n ( κ ζ , ζ ) = 0.388 × 10 8 ε 1 / 3 χ t ζ 2 κ ζ 11 / 3 [ 1 + 2.35 ( κ ζ l 0 ) 2 / 3 ] f ( κ ζ , ϖ ) ,
f ( κ ζ , ϖ ) = exp ( A T δ ) + ϖ 2 exp ( A S δ ) 2 ϖ 1 exp ( A T S δ ) ,
ρ 0 2 = 18.02 C m 2 k 2 ζ 2 z l 0 1 / 3 ( 0.483 0.835 ϖ 1 + 3.38 ϖ 2 ) ,
W ( r d , r s , z ) = ( k 2 π z ) 2 d 2 ρ s d 2 ρ d exp [ 2 ρ s 2 w 0 2 i k ρ s ρ d R 0 + i k ( ρ d r d ) z ] × exp [ ρ d 2 2 w 0 2 ρ d 2 2 σ 0 2 ρ d 2 + ρ d r d + r d 2 ρ 0 2 i k r s ( ρ d r d ) z ] .
W ( r d , r s , z ) = w 0 2 w 2 ( z ) exp [ r d 2 L 2 r s 2 w 2 ( z ) + i M ( r d r s ) ] ,
I ( r , z ) = W ( r d = 0 , r s = r , z ) = w 0 2 w 2 ( z ) exp ( 2 r 2 w 2 ( z ) ) .
A | E A ( r ) | 2 d r = π w 0 2 2 [ 1 exp ( D 2 2 w 2 ( z ) ) ] ,
η 1 = 4 ω 0 2 λ 2 f 2 w 2 ( z ) [ 1 exp ( D 2 2 w 2 ( z ) ) ] 0 D / 2 0 D / 2 0 2 π 0 2 π exp [ ( L + π 2 ω 0 2 2 λ 2 f 2 ) r d 2 ( 2 w 2 ( z ) + 2 π 2 ω 0 2 λ 2 f 2 ) r s 2 ] exp [ i M r d r s cos ( φ d φ s ) ] r d r s d r d d r s d φ d d φ s .
0 2 π 0 2 π exp [ i M r d r s cos ( φ d φ s ) ] d φ d d φ s = 4 π 2 J 0 ( M r d r s ) ,
η 1 = 16 π 2 ω 0 2 λ 2 f 2 w 2 ( z ) [ 1 exp ( D 2 2 w 2 ( z ) ) ] 0 D / 2 0 D / 2 exp [ ( L + π 2 ω 0 2 2 λ 2 f 2 ) r d 2 ( 2 w 2 ( z ) + 2 π 2 ω 0 2 λ 2 f 2 ) r s 2 ] J 0 [ M r d r s ] r d r s d r d d r s .
η 1 = D 4 π 2 ω 0 2 λ 2 f 2 w 2 ( z ) [ 1 exp ( D 2 2 w 2 ( z ) ) ] 0 1 0 1 exp [ ( D 2 L 4 + D 2 π 2 ω 0 2 8 λ 2 f 2 ) x 1 2 ( D 2 2 w 2 ( z ) + D 2 π 2 ω 0 2 2 λ 2 f 2 ) x 2 2 ] J 0 ( M D 2 x 1 x 2 4 ) x 1 x 2 d x 1 d x 2 .
η 2 = 2 D 2 π 2 ω 0 2 λ 2 f 2 0 1 0 1 exp [ ( D 2 L 4 D 2 8 w 2 ( z ) + D 2 π 2 ω 0 2 8 λ 2 f 2 ) x 1 2 D 2 π 2 ω 0 2 2 λ 2 f 2 x 2 2 ] × J 0 ( M D 2 x 1 x 2 4 ) x 1 x 2 d x 1 d x 2 .

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