An interface-enriched finite element method for electromagnetic analysis and optimization of 2D problems

Abstract

Nanophotonics is the study of structures’ interaction with light with features at or below the nanometer scale. It has gained the interest of many researchers, as it can be used to control the flow of light very effectively in the design of, e.g., solar cells, highly efficient biosensors or lasers. The design of such devices can be non-intuitive and complex and therefore computational tools like topology optimization techniques have been used to improve their designs. However, the topology optimization methods used in the literature often use a density-based representation of the geometry, which often leads to jagged edges. It has been shown in the literature that jagged edges can deteriorate the accuracy of simulation results. Using a level-set method in combination with an enriched finite element method offers a smoother boundary representation than the often used density-based methods. This work aims to develop an analysis and level set optimization for 2D electromagnetic scattering and eigenvalue problems using an enriched finite element method. Furthermore, we showcase that even for a non-conforming discretization, the enriched finite element method achieves the same convergence properties as the standard finite element method with fitted meshes. Finally, we perform topology optimization on the design of both a 2D meta lens and 2D reflector, maximizing their ability to focus light onto a point, using a level set method to define the geometry in combination with the enriched method used in the analysis.