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    This study introduces a new conformal transformation optics method using geodesic lenses for continuous refractive index profiles. This approach enables perfect performance for devices like conformal transparency and invisible cloaks.

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    Area of Science:

    • Optics
    • Materials Science

    Background:

    • Conformal transformation optics manipulates light using inhomogeneous dielectrics.
    • Discontinuous refractive index profiles at branch cuts limit device functionality.

    Purpose of the Study:

    • To develop a novel conformal transformation optics method addressing refractive index discontinuities.
    • To achieve high-performance optical devices with continuous dielectric profiles.

    Main Methods:

    • Utilizing geodesic lenses with special closed surfaces for continuous refractive index profiles.
    • Demonstrating conformal transparency and reflection.
    • Achieving conformal invisible cloaks using perfect conductors.

    Main Results:

    • The proposed method ensures continuous refractive index profiles, leading to near-perfect device performance.
    • Conformal transparency (invisibility without a cloaking region) was successfully demonstrated.
    • Conformal invisible cloaks were achieved through two distinct methods.

    Conclusions:

    • The geodesic lens-based conformal transformation optics offers a robust solution for designing advanced optical devices.
    • This method shows potential for applications in other wave phenomena governed by the Helmholtz equation in 2D.