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Reverse ray tracing for transformation optics.

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    This study introduces 3D reverse ray tracing for transformation optics, efficiently calculating illuminance in complex optical systems with extreme inhomogeneity and anisotropy. This novel method overcomes limitations of traditional ray tracing for advanced optical device design.

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    Area of Science:

    • Optics and Photonics
    • Computational Physics
    • Materials Science

    Background:

    • Ray tracing is crucial for optical system performance prediction.
    • Hamiltonian equations govern ray tracing in transformation optics but are complex with inhomogeneous and anisotropic media.
    • Existing methods struggle with extreme inhomogeneity and anisotropy.

    Purpose of the Study:

    • To present a novel 3D reverse ray tracing method for transformation optics.
    • To address challenges in tracing rays through highly inhomogeneous and anisotropic optical devices.
    • To efficiently calculate illuminance in transformation optics systems.

    Main Methods:

    • Developed a 3D reverse ray tracing approach based on Fermat's principle and a sweeping method.
    • Obtained the eikonal function using the sweeping method.
    • Calculated wave vectors from the gradient of the eikonal function to determine illuminance.

    Main Results:

    • Successfully applied 3D reverse ray tracing to three transformation optics cases with inhomogeneous and anisotropic indices.
    • Demonstrated efficient calculation of ray trajectories and illuminance.
    • Validated the method's effectiveness for systems with symmetric positive definite material property tensors.

    Conclusions:

    • 3D reverse ray tracing offers an efficient alternative to solving ordinary differential equations for ray tracing in transformation optics.
    • The method is suitable for analyzing optical systems with complex material properties.
    • This technique advances the design and analysis of transformation optics devices.