Abstract

This paper presents the joint characteristic function of the first- and second-order polarization-modedispersion (PMD) vectors in installed optical fibers that are almost linearly birefringent. The joint characteristic function is a Fourier transform of the joint probability density function of these PMD vectors. We regard the random fiber birefringence components as white Gaussian processes and use a Fokker-Planck method. In the limit of a large transmission distance, our joint characteristic function agrees with the previous joint characteristic function obtained for highly birefringent fibers. However, their differences can be noticeable for practical transmission distances.

© 2010 Optical Society of Korea

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  1. C. D. Poole and J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications III-A, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, CA, USA, 1997), Chapter 6.
  2. H. Kogelnik and R. M. Jopson, “Polarization-mode dispersion,” in Optical Fiber Telecommunications IVB Systems and Impairments, I. P. Kaminow and T. Li, eds. (Academic, San Diego, CA, USA, 2002), Chapter 15.
  3. H. Jang, K. Kim, J. Lee, and J. Jeong, “Theoretical investigation of first-order and second-order polarization-mode dispersion tolerance on various modulation formats in 40 Gb/s transmission systems with FEC coding,” J. Opt. Soc. Korea 13, 227-233 (2009).
    [CrossRef]
  4. G. J. Foschini and L. A. Shepp, “Closed form characteristic functions for certain random variables related to Brownian motion,” in Stochastic Analysis, Liber Amicorum for Moshe Zakai (Academic, New York, USA, 1991), pp. 169-187.
  5. G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” IEEE J. Lightwave Technol. 9, 1439-1456 (1991).
    [CrossRef]
  6. G. J. Foschini, R. M. Jopson, L. E. Nelson, and H. Kogelnik, “The statistics of PMD-induced chromatic fiber dispersion,” IEEE J. Lightwave Technol. 17, 1560-1565 (1999).
    [CrossRef]
  7. 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. 12, 293-295 (2000).
    [CrossRef]
  8. G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Statistics of second-order PMD depolarization,” IEEE J. Lightwave Technol. 19, 1882-1886 (2001).
    [CrossRef]
  9. J. P. Gordon, “Statistical properties of polarization mode dispersion,” in Polarization Mode Dispersion, A. Galtarossa and C. R. Menyuk, eds. (Springer, New York, USA, 2005), pp. 52-59.
  10. A. Galtarossa and L. Palmieri, “Measure of twist-induced circular birefringence in long single-mode fibers: theory and experiments,” IEEE J. Lightwave Technol. 20, 1149-1159 (2002).
    [CrossRef]
  11. H. Risken, The Fokker-planck Equation Methods of Solution and Applications, 2nd ed. (Springer-Verlag, New York, USA, 1996), Chapter 3, pp. 54-56.
  12. J. S. Lee, “Analysis of the polarization-mode-dispersion vector distribution for linearly birefringent optical fibers,” IEEE Photon. Technol. Lett. 19, 972-974 (2007).
    [CrossRef]
  13. J. S. Lee, “Derivation of the Foschini and Shepp’s joint-characteristic function for the first-and second-order polarization-mode-dispersion vectors using the Fokker-Planck method,” J. Opt. Soc. Korea 12, 240-243 (2008).
    [CrossRef]
  14. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, New York, USA, 2005), p. 130.
  15. Y. Tan, J. Yang, W. L. Kath, and C. M. Menyuk, “Transient evolution of the polarization-dispersion vector’s probability distribution,” J. Opt. Soc. Am. B 19, 992-1000 (2002).
    [CrossRef]
  16. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, New York, USA, 2005), Chapter 4.

2009 (1)

H. Jang, K. Kim, J. Lee, and J. Jeong, “Theoretical investigation of first-order and second-order polarization-mode dispersion tolerance on various modulation formats in 40 Gb/s transmission systems with FEC coding,” J. Opt. Soc. Korea 13, 227-233 (2009).
[CrossRef]

2008 (1)

J. S. Lee, “Derivation of the Foschini and Shepp’s joint-characteristic function for the first-and second-order polarization-mode-dispersion vectors using the Fokker-Planck method,” J. Opt. Soc. Korea 12, 240-243 (2008).
[CrossRef]

2007 (1)

J. S. Lee, “Analysis of the polarization-mode-dispersion vector distribution for linearly birefringent optical fibers,” IEEE Photon. Technol. Lett. 19, 972-974 (2007).
[CrossRef]

2005 (3)

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, New York, USA, 2005), p. 130.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, New York, USA, 2005), Chapter 4.

J. P. Gordon, “Statistical properties of polarization mode dispersion,” in Polarization Mode Dispersion, A. Galtarossa and C. R. Menyuk, eds. (Springer, New York, USA, 2005), pp. 52-59.

2002 (3)

A. Galtarossa and L. Palmieri, “Measure of twist-induced circular birefringence in long single-mode fibers: theory and experiments,” IEEE J. Lightwave Technol. 20, 1149-1159 (2002).
[CrossRef]

H. Kogelnik and R. M. Jopson, “Polarization-mode dispersion,” in Optical Fiber Telecommunications IVB Systems and Impairments, I. P. Kaminow and T. Li, eds. (Academic, San Diego, CA, USA, 2002), Chapter 15.

Y. Tan, J. Yang, W. L. Kath, and C. M. Menyuk, “Transient evolution of the polarization-dispersion vector’s probability distribution,” J. Opt. Soc. Am. B 19, 992-1000 (2002).
[CrossRef]

2001 (1)

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Statistics of second-order PMD depolarization,” IEEE J. Lightwave Technol. 19, 1882-1886 (2001).
[CrossRef]

2000 (1)

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. 12, 293-295 (2000).
[CrossRef]

1999 (1)

G. J. Foschini, R. M. Jopson, L. E. Nelson, and H. Kogelnik, “The statistics of PMD-induced chromatic fiber dispersion,” IEEE J. Lightwave Technol. 17, 1560-1565 (1999).
[CrossRef]

1997 (1)

C. D. Poole and J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications III-A, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, CA, USA, 1997), Chapter 6.

1996 (1)

H. Risken, The Fokker-planck Equation Methods of Solution and Applications, 2nd ed. (Springer-Verlag, New York, USA, 1996), Chapter 3, pp. 54-56.

1991 (2)

G. J. Foschini and L. A. Shepp, “Closed form characteristic functions for certain random variables related to Brownian motion,” in Stochastic Analysis, Liber Amicorum for Moshe Zakai (Academic, New York, USA, 1991), pp. 169-187.

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

IEEE J. Lightwave Technol. (4)

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

G. J. Foschini, R. M. Jopson, L. E. Nelson, and H. Kogelnik, “The statistics of PMD-induced chromatic fiber dispersion,” IEEE J. Lightwave Technol. 17, 1560-1565 (1999).
[CrossRef]

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Statistics of second-order PMD depolarization,” IEEE J. Lightwave Technol. 19, 1882-1886 (2001).
[CrossRef]

A. Galtarossa and L. Palmieri, “Measure of twist-induced circular birefringence in long single-mode fibers: theory and experiments,” IEEE J. Lightwave Technol. 20, 1149-1159 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J. S. Lee, “Analysis of the polarization-mode-dispersion vector distribution for linearly birefringent optical fibers,” IEEE Photon. Technol. Lett. 19, 972-974 (2007).
[CrossRef]

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. 12, 293-295 (2000).
[CrossRef]

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

Journal of the Optical Society of Korea (2)

J. S. Lee, “Derivation of the Foschini and Shepp’s joint-characteristic function for the first-and second-order polarization-mode-dispersion vectors using the Fokker-Planck method,” J. Opt. Soc. Korea 12, 240-243 (2008).
[CrossRef]

H. Jang, K. Kim, J. Lee, and J. Jeong, “Theoretical investigation of first-order and second-order polarization-mode dispersion tolerance on various modulation formats in 40 Gb/s transmission systems with FEC coding,” J. Opt. Soc. Korea 13, 227-233 (2009).
[CrossRef]

Other (7)

G. J. Foschini and L. A. Shepp, “Closed form characteristic functions for certain random variables related to Brownian motion,” in Stochastic Analysis, Liber Amicorum for Moshe Zakai (Academic, New York, USA, 1991), pp. 169-187.

C. D. Poole and J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications III-A, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, CA, USA, 1997), Chapter 6.

H. Kogelnik and R. M. Jopson, “Polarization-mode dispersion,” in Optical Fiber Telecommunications IVB Systems and Impairments, I. P. Kaminow and T. Li, eds. (Academic, San Diego, CA, USA, 2002), Chapter 15.

J. P. Gordon, “Statistical properties of polarization mode dispersion,” in Polarization Mode Dispersion, A. Galtarossa and C. R. Menyuk, eds. (Springer, New York, USA, 2005), pp. 52-59.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, New York, USA, 2005), p. 130.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, New York, USA, 2005), Chapter 4.

H. Risken, The Fokker-planck Equation Methods of Solution and Applications, 2nd ed. (Springer-Verlag, New York, USA, 1996), Chapter 3, pp. 54-56.

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