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    Area of Science:

    • Nonlinear Optics
    • Optical Cavities
    • Dynamical Systems

    Background:

    • Passive optical cavities exhibit complex dynamics.
    • Modulational instability is a key phenomenon in nonlinear systems.
    • The Ikeda map models nonlinear optical phenomena.

    Purpose of the Study:

    • Investigate modulational instability in inhomogeneous passive cavities.
    • Analyze the generation of temporal patterns.
    • Compare analytical and numerical findings with existing models.

    Main Methods:

    • Modeling the system using the Ikeda map.
    • Applying Floquet theory for analytical solutions.
    • Performing numerical simulations of the Ikeda map.

    Main Results:

    • Identified parametric instabilities arising from cavity boundary conditions and modulated fiber dispersion.
    • Observed the generation of simple and period-doubled temporal patterns.
    • Validated analytical results with numerical simulations.

    Conclusions:

    • The Ikeda map effectively models temporal pattern generation in passive cavities.
    • Floquet theory provides accurate analytical predictions.
    • Highlighted limitations of the mean-field Lugiato-Lefever model for inhomogeneous systems.