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    Area of Science:

    • Optics and Photonics
    • Computational Physics
    • Materials Science

    Background:

    • Periodic structures are crucial in optics, but modeling incoherent effects is challenging.
    • Existing methods for incoherent effects are often imprecise or computationally intensive, relying on averaging coherent responses.
    • There is a need for rigorous and efficient methods to model optical phenomena in periodic structures with incoherent effects.

    Purpose of the Study:

    • To present a novel and computationally efficient approach for modeling incoherent effects in laterally periodic structures.
    • To provide a rigorous method that overcomes the limitations of existing averaging techniques for incoherent optical phenomena.
    • To explain complex light-structure interactions, such as those between diffraction gratings and thick substrates.

    Main Methods:

    • Utilizing scattering matrix formalism to describe the optical response of the structures.
    • Applying incoherent wave summation through infinite geometric series.
    • Incorporating generalized Mueller matrix calculus for comprehensive analysis.
    • Combining the novel method with existing coherent modeling techniques for periodic structures.

    Main Results:

    • The developed method demonstrates significantly faster computational performance compared to traditional averaging-based incoherent methods.
    • The approach provides a rigorous framework for modeling incoherent effects, validated against experimental spectroscopic data.
    • The new method successfully explains phenomena arising from the interaction of diffraction gratings with thick substrates.

    Conclusions:

    • The proposed method offers a rigorous, efficient, and versatile tool for modeling incoherent optical effects in periodic structures.
    • This approach enhances the understanding of light interactions in complex optical systems, particularly those involving diffraction gratings and substrates.
    • The computational efficiency makes this method suitable for a wider range of practical optical applications.