Abstract

Efficient coupling of coherent plane waves into single-mode fibers is a key technology for free-space optical communication at 1550nm. Here we deal with the influence of random angular jitter on a plane wave to single-mode fiber coupling. The expression of mean-coupling efficiency in the presence of random jitter is handled in the pupil plane. First, an analytical expression of the mean-coupling efficiency is derived for the zero bias error case. Then the bias error was taken into account. By minimizing the coupling efficiency penalty, the optimum value of design parameter β of fiber-coupled optical systems in the presence of random jitter is obtained. The results obtained here will be useful in facilitating parametric estimation and optimization of fiber-coupled optical systems.

© 2009 Optical Society of America

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References

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  1. V. W. S. Chan, “Optical space communications,” IEEE J. Sel. Top. Quantum Electron. 6, 959-975 (2000).
    [CrossRef]
  2. D. A. Rockwell and G. S. Mecherle, “Wavelength selection for optical wireless communications systems,” Proc. SPIE 4530, 27-35 (2001).
  3. T. Araki, S. Tajima, and Y. Tajima, “High power optical amplifier for optical inter-orbit communications,” Proc. SPIE 2699, 266-277 (1996).
  4. T. Araki, S. Nakamori, and M. Furuya, “Latest results and trade-off of high power optical fiber amplifiers for optical inter-orbit communications,” Proc. SPIE 3266, 42-48(1998).
  5. J. C. Livas, S. B. Alexander, and E. S. Kintzer, “Gbps-class optical communications systems for free-space applications,” Proc. SPIE 1866, 148-157 (1993).
  6. A. Polishuk and S. Arnon, “Optimization of a laser satellite communication system with an optical preamplifier,” J. Opt. Soc. Am. A 21, 1307-1315 (2004).
    [CrossRef]
  7. M. Toyoshima, T. Jono, K. Nakagawa, and A. Yamamoto, “Optimum divergence angle of a Gaussian beam wave in the presence of random jitter in free-space laser communication systems,” J. Opt. Soc. Am. A 19, 567-571(2002).
    [CrossRef]
  8. C. C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252-260 (1989).
  9. S. Arnon, S. R. Rotman, and N. S. Kopeika, “Performance limitations of a free-space optical communication satellite network owing to vibrations: heterodyne detection,” Appl. Opt. 37, 6366-6374 (1998).
    [CrossRef]
  10. M. Toyoshima, “Maximum fiber coupling efficiency and optimum beam size in the presence of random angular jitter for free-space laser systems and their applications,” J. Opt. Soc. Am. A 23, 2246-2250 (2006).
    [CrossRef]
  11. C. Ruilier, “A study of degraded light coupling into single-mode fibers,” Proc. SPIE 3350, 319-329 (1998).
  12. 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]
  13. S. Thibault and J. Lacoursière, “Advanced fiber coupling technologies for space and astronomical applications,” Proc. SPIE 5578, 40-51 (2004).
  14. J. A. Buck, Fundamentals of Optical Fibers (Wiley, 1995).
  15. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, 2000).

2006 (1)

2004 (2)

S. Thibault and J. Lacoursière, “Advanced fiber coupling technologies for space and astronomical applications,” Proc. SPIE 5578, 40-51 (2004).

A. Polishuk and S. Arnon, “Optimization of a laser satellite communication system with an optical preamplifier,” J. Opt. Soc. Am. A 21, 1307-1315 (2004).
[CrossRef]

2002 (2)

2001 (1)

D. A. Rockwell and G. S. Mecherle, “Wavelength selection for optical wireless communications systems,” Proc. SPIE 4530, 27-35 (2001).

2000 (1)

V. W. S. Chan, “Optical space communications,” IEEE J. Sel. Top. Quantum Electron. 6, 959-975 (2000).
[CrossRef]

1998 (3)

S. Arnon, S. R. Rotman, and N. S. Kopeika, “Performance limitations of a free-space optical communication satellite network owing to vibrations: heterodyne detection,” Appl. Opt. 37, 6366-6374 (1998).
[CrossRef]

T. Araki, S. Nakamori, and M. Furuya, “Latest results and trade-off of high power optical fiber amplifiers for optical inter-orbit communications,” Proc. SPIE 3266, 42-48(1998).

C. Ruilier, “A study of degraded light coupling into single-mode fibers,” Proc. SPIE 3350, 319-329 (1998).

1996 (1)

T. Araki, S. Tajima, and Y. Tajima, “High power optical amplifier for optical inter-orbit communications,” Proc. SPIE 2699, 266-277 (1996).

1993 (1)

J. C. Livas, S. B. Alexander, and E. S. Kintzer, “Gbps-class optical communications systems for free-space applications,” Proc. SPIE 1866, 148-157 (1993).

1989 (1)

C. C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252-260 (1989).

Alexander, S. B.

J. C. Livas, S. B. Alexander, and E. S. Kintzer, “Gbps-class optical communications systems for free-space applications,” Proc. SPIE 1866, 148-157 (1993).

Araki, T.

T. Araki, S. Nakamori, and M. Furuya, “Latest results and trade-off of high power optical fiber amplifiers for optical inter-orbit communications,” Proc. SPIE 3266, 42-48(1998).

T. Araki, S. Tajima, and Y. Tajima, “High power optical amplifier for optical inter-orbit communications,” Proc. SPIE 2699, 266-277 (1996).

Arnon, S.

Buck, J. A.

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

Chan, V. W. S.

V. W. S. Chan, “Optical space communications,” IEEE J. Sel. Top. Quantum Electron. 6, 959-975 (2000).
[CrossRef]

Chen, C. C.

C. C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252-260 (1989).

Furuya, M.

T. Araki, S. Nakamori, and M. Furuya, “Latest results and trade-off of high power optical fiber amplifiers for optical inter-orbit communications,” Proc. SPIE 3266, 42-48(1998).

Gardner, C. S.

C. C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252-260 (1989).

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, 2000).

Jono, T.

Kintzer, E. S.

J. C. Livas, S. B. Alexander, and E. S. Kintzer, “Gbps-class optical communications systems for free-space applications,” Proc. SPIE 1866, 148-157 (1993).

Kopeika, N. S.

Lacoursière, J.

S. Thibault and J. Lacoursière, “Advanced fiber coupling technologies for space and astronomical applications,” Proc. SPIE 5578, 40-51 (2004).

Leeb, W. R.

Livas, J. C.

J. C. Livas, S. B. Alexander, and E. S. Kintzer, “Gbps-class optical communications systems for free-space applications,” Proc. SPIE 1866, 148-157 (1993).

Mecherle, G. S.

D. A. Rockwell and G. S. Mecherle, “Wavelength selection for optical wireless communications systems,” Proc. SPIE 4530, 27-35 (2001).

Nakagawa, K.

Nakamori, S.

T. Araki, S. Nakamori, and M. Furuya, “Latest results and trade-off of high power optical fiber amplifiers for optical inter-orbit communications,” Proc. SPIE 3266, 42-48(1998).

Polishuk, A.

Rockwell, D. A.

D. A. Rockwell and G. S. Mecherle, “Wavelength selection for optical wireless communications systems,” Proc. SPIE 4530, 27-35 (2001).

Rotman, S. R.

Ruilier, C.

C. Ruilier, “A study of degraded light coupling into single-mode fibers,” Proc. SPIE 3350, 319-329 (1998).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, 2000).

Tajima, S.

T. Araki, S. Tajima, and Y. Tajima, “High power optical amplifier for optical inter-orbit communications,” Proc. SPIE 2699, 266-277 (1996).

Tajima, Y.

T. Araki, S. Tajima, and Y. Tajima, “High power optical amplifier for optical inter-orbit communications,” Proc. SPIE 2699, 266-277 (1996).

Thibault, S.

S. Thibault and J. Lacoursière, “Advanced fiber coupling technologies for space and astronomical applications,” Proc. SPIE 5578, 40-51 (2004).

Toyoshima, M.

Wallner, O.

Winzer, P. J.

Yamamoto, A.

Appl. Opt. (2)

IEEE J. Sel. Top. Quantum Electron. (1)

V. W. S. Chan, “Optical space communications,” IEEE J. Sel. Top. Quantum Electron. 6, 959-975 (2000).
[CrossRef]

IEEE Trans. Commun. (1)

C. C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252-260 (1989).

J. Opt. Soc. Am. A (3)

Proc. SPIE (6)

C. Ruilier, “A study of degraded light coupling into single-mode fibers,” Proc. SPIE 3350, 319-329 (1998).

D. A. Rockwell and G. S. Mecherle, “Wavelength selection for optical wireless communications systems,” Proc. SPIE 4530, 27-35 (2001).

T. Araki, S. Tajima, and Y. Tajima, “High power optical amplifier for optical inter-orbit communications,” Proc. SPIE 2699, 266-277 (1996).

T. Araki, S. Nakamori, and M. Furuya, “Latest results and trade-off of high power optical fiber amplifiers for optical inter-orbit communications,” Proc. SPIE 3266, 42-48(1998).

J. C. Livas, S. B. Alexander, and E. S. Kintzer, “Gbps-class optical communications systems for free-space applications,” Proc. SPIE 1866, 148-157 (1993).

S. Thibault and J. Lacoursière, “Advanced fiber coupling technologies for space and astronomical applications,” Proc. SPIE 5578, 40-51 (2004).

Other (2)

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

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, 2000).

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Figures (8)

Fig. 1
Fig. 1

Coupling geometry.

Fig. 2
Fig. 2

Incident beam tilt by angles θ results in a lateral shift of the focused mode E o ( r ) by Δ r = θ f in the coupling plane, which is equivalent to lateral offset Δ r of the fiber axis from the optical axis of the lens.

Fig. 3
Fig. 3

Fiber coupling efficiency as a function of random jitter σ normalized by mode field radius ω 0 for different design parameters β.

Fig. 4
Fig. 4

Fiber coupling efficiency as a function of design parameter β and random jitter σ normalized by mode field radius ω 0 .

Fig. 5
Fig. 5

Relationship between optimum design parameter β and random jitter σ normalized by mode field radius ω 0 .

Fig. 6
Fig. 6

Maximum coupling efficiency as a function of normalized random jitter σ / ω 0 when design parameter β is optimum.

Fig. 7
Fig. 7

Optimum value of design parameter β as a function of normalized bias error r 0 / ω 0 and random jitter σ / ω 0 .

Fig. 8
Fig. 8

Maximum coupling efficiency as a function of normalized bias error r 0 / ω 0 and random jitter σ / ω 0 when design parameter β is optimum.

Equations (19)

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η = | E A * ( r ) F A ( r ) d s | 2 | E A ( r ) | 2 d s · | F A ( r ) | 2 d s ,
f ( θ , ϕ ) = θ σ 2 exp ( θ 2 + ϕ 2 2 σ 2 ) I 0 ( θ ϕ σ 2 ) ,
f ( θ ) | ϕ = 0 = θ σ 2 exp ( θ 2 2 σ 2 ) .
f ( Δ r ) = Δ r σ 2 exp ( Δ r 2 2 σ 2 ) .
F A ( r ) = 2 π ω a 2 exp ( r 2 ω a 2 ) exp [ j 2 π λ f cos ( θ Ω ) r Δ r ] ,
η = | E A ( r ) F A ( r ) d s | 2 | E A ( r ) | 2 d s | F A ( r ) | 2 d s = | E A ( r ) F A ( r ) f ( Δ r ) r d r d θ d Δ r | 2 | E A ( r ) | 2 d s .
η = 1 π R 2 | 2 π ω a 2 0 R 0 0 2 π Δ r σ 2 exp [ r 2 ω a 2 + j 2 π λ f r Δ r cos ( θ Ω ) Δ r 2 2 σ 2 ] r d θ d Δ r d r | 2 .
J 0 ( x ) = 1 2 π 0 2 π exp ( i x cos θ ) d θ .
η = 1 π R 2 | 2 2 π ω a 0 R exp [ ( 2 π 2 σ 2 λ 2 f 2 1 ω a 2 ) r 2 ] r d r | 2 .
η = 2 { [ 2 ( σ ω 0 ) 2 + 1 ] 2 β 2 } ( 1 exp { [ ( σ ω 0 ) 2 + 1 ] β 2 } ) 2 .
η = 2 β 2 [ 1 exp ( β 2 ) ] 2 .
d η d β = ( 2 x + 1 ) e x 1 ,
β = 1.2564 2 σ 2 ω 0 2 + 1 .
η ( σ ω 0 ) | max = 0.8145 1 2 σ 2 ω 0 2 + 1 .
f ( Δ r , r 0 ) = Δ r σ 2 exp ( Δ r 2 + r 0 2 2 σ 2 ) I 0 ( Δ r , r 0 σ 2 ) .
η = 1 π R 2 | 2 π ω a 2 exp ( r 0 2 2 σ 2 ) 0 R 0 Δ r σ 2 exp ( r 2 ω a 2 Δ r 2 2 σ 2 ) 2 π J 0 ( 2 π λ f r Δ r ) I 0 ( Δ r , r 0 σ 2 ) r d Δ r d r | 2 .
0 x e α x 2 I ν ( β x ) J ν ( γ x ) d x = 1 2 α exp ( β 2 γ 2 4 α ) J ν ( γ β 2 α ) , [ Re α > 0 , Re ν > 1 ] .
η = 1 π R 2 | 2 2 π ω a 0 R exp [ ( 2 π 2 σ 2 λ 2 f 2 1 ω a 2 ) r 2 ] J 0 ( 2 π λ f r 0 r ) r d r | 2 .
η = 8 β 2 | 0 1 exp { β 2 [ 2 ( σ ω 0 ) 2 + 1 ] ρ 2 } J 0 ( 2 r 0 ω 0 β ρ ) ρ d ρ | 2 .

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