Abstract

We characterize the joint two-time statistics of the polarization-mode dispersion (PMD) vector. Good agreement with experimental PMD measurements taken on an installed system is achieved. The results can be used to obtain the temporal evolution of the average penalty of a system close to an outage condition.

© 2007 Optical Society of America

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References

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  1. C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, IEEE Photon. Technol. Lett. 3, 68 (1991).
    [CrossRef]
  2. A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 12, 1713 (2003).
    [CrossRef]
  3. A. Mecozzi, Opt. Lett. 29, 1482 (2004).
    [CrossRef] [PubMed]
  4. M. Karlsson, J. Brentel, and P. A. Andrekson, J. Lightwave Technol. 18, 941 (2000).
    [CrossRef]
  5. C. W. Gardiner, Stochastic Methods for Physics, Chemistry and Natural Sciences (Springer-Verlag, 1983).
  6. M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, J. Lightwave Technol. 24, 4584 (2006).
    [CrossRef]
  7. M. Shtaif, IEEE Photon. Technol. Lett. 15, 51 (2003).
    [CrossRef]

2006 (1)

2004 (1)

2003 (2)

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 12, 1713 (2003).
[CrossRef]

M. Shtaif, IEEE Photon. Technol. Lett. 15, 51 (2003).
[CrossRef]

2000 (1)

1991 (1)

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, IEEE Photon. Technol. Lett. 3, 68 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, IEEE Photon. Technol. Lett. 3, 68 (1991).
[CrossRef]

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 12, 1713 (2003).
[CrossRef]

M. Shtaif, IEEE Photon. Technol. Lett. 15, 51 (2003).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Lett. (1)

Other (1)

C. W. Gardiner, Stochastic Methods for Physics, Chemistry and Natural Sciences (Springer-Verlag, 1983).

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Figures (3)

Fig. 1
Fig. 1

Filled circles are the plot of the normalized ACF of the PMD vector extracted from the experimental data, while the solid curve is the fitting curve Eq. (5). The inset shows the same plot in a semilogarithmic scale.

Fig. 2
Fig. 2

Circles, squares, and diamonds are the plot of the averages τ p 2 ( t ) τ ̂ t , τ o 2 ( t ) τ ̂ t and the (constant) sum of the two, respectively, extracted from the experimental data. The fitting curves are the plot of Eqs. (19, 20). Reported quantities are normalized to τ rms 2 .

Fig. 3
Fig. 3

Equation (24) normalized to τ 2 = 2 τ rms 2 3 is plotted by solid curve for τ ( t ) = τ rms 2 and τ ( t ) = 2 τ rms . Circles are the result of a Monte Carlo simulation based on the use of the Brownian Bridge method.

Equations (24)

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d τ ( z ; t ) = ω d W ( z ; t ) × τ ( z ; t ) + d W ( z ; t ) 1 3 ω 2 [ 1 + ϵ ( 0 ) ] τ ( z ; t ) d z ,
d W ( z ; t ) d W ( z ; t ) = [ 1 + ϵ ( t t ) ] δ ( z z ) d z d z ,
d τ t τ t = 2 3 ω 2 [ ϵ ( 0 ) ϵ ( t t ) ] τ t τ t d z + [ 1 + ϵ ( t t ) ] d z ,
τ t τ t = 3 [ 1 + ϵ ( t t ) ] 2 ω 2 [ ϵ ( 0 ) ϵ ( t t ) ] × { 1 exp [ 2 ω 2 L 3 [ ϵ ( 0 ) ϵ ( t t ) ] ] } .
τ t τ t τ 2 t d t t [ 1 exp ( t t t d ) ] ,
ϵ ( t t ) = D t c 2 exp ( t t t c ) ,
d τ t = ω d W ( z ; t , t ) × τ t + d W ( z ; t ) 2 3 ω 2 [ ϵ ( 0 ) ϵ ( t t ) ] τ t d z ,
d W ( z ; t , t ) d W ( z ; t , t ) = 2 [ ϵ ( 0 ) ϵ ( t t ) ] × δ ( z z ) d z d z ,
d W ( z ; t ) d W ( z ; t ) δ ( z z ) d z d z ,
d τ t = 2 ω [ ϵ ( 0 ) ϵ ( t t ) ] 1 2 d W ( z ) × τ t 2 3 ω 2 [ ϵ ( 0 ) ϵ ( t t ) ] τ t d z + d W ( z ) ,
d τ t = ( 3 t t t d L ) 1 2 d W ( z ) × τ t t t t d L τ t d z + d W ( z ) .
τ t τ t = τ t 1 exp ( θ ) θ ,
τ p 2 ( t ) τ t = f + τ t 2 g p ,
τ o 2 ( t ) τ t = 2 f + τ t 2 g o ,
f = τ 2 3 θ { θ 2 + 6 [ 1 exp ( θ ) ] 3 θ } ,
g p = 2 3 θ + exp ( 3 θ ) 1 9 θ 2 ,
g o = 2 6 θ exp ( 3 θ ) + 9 exp ( θ ) 8 9 θ 2 ,
τ t 2 τ t = τ 2 + 2 ( τ t 2 τ 2 ) θ 1 + exp ( θ ) θ 2 .
τ p 2 ( t ) τ ̂ t = τ 2 ( 1 3 + F ) ,
τ o 2 ( t ) τ ̂ t = τ 2 ( 2 3 F ) ,
F = 2 2 3 exp ( θ ) + exp ( 3 θ ) 9 θ 2 .
τ 2 ( t ) τ t = [ τ t 2 ( τ t s ̂ ) 2 ] τ t ,
τ 2 ( t ) τ t = τ t 2 τ t ( s ̂ τ ̂ t ) 2 τ p 2 ( t ) τ t [ τ o ( t ) s ] 2 τ t ,
τ 2 ( t ) τ t = [ 1 τ 2 ( t ) 2 τ t 2 ] τ o 2 ( t ) τ t + τ 2 ( t ) τ t 2 τ p 2 ( t ) τ t .

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