To determine an effective optimization strategy and facilitate the manufacture of optical metalenses, this paper extends the material-field series-expansion (MFSE) method for the topology design of metalenses. A new anisotropic material-field function with a spatially anisotropic correlation is introduced to describe the structural topology in a narrow design domain. The topological features can be implicitly controlled by material-field correlation lengths in different directions. Then, a generalized sigmoid projection is introduced to construct an interpolation relationship between the unbounded material-field value and the relative permittivity. Based on the series expansion technique, the number of design variables is greatly reduced in this topology optimization process without requiring additional material-field bounded constraints. The MFSE-based metalens design problem is efficiently solved by using a gradient-based algorithm incorporating design sensitivity analysis. Numerical examples demonstrate that the proposed optimization algorithm can successfully obtain an optimized and easy-to-manufacture design in optics inverse design problems.
Topology optimization is among the most effective tools for innovative and lightweight structural designs. Multi-material design is considered to achieve better structural performance than single-material design. To significantly reduce the design space dimensionality and facilitate the optimization of multi-material structural design problems, this study proposes an effective topological representation and dimensionality reduction approach based on the material-field series expansion (MFSE) model. In the proposed method, a specified number of material phases is described within a single material field with a piecewise Heaviside projection function. The topology optimization problem is solved by determining the optimal MFSE coefficients. Owing to the single material-field topological description and series expansion, the number of design variables is independent of the finite element mesh and the number of material phases. In terms of dimensionality reduction, the proposed method outperformed all reported state-of-the-art algorithms for multi-material topology optimization. The validity and universality of the proposed method are illustrated in two- and three-dimensional numerical examples.
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