Abstract

I present numerical simulations of the average transfer function of polarization mode dispersion (PMD) in optical fibers conditioned on various given values of the differential group delay (DGD). I find that even fibers with relatively small mean DGD can exhibit significant coupling between the two principal states of polarization. The average frequency dependence of this coupling can be approximated by a generic analytic function that deviates substantially from the quadratic frequency dependence that is often assumed in second-order PMD models. Finally, I define an extended transfer matrix for first-order PMD that describes the average frequency dependence of all PMD-induced distortions as a function of the DGD and show that this matrix is much better suited for optical PMD compensation than that of a conventional first- and second-order PMD model.

© 2005 Optical Society of America

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References

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  1. H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), p. 725.
    [CrossRef]
  2. E. Forestieri and L. Vincetti, J. Lightwave Technol. 19, 1898 (2001).
    [CrossRef]
  3. F. Heismann, IEEE Photonics Technol. Lett. 16, 2616 (2004).
    [CrossRef]
  4. M. Shtaif and M. Boroditsky, IEEE Photonics Technol. Lett. 15, 1369 (2003).
    [CrossRef]
  5. H. Kogelnik, L. E. Nelson, and P. J. Winzer, IEEE Photonics Technol. Lett. 16, 1053 (2004).
    [CrossRef]
  6. F. Heismann, IEEE Photonics Technol. Lett. 16, 1658 (2004).
    [CrossRef]
  7. G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, J. Lightwave Technol. 19, 1882 (2001).
    [CrossRef]
  8. F. Heismann, in Optical Fiber Communication Conference on CD-ROM (Optical Society of America, Washington, D.C., 2005), paper OThT7.

2004 (3)

F. Heismann, IEEE Photonics Technol. Lett. 16, 2616 (2004).
[CrossRef]

H. Kogelnik, L. E. Nelson, and P. J. Winzer, IEEE Photonics Technol. Lett. 16, 1053 (2004).
[CrossRef]

F. Heismann, IEEE Photonics Technol. Lett. 16, 1658 (2004).
[CrossRef]

2003 (1)

M. Shtaif and M. Boroditsky, IEEE Photonics Technol. Lett. 15, 1369 (2003).
[CrossRef]

2001 (2)

Boroditsky, M.

M. Shtaif and M. Boroditsky, IEEE Photonics Technol. Lett. 15, 1369 (2003).
[CrossRef]

Forestieri, E.

Foschini, G. J.

Heismann, F.

F. Heismann, IEEE Photonics Technol. Lett. 16, 2616 (2004).
[CrossRef]

F. Heismann, IEEE Photonics Technol. Lett. 16, 1658 (2004).
[CrossRef]

F. Heismann, in Optical Fiber Communication Conference on CD-ROM (Optical Society of America, Washington, D.C., 2005), paper OThT7.

Jopson, R. M.

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, J. Lightwave Technol. 19, 1882 (2001).
[CrossRef]

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), p. 725.
[CrossRef]

Kogelnik, H.

H. Kogelnik, L. E. Nelson, and P. J. Winzer, IEEE Photonics Technol. Lett. 16, 1053 (2004).
[CrossRef]

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, J. Lightwave Technol. 19, 1882 (2001).
[CrossRef]

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), p. 725.
[CrossRef]

Nelson, L. E.

H. Kogelnik, L. E. Nelson, and P. J. Winzer, IEEE Photonics Technol. Lett. 16, 1053 (2004).
[CrossRef]

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, J. Lightwave Technol. 19, 1882 (2001).
[CrossRef]

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), p. 725.
[CrossRef]

Shtaif, M.

M. Shtaif and M. Boroditsky, IEEE Photonics Technol. Lett. 15, 1369 (2003).
[CrossRef]

Vincetti, L.

Winzer, P. J.

H. Kogelnik, L. E. Nelson, and P. J. Winzer, IEEE Photonics Technol. Lett. 16, 1053 (2004).
[CrossRef]

IEEE Photonics Technol. Lett. (4)

F. Heismann, IEEE Photonics Technol. Lett. 16, 2616 (2004).
[CrossRef]

M. Shtaif and M. Boroditsky, IEEE Photonics Technol. Lett. 15, 1369 (2003).
[CrossRef]

H. Kogelnik, L. E. Nelson, and P. J. Winzer, IEEE Photonics Technol. Lett. 16, 1053 (2004).
[CrossRef]

F. Heismann, IEEE Photonics Technol. Lett. 16, 1658 (2004).
[CrossRef]

J. Lightwave Technol. (2)

Other (2)

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), p. 725.
[CrossRef]

F. Heismann, in Optical Fiber Communication Conference on CD-ROM (Optical Society of America, Washington, D.C., 2005), paper OThT7.

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Figures (3)

Fig. 1
Fig. 1

Simulations of the mean frequency dependence of phases φ, ψ, and η in Eq. (1) conditioned on a DGD of Δ τ = 1.6 Δ τ and averaged over more than 30,000 independent samples (solid curves). Dotted line, first-order approximation of φ Δ τ ; dashed curve, quadratic approximation (2) of η Δ τ .

Fig. 2
Fig. 2

Mean frequency dependence of η conditioned on Δ τ ̃ = 0.1 , 0.5 , 1.0 , 1.5 , 2.0 , 2.5 . The dots represent the simulation results, averaged over at least 10,000 independent samples, and the curves display the fits obtained from expression (3). Also shown are the standard deviations of η for Δ τ ̃ = 0.1 , 0.5 , 1.0 .

Fig. 3
Fig. 3

Frequency dependence of the real and imaginary parts of the elements of the overall transfer matrix with and without PMD compensation (represented by curves and dots, respectively). The main diagram shows the mean values, averaged over more than 30,000 independent samples, while the inset displays the corresponding standard deviations. The bold solid curves were obtained with a first-order compensator generating the mean phases φ Δ τ , η Δ τ , and ψ 0 , whereas the dashed curves were obtained with a combined first- and second-order PMD compensator generating φ = τ Δ ω τ ω Δ ω 2 2 , η = τ ω Δ ω 2 2 , and ψ 0 .

Equations (3)

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D ( Δ ω ) = [ cos η exp ( j φ ) j sin η exp ( j ψ ) j sin η exp ( j ψ ) cos η exp ( j φ ) ] ,
η Δ τ τ ω Δ τ Δ τ 2 Δ ω ̃ 2 2 ,
η Δ τ π 4 tanh [ f 2 ( ξ ) ] ,

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