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Mode solver based on Gegenbauer polynomial expansion for cylindrical structures with arbitrary cross sections.

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    A new modal method efficiently computes eigenmodes for cylindrical structures with complex cross sections. This technique, using Hertz potentials and Gegenbauer expansion, accurately solves for both conducting and dielectric materials.

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    Area of Science:

    • Computational Electromagnetics
    • Numerical Analysis
    • Applied Physics

    Background:

    • Accurate computation of eigenmodes is crucial for analyzing electromagnetic wave propagation in various structures.
    • Traditional methods can be computationally intensive or limited in handling arbitrary cross-sectional geometries.
    • The need for efficient and versatile numerical techniques for modal analysis persists.

    Purpose of the Study:

    • To develop and present a novel modal method for calculating eigenmodes of cylindrical structures.
    • To address the challenge of arbitrary cross-sectional profiles in modal analysis.
    • To demonstrate the efficiency and accuracy of the proposed method for different material types.

    Main Methods:

    • Introduced a new coordinate system tailored to arbitrary cross-sectional profiles.
    • Formulated a matrix eigenvalue equation derived using Hertz potentials.
    • Employed the modal method based on Gegenbauer expansion (MMGE) for numerical solutions.
    • Developed a complex coordinate version of MMGE for dielectric structures.

    Main Results:

    • The modal method successfully computes eigenmodes as eigenvectors of the derived matrix eigenvalue equation.
    • MMGE proved to be an efficient numerical tool for solving the eigenvalue problem.
    • Results were validated against known solutions for both perfectly conducting and dielectric cylindrical structures.

    Conclusions:

    • The presented modal method, particularly MMGE, offers an efficient and accurate approach for eigenmode computation.
    • The method's adaptability to arbitrary cross sections and dielectric properties enhances its applicability.
    • This technique provides a valuable tool for the analysis of complex electromagnetic structures.