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Analytical expression for Risken-Nummedal-Graham-Haken instability threshold in quantum cascade lasers.

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    A new analytical expression determines the threshold for Risken-Nummedal-Graham-Haken (RNGH) multimode instability in quantum cascade lasers (QCLs). This model aids in analyzing QCL dynamics and predicting instability thresholds, aligning with experimental findings.

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    Area of Science:

    • Quantum optics
    • Semiconductor lasers
    • Solid-state physics

    Background:

    • Quantum cascade lasers (QCLs) are crucial for mid-infrared applications.
    • Understanding multimode instabilities is key to optimizing QCL performance.
    • The Risken-Nummedal-Graham-Haken (RNGH) instability affects laser dynamics.

    Purpose of the Study:

    • Derive a closed-form expression for the RNGH instability threshold in Fabry-Pérot (FP) cavity QCLs.
    • Develop a versatile analytical tool for QCL dynamic behavior analysis.
    • Provide a method for practical estimation of the RNGH instability threshold.

    Main Methods:

    • Developed a theoretical model for FP cavity lasers including carrier coherence and population gratings.
    • Incorporated carrier diffusion effects on grating relaxation.
    • Applied second-order bi-orthogonal perturbation theory to analyze the RNGH instability threshold.
    • Validated the analytical solution through numerical simulations.

    Main Results:

    • Obtained a simple, closed-form analytical expression for the RNGH instability threshold.
    • The model accurately predicts a low RNGH instability threshold in QCLs.
    • Analytical results show excellent agreement with numerical simulations and existing experimental data.

    Conclusions:

    • The derived analytical expression offers a practical tool for QCL analysis.
    • The model's predictions of low RNGH instability thresholds are experimentally validated.
    • This work facilitates better understanding and design of stable QCLs.