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Extended and localized Hopf-Turing mixed-mode in non-instantaneous Kerr cavities.

M Ouali, S Coulibaly, M Taki

    Optics Express
    |April 7, 2017
    PubMed
    Summary

    Researchers found stable mixed-mode solutions in a ring cavity with a non-instantaneous Kerr medium. These solutions exhibit spatio-temporal dynamics, appearing as either extended or localized patterns.

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    Area of Science:

    • Nonlinear optics
    • Optical cavity dynamics
    • Complex systems

    Background:

    • Ring cavities are fundamental in nonlinear optics.
    • Non-instantaneous Kerr media exhibit delayed nonlinear responses.
    • Modulational instability and self-pulsing are key phenomena in optical systems.

    Purpose of the Study:

    • Investigate spatio-temporal dynamics in a driven ring cavity with a non-instantaneous Kerr medium.
    • Identify and characterize stable mixed-mode solutions.
    • Analyze the transition from stationary to mixed-mode solutions.

    Main Methods:

    • Numerical simulations of the ring cavity dynamics.
    • Analysis of Turing (modulational) instability.
    • Study of Andronov-Hopf bifurcations (self-pulsing).

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  • Construction of bifurcation diagrams.

    • Main Results:

    • Existence of stable mixed-mode solutions, both extended and localized.
    • Mixed-mode solutions arise from the interaction of Turing instability and self-pulsing.
    • Numerical description of the transition to mixed-mode solutions.
    • Demonstration of stable, spatially localized, time-periodic oscillations.

    Conclusions:

    • Stable mixed-mode solutions, including localized ones, exist in this system.
    • The interplay between instabilities governs the observed dynamics.
    • Bifurcation analysis provides a framework for understanding solution transitions.