Anisotropic material-field series expansion for the topological design of optical metalens

• Published in: Optics express 2022-05, Vol.30 (10), p.16459-16478
• Main Authors: Sun, Zhaoyou, Liu, Pai, Luo, Yangjun
• Format: Article
• Language: English
• ISSN: 1094-4087; 1094-4087
• DOI: 10.1364/OE.457715

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.