Modulational instability in nonlocal nonlinear Kerr media

Wieslaw Krolikowski, Ole Bang, Jens Juul Rasmussen, and John Wyller
Phys. Rev. E 64, 016612 – Published 26 June 2001
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Abstract

We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function. For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose-Einstein condensates.

  • Received 4 March 2001

DOI:https://doi.org/10.1103/PhysRevE.64.016612

©2001 American Physical Society

Authors & Affiliations

Wieslaw Krolikowski

  • Australian Photonics Cooperative Research Centre, Laser Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia

Ole Bang

  • Department of Informatics and Mathematical Modeling, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark

Jens Juul Rasmussen

  • Risø National Laboratory, Optics and Fluid Dynamics Department, OFD - 128, P.O. Box 49, DK-4000 Roskilde, Denmark

John Wyller

  • Department of Mathematical Sciences, Agricultural University of Norway, P.O. Box 5065, N-1432 Ås, Norway

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Vol. 64, Iss. 1 — July 2001

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