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

Stanislav A. Derevyanko; Sergei K. Turitsyn; Dennis A. Yakushev

doi:10.1364/JOSAB.22.000743

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

Aston Institute of Photonic Technologies (AiPT)

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	743-752
Number of pages	10
Journal	Journal of the Optical Society of America B
Volume	22
Issue number	4
DOIs	https://doi.org/10.1364/JOSAB.22.000743
Publication status	Published - 2005

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

Access to Document

10.1364/JOSAB.22.000743

Fokker–Planck equation approach to the description of soliton statistics in optical fiber transmission systems
© 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.
Final published version, 175 KB

Cite this

@article{bd889a788ffb44098798c53540af6b3f,

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

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.",

keywords = "Fokker-Planck equation, optical solitons, statistical analysis, optical fibre communication, superradiance, WKB calculations ",

author = "Derevyanko, {Stanislav A.} and Turitsyn, {Sergei K.} and Yakushev, {Dennis A.}",

note = "{\textcopyright} 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.",

year = "2005",

doi = "10.1364/JOSAB.22.000743",

language = "English",

volume = "22",

pages = "743--752",

journal = "Journal of the Optical Society of America B",

issn = "0740-3224",

publisher = "The Optical Society",

number = "4",

}

TY - JOUR

T1 - Fokker-Planck equation approach to the description of soliton statistics in optical fiber transmission systems

AU - Derevyanko, Stanislav A.

AU - Turitsyn, Sergei K.

AU - Yakushev, Dennis A.

N1 - © 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.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - Fokker-Planck equation

KW - optical solitons

KW - statistical analysis

KW - optical fibre communication

KW - superradiance

KW - WKB calculations

UR - http://www.scopus.com/inward/record.url?scp=18244363592&partnerID=8YFLogxK

UR - http://www.opticsinfobase.org/josab/abstract.cfm?uri=josab-22-4-743

U2 - 10.1364/JOSAB.22.000743

DO - 10.1364/JOSAB.22.000743

M3 - Article

AN - SCOPUS:18244363592

SN - 0740-3224

VL - 22

SP - 743

EP - 752

JO - Journal of the Optical Society of America B

JF - Journal of the Optical Society of America B

IS - 4

ER -

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

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this