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    This study introduces a theory for designing graded index lenses on curved surfaces, simplifying fabrication. The method ensures isotropic material properties, making advanced optical designs more accessible.

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    Area of Science:

    • Optics and Photonics
    • Materials Science

    Background:

    • Graded index lenses offer unique optical properties but are typically designed for flat surfaces.
    • Fabricating complex refractive index profiles on curved surfaces presents significant challenges.

    Purpose of the Study:

    • To develop a theoretical framework for mapping graded index lenses onto arbitrary rotationally symmetric curved surfaces.
    • To demonstrate the design of Luneburg and Maxwell fish-eye lenses on various curved substrates.
    • To explore the fabrication of surface-wave lenses with isotropic and homogenous dielectric layers.

    Main Methods:

    • Theoretical mapping of graded index lenses to curved surfaces.
    • Full-wave simulations using waveguide structures to validate lens performance.
    • Transformation of refractive index profiles for surface-wave lens design.

    Main Results:

    • The theory successfully maps Luneburg and Maxwell fish-eye lenses onto diverse curved surfaces.
    • All designs inherently satisfy isotropic permittivity requirements.
    • Simulations confirm the performance of mapped lenses in a waveguide setup.
    • Surface-wave lenses with isotropic and homogenous dielectric layers were designed, showing fabrication feasibility.

    Conclusions:

    • The presented theory provides a versatile method for designing graded index lenses on curved surfaces.
    • The approach simplifies the realization of complex optical functionalities on non-planar substrates.
    • The demonstrated designs highlight the potential for easier fabrication of advanced optical components.