Anisotropic material-field series expansion for the topological design of optical metalens
Zhaoyou Sun, Pai Liu, Yangjun Luo
Abstract
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.