Abstract

We propose a feed-forward polarization mode dispersion (PMD) compensator with three segments that is capable of compensating for the first- and second-order PMD in a transmission fiber. All control parameters are analytically obtained by the PMD concatenated rules. The influence of all possible perturbations on the compensation is investigated with Monte Carlo simulations. The main advantage of our PMD compensation module over the models reported so far is that it shows excellent robustness to all possible perturbations.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Büllow, “System outage probability due to first- and second-order PMD,” IEEE Photon. Technol. Lett. 10, 696–698 (1998).
    [Crossref]
  2. P. Ciprut, B. Gisin, N. Gisin, R. Passy, P. Von Der Weid, F. Prieto, C. W. Zimmer, “Second-order polarization mode dispersion: impact on analog and digital transmissions,” J. Lightwave Technol. 16, 757–771 (1998).
    [Crossref]
  3. L. E. Nelson, R. M. Jopson, H. Kogelnik, “Polarization mode dispersion penalties associated with rotation of principal states of polarization in optical fiber,” in Proceedings of the Optical Fiber Communication Conference, Vol. 37 of the OSA Proceedings Series (Optical Society of America, Washington, D.C., 2000), pp. 25–27.
  4. G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Statistics of second-order PMD depolarization,” J. Lightwave Technol. 19, 1882–1886 (2001).
    [Crossref]
  5. H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson, P. A. Andrekson, “A comparison between different PMD compensation techniques,” J. Lightwave Technol. 20, 368–378 (2002).
    [Crossref]
  6. P. C. Chou, J. M. Fini, H. A. Haus, “Demonstration of a feed-forward PMD compensation technique,” IEEE Photon. Technol. Lett. 14, 161–163 (2002).
    [Crossref]
  7. R. M. Jopson, L. E. Nelson, H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
    [Crossref]
  8. L. E. Nelson, R. M. Jopson, H. Kogelnik, G. J. Foschini, “Measurement of depolarization and scaling associated with second-order polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 11, 1614–1616 (1999).
    [Crossref]
  9. P. B. Phua, J. M. Fini, H. A. Haus, E. P. Ippen, “New 1st and 2nd order PMD characterization using time-averaged state-of-polarization variation with signal’s bandwidth,” in Proceedings of OSA Annual Meeting (Optical Society of America, Washington, D.C., 2001), paper TuY4.
  10. P. B. Phua, H. A. Haus, “Deterministic approach to first- and second-order PMD compensation,” IEEE Photon. Technol. Lett. 14, 1270–1272 (2002).
    [Crossref]
  11. J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” in Proc. Natl. Acad. Sci. 97, 4541–4550 (2000).
    [Crossref]
  12. G. J. Foschini, C. D. Poole, “Statistical theory of polarization mode dispersion in single-mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
    [Crossref]
  13. G. J. Foschini, R. M. Jopson, L. E. Nelson, H. Kogelnik, “The statistics of PMD-induced chromatic fiber dispersion,” J. Lightwave Technol. 17, 1560–1565 (1999).
    [Crossref]
  14. G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12, 293–295 (2000).
    [Crossref]
  15. P. B. Phua, H. A. Haus, “A deterministically controlled four-segment polarization-mode dispersion emulator,” J. Lightwave Technol. 20, 1132–1140 (2002).
    [Crossref]

2002 (4)

H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson, P. A. Andrekson, “A comparison between different PMD compensation techniques,” J. Lightwave Technol. 20, 368–378 (2002).
[Crossref]

P. C. Chou, J. M. Fini, H. A. Haus, “Demonstration of a feed-forward PMD compensation technique,” IEEE Photon. Technol. Lett. 14, 161–163 (2002).
[Crossref]

P. B. Phua, H. A. Haus, “Deterministic approach to first- and second-order PMD compensation,” IEEE Photon. Technol. Lett. 14, 1270–1272 (2002).
[Crossref]

P. B. Phua, H. A. Haus, “A deterministically controlled four-segment polarization-mode dispersion emulator,” J. Lightwave Technol. 20, 1132–1140 (2002).
[Crossref]

2001 (1)

2000 (2)

G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12, 293–295 (2000).
[Crossref]

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” in Proc. Natl. Acad. Sci. 97, 4541–4550 (2000).
[Crossref]

1999 (3)

R. M. Jopson, L. E. Nelson, H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
[Crossref]

L. E. Nelson, R. M. Jopson, H. Kogelnik, G. J. Foschini, “Measurement of depolarization and scaling associated with second-order polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 11, 1614–1616 (1999).
[Crossref]

G. J. Foschini, R. M. Jopson, L. E. Nelson, H. Kogelnik, “The statistics of PMD-induced chromatic fiber dispersion,” J. Lightwave Technol. 17, 1560–1565 (1999).
[Crossref]

1998 (2)

1991 (1)

G. J. Foschini, C. D. Poole, “Statistical theory of polarization mode dispersion in single-mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
[Crossref]

Andrekson, P. A.

Büllow, H.

H. Büllow, “System outage probability due to first- and second-order PMD,” IEEE Photon. Technol. Lett. 10, 696–698 (1998).
[Crossref]

Chou, P. C.

P. C. Chou, J. M. Fini, H. A. Haus, “Demonstration of a feed-forward PMD compensation technique,” IEEE Photon. Technol. Lett. 14, 161–163 (2002).
[Crossref]

Ciprut, P.

Fini, J. M.

P. C. Chou, J. M. Fini, H. A. Haus, “Demonstration of a feed-forward PMD compensation technique,” IEEE Photon. Technol. Lett. 14, 161–163 (2002).
[Crossref]

P. B. Phua, J. M. Fini, H. A. Haus, E. P. Ippen, “New 1st and 2nd order PMD characterization using time-averaged state-of-polarization variation with signal’s bandwidth,” in Proceedings of OSA Annual Meeting (Optical Society of America, Washington, D.C., 2001), paper TuY4.

Foschini, G. J.

G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Statistics of second-order PMD depolarization,” J. Lightwave Technol. 19, 1882–1886 (2001).
[Crossref]

G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12, 293–295 (2000).
[Crossref]

L. E. Nelson, R. M. Jopson, H. Kogelnik, G. J. Foschini, “Measurement of depolarization and scaling associated with second-order polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 11, 1614–1616 (1999).
[Crossref]

G. J. Foschini, R. M. Jopson, L. E. Nelson, H. Kogelnik, “The statistics of PMD-induced chromatic fiber dispersion,” J. Lightwave Technol. 17, 1560–1565 (1999).
[Crossref]

G. J. Foschini, C. D. Poole, “Statistical theory of polarization mode dispersion in single-mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
[Crossref]

Gisin, B.

Gisin, N.

Gordon, J. P.

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” in Proc. Natl. Acad. Sci. 97, 4541–4550 (2000).
[Crossref]

Haus, H. A.

P. C. Chou, J. M. Fini, H. A. Haus, “Demonstration of a feed-forward PMD compensation technique,” IEEE Photon. Technol. Lett. 14, 161–163 (2002).
[Crossref]

P. B. Phua, H. A. Haus, “A deterministically controlled four-segment polarization-mode dispersion emulator,” J. Lightwave Technol. 20, 1132–1140 (2002).
[Crossref]

P. B. Phua, H. A. Haus, “Deterministic approach to first- and second-order PMD compensation,” IEEE Photon. Technol. Lett. 14, 1270–1272 (2002).
[Crossref]

P. B. Phua, J. M. Fini, H. A. Haus, E. P. Ippen, “New 1st and 2nd order PMD characterization using time-averaged state-of-polarization variation with signal’s bandwidth,” in Proceedings of OSA Annual Meeting (Optical Society of America, Washington, D.C., 2001), paper TuY4.

Ippen, E. P.

P. B. Phua, J. M. Fini, H. A. Haus, E. P. Ippen, “New 1st and 2nd order PMD characterization using time-averaged state-of-polarization variation with signal’s bandwidth,” in Proceedings of OSA Annual Meeting (Optical Society of America, Washington, D.C., 2001), paper TuY4.

Jopson, R. M.

G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Statistics of second-order PMD depolarization,” J. Lightwave Technol. 19, 1882–1886 (2001).
[Crossref]

G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12, 293–295 (2000).
[Crossref]

G. J. Foschini, R. M. Jopson, L. E. Nelson, H. Kogelnik, “The statistics of PMD-induced chromatic fiber dispersion,” J. Lightwave Technol. 17, 1560–1565 (1999).
[Crossref]

L. E. Nelson, R. M. Jopson, H. Kogelnik, G. J. Foschini, “Measurement of depolarization and scaling associated with second-order polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 11, 1614–1616 (1999).
[Crossref]

R. M. Jopson, L. E. Nelson, H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
[Crossref]

L. E. Nelson, R. M. Jopson, H. Kogelnik, “Polarization mode dispersion penalties associated with rotation of principal states of polarization in optical fiber,” in Proceedings of the Optical Fiber Communication Conference, Vol. 37 of the OSA Proceedings Series (Optical Society of America, Washington, D.C., 2000), pp. 25–27.

Karlsson, M.

Kogelnik, H.

G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Statistics of second-order PMD depolarization,” J. Lightwave Technol. 19, 1882–1886 (2001).
[Crossref]

G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12, 293–295 (2000).
[Crossref]

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” in Proc. Natl. Acad. Sci. 97, 4541–4550 (2000).
[Crossref]

L. E. Nelson, R. M. Jopson, H. Kogelnik, G. J. Foschini, “Measurement of depolarization and scaling associated with second-order polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 11, 1614–1616 (1999).
[Crossref]

R. M. Jopson, L. E. Nelson, H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
[Crossref]

G. J. Foschini, R. M. Jopson, L. E. Nelson, H. Kogelnik, “The statistics of PMD-induced chromatic fiber dispersion,” J. Lightwave Technol. 17, 1560–1565 (1999).
[Crossref]

L. E. Nelson, R. M. Jopson, H. Kogelnik, “Polarization mode dispersion penalties associated with rotation of principal states of polarization in optical fiber,” in Proceedings of the Optical Fiber Communication Conference, Vol. 37 of the OSA Proceedings Series (Optical Society of America, Washington, D.C., 2000), pp. 25–27.

Nelson, L. E.

G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Statistics of second-order PMD depolarization,” J. Lightwave Technol. 19, 1882–1886 (2001).
[Crossref]

G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12, 293–295 (2000).
[Crossref]

G. J. Foschini, R. M. Jopson, L. E. Nelson, H. Kogelnik, “The statistics of PMD-induced chromatic fiber dispersion,” J. Lightwave Technol. 17, 1560–1565 (1999).
[Crossref]

R. M. Jopson, L. E. Nelson, H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
[Crossref]

L. E. Nelson, R. M. Jopson, H. Kogelnik, G. J. Foschini, “Measurement of depolarization and scaling associated with second-order polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 11, 1614–1616 (1999).
[Crossref]

L. E. Nelson, R. M. Jopson, H. Kogelnik, “Polarization mode dispersion penalties associated with rotation of principal states of polarization in optical fiber,” in Proceedings of the Optical Fiber Communication Conference, Vol. 37 of the OSA Proceedings Series (Optical Society of America, Washington, D.C., 2000), pp. 25–27.

Passy, R.

Phua, P. B.

P. B. Phua, H. A. Haus, “Deterministic approach to first- and second-order PMD compensation,” IEEE Photon. Technol. Lett. 14, 1270–1272 (2002).
[Crossref]

P. B. Phua, H. A. Haus, “A deterministically controlled four-segment polarization-mode dispersion emulator,” J. Lightwave Technol. 20, 1132–1140 (2002).
[Crossref]

P. B. Phua, J. M. Fini, H. A. Haus, E. P. Ippen, “New 1st and 2nd order PMD characterization using time-averaged state-of-polarization variation with signal’s bandwidth,” in Proceedings of OSA Annual Meeting (Optical Society of America, Washington, D.C., 2001), paper TuY4.

Poole, C. D.

G. J. Foschini, C. D. Poole, “Statistical theory of polarization mode dispersion in single-mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
[Crossref]

Prieto, F.

Samuelsson, R.

Sunnerud, H.

Von Der Weid, P.

Xie, C.

Zimmer, C. W.

IEEE Photon. Technol. Lett. (6)

H. Büllow, “System outage probability due to first- and second-order PMD,” IEEE Photon. Technol. Lett. 10, 696–698 (1998).
[Crossref]

P. C. Chou, J. M. Fini, H. A. Haus, “Demonstration of a feed-forward PMD compensation technique,” IEEE Photon. Technol. Lett. 14, 161–163 (2002).
[Crossref]

R. M. Jopson, L. E. Nelson, H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
[Crossref]

L. E. Nelson, R. M. Jopson, H. Kogelnik, G. J. Foschini, “Measurement of depolarization and scaling associated with second-order polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 11, 1614–1616 (1999).
[Crossref]

P. B. Phua, H. A. Haus, “Deterministic approach to first- and second-order PMD compensation,” IEEE Photon. Technol. Lett. 14, 1270–1272 (2002).
[Crossref]

G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12, 293–295 (2000).
[Crossref]

J. Lightwave Technol. (6)

Proc. Natl. Acad. Sci. (1)

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” in Proc. Natl. Acad. Sci. 97, 4541–4550 (2000).
[Crossref]

Other (2)

L. E. Nelson, R. M. Jopson, H. Kogelnik, “Polarization mode dispersion penalties associated with rotation of principal states of polarization in optical fiber,” in Proceedings of the Optical Fiber Communication Conference, Vol. 37 of the OSA Proceedings Series (Optical Society of America, Washington, D.C., 2000), pp. 25–27.

P. B. Phua, J. M. Fini, H. A. Haus, E. P. Ippen, “New 1st and 2nd order PMD characterization using time-averaged state-of-polarization variation with signal’s bandwidth,” in Proceedings of OSA Annual Meeting (Optical Society of America, Washington, D.C., 2001), paper TuY4.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Scheme of the three-segment PMD compensator. τ 0 and τ are the observed first- and second-order PMD vectors of the transmission fiber. τ and τ ω are the PMD vectors after the compensator.

Fig. 2
Fig. 2

Geometric illustration of the solutions of vector C 1 τ 1 .

Fig. 3
Fig. 3

Detailed compositions of the three PCs.

Fig. 4
Fig. 4

Illustration of the derivation of the control parameters θ11 and θ12. In the figure, A = a î + b ĵ , A (1) = T 111)A.

Fig. 5
Fig. 5

Depiction of the compensation procedure of τ ω′. α is the angle between τ 2 and τ(2) and β is the required angle between τ 2 and τ(3) to satisfy Eq. (11). In steps (1) and (2), the transformation of τ′ is not shown for simplicity.

Fig. 6
Fig. 6

Probability densities of the first- and second-order PMD magnitudes of the transmission fiber.

Fig. 7
Fig. 7

Probability densities of the first- and second-order PMD magnitudes after the compensator for standard deviations σfix of 0.05 fs.

Fig. 8
Fig. 8

Probability densities of the first- and second-order PMD magnitudes after the compensator for standard deviations σangij of (a) σang11 = 0.5°, σang12 = 0.5°, σang21 = 0.1°, σang22 = 0.5°, σang23 = 0.1°, σang31 = 0.5°, σang32 = 0.5°; (b) σang11 = 0.2°, σang12 = 0.2°, σang21 = 0.2°, σang22 = 0.2°, σang23 = 0.2°, σang31 = 0.2°, σang32 = 0.2°.

Fig. 9
Fig. 9

Probability densities of the first- and second-order PMD magnitudes after (a) the proposed compensator and (b) the compensator that employs variable DGD module as the first segment for the following perturbation parameters: σfix = 0.01 fs, τres = 0.6 ps, σangij = 0.2°.

Tables (1)

Tables Icon

Table 1 Metric Parameters Corresponding to Perturbations in Different Tunable Phase Shiftersa

Equations (17)

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

τ=τ1+R1C1τ0,
τω=τ1R1C1τ0+R1C1τ0ω,
τ=τ2+R2C2τ,
τω=τ2R2C2τ+R2C2τω,
τ=τ3+R3C3τ,
τω=τ3R3C3τ+R3C3τω.
C1τ1 · τ0ω=-τ0 · τ0ω.
P|τ0|x=8π2τm2xτm2 exp-2x/τm2π,
P|τ0ω|x=8πτm24xτm2tanh4x/τm2sech4x/τm2,
C1τ1=aiˆ+bjˆ,
τ2·C2τ+C2τω=0,
C3τ=-τ3.
T1θ=1000cos θ-sin θ0sin θcos θ,
T2θ=cos θ0-sin θ010sin θ0cos θ,
r1=E|τ|/τm,
r2=E|τω|/E|τ0ω|,
Rj|τj|=1000cosω|τj|-sinω|τj|0sinω|τj|cosω|τj|, j=1, 2.

Metrics