Modulational instability in nonlocal nonlinear Kerr media

Wieslaw Krolikowski, Ole Bang, Jens Juul Rasmussen, John Wyller

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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.
    Original languageEnglish
    JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
    Volume64
    Issue number1
    Pages (from-to)016612
    ISSN1063-651X
    DOIs
    Publication statusPublished - 2001

    Bibliographical note

    Copyright (2001) American Physical Society

    Keywords

    • LATTICES
    • SCHRODINGER-EQUATION; SOLITONS
    • DYNAMICS
    • BOSE-EINSTEIN CONDENSATION

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