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    A new bilinear parameterization enhances the C method for analyzing deep and smooth grating profiles. This advancement allows for accurate numerical results, overcoming previous limitations and improving computational stability.

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    Area of Science:

    • Optics and Photonics
    • Computational Electromagnetics

    Background:

    • The C method is a coordinate transformation technique used for analyzing diffraction gratings.
    • Previous limitations of the C method restricted its application to gratings with shallow profiles.

    Purpose of the Study:

    • To propose a simple variable transformation for the C method.
    • To enable the analysis of deep and smooth grating profiles using the C method.

    Main Methods:

    • A bilinear parameterization using two joined straight-line segments per grating period was introduced.
    • This parameterization was applied within the framework of the C method.

    Main Results:

    • The enhanced C method achieved convergent numerical results for gratings with a groove depth-to-period ratio as high as 10.
    • The method demonstrated practical elimination of divergent results caused by large truncation numbers.

    Conclusions:

    • The proposed bilinear parameterization significantly extends the applicability of the C method to complex grating profiles.
    • This method offers improved accuracy and computational stability for grating analysis.