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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 4 — Apr. 1, 2007
  • pp: 773–787

Fundamental laws of parametric gain in periodic dispersion-managed optical links

Paolo Serena, Alberto Bononi, and Alessandra Orlandini  »View Author Affiliations

JOSA B, Vol. 24, Issue 4, pp. 773-787 (2007)

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A general theory of the parametric gain of amplified spontaneous emission (ASE) noise in periodic dispersion-managed (DM) optical links is presented, based on a linearization of the nonlinear Schrödinger equation around a constant-wave input signal. Closed-form expressions are presented of the in-phase and quadrature ASE power spectral densities (PSDs), valid in the limit of infinitely many spans, for a limited total cumulated nonlinear phase and in-line dispersion, a typical case for nonsoliton systems. PSDs are shown to solely depend on the in-line cumulated dispersion and on the so-called DM kernel. Kernel expressions for both typical terrestrial and submarine DM links are provided. By Taylor expanding the kernel in frequency, we introduce a definition of DM map strength that is more appropriate for limited nonlinear phase DM systems with lossy transmission fibers than the standard definition for soliton systems. Various important special cases of PSDs are discussed in detail. Novel insights, to our knowledge, into the effect of a postdispersion-compensating fiber on such PSDs are included. Finally, examples of application of the PSD formulas to the performance evaluation of both on–off keying and differential phase keying modulated systems are provided.

© 2007 Optical Society of America

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

ToC Category:
Fiber Optics and Optical Communications

Original Manuscript: September 13, 2006
Revised Manuscript: November 29, 2006
Manuscript Accepted: December 4, 2006
Published: March 15, 2007

Paolo Serena, Alberto Bononi, and Alessandra Orlandini, "Fundamental laws of parametric gain in periodic dispersion-managed optical links," J. Opt. Soc. Am. B 24, 773-787 (2007)

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  2. R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, "Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization," J. Lightwave Technol. 20, 389-400 (2002). [CrossRef]
  3. B. Xu and M. Brandt-Pearce, "Optical fiber parametric-gain-induced noise coloring and amplification by modulated signals," J. Opt. Soc. Am. B 21, 499-513 (2004). [CrossRef]
  4. P. Serena, A. Bononi, J. C. Antona, and S. Bigo, "Parametric gain in the strongly nonlinear regime and its impact on 10-Gb/s NRZ systems with forward-error correction," J. Lightwave Technol. 23, 2352-2363 (2005). [CrossRef]
  5. A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "New analytical results on fiber parametric gain and its effects on ASE noise," IEEE Photon. Technol. Lett. 9, 535-537 (1997). [CrossRef]
  6. R. Hui, M. O'Sullivan, A. Robinson, and M. Taylor, "Modulation instability and its impact in multispan optical amplified IMDD systems: theory and experiments," J. Lightwave Technol. 15, 1071-1082 (1997). [CrossRef]
  7. C. Lorattanasane and K. Kikuchi, "Parametric instability of optical amplifier noise in long-distance optical transmission systems," IEEE J. Quantum Electron. 33, 1068-1074 (1997). [CrossRef]
  8. M. Karlsson, "Modulation instability in lossy optical fibers," J. Opt. Soc. Am. B 12, 2071-2078 (1995).
  9. F. Matera, A. Mecozzi, M. Romagnoli, and M. Settembre, "Sideband instability induced by periodic power variation in long-distance fiber links," Opt. Lett. 18, 1499-1501 (1993). [CrossRef] [PubMed]
  10. N. J. Smith and N. J. Doran, "Modulation instabilities in fibers with periodic dispersion management," Opt. Lett. 21, 570-572 (1996). [CrossRef] [PubMed]
  11. M. Midrio, P. Franco, and M. Romagnoli, "Noise statistics in transmission systems with grating dispersion compensation," J. Opt. Soc. Am. B 15, 2748-2756 (1998). [CrossRef]
  12. E. Ciaramella and M. Tamburrini, "Modulation instability in long amplified links with strong dispersion compensation," IEEE Photon. Technol. Lett. 11, 1608-1610 (1999). [CrossRef]
  13. C. J. McKinstrie, S. Radic, and A. R. Chaplyvy, "Parametric amplifiers driven by two pump waves," IEEE J. Sel. Top. Quantum Electron. 8, 538-547 (2002). [CrossRef]
  14. J. M. Chávez Boggio, S. Tenenbaum, and H. L. Fragnito, "Amplification of broadband noise pumped by two lasers in optical fibers," J. Opt. Soc. Am. B 18, 1428-1435 (2001). [CrossRef]
  15. F. Consolandi, C. De Angelis, A.-D. Capobianco, and A. Tonello, "Parametric gain in fiber systems with periodic dispersion management," Opt. Commun. 208, 309-320 (2002). [CrossRef]
  16. P. Serena, A. Orlandini, and A. Bononi, "Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightwave Technol. 24, 2026-2037 (2006). [CrossRef]
  17. M. J. Ablowitz and T. Hirooka, "Managing nonlinearity in strongly dispersion-managed optical pulse transmission," J. Opt. Soc. Am. B 19, 425-439 (2002). [CrossRef]
  18. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (Mc-Graw-Hill, 1991).
  19. D. Zwillinger, Handbook of Differential Equations (Academic, 1998).
  20. H. A. Haus, "Quantum noise in a solitonlike repeater system," J. Opt. Soc. Am. B 8, 1122-1126 (1991). [CrossRef]
  21. L. C. Evans, "An introduction to stochastic differential equations," http://math.berkeley/edu/~evans/.
  22. C.-T. Chen, Linear System Theory and Design (Holt-Saunders, 1984), pp. 49-50.
  23. J.-P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990). [CrossRef] [PubMed]
  24. J. C. Bronski and J. N. Kutz, "Modulation stability of plane waves in nonreturn-to-zero communications systems with dispersion management," Opt. Lett. 21, 937-939 (1996). [CrossRef] [PubMed]
  25. M. J. Ablowitz, T. Hirooka, and T. Inoue, "Higher-order analysis of dispersion-managed transmission systems: solutions and their characteristics," J. Opt. Soc. Am. B 19, 2876-2885 (2002). [CrossRef]
  26. A comparison of DM systems with different span lengths at a constant nonlinear phase can make sense, for instance, in a metropolitan network environment where, although the fiber links are short, a big lumped loss, such as a demultiplexer or an add-drop module, is inserted at the end of each span connecting two consecutive nodes.
  27. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, 1999).
  28. A. Bononi, P. Serena, J.-C. Antona, and S. Bigo, "Implications of nonlinear interactions of signal and noise in low-OSNR transmission systems with FEC," in Optical Fiber Communication Conference, OSA Trends in Optics and Photonics Series (Optical Society of America, 2005), paper OTHW5.
  29. H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003). [CrossRef]
  30. A. Orlandini, P. Serena, and A. Bononi, "An alternative analysis of nonlinear phase noise impact on DPSK systems," in Proceedings of the IEEE European Conference on Optical Communication (IEEE, 2006), paper Th3.2.6. [CrossRef]
  31. K.-P. Ho, "Probability density of nonlinear phase noise," J. Opt. Soc. Am. B 20, 1875-1879 (2003). [CrossRef]
  32. E. Ciaramella, "Effect of non-uniform chromatic dispersion fibre link in determining system limitations due to four wave mixing," Electron. Lett. 34, 202-204 (1998). [CrossRef]
  33. M. J. Ablowitz and J. Moeser, "Dispersion management for randomly varying optical fibers," Opt. Lett. 8, 821-823 (2004). [CrossRef]
  34. G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "Parametric gain in multiwavelength systems: a new approach to noise enhancement analysis," IEEE Photon. Technol. Lett. 9, 1135-1137 (1999). [CrossRef]

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