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    This summary is machine-generated.

    Disordered thin films create structural colors. Using Ewald sphere construction, we explain why these films produce blue but not red colors, and how to achieve red structural colors.

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    Area of Science:

    • Physics
    • Materials Science
    • Optics

    Background:

    • Disordered structures with specific refractive-index distributions produce non-iridescent colors.
    • The Fourier transform of these refractive-index distributions is often spherical.

    Purpose of the Study:

    • To determine scattering direction and efficiency in thin films with disordered structures.
    • To explain the limitations and possibilities of generating structural colors (blue vs. red) using these structures.
    • To present a geometrical method for analyzing structural color generation.

    Main Methods:

    • Utilizing the Ewald sphere construction based on first-order scattering approximation.
    • Numerically synthesizing a model structure with a spherical shell in reciprocal space.
    • Comparing first-order scattering predictions with direct electromagnetic simulations.

    Main Results:

    • The Ewald sphere construction provides a geometrical explanation for why short-wavelength colors (blue) are favored over long-wavelength colors (red).
    • A synthesized model structure demonstrates the effectiveness of the Ewald sphere approach.
    • First-order scattering predictions align well with direct electromagnetic simulations for reflectivity.

    Conclusions:

    • The Ewald sphere construction is a valuable geometrical tool for understanding spectral and directional reflectivity in disordered structures.
    • Combining total internal reflection with directed scattering enables the production of long-wavelength structural colors.