Abstract

We present analytical results on the polarization-mode dispersion characteristics of single-mode birefringent fibers based on statistical properties of the backscattered signal. In particular, we calculate exactly the relationship between polarization-mode dispersion characteristics in forward propagation with respect to round-trip propagation in terms of dynamical equations, differential group delays, correlation lengths, and second-order effects. The theory applies to fibers affected by superposition of linear and circular birefringence in both the short-length and the long-length regimes.

© 1999 Optical Society of America

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  1. A. J. Rogers, “Polarization-optical time domain reflectometry: a technique for the measurement of field distributions,” Appl. Opt. 20, 1060–1074 (1981).
    [CrossRef] [PubMed]
  2. B. Y. Kim, S. S. Choi, “Analysis and measurement of birefringence in single-mode fiber using the backscattering method,” Opt. Lett. 6, 578–580 (1981).
    [CrossRef] [PubMed]
  3. E. Brinkmeyer, “Forward–backward transmission in birefringent single-mode fibers: interpretation of polarization-sensitive measurements,” Opt. Lett. 11, 575–577 (1981).
    [CrossRef]
  4. J. N. Ross, “Birefringence measurement in optical fibers by polarization optical time-domain reflectometry,” Appl. Opt. 21, 3489–3495 (1982).
    [CrossRef] [PubMed]
  5. A. Galtarossa, P. Pistolato, M. Schiano, “Measurements of stress birefringence in optical cables by polarization otdr,” presented at the European Fibre Optic Communications and Networks Conference, Brighton, UK, June 27–30, 1995.
  6. E. Collett, Polarized Light, Fundamentals and Applications (Dekker, New York, 1993).
  7. D. H. O. Beddinghton, T. G. Ellison, X. Shon, A. S. Siddiqui, S. D. Walker, “Fully polarimetric optical time domain reflectometer with one meter spatial resolution,” in Digest of 1997 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1997), paper WL24.
  8. A. Galtarossa, M. Schiano, “Complete characterization of polarization mode dispersion in erbium doped optical amplifiers,” Electron. Lett. 28, 2143–2144 (1992).
    [CrossRef]
  9. A. Galtarossa, B. A. Schrefler, M. Schiano, C. G. Someda, A. Tommasini, G. Zavarise, “Stress distribution in optical-fiber ribbons,” IEEE Photonics Technol. Lett. 9, 354–356 (1997).
    [CrossRef]
  10. C. D. Poole, J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications, I. P. Kaminow, T. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 114–155.
  11. F. Curti, B. Daino, G. De Marchis, F. Matera, “Statistical treatment of the evolution of the principal states of polarization in single-mode fibers,” J. Lightwave Technol. 8, 1162–1166 (1990).
    [CrossRef]
  12. F. Corsi, A. Galtarossa, L. Palmieri, “Experimental investigation of polarization mode dispersion properties in single-mode fibers using a new backscattering technique,” in Digest of the 1998 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1998), paper ThR4.
  13. F. Corsi, A. Galtarossa, L. Palmieri, “Polarization mode dispersion characterization of single-mode optical fiber using backscattering technique,” J. Lightwave Technol. 16, 1832–1843 (1998).
    [CrossRef]
  14. R. Ulrich, A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt. 18, 2241–2251 (1979).
    [CrossRef] [PubMed]
  15. G. J. Foschini, C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
    [CrossRef]
  16. C. D. Poole, J. H. Winters, J. A. Nagel, “Dynamical equation for polarization dispersion,” Opt. Lett. 6, 372–374 (1991).
    [CrossRef]
  17. R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,” Electron. Lett. 28, 1772–1773 (1995).
    [CrossRef]
  18. M. O. Van Deventer, “Probability density functions of optical polarization state: theory and applications,” J. Lightwave Technol. 12, 2147–2152 (1994).
    [CrossRef]
  19. S. C. Rashleigh, “Origins and control of polarization effect in single-mode fibers,” J. Lightwave Technol. 1, 312–331 (1983).
    [CrossRef]
  20. P. K. A. Wai, C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
    [CrossRef]
  21. P. K. A. Wai, C. R. Menyuk, “Polarization decorrelation in optical fibers with randomly varying birefringence,” Opt. Lett. 19, 1517–1519 (1994).
    [CrossRef] [PubMed]
  22. P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. 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]

1998

1997

A. Galtarossa, B. A. Schrefler, M. Schiano, C. G. Someda, A. Tommasini, G. Zavarise, “Stress distribution in optical-fiber ribbons,” IEEE Photonics Technol. Lett. 9, 354–356 (1997).
[CrossRef]

1996

P. K. A. Wai, C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

1995

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,” Electron. Lett. 28, 1772–1773 (1995).
[CrossRef]

1994

M. O. Van Deventer, “Probability density functions of optical polarization state: theory and applications,” J. Lightwave Technol. 12, 2147–2152 (1994).
[CrossRef]

P. K. A. Wai, C. R. Menyuk, “Polarization decorrelation in optical fibers with randomly varying birefringence,” Opt. Lett. 19, 1517–1519 (1994).
[CrossRef] [PubMed]

1992

A. Galtarossa, M. Schiano, “Complete characterization of polarization mode dispersion in erbium doped optical amplifiers,” Electron. Lett. 28, 2143–2144 (1992).
[CrossRef]

1991

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

C. D. Poole, J. H. Winters, J. A. Nagel, “Dynamical equation for polarization dispersion,” Opt. Lett. 6, 372–374 (1991).
[CrossRef]

1990

F. Curti, B. Daino, G. De Marchis, F. Matera, “Statistical treatment of the evolution of the principal states of polarization in single-mode fibers,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

1983

S. C. Rashleigh, “Origins and control of polarization effect in single-mode fibers,” J. Lightwave Technol. 1, 312–331 (1983).
[CrossRef]

1982

1981

1979

Bebbington, D. H. O.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,” Electron. Lett. 28, 1772–1773 (1995).
[CrossRef]

Beddinghton, D. H. O.

D. H. O. Beddinghton, T. G. Ellison, X. Shon, A. S. Siddiqui, S. D. Walker, “Fully polarimetric optical time domain reflectometer with one meter spatial resolution,” in Digest of 1997 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1997), paper WL24.

Brinkmeyer, E.

Choi, S. S.

Ciprut, P.

Collett, E.

E. Collett, Polarized Light, Fundamentals and Applications (Dekker, New York, 1993).

Corsi, F.

F. Corsi, A. Galtarossa, L. Palmieri, “Polarization mode dispersion characterization of single-mode optical fiber using backscattering technique,” J. Lightwave Technol. 16, 1832–1843 (1998).
[CrossRef]

F. Corsi, A. Galtarossa, L. Palmieri, “Experimental investigation of polarization mode dispersion properties in single-mode fibers using a new backscattering technique,” in Digest of the 1998 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1998), paper ThR4.

Curti, F.

F. Curti, B. Daino, G. De Marchis, F. Matera, “Statistical treatment of the evolution of the principal states of polarization in single-mode fibers,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

Daino, B.

F. Curti, B. Daino, G. De Marchis, F. Matera, “Statistical treatment of the evolution of the principal states of polarization in single-mode fibers,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

De Marchis, G.

F. Curti, B. Daino, G. De Marchis, F. Matera, “Statistical treatment of the evolution of the principal states of polarization in single-mode fibers,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

Ellison, T. G.

D. H. O. Beddinghton, T. G. Ellison, X. Shon, A. S. Siddiqui, S. D. Walker, “Fully polarimetric optical time domain reflectometer with one meter spatial resolution,” in Digest of 1997 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1997), paper WL24.

Foschini, G. J.

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

Galtarossa, A.

F. Corsi, A. Galtarossa, L. Palmieri, “Polarization mode dispersion characterization of single-mode optical fiber using backscattering technique,” J. Lightwave Technol. 16, 1832–1843 (1998).
[CrossRef]

A. Galtarossa, B. A. Schrefler, M. Schiano, C. G. Someda, A. Tommasini, G. Zavarise, “Stress distribution in optical-fiber ribbons,” IEEE Photonics Technol. Lett. 9, 354–356 (1997).
[CrossRef]

A. Galtarossa, M. Schiano, “Complete characterization of polarization mode dispersion in erbium doped optical amplifiers,” Electron. Lett. 28, 2143–2144 (1992).
[CrossRef]

A. Galtarossa, P. Pistolato, M. Schiano, “Measurements of stress birefringence in optical cables by polarization otdr,” presented at the European Fibre Optic Communications and Networks Conference, Brighton, UK, June 27–30, 1995.

F. Corsi, A. Galtarossa, L. Palmieri, “Experimental investigation of polarization mode dispersion properties in single-mode fibers using a new backscattering technique,” in Digest of the 1998 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1998), paper ThR4.

Gisin, B.

Gisin, N.

Gleeson, L. M.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,” Electron. Lett. 28, 1772–1773 (1995).
[CrossRef]

Kim, B. Y.

Matera, F.

F. Curti, B. Daino, G. De Marchis, F. Matera, “Statistical treatment of the evolution of the principal states of polarization in single-mode fibers,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

Menyuk, C. R.

P. K. A. Wai, C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

P. K. A. Wai, C. R. Menyuk, “Polarization decorrelation in optical fibers with randomly varying birefringence,” Opt. Lett. 19, 1517–1519 (1994).
[CrossRef] [PubMed]

Nagel, J.

C. D. Poole, J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications, I. P. Kaminow, T. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 114–155.

Nagel, J. A.

Palmieri, L.

F. Corsi, A. Galtarossa, L. Palmieri, “Polarization mode dispersion characterization of single-mode optical fiber using backscattering technique,” J. Lightwave Technol. 16, 1832–1843 (1998).
[CrossRef]

F. Corsi, A. Galtarossa, L. Palmieri, “Experimental investigation of polarization mode dispersion properties in single-mode fibers using a new backscattering technique,” in Digest of the 1998 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1998), paper ThR4.

Passy, R.

Pistolato, P.

A. Galtarossa, P. Pistolato, M. Schiano, “Measurements of stress birefringence in optical cables by polarization otdr,” presented at the European Fibre Optic Communications and Networks Conference, Brighton, UK, June 27–30, 1995.

Poole, C. D.

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

C. D. Poole, J. H. Winters, J. A. Nagel, “Dynamical equation for polarization dispersion,” Opt. Lett. 6, 372–374 (1991).
[CrossRef]

C. D. Poole, J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications, I. P. Kaminow, T. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 114–155.

Prieto, F.

Rashleigh, S. C.

S. C. Rashleigh, “Origins and control of polarization effect in single-mode fibers,” J. Lightwave Technol. 1, 312–331 (1983).
[CrossRef]

Rogers, A. J.

Ross, J. N.

Schiano, M.

A. Galtarossa, B. A. Schrefler, M. Schiano, C. G. Someda, A. Tommasini, G. Zavarise, “Stress distribution in optical-fiber ribbons,” IEEE Photonics Technol. Lett. 9, 354–356 (1997).
[CrossRef]

A. Galtarossa, M. Schiano, “Complete characterization of polarization mode dispersion in erbium doped optical amplifiers,” Electron. Lett. 28, 2143–2144 (1992).
[CrossRef]

A. Galtarossa, P. Pistolato, M. Schiano, “Measurements of stress birefringence in optical cables by polarization otdr,” presented at the European Fibre Optic Communications and Networks Conference, Brighton, UK, June 27–30, 1995.

Schrefler, B. A.

A. Galtarossa, B. A. Schrefler, M. Schiano, C. G. Someda, A. Tommasini, G. Zavarise, “Stress distribution in optical-fiber ribbons,” IEEE Photonics Technol. Lett. 9, 354–356 (1997).
[CrossRef]

Schuh, R. E.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,” Electron. Lett. 28, 1772–1773 (1995).
[CrossRef]

Shon, X.

D. H. O. Beddinghton, T. G. Ellison, X. Shon, A. S. Siddiqui, S. D. Walker, “Fully polarimetric optical time domain reflectometer with one meter spatial resolution,” in Digest of 1997 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1997), paper WL24.

Siddiqui, A. S.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,” Electron. Lett. 28, 1772–1773 (1995).
[CrossRef]

D. H. O. Beddinghton, T. G. Ellison, X. Shon, A. S. Siddiqui, S. D. Walker, “Fully polarimetric optical time domain reflectometer with one meter spatial resolution,” in Digest of 1997 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1997), paper WL24.

Sikora, E. S. R.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,” Electron. Lett. 28, 1772–1773 (1995).
[CrossRef]

Simon, A.

Someda, C. G.

A. Galtarossa, B. A. Schrefler, M. Schiano, C. G. Someda, A. Tommasini, G. Zavarise, “Stress distribution in optical-fiber ribbons,” IEEE Photonics Technol. Lett. 9, 354–356 (1997).
[CrossRef]

Tommasini, A.

A. Galtarossa, B. A. Schrefler, M. Schiano, C. G. Someda, A. Tommasini, G. Zavarise, “Stress distribution in optical-fiber ribbons,” IEEE Photonics Technol. Lett. 9, 354–356 (1997).
[CrossRef]

Ulrich, R.

Van Deventer, M. O.

M. O. Van Deventer, “Probability density functions of optical polarization state: theory and applications,” J. Lightwave Technol. 12, 2147–2152 (1994).
[CrossRef]

Von der Weid, J. P.

Wai, P. K. A.

P. K. A. Wai, C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

P. K. A. Wai, C. R. Menyuk, “Polarization decorrelation in optical fibers with randomly varying birefringence,” Opt. Lett. 19, 1517–1519 (1994).
[CrossRef] [PubMed]

Walker, N. G.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,” Electron. Lett. 28, 1772–1773 (1995).
[CrossRef]

Walker, S. D.

D. H. O. Beddinghton, T. G. Ellison, X. Shon, A. S. Siddiqui, S. D. Walker, “Fully polarimetric optical time domain reflectometer with one meter spatial resolution,” in Digest of 1997 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1997), paper WL24.

Winters, J. H.

Zavarise, G.

A. Galtarossa, B. A. Schrefler, M. Schiano, C. G. Someda, A. Tommasini, G. Zavarise, “Stress distribution in optical-fiber ribbons,” IEEE Photonics Technol. Lett. 9, 354–356 (1997).
[CrossRef]

Zimmer, C. W.

Appl. Opt.

Electron. Lett.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,” Electron. Lett. 28, 1772–1773 (1995).
[CrossRef]

A. Galtarossa, M. Schiano, “Complete characterization of polarization mode dispersion in erbium doped optical amplifiers,” Electron. Lett. 28, 2143–2144 (1992).
[CrossRef]

IEEE Photonics Technol. Lett.

A. Galtarossa, B. A. Schrefler, M. Schiano, C. G. Someda, A. Tommasini, G. Zavarise, “Stress distribution in optical-fiber ribbons,” IEEE Photonics Technol. Lett. 9, 354–356 (1997).
[CrossRef]

J. Lightwave Technol.

M. O. Van Deventer, “Probability density functions of optical polarization state: theory and applications,” J. Lightwave Technol. 12, 2147–2152 (1994).
[CrossRef]

S. C. Rashleigh, “Origins and control of polarization effect in single-mode fibers,” J. Lightwave Technol. 1, 312–331 (1983).
[CrossRef]

P. K. A. Wai, C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

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

F. Curti, B. Daino, G. De Marchis, F. Matera, “Statistical treatment of the evolution of the principal states of polarization in single-mode fibers,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

F. Corsi, A. Galtarossa, L. Palmieri, “Polarization mode dispersion characterization of single-mode optical fiber using backscattering technique,” J. Lightwave Technol. 16, 1832–1843 (1998).
[CrossRef]

P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. 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]

Opt. Lett.

Other

C. D. Poole, J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications, I. P. Kaminow, T. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 114–155.

A. Galtarossa, P. Pistolato, M. Schiano, “Measurements of stress birefringence in optical cables by polarization otdr,” presented at the European Fibre Optic Communications and Networks Conference, Brighton, UK, June 27–30, 1995.

E. Collett, Polarized Light, Fundamentals and Applications (Dekker, New York, 1993).

D. H. O. Beddinghton, T. G. Ellison, X. Shon, A. S. Siddiqui, S. D. Walker, “Fully polarimetric optical time domain reflectometer with one meter spatial resolution,” in Digest of 1997 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1997), paper WL24.

F. Corsi, A. Galtarossa, L. Palmieri, “Experimental investigation of polarization mode dispersion properties in single-mode fibers using a new backscattering technique,” in Digest of the 1998 Optical Fiber Conference (Optical Society of America, Washington, D.C., 1998), paper ThR4.

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