Abstract

High-speed free-space optical communication systems have recently used fiber-optic components. The received laser beam in such a system must be coupled into a single-mode fiber at the input of the receiver module. However, propagation through atmospheric turbulence degrades the spatial coherence of a laser beam and limits the fiber-coupling efficiency. We numerically evaluate the fiber-coupling efficiency for laser light distorted by atmospheric turbulence. We also investigate the use of a coherent fiber array as a receiver structure and find that a coherent fiber array that consists of seven subapertures would significantly increase the fiber-coupling efficiency.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2003 (1)

2001 (1)

2000 (2)

1999 (1)

G. Nykolak, P. F. Szajowski, G. Tourgee, H. Presby, “2.5 Gbit/s free space optical link over 4.4 km,” Electron. Lett. 35, 578–579 (1999).
[CrossRef]

1998 (3)

1996 (1)

Andrews, L. C.

Barbier, P. R.

Belmonte, A.

Benedetto, S.

L. Kazovsky, S. Benedetto, A. Willner, Optical Fiber Communication Systems (Artech House, 1996).

Bifano, T. G.

T. Weyrauch, M. A. Vorontsov, J. W. Gowens, T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” in Free-Space Laser Communication and Laser Imaging,D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE4489, 177–184 (2002).
[CrossRef]

Bruesselbach, H.

H. Bruesselbach, M. L. Minden, S. Wang, D. C. Jones, M. S. Mangir, “A coherent fiber array based laser link for atmospheric aberration mitigation and power scaling,” in Free-Space Laser Communication Technologies XVI,G. S. Mecherle, C. Y. Young, J. S. Stryjewski, eds., Proc. SPIE5338, 90–101 (2004).
[CrossRef]

Buck, J. A.

J. A. Buck, Fundamentals of Optical Fibers (Wiley, 1995).

Castellanos, D. C.

Cho, J. W.

Chung, Y.

Costello, T. P.

Gatt, P.

Gowens, J. W.

T. Weyrauch, M. A. Vorontsov, J. W. Gowens, T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” in Free-Space Laser Communication and Laser Imaging,D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE4489, 177–184 (2002).
[CrossRef]

Harvey, J. E.

Heimmermann, D. A.

Hobbs, P. C. D.

P. C. D. Hobbs, Building Electro-Optical Systems (Wiley-Interscience, 2000).
[CrossRef]

Hurh, Y. S.

Jones, D. C.

H. Bruesselbach, M. L. Minden, S. Wang, D. C. Jones, M. S. Mangir, “A coherent fiber array based laser link for atmospheric aberration mitigation and power scaling,” in Free-Space Laser Communication Technologies XVI,G. S. Mecherle, C. Y. Young, J. S. Stryjewski, eds., Proc. SPIE5338, 90–101 (2004).
[CrossRef]

Kazovsky, L.

L. Kazovsky, S. Benedetto, A. Willner, Optical Fiber Communication Systems (Artech House, 1996).

Kudielka, K. H.

Lee, D. W.

Lee, J. S.

Leeb, W. R.

Lim, J. H.

Mangir, M. S.

H. Bruesselbach, M. L. Minden, S. Wang, D. C. Jones, M. S. Mangir, “A coherent fiber array based laser link for atmospheric aberration mitigation and power scaling,” in Free-Space Laser Communication Technologies XVI,G. S. Mecherle, C. Y. Young, J. S. Stryjewski, eds., Proc. SPIE5338, 90–101 (2004).
[CrossRef]

Minden, M. L.

H. Bruesselbach, M. L. Minden, S. Wang, D. C. Jones, M. S. Mangir, “A coherent fiber array based laser link for atmospheric aberration mitigation and power scaling,” in Free-Space Laser Communication Technologies XVI,G. S. Mecherle, C. Y. Young, J. S. Stryjewski, eds., Proc. SPIE5338, 90–101 (2004).
[CrossRef]

Nykolak, G.

G. Nykolak, P. F. Szajowski, G. Tourgee, H. Presby, “2.5 Gbit/s free space optical link over 4.4 km,” Electron. Lett. 35, 578–579 (1999).
[CrossRef]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

Phillips, R. R.

Plett, M. L.

Presby, H.

G. Nykolak, P. F. Szajowski, G. Tourgee, H. Presby, “2.5 Gbit/s free space optical link over 4.4 km,” Electron. Lett. 35, 578–579 (1999).
[CrossRef]

Rush, D. W.

Rye, B. J.

Sellar, G.

Song, D. Y.

Stickley, C. M.

Stryjewski, J. S.

Szajowski, P. F.

G. Nykolak, P. F. Szajowski, G. Tourgee, H. Presby, “2.5 Gbit/s free space optical link over 4.4 km,” Electron. Lett. 35, 578–579 (1999).
[CrossRef]

Tourgee, G.

G. Nykolak, P. F. Szajowski, G. Tourgee, H. Presby, “2.5 Gbit/s free space optical link over 4.4 km,” Electron. Lett. 35, 578–579 (1999).
[CrossRef]

Vorontsov, M. A.

T. Weyrauch, M. A. Vorontsov, J. W. Gowens, T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” in Free-Space Laser Communication and Laser Imaging,D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE4489, 177–184 (2002).
[CrossRef]

Wang, S.

H. Bruesselbach, M. L. Minden, S. Wang, D. C. Jones, M. S. Mangir, “A coherent fiber array based laser link for atmospheric aberration mitigation and power scaling,” in Free-Space Laser Communication Technologies XVI,G. S. Mecherle, C. Y. Young, J. S. Stryjewski, eds., Proc. SPIE5338, 90–101 (2004).
[CrossRef]

Weeks, A. R.

Weyrauch, T.

T. Weyrauch, M. A. Vorontsov, J. W. Gowens, T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” in Free-Space Laser Communication and Laser Imaging,D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE4489, 177–184 (2002).
[CrossRef]

Willner, A.

L. Kazovsky, S. Benedetto, A. Willner, Optical Fiber Communication Systems (Artech House, 1996).

Winzer, P. J.

Xu, J.

Appl. Opt. (5)

Electron. Lett. (1)

G. Nykolak, P. F. Szajowski, G. Tourgee, H. Presby, “2.5 Gbit/s free space optical link over 4.4 km,” Electron. Lett. 35, 578–579 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Other (6)

T. Weyrauch, M. A. Vorontsov, J. W. Gowens, T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” in Free-Space Laser Communication and Laser Imaging,D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE4489, 177–184 (2002).
[CrossRef]

H. Bruesselbach, M. L. Minden, S. Wang, D. C. Jones, M. S. Mangir, “A coherent fiber array based laser link for atmospheric aberration mitigation and power scaling,” in Free-Space Laser Communication Technologies XVI,G. S. Mecherle, C. Y. Young, J. S. Stryjewski, eds., Proc. SPIE5338, 90–101 (2004).
[CrossRef]

L. C. Andrews, R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

J. A. Buck, Fundamentals of Optical Fibers (Wiley, 1995).

L. Kazovsky, S. Benedetto, A. Willner, Optical Fiber Communication Systems (Artech House, 1996).

P. C. D. Hobbs, Building Electro-Optical Systems (Wiley-Interscience, 2000).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Mutual coherence function as a function of |r1r2| for the Kolmogorov spectrum (solid curve) and the Gaussian approximation of the mutual coherence function (dashed curve), where Cn2 = 10−13 m−2/3, λ = 1.55 μm, and L = 1 km.

Fig. 2
Fig. 2

Fiber-coupling efficiency as a function of the number of speckles AR/AC over the receiver aperture. The coupling-geometry parameter a = 1.12 for the curve. The circles represent the maximum coupling efficiency that can be obtained by optimizing a for six different values of AR/AC.

Fig. 3
Fig. 3

Fiber-coupling efficiency as a function of the number of speckles AR/AC over the receiver aperture for a = 1.12. The two curves are obtained by using the mutual coherence function for the Kolmogorov spectrum (solid curve) and the Gaussian approximation to the mutual coherence function (dashed curve).

Fig. 4
Fig. 4

Fiber-coupling efficiency as a function of Cn2 for a link distance of 1 km, where DR = 10 cm, a = 1.12, and λ = 1.55 μm.

Fig. 5
Fig. 5

Fiber-coupling efficiency as a function of link distance for three different values of Cn2, where DR = 10 cm, a = 1.12, and λ = 1.55 μm.

Fig. 6
Fig. 6

Hexagonal close-packed arrangement of a coherent fiber array. The seven small circles represent subapertures of diameter dR, and the large circle represents a single receiver aperture of diameter DR.

Fig. 7
Fig. 7

Fiber-coupling efficiency and the efficiency improvement factor over a single-aperture receiver for a seven-element coherent fiber array. The results are plotted as a function of Cn2 for a link distance of 1 km, where DR = 10 cm, a = 1.12, and λ = 1.55 μm.

Fig. 8
Fig. 8

Fiber-coupling efficiency and the efficiency improvement factor over a single-aperture receiver for a seven-element coherent fiber array. The results are plotted as a function of link distance for three different values of Cn2, where DR = 10 cm, a = 1.12, and λ = 1.55 μm.

Equations (19)

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η c = P c P a = | A U i ( r ) U m * ( r ) d r | 2 A U i ( r ) 2 d r ,
η c = 1 P a A Γ i ( r 1 , r 2 ) U m * ( r 1 ) U m ( r 2 ) d r 1 d r 2 ,
Γ i ( r 1 , r 2 ) = U i ( r 1 ) U i * ( r 2 ) .
Γ i ( r 1 , r 2 ) = I 1 exp ( - 1.46 C n 2 k 2 L r 1 - r 2 5 / 3 ) ,
U m ( r ) = k W m 2 π f exp [ - ( k W m 2 f ) 2 r 2 ] ,
Γ i ( r 1 , r 2 ) = I i exp ( - r 1 - r 2 2 ρ c 2 ) ,
ρ c = ( 1.46 C n 2 k 2 L ) - 3 / 5 .
η c = 2 π W m 2 ( λ f ) 2 1 A R 0 D R / 2 0 D R / 2 0 2 π 0 2 π × exp [ - ( π W m λ f ) 2 ( r 1 2 + r 2 2 ) ] × exp ( - r 1 - r 2 5 / 3 ρ c 5 / 3 ) r 1 r 2 d θ 1 d θ 2 d r 1 d r 2 ,
r 1 - r 2 2 = r 1 2 + r 2 2 - 2 r 1 r 2 cos ( θ 1 - θ 2 )
I = 0 2 π 0 2 π exp { - [ r 1 2 + r 2 2 - 2 r 1 r 2 cos ( θ 1 - θ 2 ) ] 5 / 6 ρ c 5 / 3 } × d θ 1 d θ 2 .
I = 4 π 0 π exp { - ( r 1 2 + r 2 2 ρ c 2 ) 5 / 6 × [ 1 - 2 r 1 r 2 r 1 2 + r 2 2 cos ( θ d ) ] 5 / 6 } d θ d .
I = 4 π 0 π exp { - v 5 / 6 [ 1 - u cos ( θ d ) ] 5 / 6 } d θ d ,
v = A R A c ( x 1 2 + x 2 2 ) ,
u = 2 x 1 x 2 x 1 2 + x 2 2 .
η c = 8 a 2 π 0 1 0 1 exp [ - a 2 ( x 1 2 + x 2 2 ) ] × F ( A R A C ( x 1 2 + x 2 2 ) , 2 x 1 x 2 x 1 2 + x 2 2 ) x 1 x 2 d x 1 d x 2 ,
F ( v , u ) = 0 π exp { - v 5 / 6 [ 1 - u cos ( θ ) ] 5 / 6 } d θ .
a = D R 2 π W m λ f .
F ( v , u ) = π exp ( - v ) I 0 ( v u ) ,
η c = 8 a 2 0 1 0 1 exp [ - ( a 2 + A R A C ) ( x 1 2 + x 2 2 ) ] × I 0 ( 2 A R A C x 1 x 2 ) x 1 x 2 d x 1 d x 2 .

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