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Curvilinear coordinate method as an initial value problem: application to gratings.

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    This study presents an efficient C-method for calculating grating scattering matrices. The approach uses Maxwell

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    Area of Science:

    • Electromagnetics and Optics
    • Computational Physics

    Background:

    • Calculating the scattering matrix of gratings is crucial for understanding light-matter interactions.
    • Existing methods can be computationally intensive.

    Purpose of the Study:

    • To develop an efficient C-method for calculating the scattering matrix of gratings.
    • To provide a robust computational framework for electromagnetic scattering problems.

    Main Methods:

    • A C-method approach is employed, defining a coordinate system with horizontal planes above and below the grating.
    • Maxwell's equations are solved as an initial value problem within a defined area.
    • Fields outside this area are represented using Rayleigh expansions.

    Main Results:

    • The scattering matrix is efficiently calculated by utilizing continuity relations of field components on the horizontal planes.
    • The method provides a novel way to handle boundary conditions and field representations.

    Conclusions:

    • The proposed C-method offers an efficient and accurate way to compute grating scattering matrices.
    • This approach has potential applications in optical device design and analysis.