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Multi-functional lens based on conformal mapping.

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    A novel multi-functional lens, based on conformal mapping, offers versatile electromagnetic wave control. This gradient-index dielectric cylinder acts as a flattened Luneburg lens, Eaton lens, or waveguide bend, demonstrating excellent performance for optical systems.

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    Area of Science:

    • Electromagnetics and Optics
    • Materials Science

    Background:

    • Gradient-index (GRIN) lenses offer unique wave manipulation capabilities.
    • Traditional Luneburg and Eaton lenses have specific applications in beam steering and guiding.

    Purpose of the Study:

    • To propose and design a novel two-dimensional, multi-functional lens structure.
    • To explore its capabilities as a flattened Luneburg lens, Eaton lens, and waveguide bend.
    • To demonstrate its realization using metamaterials.

    Main Methods:

    • Conformal mapping method for lens design.
    • Gradient-index dielectric cylinder with a semi-elliptic cross-section.
    • Utilizing non-resonant metamaterials with inhomogeneous hole arrays for realization.

    Main Results:

    • The lens functions as a flattened Luneburg lens, producing highly-directive electromagnetic waves.
    • It operates as an Eaton lens, guiding beams to perform a U-turn.
    • The structure can be configured as a waveguide bend.
    • Simulation results validate excellent performance, aligning with theoretical predictions.

    Conclusions:

    • The designed multi-functional lens demonstrates versatile electromagnetic control.
    • It shows particular utility in real-world optical lens systems.
    • Metamaterial realization offers a practical pathway for implementation.