Mathematical models of higher-order polarization mode dispersion for a silica anisotropic optical waveguide
M.R. Musakaev, A.Kh. Sultanov

Full text of article: Russian language.

Abstract:
The comparative analysis of Jones-matrices-based mathematical models of higher-order polarization mode dispersion is presented. It is shown that the limited exponential model and the Taylor-series-based model do not give a good approximation of higher-order polarization mode dispersion due to the infinite ratio of the dispersion vector module to the frequency. The real-fiber polarization mode dispersion can be described more accurately using an analytical model that describes the dispersion vector as the closed-curve rotation in the Stokes space and a model in which the frequency-dependent and independent matrix elements are treated independently . In addition, an analytical expression of pulse broadening, often chosen as a quality parameter for communication systems, can be obtained with a model of the dispersion rotation in the Stokes space. The shortcoming of all the models analyzed is that they give a purely mathematical approximate description without regard for the physics of the process.

Key words:
optical waveguide, anisotropy, polarization mode dispersion (PMD), Jones matrix, Taylor series, Stokes space.

References:

  1. Rashleigh, S.C. Polarization mode dispersion in single-mode fibers / S.C. Rashleigh, R. Ulrich // Opt. Lett. – 1978. – V. 3. – P. 60-63.
  2. Matera, F. Field demonstration of 40 Gb/s soliton transmission with alternate polarizations / F. Matera, M. Settembre, M. Tamburrini, F. Favre, D. Le Guen, T. Georges, M. Henry, G. Michaud, P. Franco, A. Shiffini, M. Romagnoli, M. Guglielmucci, S. Casceli // J. Lightwave Technol. – 1999. – V. 17. – P. 2225-2234.
  3. Kolltveit, E. Single wavelength 40 Gb/s soliton field transmission experiment over 400 km of installed fiber / E. Kollweit, P.A. Andrekson, J. Brentel, B.E. Olsson, B. Bakhshi, J. Hansryd, P.O. Hedekvist, M. Karlsson, H. Sunnerud, J. Li. // Electron. Lett. – 1999. – V. 35. – P. 75-76.
  4. Sunnerud, H. Polarization-mode dispersion in high-speed fiber-optic transmission systems / H. Sunnerud, M. Karlsson, C. Xie, P.A. Andrekson // J. Lightwave Technol. – 2002. – V. 20. – P. 2204-2219.
  5. Lin, Q. Polarization mode dispersion-induced fluctuations during Raman amplifications in optical fibers / Q. Lin, Govind P. Agrawal // Opt. Lett. – 2002. – V. 27. – P. 2194-2196.
  6. Poole, C.D. Phenomenological approach to polarization dispersion in long single-mode fibres / C.D. Poole, R.E. Wagner // Electron. Lett. – 1986. – V. 22. – P. 1029-1030.
  7. Gerrard, A. Introduction to matrix methods in optics / A. Gerrard, J.M. Burch. – London: A. Wiley-Interscience pub., John Wiley & Sons, 1975. – 344 p.
  8. Foschini, G.J. Statistical theory of polarization dispersion in single mode fibers / G.J. Foschini, C.D. Poole // J. Lightwave Technol. – 1991. – V. 9. – P. 1439-1456.
  9. Foschini, G.J. The statistics of PMD-induced chromatic fiber dispersion / G.J. Foschini, R.M. Jopson, L.E. Nelson, H. Kogelnik // J. Lightwave Technol. – 1999. – V. 17. – P. 1560-1565.
  10. Karlsson, M. Polarization mode dispersion-induced pulse broadening in optical fibers / M. Karlsson // Opt. Lett. – 1998. – V. 23. – P. 688-690.
  11. Ibragimov, E. Statistical correlation between first and second-order PMD / E. Ibragimov, G. Shtengel, S. Suh // J. Lightwave Technol. – 2002. – V. 20. – P. 586-590.
  12. Bruyère, F. Impact of first and second order PMD in optical digital transmission systems / F. Bruyère // Opt. Fiber Technol. – 1996. – V. 2. – P. 269-280.
  13. Kogelnik, H. Jones matrix for second order polarization mode dispersion / H. Kogelnik, L.E. Nelson, J.P. Gordon, R.M. Jopson // Opt. Lett. – 2000. – V. 25. – P. 19-21.
  14. Penninckx, D. Jones matrix of polarization mode dispersion / D. Penninckx, V. Morenas // Opt. Lett. – 1999. – V. 24. – P. 875-877.
  15. Eyal, A. Representation of second order polarization mode dispersion / A. Eyal, W.K. Marshall, M. Tur, Y. Yariv // Electron. Lett. – 1999. – V. 35. – P. 1658-1659.
  16. Eyal, A. Statistical determination of the length dependence of high-order polarization-mode dispersion / A. Eyal, Y. Li, W.K. Marshall, A. Yariv // Opt. Lett. – 2000. – V. 25. – P. 875-877.
  17. Forestieri, E. Exact evaluation of the Jones matrix of a fiber in the presence of polarization mode dispersion of any order / E. Forestrieri, L. Vincetti // J. Lightwave Technol. – 2001. – V. 19. – P. 1898-1909.
  18. Orlandini, A. A simple and useful model for Jones matrix to evaluate higher order polarization mode dispersion effects / A. Orlandini, L. Vincetti // IEEE Photon. Technol. Lett. – 2001. – V. 13. – P. 1176-1178.
  19. Orlandini, A. Analytical evaluation of optical system impairments caused by high-order polarization mode dispersion effects / A. Orlandini, L. Vincetti // Microwave Optical Technol. Lett. – 2001. – V. 31. – P. 449-453.
  20. Heismann, F. Accurate Jones matrix expansion for all orders of polarization mode dispersion / F. Heismann // Opt. Lett. – 2003. – V. 28. – P. 2013-2015.
  21. Ferreira, M.F. Polarization mode dispersion in high-speed optical communication systems / M.F. Ferreira, S.V. Latas, M.H. Sousa, A.N. Pinto, J.F. Rocha, P.S. André, N.J. Muga, R.N. Nogueira, J.E. Machado // Fiber Integ. Opt. – 2005. – V. 24. – P. 261-28.
© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20