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Page 2 of 24 He et al. Microstructures 2023;3:2023037 https://dx.doi.org/10.20517/microstructures.2023.29

and possess physical properties beyond the capabilities of natural materials. Based on different disciplines,
[3]
[4]
acoustic meta-structures , mechanical meta-structures , electromagnetic meta-structures , and other
[2]
[5]
types can be distinguished. Acoustic meta-structures , including phononic crystals, acoustic metamaterials,
and acoustic metasurfaces, have emerged as an elegant means of manipulating acoustic and elastic waves.
Through special structural designs, researchers can achieve dynamic characteristics that are not found in
[7,8]
natural materials, enabling novel operations such as mechanical wave blocking , absorption ,
[6]
focusing [9,10] , robust energy harvesting [11,12] , negative refraction , invisibility [14,15] , topological transmission ,
[13]
[16]
and more. The significant advancement in the field of acoustic meta-structures can be attributed primarily
to the extensive research conducted on electronic crystals and photonic crystals. Matter waves and
electromagnetic waves exhibit band structures separated by bandgaps under the action of Bloch periodic
potential fields formed by the above structures. Bandgap formation is attributed to the Bragg scattering
mechanism, which results from destructive interference between scattered waves caused by periodic
structures. Phononic crystals [17,18] , which are formed by the periodic distribution of materials or structures in
space, can exhibit bandgaps that effectively block or attenuate the propagation of mechanical waves as an
extension of the aforementioned concept. The subsequent development of localized resonant phononic
crystals enables the formation of low-frequency hybridization bandgaps through scatterer resonance,
independent of the periodicity of the structure itself . The local resonance mechanism has triggered a
[19]
revolutionary innovation in the realm of acoustic metamaterials . On the one hand, the bandgap frequency
[20]
is determined by the resonant unit frequency, providing theoretical support for developing compact
structures with vibration and noise reduction functions in limited space requirements. On the other hand, it
has been proven to possess new physical properties with locally resonant parameters, resulting in equivalent
[21]
excotic properties. This has stimulated extensive research on negative mass density , negative bulk
modulus [22,23] , and double-negative parameters [24,25] .

In the past decade, guided by the goal of achieving efficient regulation of low-frequency acoustic/elastic
waves through thin and lightweight structures, researchers have developed acoustic metasurfaces by
designing subwavelength functional unit arrays to form phase gradients based on the generalized Snell's
[27]
[26]
law . Acoustic metasurfaces include reflective, absorptive, and transmissive types, which can achieve
[28]
functions such as acoustic/elastic wave focusing , cloaking [29,30] , low-frequency perfect absorption [31,32] ,
[33]
[34]
asymmetric transmission , self-bending , and so forth. Compared with phononic crystals and acoustic
metamaterials, acoustic metasurfaces have the characteristics of ultra-thin, planar, low loss, and strong
designability, which make it possible to develop extremely miniaturized acoustic functional devices.
Recently, the concept of topological insulators in condensed matter physics has been added to the design of
acoustic meta-structures for regulating mechanical waves [35-39] . Due to the existence of bandgaps, mechanical
waves within specific frequency ranges are not allowed to propagate. In these bandgaps, acoustic meta-
structures can be considered as insulators of mechanical waves. The topological properties of bandgaps can
be characterized by calculating topological invariants and can generally be classified as topological trivial
and topological non-trivial bandgaps [40,41] . On the structural boundaries with the above two bandgaps,
certain frequencies of waves within the bandgap are allowed to propagate, which are the so-called
topological edge states. Supported by topological mechanisms, topological edge states have robust
transmission characteristics, such as defect immunity, unidirectional waveguides, and backscatter
suppression effects [42,43] . The in-depth studies of topological states have broadened the application prospects
of acoustic meta-structures to a certain extent.

The research on mechanical meta-structures primarily centers around the three material parameters of
[3]
elastic modulus, shear modulus, and Poisson's ratio in order to attain exceptional static performance .