Fokker-Planck equation approach to the description of soliton statistics in optical fiber transmission systems

Stanislav A. Derevyanko*, Sergei K. Turitsyn, Dennis A. Yakushev

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We derive rigorously the Fokker-Planck equation that governs the statistics of soliton parameters in optical transmission lines in the presence of additive amplifier spontaneous emission. We demonstrate that these statistics are generally non-Gaussian. We present exact marginal probability-density functions for soliton parameters for some cases. A WKB approach is applied to describe the tails of the probability-density functions.

Original languageEnglish
Pages (from-to)743-752
Number of pages10
JournalJournal of the Optical Society of America B
Volume22
Issue number4
DOIs
Publication statusPublished - 2005

Fingerprint

Fokker-Planck equation
probability density functions
solitary waves
optical fibers
statistics
spontaneous emission
transmission lines
amplifiers

Bibliographical note

© 2005 Optical Society of America
This paper was published in Journal of the Optical Society of America B and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/josab/abstract.cfm?uri=josab-22-4-743. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Keywords

  • Fokker-Planck equation
  • optical solitons
  • statistical analysis
  • optical fibre communication
  • superradiance
  • WKB calculations

Cite this

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abstract = "We derive rigorously the Fokker-Planck equation that governs the statistics of soliton parameters in optical transmission lines in the presence of additive amplifier spontaneous emission. We demonstrate that these statistics are generally non-Gaussian. We present exact marginal probability-density functions for soliton parameters for some cases. A WKB approach is applied to describe the tails of the probability-density functions.",
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Fokker-Planck equation approach to the description of soliton statistics in optical fiber transmission systems. / Derevyanko, Stanislav A.; Turitsyn, Sergei K.; Yakushev, Dennis A.

In: Journal of the Optical Society of America B, Vol. 22, No. 4, 2005, p. 743-752.

Research output: Contribution to journalArticle

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AU - Derevyanko, Stanislav A.

AU - Turitsyn, Sergei K.

AU - Yakushev, Dennis A.

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