Abstract

The probability distribution of the differential group delay (DGD) at any fiber length is determined by use of a physically reasonable model of the fiber birefringence. We show that if the fiber correlation length is of the same order as or larger than the beat length, the DGD distribution approaches a Maxwellian in roughly 30 fiber correlation lengths, corresponding to a couple of kilometers in realistic cases. We also find that the probability distribution function of the polarization dispersion vector at the output of the fiber depends on the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances.

© 2001 Optical Society of America

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References

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  1. G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
    [CrossRef]
  2. N. Gisin, Opt. Commun. 86, 37 (1991).
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  3. N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
    [CrossRef]
  4. P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
    [CrossRef]
  5. A. Galtarossa, L. Palmieri, M. Schiano, and T. Tambosso, Opt. Lett. 25, 1322 (2000).
    [CrossRef]
  6. L. Arnold, Stochastic Differential Equations, Theory and Applications (Wiley, New York, 1974).
  7. P. K. A. Wai, W. L. Kath, C. R. Menyuk, and J. W. Zhang, J. Opt. Soc. Am. B 16, 2967 (1997).
    [CrossRef]
  8. G. Strang, SIAM J. Numer. Anal. 5, 506 (1968).
    [CrossRef]

2000 (1)

1997 (1)

P. K. A. Wai, W. L. Kath, C. R. Menyuk, and J. W. Zhang, J. Opt. Soc. Am. B 16, 2967 (1997).
[CrossRef]

1996 (1)

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

1995 (1)

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

1991 (2)

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

N. Gisin, Opt. Commun. 86, 37 (1991).
[CrossRef]

1968 (1)

G. Strang, SIAM J. Numer. Anal. 5, 506 (1968).
[CrossRef]

Arnold, L.

L. Arnold, Stochastic Differential Equations, Theory and Applications (Wiley, New York, 1974).

Blasco, P.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Distl, R.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Foschini, G. J.

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Galtarossa, A.

Gilgen, H.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Gisin, N.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

N. Gisin, Opt. Commun. 86, 37 (1991).
[CrossRef]

Kath, W. L.

P. K. A. Wai, W. L. Kath, C. R. Menyuk, and J. W. Zhang, J. Opt. Soc. Am. B 16, 2967 (1997).
[CrossRef]

Keys, R.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Krause, E.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Larsen, C. C.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Menyuk, C. R.

P. K. A. Wai, W. L. Kath, C. R. Menyuk, and J. W. Zhang, J. Opt. Soc. Am. B 16, 2967 (1997).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Morl, K.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Palmieri, L.

Passy, R.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Pelayo, J.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Perny, B.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Poole, C. D.

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Schiano, M.

Strang, G.

G. Strang, SIAM J. Numer. Anal. 5, 506 (1968).
[CrossRef]

Tambosso, T.

Van Deventer, M. O.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Vobian, J.

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

Wai, P. K. A.

P. K. A. Wai, W. L. Kath, C. R. Menyuk, and J. W. Zhang, J. Opt. Soc. Am. B 16, 2967 (1997).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Zhang, J. W.

P. K. A. Wai, W. L. Kath, C. R. Menyuk, and J. W. Zhang, J. Opt. Soc. Am. B 16, 2967 (1997).
[CrossRef]

J. Lightwave Technol. (2)

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

P. K. A. Wai, W. L. Kath, C. R. Menyuk, and J. W. Zhang, J. Opt. Soc. Am. B 16, 2967 (1997).
[CrossRef]

Opt. Commun. (1)

N. Gisin, Opt. Commun. 86, 37 (1991).
[CrossRef]

Opt. Lett. (1)

Pure Appl. Opt. (1)

N. Gisin, R. Passy, P. Blasco, M. O. Van Deventer, R. Distl, H. Gilgen, B. Perny, R. Keys, E. Krause, C. C. Larsen, K. Morl, J. Pelayo, and J. Vobian, Pure Appl. Opt. 4, 511 (1995).
[CrossRef]

SIAM J. Numer. Anal. (1)

G. Strang, SIAM J. Numer. Anal. 5, 506 (1968).
[CrossRef]

Other (1)

L. Arnold, Stochastic Differential Equations, Theory and Applications (Wiley, New York, 1974).

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Figures (1)

Fig. 1
Fig. 1

(a)–(g) Probability distribution function pτ,Z of the DGD at various distances. The dashed curves in (f) and (g) are Maxwellian distributions. The distance is normalized to the fiber correlation length, hfiber, and the DGD is normalized to 2bhfiber. (h) Contour plot showing the angular dependence of probability distribution P for dispersion vector Ω¯ at Z=100.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

Ωz,ωz=Wz,ωω+Wz,ω×Ωz,ω,
Ω̃=H1zΩ,Ω̃=H2zΩ̃.
ddz(Ω^1Ω^2Ω^3)=gθ(Ω^2cos2bz-Ω^3sin2bz-Ω^1cos2bzΩ^1sin2bz)+(2b00),
PZ=12Ω¯1Ω¯2-Ω¯2Ω¯12+Ω¯1Ω¯3-Ω¯3Ω¯12P-PΩ¯1.
Ω¯1=τcosϕ,Ω¯2=τsinϕcosψ,Ω¯3=τsinϕsinψ,
PZ=12sinϕϕsinϕPϕ+121sin2ϕ-12Pψ2-cosϕPτ-sinϕτPϕ.
Pτ,ϕ,ψ,0=D3π3/2exp-D2τ2,

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