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    We developed a new subpixel-smoothed projection (SSP) method for topology optimization (TopOpt) that improves convergence and simplifies calculations. This differentiable binarization technique enhances performance in photonics inverse-design problems.

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    Area of Science:

    • Computational Engineering
    • Materials Science
    • Optics and Photonics

    Background:

    • Traditional topology optimization (TopOpt) methods for differentiable binarization face challenges with near-non-differentiability and slow convergence.
    • Existing projection schemes in TopOpt struggle to efficiently improve binarization during optimization.

    Purpose of the Study:

    • To introduce a novel "subpixel-smoothed projection" (SSP) formulation as a superior alternative for differentiable binarization in topology optimization.
    • To enable smooth transitions between density-based TopOpt and level-set methods for improved shape evolution.

    Main Methods:

    • Developed the SSP formulation, which utilizes both the filtered design field and its spatial gradient.
    • Implemented SSP as a drop-in replacement for existing projection schemes in topology optimization.
    • Validated the method across finite-difference, Fourier-modal, and finite-element computational approaches.

    Main Results:

    • The SSP method overcomes limitations of previous schemes, achieving smooth transitions and faster convergence.
    • Demonstrated effectiveness on various photonics inverse-design problems.
    • Achieved greater simplicity in the optimization process compared to traditional methods.

    Conclusions:

    • The subpixel-smoothed projection (SSP) formulation offers a significant advancement in differentiable binarization for topology optimization.
    • SSP provides a more robust and efficient approach for inverse-design problems, particularly in photonics.