Phonon Engineering of Micro‐ and Nanophononic Crystals and Acoustic Metamaterials: A Review

Abstract

Figure 2. a,e) Experimental specimens of a regular Kagome lattice (a) and a topological Kagome lattice (e). b,f ) Isofrequency contours (first phaseconstant surface in the first Brillouin zone) of regular (b) and topological (f ) Kagome lattices calculated from FEA. c,g) Group velocity isofrequency contours (frequency increasing from dark red to bright yellow) highlighting symmetric or asymmetric directivity of regular (c) and topological (g) lattices. d,h) Snapshots of experimentally acquired wave fields in regular (d) and topological (h) lattices, confirming symmetric or asymmetric propagation. Colors denotes the magnitude of the scan point velocities, normalized by the largest value at the considered instants. a-h) Reproduced with permission. [40]

In-Gap Edge and Domain-Wall States in Largely Perturbed Phononic Su–Schrieffer–Heeger Lattices

“…They have thus attracted significant attention. Moreover, in recent years, these topologically protected non-dissipative localized states have inspired studies of classical analogs of TIs in photonic [3][4][5][6][7], magnetic [8][9][10], and mechanical [11][12][13][14][15][16][17] systems.…”

“…In mechanical systems, a similar topological invariant can also be derived from the spectral evolution of eigenvectors of the dynamical matrix (or the compatibility matrix) from a unit cell analysis. The integer topological invariant can then inform the numbers and types of topologically protected surface/edge/corner states confining static deformation [18][19][20][21][22] or vibration [11,[13][14][15][16][17][23][24][25] within a bulk bandgap (which is a frequency range with no eigenfrequency solutions, i.e., bulk wave propagation) when a material/structure with a non-zero topological invariant, i.e., a topologically non-trivial phase, forms a domain wall with another domain characterized by a zero-topological invariant, i.e., a topologically trivial phase, including vacuum. Such a bulk property reflected as surface/edge/corner states at a domain wall or edge is usually referred to as the bulk-edge correspondence.…”

Metamaterial control of the surface acoustic wave streaming jet

“…In the work presented here we show that a phononic metamaterial can be used to control the Rayleigh angle of the streaming jet. Metamaterials are a new class of artificial material that can be engineered to possess properties that do not exist in natural materials, and have been increasingly used to control and manipulate the propagation of phonons, including SAWs, at the micro-and nano-scales [15].…”

Boundary effect on in-gap edge states in nonlocal Su-Schrieffer-Heeger model

“…In phononic systems, TIs can emulate phenomena such as the quantum Hall effect 4,5 , quantum spin Hall effect 6,7 , and quantum Valley Hall effect 8,9 , where the dynamics of vibrations reveal intriguing topological properties. These properties manifest as protected states localized at surfaces, edges, or corners, effectively confining deformations [10][11][12][13][14][15][16] . Such characteristics, inherent in topological mechanical materials, find utility across various mechanical setups, including resonators and waveguides.…”