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Efficient rational Chebyshev pseudo-spectral method with domain decomposition for optical waveguides modal analysis.

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    We introduce a novel rational Chebyshev multi-domain pseudo-spectral method (RC-MDPSM) for optical waveguide modal analysis. This method efficiently handles semi-infinite domains and accurately models leaky modes without absorbing boundary conditions.

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    Area of Science:

    • Photonics and Optical Engineering
    • Computational Electromagnetics
    • Waveguide Theory

    Background:

    • Accurate modal analysis of optical waveguides is crucial for designing photonic devices.
    • Existing methods often struggle with semi-infinite computational domains and accurately modeling leaky modes.
    • The use of Perfectly Matched Layers (PML) can be computationally expensive and introduce numerical challenges.

    Purpose of the Study:

    • To develop a computationally efficient and accurate method for the modal analysis of optical waveguides.
    • To introduce rational Chebyshev basis functions for handling semi-infinite subdomains in waveguide analysis.
    • To accurately model leaky modes in optical waveguides, especially those with small imaginary parts of the refractive index.

    Main Methods:

    • Proposal of a rational Chebyshev multi-domain pseudo-spectral method (RC-MDPSM).
    • Introduction of rational Chebyshev basis functions for semi-infinite computational subdomains.
    • Employment of an optimized algebraic map to enhance basis function efficiency and eliminate PML-like conditions.
    • Derivation of a specific boundary condition for leaky modes at the guide-substrate interface.

    Main Results:

    • The RC-MDPSM demonstrates high accuracy and computational efficiency.
    • The method effectively handles semi-infinite computational domains without PML.
    • Accurate modeling of leaky modes, even with very small imaginary parts of the refractive index, is achieved.
    • Validation through analysis of high-index contrast dielectric, plasmonic waveguides, and the ARROW structure.

    Conclusions:

    • The RC-MDPSM offers a robust and efficient solution for optical waveguide modal analysis.
    • The use of rational Chebyshev basis functions and a specialized leaky mode boundary condition significantly improves accuracy and efficiency.
    • This technique provides a valuable tool for the design and analysis of advanced photonic and plasmonic devices.