Abstract

We elaborate on a recently proposed model of the temporal dependence of polarization mode dispersion in long fiber links. We evaluate the probability that a channel of a wavelength-division multiplexed system never incurs an outage, and the range of frequency over which the parameters that characterize the temporal statistics of the differential group delay are correlated.

© 2004 Optical Society of America

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References

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  1. M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, presented at the 30th European Conference on Optical Communication, Stockholm, Sweden, September 5–9, 2004, paper We1.4.1.
  2. M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, C. Antonelli, and A. Mecozzi, “Outage probabilities for fiber routes with finite number of degrees of freedom,” IEEE Photon. Technol. Lett. (to be published).
  3. M. Karlsson, J. Lightwave Technol. 19, 324 (2001).
    [CrossRef]
  4. C. Antonelli and A. Mecozzi, IEEE Photon. Technol. Lett. 16, 1840 (2004).
    [CrossRef]
  5. J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
    [CrossRef]
  6. M. Karlsson and J. Brentel, Opt. Lett. 24, 939 (1999).
    [CrossRef]
  7. M. Shtaif, A. Mecozzi, and J. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
    [CrossRef]
  8. M. Shtaif and A. Mecozzi, Opt. Lett. 25, 707 (2000).
    [CrossRef]

2004 (1)

C. Antonelli and A. Mecozzi, IEEE Photon. Technol. Lett. 16, 1840 (2004).
[CrossRef]

2001 (1)

2000 (3)

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, and J. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif and A. Mecozzi, Opt. Lett. 25, 707 (2000).
[CrossRef]

1999 (1)

Antonelli, C.

C. Antonelli and A. Mecozzi, IEEE Photon. Technol. Lett. 16, 1840 (2004).
[CrossRef]

M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, C. Antonelli, and A. Mecozzi, “Outage probabilities for fiber routes with finite number of degrees of freedom,” IEEE Photon. Technol. Lett. (to be published).

Boroditsky, M.

M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, C. Antonelli, and A. Mecozzi, “Outage probabilities for fiber routes with finite number of degrees of freedom,” IEEE Photon. Technol. Lett. (to be published).

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, presented at the 30th European Conference on Optical Communication, Stockholm, Sweden, September 5–9, 2004, paper We1.4.1.

Brentel, J.

Brodsky, M.

M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, C. Antonelli, and A. Mecozzi, “Outage probabilities for fiber routes with finite number of degrees of freedom,” IEEE Photon. Technol. Lett. (to be published).

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, presented at the 30th European Conference on Optical Communication, Stockholm, Sweden, September 5–9, 2004, paper We1.4.1.

Frigo, N. J.

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, presented at the 30th European Conference on Optical Communication, Stockholm, Sweden, September 5–9, 2004, paper We1.4.1.

M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, C. Antonelli, and A. Mecozzi, “Outage probabilities for fiber routes with finite number of degrees of freedom,” IEEE Photon. Technol. Lett. (to be published).

Gordon, J. P.

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
[CrossRef]

Karlsson, M.

Kogelnik, H.

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
[CrossRef]

Magill, P.

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, presented at the 30th European Conference on Optical Communication, Stockholm, Sweden, September 5–9, 2004, paper We1.4.1.

M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, C. Antonelli, and A. Mecozzi, “Outage probabilities for fiber routes with finite number of degrees of freedom,” IEEE Photon. Technol. Lett. (to be published).

Mecozzi, A.

C. Antonelli and A. Mecozzi, IEEE Photon. Technol. Lett. 16, 1840 (2004).
[CrossRef]

M. Shtaif, A. Mecozzi, and J. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif and A. Mecozzi, Opt. Lett. 25, 707 (2000).
[CrossRef]

M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, C. Antonelli, and A. Mecozzi, “Outage probabilities for fiber routes with finite number of degrees of freedom,” IEEE Photon. Technol. Lett. (to be published).

Nagel, J.

M. Shtaif, A. Mecozzi, and J. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

Shtaif, M.

M. Shtaif, A. Mecozzi, and J. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif and A. Mecozzi, Opt. Lett. 25, 707 (2000).
[CrossRef]

Tur, M.

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, presented at the 30th European Conference on Optical Communication, Stockholm, Sweden, September 5–9, 2004, paper We1.4.1.

IEEE Photon. Technol. Lett. (2)

C. Antonelli and A. Mecozzi, IEEE Photon. Technol. Lett. 16, 1840 (2004).
[CrossRef]

M. Shtaif, A. Mecozzi, and J. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Lett. (2)

Proc. Natl. Acad. Sci. USA (1)

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
[CrossRef]

Other (2)

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, presented at the 30th European Conference on Optical Communication, Stockholm, Sweden, September 5–9, 2004, paper We1.4.1.

M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, C. Antonelli, and A. Mecozzi, “Outage probabilities for fiber routes with finite number of degrees of freedom,” IEEE Photon. Technol. Lett. (to be published).

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Figures (2)

Fig. 1
Fig. 1

Complement to one of the fraction of channels Cτout that never experience an outage versus τout/τ. Dashed curve, Gaussian approximation [Eq. (4)]; solid curve, exact result with N=5 (or four hinges); dotted curve, Gaussian approximation [Eq. (4)]; dashed–dotted curve, exact result with N=10 (or nine hinges).

Fig. 2
Fig. 2

Normalized autocorrelation function for τmaxω. Points refer to results of Monte Carlo simulation for three values of N. The analytical result follows from Eq. (10).

Equations (15)

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τkω=Δτkω+RkωRkτk-1ω,
τ=k=1NΔτk,
τmax=k=1NΔτk.
Cτout=1-12erfcτout-τmax2σmax,
τmax=N83πτ21/2,
σmax2=1-83πτ2.
τmaxωτmax0=h=1Nk=1NΔτhωΔτk0.
ΔτhωΔτh03π-8π2ω2-6Nω4τ2×1-exp-ω2τ23N+8τ23πN
τmaxωτmax01-83πFω2τ2N+8N3πτ2,
Fx=6x-18x21-exp-x3.
Eτ2=k=1NΔτk2.
PEτ2=Eτ23N/2-123N/2s3N/2Γ3N/2 exp-Eτ22s,
σ=23Nτ2.
Δτh2ωΔτh20=2τ223N2Fω2τ2N+τ22N2,
Eτ2ωEτ20=2τ223N2Fω2τ2N+τ22.

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