Browse > Article
http://dx.doi.org/10.3807/JOSK.2010.14.3.228

Joint-characteristic Function of the First- and Second-order Polarization-mode-dispersion Vectors in Linearly Birefringent Optical Fibers  

Lee, Jae-Seung (Department of Electronic Engineering, Kwangwoon University)
Publication Information
Journal of the Optical Society of Korea / v.14, no.3, 2010 , pp. 228-234 More about this Journal
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.
Keywords
Polarization mode dispersion; Optical fiber; Optical fiber transmission; Optical communication;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
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).   과학기술학회마을   DOI   ScienceOn
2 G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, New York, USA, 2005), p. 130.
3 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).   DOI   ScienceOn
4 G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, New York, USA, 2005), Chapter 4.
5 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.
6 G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” IEEE J. Lightwave Technol. 9, 1439-1456 (1991).   DOI   ScienceOn
7 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).   DOI   ScienceOn
8 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).   DOI   ScienceOn
9 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).   DOI   ScienceOn
10 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.
11 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).   DOI   ScienceOn
12 H. Risken, The Fokker-planck Equation Methods of Solution and Applications, 2nd ed. (Springer-Verlag, New York, USA, 1996), Chapter 3, pp. 54-56.
13 J. S. Lee, “Analysis of the polarization-mode-dispersion vector distribution for linearly birefringent optical fibers,” IEEE Photon. Technol. Lett. 19, 972-974 (2007).   DOI   ScienceOn
14 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).   과학기술학회마을   DOI   ScienceOn
15 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.
16 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.