Abstract

Polarization mode dispersion (PMD) compensation is addressed by decomposition of a fiber’s Jones matrix into amplitude and phase responses, which are then compensated for separately. Cubic and higher-order phase compensation substantially reduce the cumulative probability at a given system penalty over first-order PMD compensation, as demonstrated for a 40Gbit/s non-return-to-zero signal and a fiber PMD with a differential group delay of 20 ps (rms). Single-stage all-pass filters provide tunable compensation that is comparable to that obtained with a variable-delay line, and multistage all-pass filters are well suited for higher-order phase compensation.

© 2000 Optical Society of America

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  1. T. Ozeki and T. Kudo, in Optical Fiber Communication and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper WI9.
  2. C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.
  3. C. Poole and R. Wagner, Electron. Lett. 22, 1029 (1986).
    [CrossRef]
  4. C. Madsen and G. Lenz, IEEE Photon. Technol. Lett. 10, 994 (1998).
    [CrossRef]
  5. C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, in Integrated Photonics Research, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper RTuA1.
  6. C. Madsen, J. Walker, J. Ford, K. Goossen, and G. Lenz, presented at the European Conference on Optical Communications, Nice, France, September 27–30, 1999.
  7. C. Madsen and J. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
    [CrossRef]
  8. C. Anderson and J. Lyle, Electron. Lett. 30, 71 (1994).
    [CrossRef]

1999

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, in Integrated Photonics Research, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper RTuA1.

1993

T. Ozeki and T. Kudo, in Optical Fiber Communication and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper WI9.

Bruce, A.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, in Integrated Photonics Research, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper RTuA1.

Cappuzzo, M.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, in Integrated Photonics Research, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper RTuA1.

Farbert, A.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Feise, G.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Fischer, G.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Ford, J.

C. Madsen, J. Walker, J. Ford, K. Goossen, and G. Lenz, presented at the European Conference on Optical Communications, Nice, France, September 27–30, 1999.

Glingener, C.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Gomez, L.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, in Integrated Photonics Research, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper RTuA1.

Goossen, K.

C. Madsen, J. Walker, J. Ford, K. Goossen, and G. Lenz, presented at the European Conference on Optical Communications, Nice, France, September 27–30, 1999.

Herrmann, H.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Hinz, S.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Kudo, T.

T. Ozeki and T. Kudo, in Optical Fiber Communication and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper WI9.

Lenz, G.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, in Integrated Photonics Research, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper RTuA1.

C. Madsen, J. Walker, J. Ford, K. Goossen, and G. Lenz, presented at the European Conference on Optical Communications, Nice, France, September 27–30, 1999.

Madsen, C.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, in Integrated Photonics Research, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper RTuA1.

C. Madsen, J. Walker, J. Ford, K. Goossen, and G. Lenz, presented at the European Conference on Optical Communications, Nice, France, September 27–30, 1999.

C. Madsen and J. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
[CrossRef]

Mirvoda, V.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Noe, R.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Ozeki, T.

T. Ozeki and T. Kudo, in Optical Fiber Communication and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper WI9.

Ricken, R.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Sandel, D.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Schopflin, A.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Scotti, R.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, in Integrated Photonics Research, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper RTuA1.

Sohler, W.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Walker, J.

C. Madsen, J. Walker, J. Ford, K. Goossen, and G. Lenz, presented at the European Conference on Optical Communications, Nice, France, September 27–30, 1999.

Wehrmann, F.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Yoshida-Dierolf, M.

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

Zhao, J.

C. Madsen and J. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
[CrossRef]

1993 OSA Technical Digest Series

T. Ozeki and T. Kudo, in Optical Fiber Communication and International Conference on Integrated Optics and Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper WI9.

1999 OSA Technical Digest Series

C. Glingener, A. Schopflin, A. Farbert, G. Fischer, R. Noe, D. Sandel, S. Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, R. Ricken, W. Sohler, and F. Wehrmann, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper PD-29.

1999 OSA Technical Digest Series

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, in Integrated Photonics Research, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper RTuA1.

Other

C. Madsen, J. Walker, J. Ford, K. Goossen, and G. Lenz, presented at the European Conference on Optical Communications, Nice, France, September 27–30, 1999.

C. Madsen and J. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
[CrossRef]

C. Anderson and J. Lyle, Electron. Lett. 30, 71 (1994).
[CrossRef]

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

C. Madsen and G. Lenz, IEEE Photon. Technol. Lett. 10, 994 (1998).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematics of (a) PMD compensator, (b) a multistage APF consisting of cascaded ring resonators, and (c) a two-stage FIR 2×2 filter.

Fig. 2
Fig. 2

Cumulative probability distribution for receiver power penalty and various orders of phase-compensating filters. In addition, the case in which the polarization controller setting is such that P1ω0=1 and there is perfect phase compensation is shown.

Fig. 3
Fig. 3

Cumulative probability distribution versus receiver power penalty for two standard PMD compensating filters compared with an APF approach.

Equations (4)

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

Mω=uω-v*ωvωu*ω.
M-1ω=u*ωv*ω-vωuω=Uωexp-jΦUωVωexp-jΦVω-VωexpjΦVωUωexpjΦUω.
Fω=gω-h*ωhωg*ω=GωexpjΦGω-Hωexp-jΦHωHωexpjΦHω-Gωexp-jΦGω.
FωMωPω0PωexpjωTd10 or 10,

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