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    This study numerically analyzes actual-size concave gratings with random structures using the difference-field boundary element method (DFBEM). The DFBEM efficiently calculates diffraction efficiency and polarization effects for non-periodic gratings.

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    Area of Science:

    • Optics and electromagnetics
    • Computational physics
    • Diffraction gratings

    Background:

    • Numerical electromagnetic analysis of Maxwell's equations provides accurate diffracted fields.
    • Analyzing large, non-periodic structures like actual-size gratings is computationally expensive.
    • Previous studies have limitations due to high computational costs for complex grating analysis.

    Purpose of the Study:

    • To numerically analyze an actual-size concave grating with structural randomness.
    • To investigate the feasibility of using the difference-field boundary element method (DFBEM) for such analyses.
    • To explore the relationship between structural randomness and diffraction efficiency, including polarization effects.

    Main Methods:

    • Application of the difference-field boundary element method (DFBEM) for numerical analysis.
    • Analysis of an actual-size concave grating with 10,000 random blazed grooves.
    • Estimation of computation result accuracy.

    Main Results:

    • The DFBEM efficiently provides vectorial diffracted and scattered waves.
    • Demonstration of the method's capability for analyzing large, non-periodic gratings.
    • Established relations between the degree of structural randomness and diffraction efficiency, considering polarization.

    Conclusions:

    • The DFBEM is a computationally efficient method for analyzing actual-size, non-periodic concave gratings.
    • Structural randomness significantly impacts diffraction efficiency and polarization characteristics.
    • This approach enables detailed analysis of complex gratings previously limited by computational resources.