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Modal spectral element method with modified Legendre polynomials to analyze binary crossed gratings.

Gérard Granet

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |May 3, 2023
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    Summary

    The modal spectral element method (SEM) was extended to analyze complex binary crossed gratings. This powerful technique accurately models advanced grating structures, offering a versatile alternative for optical component design.

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    Area of Science:

    • Optics and photonics
    • Computational electromagnetics
    • Materials science

    Background:

    • Previous work established the modal spectral element method (SEM) for lamellar gratings.
    • The SEM utilizes a hierarchical basis of modified Legendre polynomials for high accuracy.

    Purpose of the Study:

    • Extend the modal spectral element method (SEM) to analyze general binary crossed gratings.
    • Demonstrate the geometric versatility of the SEM for non-aligned grating patterns.
    • Validate the extended SEM against established methods like the Fourier modal method (FMM).

    Main Methods:

    • Applied the modal spectral element method (SEM) with modified Legendre polynomials.
    • Investigated binary crossed gratings with patterns not aligned to cell boundaries.
    • Validated results by comparing with the Fourier modal method (FMM) for anisotropic gratings and FMM with adaptive spatial resolution for a silver film square-hole array.

    Main Results:

    • The SEM successfully analyzes general binary crossed gratings, demonstrating significant geometric versatility.
    • The method shows excellent agreement with the FMM for anisotropic crossed gratings.
    • Validation against FMM with adaptive spatial resolution confirms accuracy for complex structures like silver film arrays.

    Conclusions:

    • The extended modal spectral element method (SEM) is a powerful and versatile tool for analyzing complex binary crossed gratings.
    • This approach offers high accuracy and can handle intricate grating geometries.
    • The SEM provides a robust alternative for the rigorous analysis of diffractive optical elements.