Abstract

We demonstrate that within the framework of the hinge model, the polarization mode dispersion (PMD) vector correlation function averaged over time and wavelength is only appreciably affected by the position of the last hinge. Further, the correlation function width is found within the context of a standard hinge model to decrease nearly monotonically with the number of hinges. We finally derive, through a theoretical analysis, an upper bound for the mean squared differential group delay of the last fiber section in the link in terms of the correlation function.

© 2013 Optical Society of America

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References

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  1. G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
    [CrossRef]
  2. H. Kogelnik, R. M. Jopson, and L. E. Nelson, “Polarization mode dispersion,” in Optical Fiber Telecommunications (Academic, 2002), Vol. 4b, Chap. 15.
  3. M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, “Polarization mode dispersion of installed fibers,” J. Lightwave Technol. 24, 4584–4599 (2006).
    [CrossRef]
  4. C. Antonelli and A. Mecozzi, “Statistics of the DGD in PMD emulators,” IEEE Photon. Technol. Lett. 16, 1840–1842 (2004).
    [CrossRef]
  5. H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, “First-order PMD outage for the hinge model,” IEEE Photon. Technol. Lett. 17, 1208–1210(2005).
    [CrossRef]
  6. C. Antonelli and A. Mecozzi, “Theoretical characterization and system impact of the hinge model of PMD,” J. Lightwave Technol. 24, 4064–4074 (2006).
    [CrossRef]
  7. J. Li, G. Biondini, W. L. Kath, and H. Kogelnik, “Outage statistics in a waveplate hinge model of polarization mode dispersion,” J. Lightwave Technol. 28, 1958–1968 (2010).
    [CrossRef]
  8. J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
    [CrossRef]

2010 (1)

2006 (2)

2005 (1)

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, “First-order PMD outage for the hinge model,” IEEE Photon. Technol. Lett. 17, 1208–1210(2005).
[CrossRef]

2004 (1)

C. Antonelli and A. Mecozzi, “Statistics of the DGD in PMD emulators,” IEEE Photon. Technol. Lett. 16, 1840–1842 (2004).
[CrossRef]

2000 (1)

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

1991 (1)

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

Antonelli, C.

C. Antonelli and A. Mecozzi, “Theoretical characterization and system impact of the hinge model of PMD,” J. Lightwave Technol. 24, 4064–4074 (2006).
[CrossRef]

C. Antonelli and A. Mecozzi, “Statistics of the DGD in PMD emulators,” IEEE Photon. Technol. Lett. 16, 1840–1842 (2004).
[CrossRef]

Biondini, G.

Boroditsky, M.

M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, “Polarization mode dispersion of installed fibers,” J. Lightwave Technol. 24, 4584–4599 (2006).
[CrossRef]

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, “First-order PMD outage for the hinge model,” IEEE Photon. Technol. Lett. 17, 1208–1210(2005).
[CrossRef]

Brodsky, M.

M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, “Polarization mode dispersion of installed fibers,” J. Lightwave Technol. 24, 4584–4599 (2006).
[CrossRef]

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, “First-order PMD outage for the hinge model,” IEEE Photon. Technol. Lett. 17, 1208–1210(2005).
[CrossRef]

Foschini, G. J.

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

Frigo, N. J.

Gordon, J. P.

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

Jopson, R. M.

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, “First-order PMD outage for the hinge model,” IEEE Photon. Technol. Lett. 17, 1208–1210(2005).
[CrossRef]

H. Kogelnik, R. M. Jopson, and L. E. Nelson, “Polarization mode dispersion,” in Optical Fiber Telecommunications (Academic, 2002), Vol. 4b, Chap. 15.

Kath, W. L.

Kogelnik, H.

J. Li, G. Biondini, W. L. Kath, and H. Kogelnik, “Outage statistics in a waveplate hinge model of polarization mode dispersion,” J. Lightwave Technol. 28, 1958–1968 (2010).
[CrossRef]

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, “First-order PMD outage for the hinge model,” IEEE Photon. Technol. Lett. 17, 1208–1210(2005).
[CrossRef]

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

H. Kogelnik, R. M. Jopson, and L. E. Nelson, “Polarization mode dispersion,” in Optical Fiber Telecommunications (Academic, 2002), Vol. 4b, Chap. 15.

Li, J.

Mecozzi, A.

C. Antonelli and A. Mecozzi, “Theoretical characterization and system impact of the hinge model of PMD,” J. Lightwave Technol. 24, 4064–4074 (2006).
[CrossRef]

C. Antonelli and A. Mecozzi, “Statistics of the DGD in PMD emulators,” IEEE Photon. Technol. Lett. 16, 1840–1842 (2004).
[CrossRef]

Nelson, L. E.

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, “First-order PMD outage for the hinge model,” IEEE Photon. Technol. Lett. 17, 1208–1210(2005).
[CrossRef]

H. Kogelnik, R. M. Jopson, and L. E. Nelson, “Polarization mode dispersion,” in Optical Fiber Telecommunications (Academic, 2002), Vol. 4b, Chap. 15.

Poole, C. D.

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

Tur, M.

Winzer, P. J.

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, “First-order PMD outage for the hinge model,” IEEE Photon. Technol. Lett. 17, 1208–1210(2005).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

C. Antonelli and A. Mecozzi, “Statistics of the DGD in PMD emulators,” IEEE Photon. Technol. Lett. 16, 1840–1842 (2004).
[CrossRef]

H. Kogelnik, P. J. Winzer, L. E. Nelson, R. M. Jopson, M. Boroditsky, and M. Brodsky, “First-order PMD outage for the hinge model,” IEEE Photon. Technol. Lett. 17, 1208–1210(2005).
[CrossRef]

J. Lightwave Technol. (4)

Proc. Natl. Acad. Sci. U.S.A. (1)

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

Other (1)

H. Kogelnik, R. M. Jopson, and L. E. Nelson, “Polarization mode dispersion,” in Optical Fiber Telecommunications (Academic, 2002), Vol. 4b, Chap. 15.

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Figures (6)

Fig. 1.
Fig. 1.

Series of fiber sections, S1,,S6, connected through hinges H1,,H6.

Fig. 2.
Fig. 2.

Averaged correlation function for different hinge conditions as a function of the correlation time interval.

Fig. 3.
Fig. 3.

Same as Fig. 2 but for seven hinges.

Fig. 4.
Fig. 4.

Averaged correlation function for different number of hinges as a function of the correlation time interval.

Fig. 5.
Fig. 5.

Same as Fig. 4 but for anisotropic random hinges.

Fig. 6.
Fig. 6.

Same as Fig. 2 but for anisotropic random hinges.

Equations (10)

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C(α)=E[1T0Tτ⃗(t)τ⃗(t+α)dt],
τ⃗(t)=τ⃗n+RnHn1(t)τ⃗n1+RnHn1(t)Rn1Hn2(t)τ⃗n2+,
C(α)=E[τN2]+13i=1N1E[τi2]gi(α).
gi(α)=E[Tr(1T0TdαHN1(t)RN1HN2(t)Hi1(t)Hi1(t+α)HN2(t+α)RN1HN1(t+α))],
C(α)=E[τN2]+E[τN12]+13i=1N2E[τi2]gi(α),
dφidt=φiτci+Wi(t),
η=E[τ⃗(t)τ⃗(t+α)]=E[τn2]+13E[τn12]Tr(M1)+13E[τn22]Tr(M2)+,
ηminE[τn2]13i=1n1E[τi2].
ηminE[τn2]13(E[τ2]E[τn2])
E[τn2]34ηmin+14E[τ2].

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