Abstract

Polarization dispersion in single-mode fiber that contains arbitrary birefringence is described through a vector differential equation. Monte-Carlo simulations using this equation show good agreement with experimental measurements in a randomly birefringent fiber and with a previously reported analytic expression for the length dependence of the dispersion. We also correct an error made in earlier research and show that the probability density function for the magnitude of the dispersion at long lengths is Maxwellian rather than Gaussian as previously reported.

© 1991 Optical Society of America

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References

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  1. C. D. Poole, Opt. Lett. 13, 687 (1988).
    [CrossRef] [PubMed]
  2. C. D. Poole, Opt. Lett. 14, 523 (1989).
    [CrossRef] [PubMed]
  3. F. Curti, B. Daino, G. De Marchis, F. Matera, IEEE J. Lightwave Technol. 8, 1162 (1990).
    [CrossRef]
  4. C. D. Poole, R. W. Tkach, A. R. Chraplyvy, D. A. Fishman, IEEE Photon. Technol. Lett. 3, 70 (1991).
    [CrossRef]
  5. C. D. Poole, R. E. Wagner, Electron. Lett. 22, 1029 (1986).
    [CrossRef]
  6. C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
    [CrossRef]
  7. D. Andresciani, F. Curti, F. Matera, B. Daino, Opt. Lett. 12, 844 (1987).
    [CrossRef] [PubMed]
  8. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).
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    [CrossRef] [PubMed]
  10. R. Ulrich, Opt. Lett. 1, 109 (1977).
    [CrossRef] [PubMed]
  11. W. Eickhoff, Y. Yen, R. Ulrich, Appl. Opt. 20, 3428 (1981).
    [CrossRef] [PubMed]
  12. R. F. Fox, Phys. Rep. 48, 179 (1978).
    [CrossRef]

1991 (1)

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, D. A. Fishman, IEEE Photon. Technol. Lett. 3, 70 (1991).
[CrossRef]

1990 (1)

F. Curti, B. Daino, G. De Marchis, F. Matera, IEEE J. Lightwave Technol. 8, 1162 (1990).
[CrossRef]

1989 (1)

1988 (2)

C. D. Poole, Opt. Lett. 13, 687 (1988).
[CrossRef] [PubMed]

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

1987 (1)

1986 (1)

C. D. Poole, R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

1981 (1)

1979 (1)

1978 (1)

R. F. Fox, Phys. Rep. 48, 179 (1978).
[CrossRef]

1977 (1)

Andresciani, D.

Bergano, N. S.

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

Chraplyvy, A. R.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, D. A. Fishman, IEEE Photon. Technol. Lett. 3, 70 (1991).
[CrossRef]

Curti, F.

F. Curti, B. Daino, G. De Marchis, F. Matera, IEEE J. Lightwave Technol. 8, 1162 (1990).
[CrossRef]

D. Andresciani, F. Curti, F. Matera, B. Daino, Opt. Lett. 12, 844 (1987).
[CrossRef] [PubMed]

Daino, B.

F. Curti, B. Daino, G. De Marchis, F. Matera, IEEE J. Lightwave Technol. 8, 1162 (1990).
[CrossRef]

D. Andresciani, F. Curti, F. Matera, B. Daino, Opt. Lett. 12, 844 (1987).
[CrossRef] [PubMed]

De Marchis, G.

F. Curti, B. Daino, G. De Marchis, F. Matera, IEEE J. Lightwave Technol. 8, 1162 (1990).
[CrossRef]

Eickhoff, W.

Fishman, D. A.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, D. A. Fishman, IEEE Photon. Technol. Lett. 3, 70 (1991).
[CrossRef]

Fox, R. F.

R. F. Fox, Phys. Rep. 48, 179 (1978).
[CrossRef]

Matera, F.

F. Curti, B. Daino, G. De Marchis, F. Matera, IEEE J. Lightwave Technol. 8, 1162 (1990).
[CrossRef]

D. Andresciani, F. Curti, F. Matera, B. Daino, Opt. Lett. 12, 844 (1987).
[CrossRef] [PubMed]

Poole, C. D.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, D. A. Fishman, IEEE Photon. Technol. Lett. 3, 70 (1991).
[CrossRef]

C. D. Poole, Opt. Lett. 14, 523 (1989).
[CrossRef] [PubMed]

C. D. Poole, Opt. Lett. 13, 687 (1988).
[CrossRef] [PubMed]

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

C. D. Poole, R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

Schulte, H. J.

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

Simon, A.

Tkach, R. W.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, D. A. Fishman, IEEE Photon. Technol. Lett. 3, 70 (1991).
[CrossRef]

Ulrich, R.

Wagner, R. E.

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

C. D. Poole, R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

Yen, Y.

Appl. Opt. (2)

Electron. Lett. (1)

C. D. Poole, R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

IEEE J. Lightwave Technol. (2)

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

F. Curti, B. Daino, G. De Marchis, F. Matera, IEEE J. Lightwave Technol. 8, 1162 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, D. A. Fishman, IEEE Photon. Technol. Lett. 3, 70 (1991).
[CrossRef]

Opt. Lett. (4)

Phys. Rep. (1)

R. F. Fox, Phys. Rep. 48, 179 (1978).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

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Figures (4)

Fig. 1
Fig. 1

Relative rms delay time versus normalized length. Experimental data points are taken from Ref. 3.

Fig. 2
Fig. 2

Experimental setup. ECL, external-cavity laser.

Fig. 3
Fig. 3

Probability density functions for polarization dispersion vector Ω. (a) Vector components Ω1,2,3 compared with Gaussian distribution. (b) Differential delay time Δτ = |Ω| compared with Maxwell distribution. Histograms are experimental, dashed curves are theoretical, and points are simulation results.

Fig. 4
Fig. 4

Autocorrelation function for the dispersion vector versus normalized frequency.

Equations (5)

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s ^ / z = W ( ω , z ) × s ^ ,
s ^ / ω = Ω ( ω , z ) × s ^ ,
Ω ( z , ω ) / z = W ( z , ω ) / ω + W ( z , ω ) × Ω ( z , ω ) .
Δ τ rms ( z ) Δ τ 0 = 1 2 h z [ exp ( - 2 h z ) - 1 + 2 h z ] 1 / 2 ,
h = - + κ * ( x ) κ ( x - u ) exp ( - i Δ β u ) d u .

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