Topology optimization of metasurfaces for anomalous reflection of longitudinal elastic waves

Abstract

A numerical method based on topology optimization is developed for designing a metasurface that anomalously reflects longitudinal elastic waves. While the analysis and design of metasurfaces and metamaterials have received much attention recently, no numerical method to design elastic metasurfaces for anomalous reflection has been explored. Here, we formulate a density-based topology optimization suitable for finding a set of phase-delaying unit cells forming a metasurface that anomalously reflects longitudinal waves impinged upon it. Each unit cell is designed to yield the specific phase delay between the incident and reflected elastic waves. The transfer matrix approach using the averaged finite element results is employed to efficiently and accurately calculate the phase delay while the wave phenomena are analyzed by the finite element analysis. As case studies, metasurfaces converting normally incident longitudinal waves to anomalously reflected longitudinal waves were designed. Various target anomalous reflection angles were considered including the extreme reflection angle of 90°. To investigate the numerical aspect of the developed method, we investigated the effect of the sizes of the unit cells, both along the perpendicular and normal directions to the wave incidence. The mesh dependence issue was also investigated. Finally, we applied the developed topology optimization method to design metasurfaces for wave focusing and trapping in a waveguide.