Abstract

We calculate the asymptotic first-order polarization mode dispersion statistics of constantly spun fibers. We show that in the long length regime the mean differential group delay of constantly spun fibers grows linearly with distance at the same rate as for unspun fibers. Conversely, the short length regime of constantly spun fibers may be much longer, even for limited spin rates.

© 2003 Optical Society of America

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References

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  1. M.-J. Li and D. A. Nolan, Opt. Lett. 23, 1659 (1998).
    [CrossRef]
  2. A. Galtarossa, L. Palmieri, and A. Pizzinat, J. Lightwave Technol. 19, 1502 (2001).
    [CrossRef]
  3. X. Chen, M.-J. Li, and D. A. Nolan, Opt. Lett. 27, 294 (2002).
    [CrossRef]
  4. A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, Opt. Lett. 28, 390 (2003).
    [CrossRef] [PubMed]
  5. R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, Electron. Lett. 28, 1772 (1995).
    [CrossRef]
  6. X. Chen, M.-J. Li, and D. A. Nolan, Opt. Lett. 27, 1595 (2002).
    [CrossRef]
  7. P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
    [CrossRef]
  8. A. Galtarossa and L. Palmieri, in Optical Fiber Communication Conference (OFC), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper WA4.
  9. A. Pizzinat, L. Palmieri, B. S. Marks, C. R. Menyuk, and A. Galtarossa, “Analytical treatment of randomly-birefringent periodically-spun fibers,” J. Lightwave Technol. (to be published).
  10. L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations (Springer-Verlag, Berlin, 1971).
    [CrossRef]
  11. A. Galtarossa, P. Griggio, A. Pizzinat, and L. Palmieri, Opt. Lett. 27, 692 (2002).
    [CrossRef]
  12. Y. Tan, J. Yang, W. L. Kath, and C. R. Menyuk, J. Opt. Soc. Am. A 19, 992 (2002).
    [CrossRef]

2003 (1)

2002 (4)

2001 (1)

A. Galtarossa, L. Palmieri, and A. Pizzinat, J. Lightwave Technol. 19, 1502 (2001).
[CrossRef]

1998 (1)

1996 (1)

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

1995 (1)

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, Electron. Lett. 28, 1772 (1995).
[CrossRef]

Bebbington, D. H. O.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, Electron. Lett. 28, 1772 (1995).
[CrossRef]

Cesari, L.

L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations (Springer-Verlag, Berlin, 1971).
[CrossRef]

Chen, X.

Galtarossa, A.

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, Opt. Lett. 28, 390 (2003).
[CrossRef] [PubMed]

A. Galtarossa, P. Griggio, A. Pizzinat, and L. Palmieri, Opt. Lett. 27, 692 (2002).
[CrossRef]

A. Galtarossa, L. Palmieri, and A. Pizzinat, J. Lightwave Technol. 19, 1502 (2001).
[CrossRef]

A. Pizzinat, L. Palmieri, B. S. Marks, C. R. Menyuk, and A. Galtarossa, “Analytical treatment of randomly-birefringent periodically-spun fibers,” J. Lightwave Technol. (to be published).

A. Galtarossa and L. Palmieri, in Optical Fiber Communication Conference (OFC), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper WA4.

Gleeson, L. M.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, Electron. Lett. 28, 1772 (1995).
[CrossRef]

Griggio, P.

Kath, W. L.

Y. Tan, J. Yang, W. L. Kath, and C. R. Menyuk, J. Opt. Soc. Am. A 19, 992 (2002).
[CrossRef]

Li, M.-J.

Marks, B. S.

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, Opt. Lett. 28, 390 (2003).
[CrossRef] [PubMed]

A. Pizzinat, L. Palmieri, B. S. Marks, C. R. Menyuk, and A. Galtarossa, “Analytical treatment of randomly-birefringent periodically-spun fibers,” J. Lightwave Technol. (to be published).

Menyuk, C. R.

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, Opt. Lett. 28, 390 (2003).
[CrossRef] [PubMed]

Y. Tan, J. Yang, W. L. Kath, and C. R. Menyuk, J. Opt. Soc. Am. A 19, 992 (2002).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

A. Pizzinat, L. Palmieri, B. S. Marks, C. R. Menyuk, and A. Galtarossa, “Analytical treatment of randomly-birefringent periodically-spun fibers,” J. Lightwave Technol. (to be published).

Nolan, D. A.

Palmieri, L.

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, Opt. Lett. 28, 390 (2003).
[CrossRef] [PubMed]

A. Galtarossa, P. Griggio, A. Pizzinat, and L. Palmieri, Opt. Lett. 27, 692 (2002).
[CrossRef]

A. Galtarossa, L. Palmieri, and A. Pizzinat, J. Lightwave Technol. 19, 1502 (2001).
[CrossRef]

A. Galtarossa and L. Palmieri, in Optical Fiber Communication Conference (OFC), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper WA4.

A. Pizzinat, L. Palmieri, B. S. Marks, C. R. Menyuk, and A. Galtarossa, “Analytical treatment of randomly-birefringent periodically-spun fibers,” J. Lightwave Technol. (to be published).

Pizzinat, A.

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, Opt. Lett. 28, 390 (2003).
[CrossRef] [PubMed]

A. Galtarossa, P. Griggio, A. Pizzinat, and L. Palmieri, Opt. Lett. 27, 692 (2002).
[CrossRef]

A. Galtarossa, L. Palmieri, and A. Pizzinat, J. Lightwave Technol. 19, 1502 (2001).
[CrossRef]

A. Pizzinat, L. Palmieri, B. S. Marks, C. R. Menyuk, and A. Galtarossa, “Analytical treatment of randomly-birefringent periodically-spun fibers,” J. Lightwave Technol. (to be published).

Schuh, R. E.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, Electron. Lett. 28, 1772 (1995).
[CrossRef]

Siddiqui, A. S.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, Electron. Lett. 28, 1772 (1995).
[CrossRef]

Sikora, E. S. R.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, Electron. Lett. 28, 1772 (1995).
[CrossRef]

Tan, Y.

Y. Tan, J. Yang, W. L. Kath, and C. R. Menyuk, J. Opt. Soc. Am. A 19, 992 (2002).
[CrossRef]

Wai, P. K. A.

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Walker, N. G.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, Electron. Lett. 28, 1772 (1995).
[CrossRef]

Yang, J.

Y. Tan, J. Yang, W. L. Kath, and C. R. Menyuk, J. Opt. Soc. Am. A 19, 992 (2002).
[CrossRef]

Electron. Lett. (1)

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, Electron. Lett. 28, 1772 (1995).
[CrossRef]

J. Lightwave Technol. (1)

A. Galtarossa, L. Palmieri, and A. Pizzinat, J. Lightwave Technol. 19, 1502 (2001).
[CrossRef]

J. Lightwave Technol. (2)

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

A. Pizzinat, L. Palmieri, B. S. Marks, C. R. Menyuk, and A. Galtarossa, “Analytical treatment of randomly-birefringent periodically-spun fibers,” J. Lightwave Technol. (to be published).

J. Opt. Soc. Am. A (1)

Y. Tan, J. Yang, W. L. Kath, and C. R. Menyuk, J. Opt. Soc. Am. A 19, 992 (2002).
[CrossRef]

Opt. Lett. (5)

OSA Trends in Optics and Photonics Series (1)

A. Galtarossa and L. Palmieri, in Optical Fiber Communication Conference (OFC), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper WA4.

Other (1)

L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations (Springer-Verlag, Berlin, 1971).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Evolution of Δτ2z for a fiber with LB=8.86 m and LF=20 m. Curve (a) corresponds to the unspun fiber; curves (b) and (c) refer to constantly spun fibers with p=5 m and p=2.5 m, respectively.

Fig. 2
Fig. 2

Solid curves represent the pdfs of Δτ for 100,000 fiber realizations with LB=10 m, LF=20 m, and p=5 m. Dashed curves represent the Maxwellian distribution corresponding to the mean values of the ensembles.

Fig. 3
Fig. 3

pdf of Ω3 in the same conditions as in Fig. 2. The solid curves are obtained with the RMM, and the dashed curves correspond to Gaussian distributions with first and second moments calculated as in the text.

Equations (8)

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

βlz=bzcos2θz,sin2θz,0T,
dΩdz=-2σ22α00-2α0-2σ2-b0b0Ω+bω00=QΩ+u.
Ω=expQz0zexp-Qz·udz=Q-1expQz-Iu,
Δτ2=2βωe1·Q-12expQz-Qz-Iu,
Δτ22b2LFω2z-2b2LF2ω21+4α02b2.
LT=LF1+4LB2p2.
Ω1=b2σ2ω, Ω2=0, Ω3=-α0σ2ω.
Ω1f=cos2α0zexp-2σ2zb2σ2ω, Ω2f=sin2α0zexp-2σ2zb2σ2ω.

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