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Three-dimensional quasi-conformal transformation optics through numerical optimization.

Mateus A F C Junqueira, Lucas H Gabrielli, Felipe Beltrán-Mejía

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    Summary
    This summary is machine-generated.

    This study presents a novel method for 3D quasi-conformal transformation optics, enabling precise control over light manipulation. The technique achieves arbitrarily small anisotropy, ensuring modal preservation in waveguide designs.

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    Area of Science:

    • Optics and Photonics
    • Computational Electromagnetics
    • Materials Science

    Background:

    • Transformation optics (TO) enables novel electromagnetic devices by controlling light propagation through material properties.
    • Achieving 3D quasi-conformal transformations in TO traditionally faces challenges with boundary conditions and anisotropy.
    • Parametrization and numerical optimization offer potential solutions for complex 3D TO designs.

    Purpose of the Study:

    • To demonstrate a method for 3D quasi-conformal transformation optics without sliding boundary conditions.
    • To validate the proposed technique using numerical optimization and a quasi-Newton method.
    • To investigate the impact of parametrization on achieving low anisotropy in 3D TO.

    Main Methods:

    • Utilizing parametrization and numerical optimization to design 3D transformation optics.
    • Implementing a quasi-Newton method for the optimization process.
    • Validating the technique through simulations of two cylindrical waveguide bends.

    Main Results:

    • Successfully achieved 3D quasi-conformal transformation optics.
    • Demonstrated that increasing parametrization degrees of freedom reduces average anisotropy.
    • Showcased arbitrarily small average anisotropy is attainable.
    • Confirmed modal preservation in waveguide simulations when residual anisotropy is negligible.

    Conclusions:

    • The proposed parametrization and optimization method is effective for 3D quasi-conformal transformation optics.
    • This approach overcomes limitations of sliding boundary conditions.
    • The technique offers precise control over anisotropy, crucial for advanced optical device design.