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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 29, Iss. 8 — Aug. 1, 2012
  • pp: 1930–1936

Modulation instability, Cherenkov radiation, and Fermi–Pasta–Ulam recurrence

Jose M. Soto-Crespo, Adrian Ankiewicz, Natasha Devine, and Nail Akhmediev  »View Author Affiliations

JOSA B, Vol. 29, Issue 8, pp. 1930-1936 (2012)

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We study, numerically, the influence of third-order dispersion (TOD) on modulation instability (MI) in optical fibers described by the extended nonlinear Schrödinger equation. We consider two MI scenarios. One starts with a continuous wave (CW) with a small amount of white noise, while the second one starts with a CW with a small harmonic perturbation at the highest value of the growth rate. In each case, the MI spectra show an additional spectral feature that is caused by Cherenkov radiation. We give an analytic expression for its frequency. Taking a single frequency of modulation instead of a noisy CW leads to the Fermi–Pasta–Ulam (FPU) recurrence dynamics. In this case, the radiation spectral feature multiplies due to the four-wave mixing process. FPU recurrence dynamics is quite pronounced at small values of TOD, disappears at intermediate values, and is restored again at high TOD when the Cherenkov frequency enters the MI band. Our results may lead to a better understanding of the role of TOD in optical fibers.

© 2012 Optical Society of America

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(190.3100) Nonlinear optics : Instabilities and chaos
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Nonlinear Optics

Original Manuscript: May 7, 2012
Manuscript Accepted: June 3, 2012
Published: July 13, 2012

Jose M. Soto-Crespo, Adrian Ankiewicz, Natasha Devine, and Nail Akhmediev, "Modulation instability, Cherenkov radiation, and Fermi–Pasta–Ulam recurrence," J. Opt. Soc. Am. B 29, 1930-1936 (2012)

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