Localized Beating between Dynamically Generated Frequencies

G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, and A. G. Vladimirov
Phys. Rev. Lett. 102, 043905 – Published 29 January 2009

Abstract

We analyze the beating between intrinsic frequencies that are simultaneously generated by a modulation (Turing) instability in a nonlinear extended system. The model studied is that of a coherently driven photonic crystal fiber cavity. Beating in the form of a slow modulation of fast intensity oscillations is found to be stable for a wide range of parameters. We find that such beating can also be localized and contain only a finite number of slow modulations. These structures consist of dips in the amplitude of the fast intensity oscillations, which can either be isolated or regularly spaced. An asymptotic analysis close to the modulation instability threshold allows us to explain this phenomenon as a manifestation of homoclinic snaking for dissipative localized structures.

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  • Received 16 May 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.043905

©2009 American Physical Society

Authors & Affiliations

G. Kozyreff1, M. Tlidi1, A. Mussot2, E. Louvergneaux2, M. Taki2, and A. G. Vladimirov3

  • 1Optique Nonlinéaire Théorique, Université libre de Bruxelles (U.L.B.), C.P. 231, Campus Plaine, B-1050 Bruxelles, Belgium
  • 2Laboratoire de Physique des Lasers, Atomes et Molécules, CNRS UMR 8523, Centre d’Etudes et de Recherche Lasers et Applications, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d’Ascq, France
  • 3Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany

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Issue

Vol. 102, Iss. 4 — 30 January 2009

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