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    Linear-stability analysis for spatiotemporal modulation instability (MI) is equivalent to coupled-wave analysis of parametric amplification. This reveals a two-wave structure and offers insights into high-order dispersion effects in MIs.

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    Area of Science:

    • Nonlinear Optics
    • Wave Physics

    Background:

    • Spatiotemporal modulation instability (MI) is typically analyzed using linear-stability analysis of steady-state solutions.
    • This method treats MI as instabilities arising from weak harmonic perturbations.

    Purpose of the Study:

    • To demonstrate the physical equivalence between linear-stability analysis of MI and coupled-wave analysis.
    • To explore the role of high-order dispersion in spatiotemporal MI.

    Main Methods:

    • Developed a space-evolution transfer matrix to link MI models with coupled-wave descriptions.
    • Utilized complex harmonic trial functions within the standard MI framework.
    • Analyzed the phase dynamics of coupled off-axis waves.

    Main Results:

    • Established the physical equivalence between linear-stability analysis of spatiotemporal MI and off-axis parametric amplification.
    • Showed that harmonic trial functions correspond to coupled, exponentially growing and decreasing off-axis waves.
    • Identified new spatiotemporal MI effects driven by high-order dispersion.

    Conclusions:

    • The coupled-wave perspective provides a clearer physical understanding of spatiotemporal MI.
    • High-order dispersion significantly influences MI dynamics and can induce novel effects.
    • The developed method offers a transparent approach for incorporating high-order dispersion into MI gain calculations.