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<p>This paper presents a robust multi-objective optimization framework for the topological design of metalenses, treating the performance and the stability as two conflicting objectives. The optimization approach is formulated as maximizing expectation while minimizing the standard deviation of the figure of merit (FOM) or focal point intensity in the presence of multiple uncertainties in incident wavelength, relative permittivity and geometric deviations. The approach couples polynomial chaos expansion (PCE) for uncertainty quantification and Pareto optimal tracing to efficiently obtain a higher quality set of Pareto optimal solutions compared to the conventional multiple restart approach. The obtained robust metalens design demonstrated consistent performance under manufacturing uncertainties and variations in material properties. The obtained optimized solutions provide valuable insights regarding optimal topologies and their trade-offs between performance and stability. Further, the results also indicate that there is no significant performance drop-off between 2D and 1D optimized device designs, making the 1D designs more attractive due to its simpler geometries for manufacturability. Additionally, this study observed that eroded designs are less stable than dilated ones, suggesting a biased sensitivity of the topology to underexposure in nano-lithography techniques.</p>

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Multi-objective robust topology optimization of metalenses via Pareto optimal tracing and polynomial chaos

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Muhammad Subhan Arifin,
  • Nathan,
  • Lavi Rizki Zuhal,
  • Afriyanti Sumboja,
  • Pramudita Satria Palar

摘要

This paper presents a robust multi-objective optimization framework for the topological design of metalenses, treating the performance and the stability as two conflicting objectives. The optimization approach is formulated as maximizing expectation while minimizing the standard deviation of the figure of merit (FOM) or focal point intensity in the presence of multiple uncertainties in incident wavelength, relative permittivity and geometric deviations. The approach couples polynomial chaos expansion (PCE) for uncertainty quantification and Pareto optimal tracing to efficiently obtain a higher quality set of Pareto optimal solutions compared to the conventional multiple restart approach. The obtained robust metalens design demonstrated consistent performance under manufacturing uncertainties and variations in material properties. The obtained optimized solutions provide valuable insights regarding optimal topologies and their trade-offs between performance and stability. Further, the results also indicate that there is no significant performance drop-off between 2D and 1D optimized device designs, making the 1D designs more attractive due to its simpler geometries for manufacturability. Additionally, this study observed that eroded designs are less stable than dilated ones, suggesting a biased sensitivity of the topology to underexposure in nano-lithography techniques.