Metamaterials beyond electromagnetism

TLDR

Metamaterials are engineered, densely packed structures that, while often linked to negative refractive indices and cloaking in electromagnetism, also extend to thermodynamics, mechanics, acoustics, fluid dynamics, and quantum mechanics. The review surveys metamaterial concepts, analogies, and differences to electromagnetism, summarizing current theory and experimental advances from an experimentalist’s perspective. It covers both homogeneous and transformation‑based inhomogeneous architectures, citing examples such as thermal, acoustic, mechanical, seismic, and flexural wave cloaks, concentrators, inverters, and auxetic or pentamode structures.

Abstract

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.