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    Area of Science:

    • Electromagnetics and Optics
    • Computational Physics
    • Materials Science

    Background:

    • Electromagnetic field descriptions are crucial for understanding wave interactions.
    • Composite dielectric gratings with conducting strips present complex scattering challenges.
    • Existing numerical methods may require refinement for such intricate structures.

    Purpose of the Study:

    • To introduce a novel numerical method for analyzing electromagnetic scattering from composite dielectric gratings.
    • To utilize scattering factors within the shadow theory framework for enhanced analysis.
    • To investigate the scattering properties and energy losses in gratings with embedded conducting strips.

    Main Methods:

    • Development of a numerical method based on scattering factors for composite gratings.
    • Introduction of primary and secondary field scattering factors.
    • Application of the Galerkin procedure to determine surface electric currents.
    • Calculation of total field scattering factors and Joule losses.

    Main Results:

    • The method successfully calculates scattering factors and Joule losses for both propagating and evanescent wave incidences.
    • Numerical examples demonstrate the scattering properties of asymmetric multiple plane gratings with conducting strips.
    • Symmetries in diffraction efficiencies and scattering factors are observed, consistent with reciprocity principles for resistive gratings.

    Conclusions:

    • The scattering factor method provides an effective approach for analyzing complex grating structures.
    • The study validates the application of shadow theory in describing electromagnetic interactions.
    • The findings contribute to the understanding of wave propagation and energy dissipation in engineered optical materials.