Design of metasurfaces in 3D for omnidirectional band gaps: The scalar wave case

We discuss a comprehensive process for designing the material properties of three-dimensional periodic structures that are tasked to exhibit user-defined omnidirectional band gaps. To this end, we build upon the framework first posited in Goh and Kallivokas (2019) for two-dimensional metamaterials, and aim at engineering the dispersive properties of a metamaterial's 3D unit cell using an inverse medium approach. The inversion is driven by forcing the vanishing of trial group velocities at the target band gap frequencies, subject to the satisfaction of the Floquet-Bloch eigenvalue problem defined over the unit cell's IBZ. Omnidirectionality is controlled by enforcing the vanishing of the group velocities along the IBZ's high-symmetry lines. Using an adjoint method, the unit cell's properties are iteratively updated until the design goal is attained. Numerical examples for acoustic metamaterials and metasurfaces demonstrate the methodology.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

We discuss a comprehensive process for designing the material properties of three-dimensional periodic structures that exhibit user-defined omnidirectional band gaps. The process involves an inverse medium approach, forcing the vanishing of trial group velocities at the target band gap frequencies to achieve the desired properties. Numerical examples for acoustic metamaterials and metasurfaces demonstrate the methodology.