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    We present a new model for Kerr optical cavities that accurately describes multiple resonances, predicting complex phenomena like super-cavity solitons and multiple nonlinear states.

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    Area of Science:

    • Nonlinear optics
    • Quantum optics
    • Cavity optomechanics

    Background:

    • The Lugiato-Lefever equation is a standard model for describing nonlinear optical phenomena in cavities.
    • However, it typically considers only a single resonance, limiting its applicability to high-intensity or high-nonlinearity regimes.
    • Exciting multiple cavity resonances can lead to complex dynamics and novel phenomena.

    Purpose of the Study:

    • To develop a new theoretical model that extends the Lugiato-Lefever equation to include multiple resonances in Kerr optical cavities.
    • To validate the model's accuracy against the exact Ikeda map.
    • To investigate the prediction of complex nonlinear phenomena.

    Main Methods:

    • Extension of the Lugiato-Lefever equation to incorporate multiple cavity resonances.
    • Quantitative comparison with the exact Ikeda map in both stationary and dynamical regimes.
    • Analysis of model predictions for phenomena like super-cavity solitons and multiple nonlinear states.

    Main Results:

    • The proposed model shows perfect quantitative agreement with the exact Ikeda map.
    • The model accurately describes systems with a small number of resonances.
    • It successfully predicts the onset of complex phenomena, including super-cavity solitons and the coexistence of multiple nonlinear states.

    Conclusions:

    • The new model provides an accurate analytical tool for understanding nonlinear phenomena in Kerr cavities with multiple resonances.
    • It is particularly relevant for high-intensity or high-nonlinearity regimes where multiple resonances are excited.
    • This work is crucial for the future study of novel nonlinear dynamics in optical cavities.