Combinatorics

Physics

Topology (electrical circuits)

Mathematics

Optics

Metamaterial

Diffraction

Reciprocal lattice

Journal of Applied Physics

Waves are generally characterized by angular frequency ω and wavevector k. Accordingly, this tutorial is structured into two parts, one on resonance-based acoustic metamaterials, in the frequency domain, and one on topological acoustics, based on the wavevector domain as topological structures inherently involve spatial configurations that are a step beyond the simple periodic lattices. Each part will begin with a brief introduction of the basic principles, followed by two examples described in detail. In the first part, we present decorated membrane resonators and the broadband optimal acoustic absorption structures, the latter being crucial for the potential applications of acoustic metamaterials. In the second part, we discuss how to construct the Dirac cone, a special type of dispersion from either accidental degeneracy or symmetry protection, which can be shown to lead to negative, zero, or positive refractive indices. The shifting and gapping of these Dirac cones in the reciprocal space can result in effects on acoustic waves similar to that of a magnetic field on an electron. More generally, they lead to edge states resulting from a real-space gauge field as well as topological bandgaps.

Acoustic metamaterials