Abstract

Spatially resolved measurements of polarization properties of fiber optic link-such as birefringence, polarization-mode dispersion (PMD) and polarization dependent loss (PDL)-may be effectively performed using polarization sensitive reflectometric techniques. In particular, this paper focuses on polarization-OTDR and reviews its theory and applications. Special emphasis is given to the use of optical reflectometry as a tool to characterize fiber birefringence. This allows to inspect the fiber while cabled and, consequently, to test and improve the cabling process. In addition, it also allows to define reliable mathematical models, which are essential for the design of low polarization mode dispersion fibers. The application of polarization-OTDR to polarization mode dispersion and polarization dependent loss measurements is also discussed.

© 2004 IEEE

PDF Article

References

  • View by:
  • |

  1. C. G. Someda, Electromagnetic Waves, London: Chapman and Hall, 1998.
  2. D. Marcuse, "Coupled-mode theory for anisotropic optical waveguides", Bell Syst. Technol. J., vol. 54, pp. 985-995, 1975.
  3. R. Ulrich and A. Simon, "Polarization optics of twisted single-mode fibers", Appl. Opt., vol. 18, pp. 2241-2251, 1979.
  4. S. C. Rashleigh and R. Ulrich, "Polarization mode dispersion in single-mode fibers", Opt. Lett., vol. 2, pp. 60-62, 1978.
  5. H. Kogelnik, R. M. Jopson and L. E. Nelson, "Polarization-mode dispersion," in Optical Fiber Telecommunications, IV B, I. P. Kaminow, and T. Li, Eds. San Diego, CA: Academic, 2002.
  6. E. Collett, Polarized Light, Fundamentals and Applications, New York: Dekker, 1993.
  7. S. C. Rashleigh, "Origins and control of polarization effect in single-mode fibers", J. Lightwave Technol., vol. 1, pp. 312-331, 1983.
  8. G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers", J. Lightwave Technol., vol. 9, pp. 1439-1456, 1991.
  9. M. Karlsson and J. Brentel, "Autocorrelation function of the polarization-mode dispersion vector", Opt. Lett., vol. 24, pp. 939-941, 1999.
  10. G. J. Foschini, R. M. Jopson, L. E. Nelson and H. Kogelnik, "The statistics of PMD-induced chromatic fiber dispersion", J. Lightwave Technol., vol. 17, pp. 1560-1565, 1999.
  11. M. Shtaif, A. Mecozzi and J. A. Nagel, "Mean-square magnitude of all orders of polarization mode dispersion and the relation with the bandwidth of the principal states", IEEE Photon. Technol. Lett., vol. 12, pp. 53-55, 2000 .
  12. G. J. Foschini, L. E. Nelson, R. M. Jopson and H. Kogelnik, "Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion", IEEE Photon. Technol. Lett., vol. 12, pp. 293 -295, 2000.
  13. A. Bononi and A. Vannucci, "Statistics of the Jones matrix of fibers affected by polarization mode dispersion", Opt. Lett., vol. 26, pp. 675-677, 2001.
  14. A. J. Barlow, J. J. Ramskov-Hansen and D. N. Payne, "Birefringence and polarization mode-dispersion in spun single-mode fibers", Appl. Opt., vol. 20, pp. 2962 -2968, 1981.
  15. M. J. Li and D. A. Nolan, "Fiber spin-profile designs for producing fibers with low polarization mode dispersion", Opt. Lett, vol. 23, pp. 1659-1661, 1998.
  16. A. Galtarossa, P. Griggio, A. Pizzinat and L. Palmieri, "Calculation of mean differential group delay of periodically spun randomly birefringent fibers", Opt. Lett. , vol. 27, pp. 692-694, 2002.
  17. A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk and A. Galtarossa, "Influence of the model for random birefringence on the differential group delay of periodically spun fibers", IEEE Photon. Technol. Lett., vol. 15, pp. 819 -821, 2003.
  18. A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks and C. R. Menyuk, "An analytical formula for the mean differential group delay of randomly-birefringent spun fibers", J. Lightwave Technol., vol. 21, pp. 1635-1643, 2003.
  19. P. K. A. Wai and C. R. Menyuk, "Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence", J. Lightwave Technol., vol. 14, pp. 148-157, 1996.
  20. P. K. A. Wai, W. L. Kath, C. R. Menyuk and J. W. Zhang, "Non-linear polarization-mode dispersion in optical fibers with randomly varying birefringence", J. Opt. Soc. Amer. B, vol. 14, pp. 2967-2979, 1997.
  21. A. J. Rogers, "Polarization-optical time domain reflectometry: a technique for the measurement of field distributions", Appl. Opt., vol. 20, pp. 1060-1074, 1981.
  22. B. Y. Kim and S. S. Choi, "Analysis and measurement of birefringence in single-mode fiber using the backscattering method", Opt. Lett., vol. 6, pp. 578-580, 1981.
  23. J. N. Ross, "Birefringence measurement in optical fibers by polarization optical time-domain reflectometry", Appl. Opt., vol. 21, pp. 3489-3495, 1982.
  24. M. Nakazawa, "Theory of backward rayleigh scattering in polarization-maintaining single-mode fibers and its application to polarization optical time domain reflectometry", IEEE J. Quantum Electron., vol. 19, pp. 854-861, 1983.
  25. R. E. Schuh, J. G. Ellison, A. S. Siddiqui and D. H. O. Bebbington, "Polarization OTDR measurements and theoretical analysis on fibers with twist and their implications for estimation of PMD", Elett. Lett., vol. 32, pp. 387-388, 1996.
  26. F. Corsi, A. Galtarossa and L. Palmieri, "Polarization mode dispersion characterization of single-mode optical fiber using backscattering technique", J. Lightwave Technol., vol. 16, pp. 1832-1843, 1998.
  27. J. G. Ellison and A. S. Siddiqui, "A fully polarimetric optical time-domain reflectometer", IEEE Photon. Technol. Lett., vol. 10, pp. 246-248, 1998.
  28. F. Corsi, A. Galtarossa and L. Palmieri, "Beat-length characterization based on backscattering analysis in randomly perturbed single-mode fibers", J. Lightwave Technol., vol. 17, pp. 1172-1178, 1999.
  29. J. G. Ellison and A. S. Siddiqui, "Automatic matrix-based analysis method for extraction of optical fiber parameters from polarimetric optical time domain reflectometry data", J. Lightwave Technol., vol. 18, pp. 1226-1232, 2000.
  30. A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, "Measurements of beat length and perturbation length in long single-mode fibers", OSA Opt. Lett., vol. 25, pp. 384-386, 2000.
  31. A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, "Statistical characterization of fiber random birefringence", OSA Opt. Lett., vol. 25, pp. 1322-1324, 2000.
  32. A. Galtarossa, L. Palmieri, A. Pizzinat, M. Schiano and T. Tambosso, "Measurement of local beat length and differential group delay in installed single-mode fibers", J. Lightwave Technol., vol. 18, pp. 1389-1394, 2000.
  33. A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, "Measurement of birefringence correlation length in long single-mode fibers", OSA Opt. Lett., vol. 26, pp. 962-964, 2001.
  34. J. G. Ellison and A. S. Siddiqui, "Using polarimetric optical time domain reflectometry to extract spun fiber parameters", IEE Proc. Optoelectron. , vol. 148, pp. 176-182, 2001.
  35. M. Wuilpart, P. Megret, M. Blondel, A. Rogers and Y. Defosse, "Measurement of the spatial distribution of birefringence in optical fibers", IEEE Photon. Technol. Lett., vol. 13, pp. 836-838, 2001.
  36. A. Galtarossa and L. Palmieri, "Measure of twist-induced circular birefringence in long single-mode fibers: theory and experiments", J. Lightwave Technol., vol. 20, pp. 1149-1159, 2002.
  37. A. Galtarossa and L. Palmieri, "Theoretical analysis of reflectometric measurements in optical fiber links affected by polarization dependent loss", J. Lightwave Technol., vol. 21, pp. 1233-1241, 2003.
  38. B. Huttner, J. Reecht, N. Gisin, R. Passy and J. P. von der Weid, "Local birefringence measurements in single-mode fibers with coherent optical frequency-domain reflectometry", IEEE Photon. Technol. Lett., vol. 10, pp. 1458-1460, 1998.
  39. M. Wegmuller, M. Legré, P. Oberson, O. Guinnard, C. Vinegoni and N. Gisin, "Analysis of the polarization evolution in a ribbon cable using high-resolution coherent ofdr", IEEE Photon. Technol. Lett., vol. 13, pp. 145 -147, 2001.
  40. M. Wegmuller, M. Legré and N. Gisin, "Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry", J. Lightwave Technol., vol. 20, pp. 828-835, 2002.
  41. N. Zou, M. Yoshida, Y. Namihira and H. Ito, "PMD measurement based on delayed self-heterodyne ofdr and experimental comparison with itu-t round robin measurements", Electron. Lett., vol. 38, pp. 115-117, 2002.
  42. M. G. Shlyagin, A. V. Khomenko and D. Tentori, "Birefringence dispersion measurement in optical fibers by wavelength scanning", Opt. Lett., vol. 20, pp. 869-871, 1995.
  43. J. Zhang, V. A. Handerek, I. Çokgör, V. Pantelic and A. J. Rogers, "Distributed sensing of polarization mode coupling in high birefringence optical fibers using intense arbitrarily polarized coherent light", J. Lightwave Technol. , vol. 15, pp. 794-801, 1997.
  44. T. Gogolla and K. Krebber, "Distributed beat length measurement in single-mode optical fibers using stimulated brillouin-scattering and frequency-domain analysis", J. Lightwave Technol., vol. 18, pp. 320-328, 2000.
  45. W. W. Hu, K. Inagaki and Y. Mizuguchi, "Measurement of birefringence in integrated optical waveguides by use of a microwave-modulated optical wave", Opt. Lett. , vol. 26, pp. 193-195, 2001.
  46. E. A. Kuzin, J. M. E. Ayala, B. I. Escamilla and J. W. Haus, "Measurements of beat length in short low-birefringence fibers", Opt. Lett., vol. 26, pp. 1134 -1136, 2001.
  47. M. Ferrario, P. Martelli, S. Pietralunga and M. Martinelli, "Experimental observation of local birefringence and axis rotation in spun fibers on a centimetric scale", in Tech. Dig. OFC, Atlanta, GA, 2003,paper WJ3.
  48. H. Sunnerud, B. E. Olsson and P. A. Andrekson, "Technique for characterization of polarization mode dispersion accumulation along optical fibers", Elett. Lett., vol. 34, pp. 397-398, 1998.
  49. F. Corsi, A. Galtarossa and L. Palmieri, "Analytical treatment of polarization dispersion in single-mode fibers by means of backscattering signal", J. Opt. Soc. Amer. A, vol. 16, pp. 574-583, 1999.
  50. F. Corsi, A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, "Continous-wave back-reflection measurement of polarization mode dispersion", IEEE Photon. Technol. Lett., vol. 11, pp. 451-453, 1999.
  51. A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, "Single-end polarization mode dispersion measurement using back-reflected spectra through a linear polarizer", J. Lightwave Technol., vol. 17, pp. 1835-1842, 1999.
  52. B. Huttner, B. Gisin and N. Gisin, "Distributed PMD measurement with a polarization-OTDR in optical fibers", J. Lightwave Technol., vol. 17, pp. 1843-1847, 1999.
  53. H. Sunnerud, B. E. Olsson, M. Karlsson, P. A. Andrekson and J. Brentel, "Polarization-mode dispersion measurements along installed optical fibers using gated backscattered light and a polarimeter", J. Lightwave Technol., vol. 18, pp. 897-904, 2000.
  54. A. O. Kleivstul and A. S. Sudbø, "Simultaneous measurement of polarization mode dispersion in several optical fibers in parallel", Electron. Lett., vol. 37, pp. 621-623, 2001.
  55. B. L. Heffner, "Automated measurement of polarization mode dispersion using jones matrix eigenanalysis", IEEE Photon. Technol. Lett., vol. 4, pp. 1066-1069, 1992.
  56. R. M. Jopson, L. E. Nelson and H. Kogelnik, "Measurement of second-order polarization-mode dispersion vectors in optical fibers", IEEE Photon. Technol. Lett., vol. 11, pp. 1153-1155, 1999.
  57. J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization mode dispersion in optical fibers", Proc. Nat. Acad. Sci., vol. 97, pp. 4541-4550, 2000.
  58. R. C. Jones, "A new calculus for the treatment of optical systems", J. Opt. Soc. Amer., vol. 37, pp. 107-112, 1947.
  59. L. Arnold, Stochastic Differential Equations, New York: Wiley, 1974.
  60. C. W. Gardiner, Handbook of Stochastic Methods, Berlin: Springer-Verlang, 1985.
  61. B. Øksendal, Stochastic Differential Equations, Berlin: Springer-Verlang, 2000.
  62. R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson and D. H. O. Bebbington, "Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers", Elett. Lett., vol. 28, pp. 1772-1773, 1995.
  63. C. D. Poole and D. L. Favin, "Polarization-mode dispersion measurement based on transmission spectra through a polarizer", J. Lightwave Technol., vol. 12, pp. 917-929, 1994.
  64. B. L. Heffner, "Influence of optical source characteristics on the measurement of polarization-mode dispersion of highly mode-coupled fibers", Opt. Lett., vol. 21, pp. 113-115, 1996.
  65. N. J. Frigo, "A generalized geometrical representation of coupled mode theory", J. Quantum Electron., vol. 22, pp. 2131-2140, 1986.
  66. N. Gisin and B. Huttner, "Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers", Opt. Commun., vol. 142, pp. 119-125, 1997.
  67. Y. Li and A. Yariv, "Solution to the dynamical equation of polarization-mode dispersion and polarization-dependent losses", J. Opt. Soc. Amer. B, vol. 17, pp. 1821-1827, 2000.
  68. N. Gisin, "Statistics of polarization dependent losses", Opt. Commun., vol. 114, pp. 399-405, 1995.
  69. A. Mecozzi and M. Shtaif, "The statistics of polarization-dependent loss in optical communication systems", IEEE Photon. Technol. Lett., vol. 14, pp. 313-315, 2002.
  70. A. Galtarossa and L. Palmieri, "The exact statistics of polarization-dependent loss in fiber optic links", IEEE Photon. Technol. Lett., vol. 15, pp. 57-59, 2003 .

Appl. Opt. (4)

J. Lightwave Technol. (17)

F. Corsi, A. Galtarossa and L. Palmieri, "Beat-length characterization based on backscattering analysis in randomly perturbed single-mode fibers", J. Lightwave Technol., vol. 17, pp. 1172-1178, 1999.

J. G. Ellison and A. S. Siddiqui, "Automatic matrix-based analysis method for extraction of optical fiber parameters from polarimetric optical time domain reflectometry data", J. Lightwave Technol., vol. 18, pp. 1226-1232, 2000.

A. Galtarossa, L. Palmieri, A. Pizzinat, M. Schiano and T. Tambosso, "Measurement of local beat length and differential group delay in installed single-mode fibers", J. Lightwave Technol., vol. 18, pp. 1389-1394, 2000.

A. Galtarossa and L. Palmieri, "Measure of twist-induced circular birefringence in long single-mode fibers: theory and experiments", J. Lightwave Technol., vol. 20, pp. 1149-1159, 2002.

A. Galtarossa and L. Palmieri, "Theoretical analysis of reflectometric measurements in optical fiber links affected by polarization dependent loss", J. Lightwave Technol., vol. 21, pp. 1233-1241, 2003.

G. J. Foschini, R. M. Jopson, L. E. Nelson and H. Kogelnik, "The statistics of PMD-induced chromatic fiber dispersion", J. Lightwave Technol., vol. 17, pp. 1560-1565, 1999.

A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks and C. R. Menyuk, "An analytical formula for the mean differential group delay of randomly-birefringent spun fibers", J. Lightwave Technol., vol. 21, pp. 1635-1643, 2003.

P. K. A. Wai and C. R. Menyuk, "Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence", J. Lightwave Technol., vol. 14, pp. 148-157, 1996.

S. C. Rashleigh, "Origins and control of polarization effect in single-mode fibers", J. Lightwave Technol., vol. 1, pp. 312-331, 1983.

G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers", J. Lightwave Technol., vol. 9, pp. 1439-1456, 1991.

F. Corsi, A. Galtarossa and L. Palmieri, "Polarization mode dispersion characterization of single-mode optical fiber using backscattering technique", J. Lightwave Technol., vol. 16, pp. 1832-1843, 1998.

M. Wegmuller, M. Legré and N. Gisin, "Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry", J. Lightwave Technol., vol. 20, pp. 828-835, 2002.

T. Gogolla and K. Krebber, "Distributed beat length measurement in single-mode optical fibers using stimulated brillouin-scattering and frequency-domain analysis", J. Lightwave Technol., vol. 18, pp. 320-328, 2000.

A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, "Single-end polarization mode dispersion measurement using back-reflected spectra through a linear polarizer", J. Lightwave Technol., vol. 17, pp. 1835-1842, 1999.

B. Huttner, B. Gisin and N. Gisin, "Distributed PMD measurement with a polarization-OTDR in optical fibers", J. Lightwave Technol., vol. 17, pp. 1843-1847, 1999.

H. Sunnerud, B. E. Olsson, M. Karlsson, P. A. Andrekson and J. Brentel, "Polarization-mode dispersion measurements along installed optical fibers using gated backscattered light and a polarimeter", J. Lightwave Technol., vol. 18, pp. 897-904, 2000.

C. D. Poole and D. L. Favin, "Polarization-mode dispersion measurement based on transmission spectra through a polarizer", J. Lightwave Technol., vol. 12, pp. 917-929, 1994.

Opt. Lett. (10)

B. L. Heffner, "Influence of optical source characteristics on the measurement of polarization-mode dispersion of highly mode-coupled fibers", Opt. Lett., vol. 21, pp. 113-115, 1996.

E. A. Kuzin, J. M. E. Ayala, B. I. Escamilla and J. W. Haus, "Measurements of beat length in short low-birefringence fibers", Opt. Lett., vol. 26, pp. 1134 -1136, 2001.

A. Bononi and A. Vannucci, "Statistics of the Jones matrix of fibers affected by polarization mode dispersion", Opt. Lett., vol. 26, pp. 675-677, 2001.

M. G. Shlyagin, A. V. Khomenko and D. Tentori, "Birefringence dispersion measurement in optical fibers by wavelength scanning", Opt. Lett., vol. 20, pp. 869-871, 1995.

M. Karlsson and J. Brentel, "Autocorrelation function of the polarization-mode dispersion vector", Opt. Lett., vol. 24, pp. 939-941, 1999.

S. C. Rashleigh and R. Ulrich, "Polarization mode dispersion in single-mode fibers", Opt. Lett., vol. 2, pp. 60-62, 1978.

A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, "Measurement of birefringence correlation length in long single-mode fibers", OSA Opt. Lett., vol. 26, pp. 962-964, 2001.

A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, "Measurements of beat length and perturbation length in long single-mode fibers", OSA Opt. Lett., vol. 25, pp. 384-386, 2000.

A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, "Statistical characterization of fiber random birefringence", OSA Opt. Lett., vol. 25, pp. 1322-1324, 2000.

B. Y. Kim and S. S. Choi, "Analysis and measurement of birefringence in single-mode fiber using the backscattering method", Opt. Lett., vol. 6, pp. 578-580, 1981.

Other (39)

M. Nakazawa, "Theory of backward rayleigh scattering in polarization-maintaining single-mode fibers and its application to polarization optical time domain reflectometry", IEEE J. Quantum Electron., vol. 19, pp. 854-861, 1983.

R. E. Schuh, J. G. Ellison, A. S. Siddiqui and D. H. O. Bebbington, "Polarization OTDR measurements and theoretical analysis on fibers with twist and their implications for estimation of PMD", Elett. Lett., vol. 32, pp. 387-388, 1996.

J. G. Ellison and A. S. Siddiqui, "Using polarimetric optical time domain reflectometry to extract spun fiber parameters", IEE Proc. Optoelectron. , vol. 148, pp. 176-182, 2001.

M. Wuilpart, P. Megret, M. Blondel, A. Rogers and Y. Defosse, "Measurement of the spatial distribution of birefringence in optical fibers", IEEE Photon. Technol. Lett., vol. 13, pp. 836-838, 2001.

B. Huttner, J. Reecht, N. Gisin, R. Passy and J. P. von der Weid, "Local birefringence measurements in single-mode fibers with coherent optical frequency-domain reflectometry", IEEE Photon. Technol. Lett., vol. 10, pp. 1458-1460, 1998.

M. Wegmuller, M. Legré, P. Oberson, O. Guinnard, C. Vinegoni and N. Gisin, "Analysis of the polarization evolution in a ribbon cable using high-resolution coherent ofdr", IEEE Photon. Technol. Lett., vol. 13, pp. 145 -147, 2001.

H. Kogelnik, R. M. Jopson and L. E. Nelson, "Polarization-mode dispersion," in Optical Fiber Telecommunications, IV B, I. P. Kaminow, and T. Li, Eds. San Diego, CA: Academic, 2002.

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

C. G. Someda, Electromagnetic Waves, London: Chapman and Hall, 1998.

D. Marcuse, "Coupled-mode theory for anisotropic optical waveguides", Bell Syst. Technol. J., vol. 54, pp. 985-995, 1975.

P. K. A. Wai, W. L. Kath, C. R. Menyuk and J. W. Zhang, "Non-linear polarization-mode dispersion in optical fibers with randomly varying birefringence", J. Opt. Soc. Amer. B, vol. 14, pp. 2967-2979, 1997.

M. Shtaif, A. Mecozzi and J. A. Nagel, "Mean-square magnitude of all orders of polarization mode dispersion and the relation with the bandwidth of the principal states", IEEE Photon. Technol. Lett., vol. 12, pp. 53-55, 2000 .

G. J. Foschini, L. E. Nelson, R. M. Jopson and H. Kogelnik, "Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion", IEEE Photon. Technol. Lett., vol. 12, pp. 293 -295, 2000.

M. J. Li and D. A. Nolan, "Fiber spin-profile designs for producing fibers with low polarization mode dispersion", Opt. Lett, vol. 23, pp. 1659-1661, 1998.

A. Galtarossa, P. Griggio, A. Pizzinat and L. Palmieri, "Calculation of mean differential group delay of periodically spun randomly birefringent fibers", Opt. Lett. , vol. 27, pp. 692-694, 2002.

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk and A. Galtarossa, "Influence of the model for random birefringence on the differential group delay of periodically spun fibers", IEEE Photon. Technol. Lett., vol. 15, pp. 819 -821, 2003.

J. Zhang, V. A. Handerek, I. Çokgör, V. Pantelic and A. J. Rogers, "Distributed sensing of polarization mode coupling in high birefringence optical fibers using intense arbitrarily polarized coherent light", J. Lightwave Technol. , vol. 15, pp. 794-801, 1997.

W. W. Hu, K. Inagaki and Y. Mizuguchi, "Measurement of birefringence in integrated optical waveguides by use of a microwave-modulated optical wave", Opt. Lett. , vol. 26, pp. 193-195, 2001.

N. Zou, M. Yoshida, Y. Namihira and H. Ito, "PMD measurement based on delayed self-heterodyne ofdr and experimental comparison with itu-t round robin measurements", Electron. Lett., vol. 38, pp. 115-117, 2002.

J. G. Ellison and A. S. Siddiqui, "A fully polarimetric optical time-domain reflectometer", IEEE Photon. Technol. Lett., vol. 10, pp. 246-248, 1998.

A. O. Kleivstul and A. S. Sudbø, "Simultaneous measurement of polarization mode dispersion in several optical fibers in parallel", Electron. Lett., vol. 37, pp. 621-623, 2001.

B. L. Heffner, "Automated measurement of polarization mode dispersion using jones matrix eigenanalysis", IEEE Photon. Technol. Lett., vol. 4, pp. 1066-1069, 1992.

R. M. Jopson, L. E. Nelson and H. Kogelnik, "Measurement of second-order polarization-mode dispersion vectors in optical fibers", IEEE Photon. Technol. Lett., vol. 11, pp. 1153-1155, 1999.

J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization mode dispersion in optical fibers", Proc. Nat. Acad. Sci., vol. 97, pp. 4541-4550, 2000.

R. C. Jones, "A new calculus for the treatment of optical systems", J. Opt. Soc. Amer., vol. 37, pp. 107-112, 1947.

L. Arnold, Stochastic Differential Equations, New York: Wiley, 1974.

C. W. Gardiner, Handbook of Stochastic Methods, Berlin: Springer-Verlang, 1985.

B. Øksendal, Stochastic Differential Equations, Berlin: Springer-Verlang, 2000.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson and D. H. O. Bebbington, "Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers", Elett. Lett., vol. 28, pp. 1772-1773, 1995.

M. Ferrario, P. Martelli, S. Pietralunga and M. Martinelli, "Experimental observation of local birefringence and axis rotation in spun fibers on a centimetric scale", in Tech. Dig. OFC, Atlanta, GA, 2003,paper WJ3.

H. Sunnerud, B. E. Olsson and P. A. Andrekson, "Technique for characterization of polarization mode dispersion accumulation along optical fibers", Elett. Lett., vol. 34, pp. 397-398, 1998.

F. Corsi, A. Galtarossa and L. Palmieri, "Analytical treatment of polarization dispersion in single-mode fibers by means of backscattering signal", J. Opt. Soc. Amer. A, vol. 16, pp. 574-583, 1999.

F. Corsi, A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, "Continous-wave back-reflection measurement of polarization mode dispersion", IEEE Photon. Technol. Lett., vol. 11, pp. 451-453, 1999.

N. J. Frigo, "A generalized geometrical representation of coupled mode theory", J. Quantum Electron., vol. 22, pp. 2131-2140, 1986.

N. Gisin and B. Huttner, "Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers", Opt. Commun., vol. 142, pp. 119-125, 1997.

Y. Li and A. Yariv, "Solution to the dynamical equation of polarization-mode dispersion and polarization-dependent losses", J. Opt. Soc. Amer. B, vol. 17, pp. 1821-1827, 2000.

N. Gisin, "Statistics of polarization dependent losses", Opt. Commun., vol. 114, pp. 399-405, 1995.

A. Mecozzi and M. Shtaif, "The statistics of polarization-dependent loss in optical communication systems", IEEE Photon. Technol. Lett., vol. 14, pp. 313-315, 2002.

A. Galtarossa and L. Palmieri, "The exact statistics of polarization-dependent loss in fiber optic links", IEEE Photon. Technol. Lett., vol. 15, pp. 57-59, 2003 .

Cited By

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