Abstract

Free-space laser communication systems use optical-fiber-based technology such as optical amplifiers, receivers, and high-speed modulators. In these systems using single-mode fibers, the fiber coupling efficiency is one of the most significant issues to be solved. Optimum relationships between a focused optical beam and mode field size of the optical fiber in the presence of random angular jitter are discussed in relation to fiber-coupled optical systems. Maximum fiber coupling efficiency is analytically derived with the optimum Airy disk radius normalized by the mode field radius as a function of random angular jitter. The fade level of fiber-coupled signals at desired fade probability is investigated. It is shown that the average bit error ratio significantly degrades with the random angular jitter normalized by the mode field radius larger than about 0.3 when the Airy disk size is optimally selected.

© 2006 Optical Society of America

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References

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2005

2004

2003

B. Moision and J. Hamkins, "Deep-space optical communications downlink budget: modulation and coding," IPN Progress Report 42-154, JPL, Pasadena, California, pp. 1-28, (Jet Propulsion Laboratory, 2003), http://tmo.jpl.nasa.gov/progresslowbarreport/42-154/154K.pdf.

2002

1998

1997

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997), Chaps. 4 and 5.

1996

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

1995

H. T. Yura, "Optimum truncation of a Gaussian beam in the presence of random jitter," J. Opt. Soc. Am. A 12, 375-379 (1995).
[CrossRef]

D. K. Jacob and M. B. Mark, "Heterodyne ladar system efficiency enhancement using single-mode optical fiber mixers," Opt. Eng. 34, 3122-3129 (1995).
[CrossRef]

1994

H. T. Yura, "LADAR detection statistics in the presence of pointing errors," Appl. Opt. 30, 6482-6498 (1994).
[CrossRef]

1991

1989

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).
[CrossRef]

1985

J. D. Barry and G. S. Mecherle, "Beam pointing error as a significant design parameter for satellite-borne, free-space optical communication systems," Opt. Eng. 24, 1049-1054 (1985).

1979

1976

D. Marcuse, "Loss analysis of single-mode fiber splices," Bell Syst. Tech. J. 56, 703-718 (1976).

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997), Chaps. 4 and 5.

Arnon, S.

Barry, J. D.

J. D. Barry and G. S. Mecherle, "Beam pointing error as a significant design parameter for satellite-borne, free-space optical communication systems," Opt. Eng. 24, 1049-1054 (1985).

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).
[CrossRef]

Davidson, F. M.

Frehlich, R. G.

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).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Hamkins, J.

B. Moision and J. Hamkins, "Deep-space optical communications downlink budget: modulation and coding," IPN Progress Report 42-154, JPL, Pasadena, California, pp. 1-28, (Jet Propulsion Laboratory, 2003), http://tmo.jpl.nasa.gov/progresslowbarreport/42-154/154K.pdf.

Jacob, D. K.

D. K. Jacob and M. B. Mark, "Heterodyne ladar system efficiency enhancement using single-mode optical fiber mixers," Opt. Eng. 34, 3122-3129 (1995).
[CrossRef]

Jono, T.

Kavaya, M. J.

Leeb, W. R.

Marcuse, D.

D. Marcuse, "Loss analysis of single-mode fiber splices," Bell Syst. Tech. J. 56, 703-718 (1976).

Mark, M. B.

D. K. Jacob and M. B. Mark, "Heterodyne ladar system efficiency enhancement using single-mode optical fiber mixers," Opt. Eng. 34, 3122-3129 (1995).
[CrossRef]

Mecherle, G. S.

J. D. Barry and G. S. Mecherle, "Beam pointing error as a significant design parameter for satellite-borne, free-space optical communication systems," Opt. Eng. 24, 1049-1054 (1985).

Moision, B.

B. Moision and J. Hamkins, "Deep-space optical communications downlink budget: modulation and coding," IPN Progress Report 42-154, JPL, Pasadena, California, pp. 1-28, (Jet Propulsion Laboratory, 2003), http://tmo.jpl.nasa.gov/progresslowbarreport/42-154/154K.pdf.

Nakagawa, K.

Nawata, K.

Polishuk, A.

Ricklin, J. C.

Saruwatari, M.

Toyoshima, M.

Winzer, P. J.

Yamamoto, A.

Yura, H. T.

H. T. Yura, "Optimum truncation of a Gaussian beam in the presence of random jitter," J. Opt. Soc. Am. A 12, 375-379 (1995).
[CrossRef]

H. T. Yura, "LADAR detection statistics in the presence of pointing errors," Appl. Opt. 30, 6482-6498 (1994).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

D. Marcuse, "Loss analysis of single-mode fiber splices," Bell Syst. Tech. J. 56, 703-718 (1976).

IEEE Trans. Commun.

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).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

D. K. Jacob and M. B. Mark, "Heterodyne ladar system efficiency enhancement using single-mode optical fiber mixers," Opt. Eng. 34, 3122-3129 (1995).
[CrossRef]

J. D. Barry and G. S. Mecherle, "Beam pointing error as a significant design parameter for satellite-borne, free-space optical communication systems," Opt. Eng. 24, 1049-1054 (1985).

Opt. Lett.

Other

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997), Chaps. 4 and 5.

B. Moision and J. Hamkins, "Deep-space optical communications downlink budget: modulation and coding," IPN Progress Report 42-154, JPL, Pasadena, California, pp. 1-28, (Jet Propulsion Laboratory, 2003), http://tmo.jpl.nasa.gov/progresslowbarreport/42-154/154K.pdf.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (6)

Fig. 1
Fig. 1

Geometry of the optical system.

Fig. 2
Fig. 2

Fiber coupling efficiency as a function of beam offset ρ normalized by mode field radius w 0 .

Fig. 3
Fig. 3

Fiber coupling efficiency as a function of beam size w 1 and random jitter σ normalized by mode field radius w 0 .

Fig. 4
Fig. 4

Optimum fiber coupling efficiency as a function of random jitter σ w 0 when beam size is optimum against mode field radius and beam offset is zero.

Fig. 5
Fig. 5

Fade level as a function of random jitter σ w 0 at various fade probabilities P F .

Fig. 6
Fig. 6

Average BER as a function of normalized jitter and the SNR parameter.

Equations (28)

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U ( r ) = exp [ j k ( f + r 2 2 f ) ] π D 2 4 λ f [ 2 J 1 ( k D r 2 f ) k D r 2 f ] ,
A ( r ) = π D 2 4 λ f [ 2 J 1 ( 3.83 r w 1 ) ( 3.83 r w 1 ) ] ,
w 0 a = 0.65 + 1.619 V 3 2 + 2.879 V 6 ,
M ( r ) = 2 π w 0 2 exp ( r 2 w 0 2 ) .
M ( r , ρ ) = 2 2 π r w 0 exp ( r 2 + ρ 2 w 0 2 ) I 0 ( 2 r ρ w 0 2 ) .
η = A ( r ) M ( r ) d r 2 A ( r ) 2 d r .
η ( ρ w 0 ) = d r 2 2 w 0 J 1 ( 3.83 r w 1 ) × exp ( r 2 + ρ 2 w 0 2 ) I 0 ( 2 r ρ w 0 2 ) 2 .
p ( r ) = r σ 2 exp ( r 2 2 σ 2 ) .
η = A ( r ) M ( r ) d r 2 A ( r ) 2 d r = d r d ρ A ( r ) M ( r , ρ ) p ( ρ ) 2 A ( r ) 2 d r .
η = d r d ρ 2 2 w 0 J 1 ( 3.83 r w 1 ) exp ( r 2 + ρ 2 w 0 2 ) × I 0 ( 2 r ρ w 0 2 ) ρ σ 2 exp ( ρ 2 2 σ 2 ) 2 .
η = d r d ρ 2 2 w 0 J 1 ( 3.83 r w 1 ) exp ( r 2 w 0 2 ) × { ρ σ 2 exp [ ρ 2 ( 1 w 0 2 + 1 2 σ 2 ) ] I 0 ( 2 r ρ w 0 2 ) } 2 .
η = d r 2 2 w 0 J 1 ( 3.83 r w 1 ) exp ( r 2 w 0 2 ) × { w 0 2 w 0 2 + 2 σ 2 exp [ 2 σ 2 r 2 w 0 2 ( w 0 2 + 2 σ 2 ) ] } 2 .
η = d r 2 2 w 0 w 0 2 + 2 σ 2 J 1 ( 3.83 r w 1 ) exp ( r 2 w 0 2 + 2 σ 2 ) 2 .
η = 2 π 1 + 2 ( σ w 0 ) 2 exp ( 3.83 2 8 1 + 2 ( σ w 0 ) 2 ( w 1 w 0 ) 2 ) × I 1 2 ( 3.83 2 8 1 + 2 ( σ w 0 ) 2 ( w 1 w 0 ) 2 ) 2 ,
η = 2 π 1 + 2 ( σ w 0 ) 2 exp ( 2 3.83 2 8 1 + 2 ( σ w 0 ) 2 ( w 1 w 0 ) 2 ) × I 1 2 2 ( 3.83 2 8 1 + 2 ( σ w 0 ) 2 ( w 1 w 0 ) 2 ) .
η = 2 π 1 + 2 ( σ w 0 ) 2 exp ( 2 z ) I 1 2 2 ( z ) ,
z = 3.83 2 8 1 + 2 ( σ w 0 ) 2 ( w 1 w 0 ) 2 .
d η d w 1 = 2 π 1 + 2 ( σ w 0 ) 2 exp ( 2 z ) ( 2 z ) I 1 2 ( z ) [ I 1 2 ( z ) I 1 2 ( z ) ] ,
I 1 2 ( z ) I 1 2 ( z ) = 0 .
2 I 1 2 ( z ) I 1 2 ( z ) I 3 2 ( z ) = 0 .
w 1 w 0 = 1.709 1 + 2 σ 2 w 0 2 .
η ( σ w 0 , w 1 w 0 ) opt = 0.8145 1 + 2 ( σ w 0 ) 2 .
P F = ρ p ( r ) d r = ρ r σ 2 exp ( r 2 2 σ 2 ) d r ,
ρ w 0 = σ 2 ( ln P F ) w 0 .
F T = 10 log [ η ( ρ w 0 ) η ( σ w 0 , w 1 w 0 ) opt ] .
F T = 10 log [ η ( σ 2 ( ln P F ) w 0 ) η ( σ w 0 , w 1 w 0 ) opt ] .
BER ( Q ) = 1 2 erfc ( Q 2 ) ,
BER = d ρ p ( ρ ) BER [ Q η ( ρ w 0 , w 1 w 0 ) opt ] = d ρ p ( ρ ) 1 2 erfc [ Q 2 η ( ρ w 0 , w 1 w 0 ) opt ] .

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