A quantum graph approach to metamaterial design

Metamaterials are materials with unique properties arising from their fine local structure, which may include resonators or other components. This structure is typically small relative to the wavelength, allowing the material to be treated as a continuum. However, the fine structure leads to intriguing dispersion relations and corresponding properties.

Modeling metamaterials is often achieved through finite element methods, which can be time-consuming due to the need for meshing in a periodic lattice. While periodicity allows for model simplification, any structural changes necessitate remeshing. To address these challenges, a rapid modeling approach was developed, incorporating numerous parameters to provide flexibility and retain essential metamaterial properties. This quantum graph method serves as an efficient way to explore ideas before transitioning to practical applications.

The accompanying illustration emphasizes the relationship between the atomic structure and wavelength. When the wavelength is comparable to the size of the structure, it can be resolved. As the wavelength increases, a continuum model emerges, which still captures aspects of the local structure, enhancing the material's intriguing characteristics.