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    We introduce an advanced penalty method for optical waveguide mode solvers, using the Adam optimizer within pseudospectral frequency-domain (PSFD) frameworks for enhanced stability and faster convergence in calculating effective indices.

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    Area of Science:

    • Photonics and Computational Electromagnetics
    • Numerical Methods for Waveguide Analysis

    Background:

    • Optical waveguide mode solvers are crucial for photonic device design.
    • Traditional methods face challenges with numerical stability and convergence at material interfaces.

    Purpose of the Study:

    • To develop a novel penalty method for optical waveguide mode solvers.
    • To enhance numerical convergence, stability, and accuracy using adaptive optimization.

    Main Methods:

    • Integration of the Adam optimizer into pseudospectral frequency-domain (PSFD) frameworks.
    • A penalty method to manage adaptable boundary fluctuations at material interfaces.
    • Calculation of effective indices for benchmark optical waveguides.

    Main Results:

    • Significantly enhanced numerical convergence and stability.
    • Improved convergence rates and robustness through adaptive penalty coefficient determination.
    • High accuracy in effective index calculations, surpassing conventional and metaheuristic methods.

    Conclusions:

    • The proposed method offers superior accuracy and speed for optical waveguide analysis.
    • It effectively minimizes numerical boundary errors while preserving PSFD spectral accuracy.
    • This approach represents a significant advancement in numerical modeling for photonics.