Abstract

The required structure and elements of polarization mode dispersion (PMD) compensators for complete second-order compensation are investigated by use of a general PMD vector formalism of concatenated PMD elements based on Mueller matrices and Stokes vectors. The investigation shows that two- and three-stage compensators with five independent parameters can compensate for polarization-dependent chromatic dispersion as well as the depolarization component of second-order PMD.

© 2002 Optical Society of America

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References

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  1. L. E. Nelson, R. M. Jopson, H. Kogelnik, and G. J. Foschini, IEEE Photon. Technol. Lett. 11, 1614 (1999).
    [CrossRef]
  2. H. Büllow, IEEE Photon. Technol. Lett. 10, 696 (1998).
    [CrossRef]
  3. H. Büllow, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 74.
  4. J. Patscher and R. Eckhardt, Electron. Lett. 33, 1157 (1997).
    [CrossRef]
  5. Q. Yu, L. Yan, Y. Xie, M. Hauer, and A. E. Willner, IEEE Photon. Technol. Lett. 13, 863 (2001).
    [CrossRef]
  6. M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
    [CrossRef]
  7. T. Kudou, M. Iguchi, M. Masuda, and T. Ozeki, J. Lightwave Technol. 18, 614 (2000).
    [CrossRef]
  8. M. Karlsson, C. Xie, H. Sunnerud, and P. A. Anderson, in Optical Fiber Communication Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper MO1.
  9. K. N. Srinivasa Rao, Linear Algebra and Group Theory for Physicists (Wiley, New York, 1996).
  10. J. P. Gorden and H. Kogelnik, Proc. Natl. Inst. Acad. Sci. USA 97, 4541 (2000).
    [CrossRef]
  11. R. Noé, H. Heidrich, and D. Hoffmann, J. Lightwave Technol. 6, 1199 (1988).
    [CrossRef]

2001 (1)

Q. Yu, L. Yan, Y. Xie, M. Hauer, and A. E. Willner, IEEE Photon. Technol. Lett. 13, 863 (2001).
[CrossRef]

2000 (3)

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

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

T. Kudou, M. Iguchi, M. Masuda, and T. Ozeki, J. Lightwave Technol. 18, 614 (2000).
[CrossRef]

1999 (1)

L. E. Nelson, R. M. Jopson, H. Kogelnik, and G. J. Foschini, IEEE Photon. Technol. Lett. 11, 1614 (1999).
[CrossRef]

1998 (1)

H. Büllow, IEEE Photon. Technol. Lett. 10, 696 (1998).
[CrossRef]

1997 (1)

J. Patscher and R. Eckhardt, Electron. Lett. 33, 1157 (1997).
[CrossRef]

1988 (1)

R. Noé, H. Heidrich, and D. Hoffmann, J. Lightwave Technol. 6, 1199 (1988).
[CrossRef]

Anderson, P. A.

M. Karlsson, C. Xie, H. Sunnerud, and P. A. Anderson, in Optical Fiber Communication Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper MO1.

Büllow, H.

H. Büllow, IEEE Photon. Technol. Lett. 10, 696 (1998).
[CrossRef]

H. Büllow, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 74.

Eckhardt, R.

J. Patscher and R. Eckhardt, Electron. Lett. 33, 1157 (1997).
[CrossRef]

Foschini, G. J.

L. E. Nelson, R. M. Jopson, H. Kogelnik, and G. J. Foschini, IEEE Photon. Technol. Lett. 11, 1614 (1999).
[CrossRef]

Gorden, J. P.

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

Hauer, M.

Q. Yu, L. Yan, Y. Xie, M. Hauer, and A. E. Willner, IEEE Photon. Technol. Lett. 13, 863 (2001).
[CrossRef]

Heidrich, H.

R. Noé, H. Heidrich, and D. Hoffmann, J. Lightwave Technol. 6, 1199 (1988).
[CrossRef]

Hoffmann, D.

R. Noé, H. Heidrich, and D. Hoffmann, J. Lightwave Technol. 6, 1199 (1988).
[CrossRef]

Iguchi, M.

Jopson, R. M.

L. E. Nelson, R. M. Jopson, H. Kogelnik, and G. J. Foschini, IEEE Photon. Technol. Lett. 11, 1614 (1999).
[CrossRef]

Karlsson, M.

M. Karlsson, C. Xie, H. Sunnerud, and P. A. Anderson, in Optical Fiber Communication Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper MO1.

Kogelnik, H.

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

L. E. Nelson, R. M. Jopson, H. Kogelnik, and G. J. Foschini, IEEE Photon. Technol. Lett. 11, 1614 (1999).
[CrossRef]

Kudou, T.

Masuda, M.

Mecozzi, A.

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

Nagel, J. A.

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

Nelson, L. E.

L. E. Nelson, R. M. Jopson, H. Kogelnik, and G. J. Foschini, IEEE Photon. Technol. Lett. 11, 1614 (1999).
[CrossRef]

Noé, R.

R. Noé, H. Heidrich, and D. Hoffmann, J. Lightwave Technol. 6, 1199 (1988).
[CrossRef]

Ozeki, T.

Patscher, J.

J. Patscher and R. Eckhardt, Electron. Lett. 33, 1157 (1997).
[CrossRef]

Shtaif, M.

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

Srinivasa Rao, K. N.

K. N. Srinivasa Rao, Linear Algebra and Group Theory for Physicists (Wiley, New York, 1996).

Sunnerud, H.

M. Karlsson, C. Xie, H. Sunnerud, and P. A. Anderson, in Optical Fiber Communication Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper MO1.

Tur, M.

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

Willner, A. E.

Q. Yu, L. Yan, Y. Xie, M. Hauer, and A. E. Willner, IEEE Photon. Technol. Lett. 13, 863 (2001).
[CrossRef]

Xie, C.

M. Karlsson, C. Xie, H. Sunnerud, and P. A. Anderson, in Optical Fiber Communication Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper MO1.

Xie, Y.

Q. Yu, L. Yan, Y. Xie, M. Hauer, and A. E. Willner, IEEE Photon. Technol. Lett. 13, 863 (2001).
[CrossRef]

Yan, L.

Q. Yu, L. Yan, Y. Xie, M. Hauer, and A. E. Willner, IEEE Photon. Technol. Lett. 13, 863 (2001).
[CrossRef]

Yu, Q.

Q. Yu, L. Yan, Y. Xie, M. Hauer, and A. E. Willner, IEEE Photon. Technol. Lett. 13, 863 (2001).
[CrossRef]

Electron. Lett. (1)

J. Patscher and R. Eckhardt, Electron. Lett. 33, 1157 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

Q. Yu, L. Yan, Y. Xie, M. Hauer, and A. E. Willner, IEEE Photon. Technol. Lett. 13, 863 (2001).
[CrossRef]

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

L. E. Nelson, R. M. Jopson, H. Kogelnik, and G. J. Foschini, IEEE Photon. Technol. Lett. 11, 1614 (1999).
[CrossRef]

H. Büllow, IEEE Photon. Technol. Lett. 10, 696 (1998).
[CrossRef]

J. Lightwave Technol. (2)

R. Noé, H. Heidrich, and D. Hoffmann, J. Lightwave Technol. 6, 1199 (1988).
[CrossRef]

T. Kudou, M. Iguchi, M. Masuda, and T. Ozeki, J. Lightwave Technol. 18, 614 (2000).
[CrossRef]

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

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

Other (3)

H. Büllow, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 74.

M. Karlsson, C. Xie, H. Sunnerud, and P. A. Anderson, in Optical Fiber Communication Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper MO1.

K. N. Srinivasa Rao, Linear Algebra and Group Theory for Physicists (Wiley, New York, 1996).

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a two-stage PMD compensator.

Fig. 2
Fig. 2

Two-stage complete second-order PMD compensator. PMF, polarization-maintaining fiber.

Fig. 3
Fig. 3

Three-stage complete second-order PMD compensator.

Equations (6)

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

Ωtot×=M2M1M2M1-1=M2M2-1+M2M1M1-1M2-1=Ω2×+M2Ω1×M2-1=Ω2+M2Ω1×.
Ωtot=Ω2+M2Ω1+Ω2×M2Ω1.
Ωtotω= Ωfω+R1-1M1-1Ω1+R2-1Ω2= Ωfω+a+b,
Ωtotω= Ωfω+R1-1M1-1Ω1+R2-1Ω2×Ωfω+R1-1M1-1R2-1Ω2×Ω1= Ωfω+a+b×Ωfω+b×a,
Ωtotω= Ωfω+R1-1M1-1×Ω1+R2-1M2-1Ω2+R3-1Ω3,
Ωtotω= Ωfω+Ωtotω×Ωfω+R1-1M1-1×R2-1M2-1Ω2+R3-1Ω3×Ω1+R2-1M2-1R3-1Ω3×Ω2.

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