Abstract

We discuss a generalized waveplate hinge model to characterize anisotropic effects associated with the hinge model of polarization-mode dispersion in installed systems. In this model, the action of the hinges is a random time-dependent rotation about a fixed axis. We obtain the probability density function of the differential group delay and the outage probability of an individual wavelength band using a combination of importance sampling and the cross-entropy method, and we then compute the noncompliant capacity ratio by averaging over wavelength bands. The results show that there are significant differences between the outage statistics predicted by isotropic and anisotropic hinge models.

© 2008 Optical Society of America

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  1. M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, Opt. Express 13, 4090 (2005).
    [CrossRef] [PubMed]
  2. M. Boroditsky, M. Brodsky, P. Magill, N. J. Frigo, C. Antonelli, and A. Mecozzi, IEEE Photon. Technol. Lett. 17, 345 (2005).
    [CrossRef]
  3. C. Antonelli and A. Mecozzi, J. Lightwave Technol. 24, 4064 (2006).
    [CrossRef]
  4. M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, J. Lightwave Technol. 24, 4584 (2006).
    [CrossRef]
  5. M. Brodsky, J. C. Martinez, N. J. Frigo, and A. Sirenko, in Proceedings of the European Conference on Optical Communication (ECOC) (IEEE, 2005), Vol. 3, p. 335.
  6. W. Shieh and H. Kogelnik, IEEE Photon. Technol. Lett. 13, 40 (2001).
    [CrossRef]
  7. J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
    [CrossRef] [PubMed]
  8. G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
    [CrossRef]
  9. S. L. Fogal, G. Biondini, and W. L. Kath, IEEE Photon. Technol. Lett. 14, 1273 (2002).
    [CrossRef]
  10. G. Biondini, W. L. Kath, and C. R. Menyuk, J. Lightwave Technol. 22, 1201 (2004).
    [CrossRef]
  11. P. T. De Boer, D. P. Kroese, S. Mannor, and R. Y. Rubinstein, Ann. Operat. Res. 134, 19 (2005).
    [CrossRef]
  12. R. Barakat, J. Phys. A 6, 796 (1973).
    [CrossRef]
  13. H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, IEEE Photon. Technol. Lett. 17, 1208 (2005).
    [CrossRef]

2006 (2)

2005 (4)

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, Opt. Express 13, 4090 (2005).
[CrossRef] [PubMed]

M. Boroditsky, M. Brodsky, P. Magill, N. J. Frigo, C. Antonelli, and A. Mecozzi, IEEE Photon. Technol. Lett. 17, 345 (2005).
[CrossRef]

P. T. De Boer, D. P. Kroese, S. Mannor, and R. Y. Rubinstein, Ann. Operat. Res. 134, 19 (2005).
[CrossRef]

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, IEEE Photon. Technol. Lett. 17, 1208 (2005).
[CrossRef]

2004 (1)

2002 (2)

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

S. L. Fogal, G. Biondini, and W. L. Kath, IEEE Photon. Technol. Lett. 14, 1273 (2002).
[CrossRef]

2001 (1)

W. Shieh and H. Kogelnik, IEEE Photon. Technol. Lett. 13, 40 (2001).
[CrossRef]

2000 (1)

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

1973 (1)

R. Barakat, J. Phys. A 6, 796 (1973).
[CrossRef]

Antonelli, C.

C. Antonelli and A. Mecozzi, J. Lightwave Technol. 24, 4064 (2006).
[CrossRef]

M. Boroditsky, M. Brodsky, P. Magill, N. J. Frigo, C. Antonelli, and A. Mecozzi, IEEE Photon. Technol. Lett. 17, 345 (2005).
[CrossRef]

Barakat, R.

R. Barakat, J. Phys. A 6, 796 (1973).
[CrossRef]

Biondini, G.

G. Biondini, W. L. Kath, and C. R. Menyuk, J. Lightwave Technol. 22, 1201 (2004).
[CrossRef]

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

S. L. Fogal, G. Biondini, and W. L. Kath, IEEE Photon. Technol. Lett. 14, 1273 (2002).
[CrossRef]

Boroditsky, M.

M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, J. Lightwave Technol. 24, 4584 (2006).
[CrossRef]

M. Boroditsky, M. Brodsky, P. Magill, N. J. Frigo, C. Antonelli, and A. Mecozzi, IEEE Photon. Technol. Lett. 17, 345 (2005).
[CrossRef]

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, IEEE Photon. Technol. Lett. 17, 1208 (2005).
[CrossRef]

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, Opt. Express 13, 4090 (2005).
[CrossRef] [PubMed]

Brodsky, M.

M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, J. Lightwave Technol. 24, 4584 (2006).
[CrossRef]

M. Boroditsky, M. Brodsky, P. Magill, N. J. Frigo, C. Antonelli, and A. Mecozzi, IEEE Photon. Technol. Lett. 17, 345 (2005).
[CrossRef]

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, IEEE Photon. Technol. Lett. 17, 1208 (2005).
[CrossRef]

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, Opt. Express 13, 4090 (2005).
[CrossRef] [PubMed]

M. Brodsky, J. C. Martinez, N. J. Frigo, and A. Sirenko, in Proceedings of the European Conference on Optical Communication (ECOC) (IEEE, 2005), Vol. 3, p. 335.

De Boer, P. T.

P. T. De Boer, D. P. Kroese, S. Mannor, and R. Y. Rubinstein, Ann. Operat. Res. 134, 19 (2005).
[CrossRef]

Fogal, S. L.

S. L. Fogal, G. Biondini, and W. L. Kath, IEEE Photon. Technol. Lett. 14, 1273 (2002).
[CrossRef]

Frigo, N. J.

M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, J. Lightwave Technol. 24, 4584 (2006).
[CrossRef]

M. Boroditsky, M. Brodsky, P. Magill, N. J. Frigo, C. Antonelli, and A. Mecozzi, IEEE Photon. Technol. Lett. 17, 345 (2005).
[CrossRef]

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, Opt. Express 13, 4090 (2005).
[CrossRef] [PubMed]

M. Brodsky, J. C. Martinez, N. J. Frigo, and A. Sirenko, in Proceedings of the European Conference on Optical Communication (ECOC) (IEEE, 2005), Vol. 3, p. 335.

Gordon, J. P.

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

Jopson, R. M.

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, IEEE Photon. Technol. Lett. 17, 1208 (2005).
[CrossRef]

Kath, W. L.

G. Biondini, W. L. Kath, and C. R. Menyuk, J. Lightwave Technol. 22, 1201 (2004).
[CrossRef]

S. L. Fogal, G. Biondini, and W. L. Kath, IEEE Photon. Technol. Lett. 14, 1273 (2002).
[CrossRef]

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

Kogelnik, H.

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, IEEE Photon. Technol. Lett. 17, 1208 (2005).
[CrossRef]

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

Kroese, D. P.

P. T. De Boer, D. P. Kroese, S. Mannor, and R. Y. Rubinstein, Ann. Operat. Res. 134, 19 (2005).
[CrossRef]

Magill, P.

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, Opt. Express 13, 4090 (2005).
[CrossRef] [PubMed]

M. Boroditsky, M. Brodsky, P. Magill, N. J. Frigo, C. Antonelli, and A. Mecozzi, IEEE Photon. Technol. Lett. 17, 345 (2005).
[CrossRef]

Mannor, S.

P. T. De Boer, D. P. Kroese, S. Mannor, and R. Y. Rubinstein, Ann. Operat. Res. 134, 19 (2005).
[CrossRef]

Martinez, J. C.

M. Brodsky, J. C. Martinez, N. J. Frigo, and A. Sirenko, in Proceedings of the European Conference on Optical Communication (ECOC) (IEEE, 2005), Vol. 3, p. 335.

Mecozzi, A.

C. Antonelli and A. Mecozzi, J. Lightwave Technol. 24, 4064 (2006).
[CrossRef]

M. Boroditsky, M. Brodsky, P. Magill, N. J. Frigo, C. Antonelli, and A. Mecozzi, IEEE Photon. Technol. Lett. 17, 345 (2005).
[CrossRef]

Menyuk, C. R.

G. Biondini, W. L. Kath, and C. R. Menyuk, J. Lightwave Technol. 22, 1201 (2004).
[CrossRef]

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

Nelson, L. E.

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, IEEE Photon. Technol. Lett. 17, 1208 (2005).
[CrossRef]

Rubinstein, R. Y.

P. T. De Boer, D. P. Kroese, S. Mannor, and R. Y. Rubinstein, Ann. Operat. Res. 134, 19 (2005).
[CrossRef]

Shieh and H. Kogelnik, W.

W. Shieh and H. Kogelnik, IEEE Photon. Technol. Lett. 13, 40 (2001).
[CrossRef]

Sirenko, A.

M. Brodsky, J. C. Martinez, N. J. Frigo, and A. Sirenko, in Proceedings of the European Conference on Optical Communication (ECOC) (IEEE, 2005), Vol. 3, p. 335.

Tur, M.

Winzer, P. J.

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, IEEE Photon. Technol. Lett. 17, 1208 (2005).
[CrossRef]

Ann. Operat. Res. (1)

P. T. De Boer, D. P. Kroese, S. Mannor, and R. Y. Rubinstein, Ann. Operat. Res. 134, 19 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, IEEE Photon. Technol. Lett. 17, 1208 (2005).
[CrossRef]

W. Shieh and H. Kogelnik, IEEE Photon. Technol. Lett. 13, 40 (2001).
[CrossRef]

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

S. L. Fogal, G. Biondini, and W. L. Kath, IEEE Photon. Technol. Lett. 14, 1273 (2002).
[CrossRef]

M. Boroditsky, M. Brodsky, P. Magill, N. J. Frigo, C. Antonelli, and A. Mecozzi, IEEE Photon. Technol. Lett. 17, 345 (2005).
[CrossRef]

J. Lightwave Technol. (3)

J. Phys. A (1)

R. Barakat, J. Phys. A 6, 796 (1973).
[CrossRef]

Opt. Express (1)

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

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

Other (1)

M. Brodsky, J. C. Martinez, N. J. Frigo, and A. Sirenko, in Proceedings of the European Conference on Optical Communication (ECOC) (IEEE, 2005), Vol. 3, p. 335.

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Figures (2)

Fig. 1
Fig. 1

Comparison of the PDF of the DGD for the waveplate hinge model (dashed curve, for two sets of hinge directions) versus that for the isotropic hinge model (solid curve). Each case uses the same set of ten sectional PMD vectors. The vertical line indicates the cut-off value τ o = 6.89 ps , which is the outage threshold for a system with a 1 dB penalty margin.

Fig. 2
Fig. 2

NCR as a function of the specified outage probability for transmission links with ten sections and a mean DGD 3.5 (top left curves) and 2.5 ps (bottom right curves). Dashed lines, NCR in the isotropic model; solid lines, NCR in the anisotropic model assuming uniform splitting ratios; dotted–dashed curves, upper bound for the NCR in the anisotropic model; vertical lines, transition between NCR = 0 and NCR = 1 in the traditional model of PMD.

Equations (6)

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

τ n + 1 = R n + 1 H n τ n + Δ τ n + 1 .
τ n + 1 = H n τ n + Δ τ n + 1 ,
H n = cos φ n I + ( 1 cos φ n ) r ̂ n r ̂ n t + sin φ n r ̂ n × ,
D ( p opt * , p * ) = E p opt * [ ln ( p opt * ( x ) p * ( x ) ) ] ,
P out = 0 γ 1 ( τ ) γ 2 ( τ ) p ( τ , γ ) d γ d τ ,
Δ γ ( τ ) = 1 + 4 α ε A 1 ( τ 0 τ ) 2

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