Dispersive Time-Delay Dynamical Systems

Alexander Pimenov, Svetlana Slepneva, Guillaume Huyet, and Andrei G. Vladimirov
Phys. Rev. Lett. 118, 193901 – Published 11 May 2017
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Abstract

We present a theoretical approach to investigate the effect of dispersion in dynamical systems commonly described by time-delay models. The introduction of a polarization equation provides a means to introduce dispersion as a distributed delay term. The expansion of this term in power series, as usually performed to study the propagation of waves in spatially extended systems, can lead to the appearance of spurious instabilities. This approach is illustrated using a long cavity laser, where in the normal dispersion regime both the experiment and theory show a stable operation, while a modulation instability, commonly referred as the Benjamin-Feir instability, is observed in the anomalous dispersion regime.

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  • Received 28 October 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.193901

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsAtomic, Molecular & Optical

Authors & Affiliations

Alexander Pimenov1,*, Svetlana Slepneva2,3, Guillaume Huyet2,3,4,5, and Andrei G. Vladimirov1,6

  • 1Weierstrass Institute, Mohrenstraße 39, Berlin 10117, Germany
  • 2Centre for Advanced Photonics and Process Analysis & Department of Physical Sciences, Cork Institute of Technology, Cork T12P928, Ireland
  • 3Tyndall National Institute, University College Cork, Lee Maltings, Dyke Parade, Cork T12R5CP, Ireland
  • 4National Research University of Information Technologies, Mechanics and Optics, 199034 Saint Petersburg, Russia
  • 5Université Côte d’Azur, CNRS, Institut de Physique de Nice, Parc Valrose, 06108 Nice cedex 2, France
  • 6Lobachevsky State University of Nizhny Novgorod, 23 Gagarina avenue, 603950 Russia

  • *Corresponding author. alexander.pimenov@wias-berlin.de

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Issue

Vol. 118, Iss. 19 — 12 May 2017

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