Abstract

A new method for obtaining the probability density function of polarization mode dispersion (PMD) conditioned on the measured PMD value at an offset optical frequency is introduced. This method is advantageous in its ability to accurately and efficiently estimate the conditional distribution far in the tails.

© 2004 Optical Society of America

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References

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  1. G. Biondini, W. L. Kath, and C. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
    [CrossRef]
  2. D. Yevick, IEEE Photon. Technol. Lett. 15, 1540 (2003).
    [CrossRef]
  3. M. Shtaif, IEEE Photon. Technol. Lett. 15, 51 (2003).
    [CrossRef]
  4. A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 15, 1713 (2003).
    [CrossRef]
  5. M. Karlsson and J. Brentel, Opt. Lett. 24, 939 (1999).
    [CrossRef]
  6. M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
    [CrossRef]
  7. G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
    [CrossRef]

2003 (3)

D. Yevick, IEEE Photon. Technol. Lett. 15, 1540 (2003).
[CrossRef]

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

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 15, 1713 (2003).
[CrossRef]

2002 (1)

G. Biondini, W. L. Kath, and C. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

2000 (1)

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

1999 (1)

1991 (1)

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

Biondini, G.

G. Biondini, W. L. Kath, and C. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

Brentel, J.

Foschini, G. J.

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

Karlsson, M.

Kath, W. L.

G. Biondini, W. L. Kath, and C. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

Mecozzi, A.

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 15, 1713 (2003).
[CrossRef]

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

Menyuk, C.

G. Biondini, W. L. Kath, and C. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

Nagel, J. A.

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

Poole, C. D.

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

Shtaif, M.

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 15, 1713 (2003).
[CrossRef]

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

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

Yevick, D.

D. Yevick, IEEE Photon. Technol. Lett. 15, 1540 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

G. Biondini, W. L. Kath, and C. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

D. Yevick, IEEE Photon. Technol. Lett. 15, 1540 (2003).
[CrossRef]

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

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 15, 1713 (2003).
[CrossRef]

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

J. Lightwave Technol. (1)

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

Opt. Lett. (1)

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Figures (4)

Fig. 1
Fig. 1

Two-dimensional PDF Q(τ,τ|τ0) obtained with the present algorithm, with 10,000 realizations of process M. The parameters are τ=2 ps, τ0=6.4 ps, and frequency separation ω/2π=150 GHz.

Fig. 2
Fig. 2

Section of the three-dimensional PDF P(τω|τ0) obtained with Q as shown in Fig. 1.

Fig. 3
Fig. 3

Section of the three-dimensional PDF P(τω|τ0) obtained with 10,000 realizations and the same parameters of Fig. 2, except for frequency separation ω/2π=300 GHz.

Fig. 4
Fig. 4

Theoretical PDF of τω with the condition τ0=0 (solid curve), and the results of the proposed numerical procedure using 10,000 realizations (filled circles).

Equations (10)

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

Cλ0,λω;z=exp16λ02z+16λω2z×exp13λ0·Mλω,
dM=I-ωdWz×M-ω23Mdz,
Cτ0,λω;z=12πz/33/2×exp16λω2z-32zτ0+Mλω/32.
Cτ0λω;z=exp16λω2z-1zλω·MTMλω-1zMTτ0·λω,
P(τω|τ0)=12π3/2detC×exp-12τω-d·C-1τω-d,
d=1zMTτ0,
C=13zz2I-MTM.
Q(τ,τ|τ0)=02πP(τω|τ0)τdϕ.
Q(τ,τ|τ0)=02πτdϕ2π3/2detC×exp-12τω-d·C-1τω-d.
P(τxeˆx+τyeˆy|τ0eˆx)=Q(τx,τy|τ0eˆx)2πτy,

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