Acoustic metamaterials and metasurfaces are a kind of artificially structured materials to manipulate advanced or unprecedented functions for acoustic waves in air, liquid, and solid from macroscale to nanoscale. Metasurfaces act as a slice of a metamaterial with subwavelength thickness being like a surface, benefitting scenarios that especially require compact design in space. In the past two decades, we witnessed significant advancements of this field as an integrative process as “design–fabrication–verification” for innovations include extreme effective parameters, invisible cloak, non-reciprocal propagation, topological insulators, among others, and for interdisciplinary research in physics, materials, engineering, and artificial intelligence. Driven by new manufacturing technologies and strong applicable demands, such as noise and vibration control, aerospace, signal processing, sensors, and non-destructive testing, the study of acoustic metamaterials and metasurfaces attracts increasing attention from both academic and industrial parts.
The objective of this Special Topic is to collect studies from prominent experts in this community; provide a comprehensive overview of the latest trends in acoustic metamaterials and metasurfaces; and guide new researchers, funding agencies, and industries in identifying valuable prospects for this field in the future.
Sound absorbers and insulators are widely demanded in daily life and industry. Acoustic metamaterials and metasurfaces are able to provide different approaches to target this functionality.
Ye et al. presented a reconfigurable ultra-sparse ventilated metamaterial absorber based on triadic cylindrical Helmholtz resonators, exhibiting low frequency sound absorption with highly sparse ventilation. They employed a coupled mode theory for three resonators to clarify the underlying physics. The designed absorber is able to achieve a sparsity level of more than 80%, with a measured wind velocity ratio higher than 95%. They installed a motor to mechanically tune the sound absorption frequency in the frequency range from 600 to 950 Hz.1
Liu et al. presented an ultra-broadband acoustic metamaterial that achieves sound absorption in the range of 400–10 000 Hz with a subwavelength thickness of 9.3 cm. They designed multiple Fabry–Pérot channels with inhomogeneous cross-sectional areas, allowing for flexible adjustment of the impedance characteristics of each channel. By critically coupling the Fabry–Pérot channels, a 27-cell broadband metamaterial is obtained with an average absorption coefficient above 90% over 400–10 000 Hz, which is verified by experiments in a square impedance tube and an alpha-cabin reverberation room.2
Krasikova et al. studied the noise-insulating properties of the periodic structures based on coupled Helmholtz resonators. By tuning the local coupling between the resonators, they showed a broad stopband covering ∼3.5 octaves (200–2100 Hz) in the transmission spectra, which is analyzed in terms of the bandgap of the corresponding periodic structures. The local coupling strength can be varied by introducing chirped structures and lossy resonators with porous inserts. The stopband engineering procedure is supported by genetic algorithm optimization, and the numerical calculations are verified by experimental measurements.3
Wang et al. proposed an acoustic absorber based on space coiling and folding metamaterials with side openings, which could effectively absorb line-spectrum noise as well as broadband noise for working in harsh environments. They developed an analytical model to study the acoustic response of space coiling and folding metamaterials, which is further validated by numerical simulations. Further experiments have demonstrated the acoustic properties of the proposed metamaterial structure and confirmed the capability of stacked space coiling and folding metamaterials for flexible control of the acoustic absorption spectrum.4
Ju et al. reported a coupled Mie resonators system constructed with two parallel waveguides connected by an aperture and two Mie resonators placed symmetrically on both sides of the aperture to demonstrate coherent perfect absorption. They exploited the incident waves of the waveguide as an effective gain so that parity–time (PT) symmetry with balanced loss and gain is realized by only passive materials. Coherent perfect absorption is observed in the PT symmetric phase and at the exceptional point but not in the broken phase. By varying the relative phase between the two incident waves, the coherent absorption can be tuned from perfect absorption to zero.5
Guan et al. demonstrated both numerically and experimentally an ultra-low-frequency sound absorber and its application in silenced ducts. The absorber comprises an array of resonant dual-spiral channel units backed by a wall, achieving ultra-low-frequency sound absorption with a fractional bandwidth of 18.3% around 73 Hz that originated from its effective near-zero modulus, with the absorbed energy dissipated through viscous losses in the unit channels. By designing a composite absorber of five units with different parameters, efficient sound absorption in a duct with an enhanced fractional bandwidth of 60.6% and an average absorptance of 0.87 is experimentally demonstrated.6
Pan et al. proposed a gradient index metamaterial consisting of radius-varied cavities in rubber for broadband underwater sound absorption. The material’s viscosity and the coupling effect among the gradient cavities contribute to broadband sound absorption with impedance matching at the interface with water. They experimentally validated the performance of broadband sound absorption from 1 to 10 kHz, which agrees well with the theoretical and numerical results. They further experimentally demonstrated the sound absorption performance with hydrostatic pressures up to 3 MPa and analyzed the mechanism of the sound absorption deviation caused by high pressures.7
Elastic metasurfaces and metamaterials show great ability to steer guided waves with abnormal functions, such as robust bandgaps, asymmetric transmission, wavefront shaping, or intelligent tasks.
Fan et al. proposed a feasible single-layered lossless metasurface for adjusting the asymmetric transmission of flexural waves. The asymmetric transmission is physically realized by the uneven diffraction of the ±1st orders in opposite fields of the designed metasurface. Their design allowed the elastic-wave behavior to switch between efficient symmetric and asymmetric transmissions. Furthermore, a high contrast ratio of transmitted energy is verified in experiments and simulations within a wide-angle range.8
Carpentier et al. investigated the ability of a metasurface made of resonant elliptical pillars to focus flexural Lamb waves in the subwavelength regime. They reported on the influence of the ellipticity parameter on the local resonances of the pillars, in particular, the monopolar compressional and dipolar bending modes that are responsible for the desired focusing effect. Both the resonances can be superimposed for a particular choice of the ellipticity parameter, allowing a phase shift of 2π in the transmission coefficient for an incident antisymmetric Lamb wave. Finally, a metasurface of gradient elliptical pillars ellipticity is designed, and its capacity to choose the focusing directionality of the transmitted wave at different targeted points is demonstrated.9
Moghaddaszadeh et al. presented an elastic neuromorphic metasurface that performs distinct classification tasks. Multiple layers of reconfigurable waveguides are phase-trained via constant weights and trainable activation functions in a manner that enables the resultant wave scattering at the readout location to focus on the correct class within the detection plane. They further demonstrated the neuromorphic system’s reconfigurability in performing two distinct tasks, eliminating the need for costly remanufacturing.10
Zeighami et al. explored the propagation characteristics of surface Rayleigh waves in a locally resonant metamaterial layer positioned on an elastic half-space. They utilized a thin-plate sample and constructed the metamaterial layer, featuring multiple rows of subwavelength resonators, by machining the resonators at one edge of the plate. Employing a piezoelectric transducer coupled to the plate and a laser vibrometer, they actuated and received the surface-like waves propagating at the plate edge. The experimental observations revealed the hybridization of the fundamental surface mode at the resonant frequency of the embedded resonators, leading to the creation of a low-frequency bandgap.11
Zhao et al. developed transformation theory to establish equivalence between curved plates of different shapes and thickness profiles. Introducing tailor-made thickness profiles on a given curved shape enables illusion effects, where flexural waves propagate as if on a flat plate or on another curved plate with a totally different configuration. They further carried out numerical simulations and experimental field mapping to confirm the effectiveness of these illusions.12
Babacic et al. utilized Brillouin light scattering to investigate the impact of symmetry breaking on GHz phonon propagation in phononic crystals made of holey silicon nanomembranes. They showed that the lattice of thimble-like holes leads to broken midplane symmetry and, hence, to anticrossing acoustic bandgaps. With the rising level of uncorrelated translational disorder, the phononic effects are gradually suppressed, starting at higher frequencies. The low-frequency partial Bragg bandgap remains robust up to the highest level of disorder.13
One-dimensional acoustic and elastic metamaterials provide a good candidate to theoretically analyze rich wave functions, such as nonlocal effect, rainbow trapping effect, maxon mode, Willis coupling, and topological interface mode.
Wang et al. introduced the concept of nonlocal effect into a monoatomic mass–spring periodic structure, leading to unique characteristics of dispersion curves. Through the incorporation of the second neighboring nonlocal effect, they observed the emergence of negative group velocity and specific points with zero group velocity within the dispersion curves for a rainbow trapping effect. Notably, with the appropriate tuning of the third neighboring nonlocal effect, they observed that multi-frequency can be localized at predetermined positions, demonstrating a multi-frequency rainbow trapping phenomenon.14
Zhang et al. observed maxon-like dispersion of ultrasonic guided waves in elastic metamaterial beams consisting of a rectangular beam and an array of cylindrical resonators. The pillars act as asymmetric resonators that induce a strong modal hybridization. They observed the strongly localized maxon mode with zero group velocity and demonstrated a unique feature of the maxon with a down-shifting peak frequency in space. To reveal the fundamental mechanism, they also conducted comprehensive numerical studies on all frieze group symmetries and key geometric parameters.15
Samak and Bilal presented an alternative design methodology for metamaterials with exotic dispersion characteristics using magnetic lattices. They provided experimental evidence for obtaining mixed positive–negative dispersion for the lowest dispersion branch without the need for non-local interactions. Their methodology provided control over the transmission region and the group velocity for both acoustic and optical branches.16
Cai et al. studied elastic topological interface states appearing between two Su–Schrieffer–Heeger-like pillared metabeams where each metabeam is constituted by a mirror symmetric hyperuniform structure. They demonstrated that this structure could open new bandgaps at low frequencies, of which some are nontrivial and can support topological interface modes. They further showed that the number of low-frequency bandgaps supporting the topological modes increases with the level of randomness, hence providing a high number of interface modes in the same structure. The robustness of the topological interface states against random perturbations in the pillars’ positions is further verified.17
Danawe and Tol presented how to tune the electro-momentum coupling arising in 1D periodic piezoelectric metamaterials with broken inversion symmetry through shunting the inherent capacitance of the individual piezoelectric layers with a resistor and an inductor in series forming a resistor–inductor–capacitor circuit. They derived a closed-form expression of the electro-momentum coupling in shunted piezoelectric metamaterials and demonstrated the ability to tailor the electro-momentum coupling coefficient and control the amplitudes and phases of the forward/backward propagating waves, yielding tunable asymmetric wave responses.18
Groby and Haberman derived closed-form expressions for the effective properties of a one-dimensional heterogeneous poroelastic medium consisting of a periodically repeating two-layer unit-cell. The Willis coupling of this periodic poroelastic medium does not vanish in the low-frequency limit. The effective wavenumber and impedance of this asymmetric lamellar material demonstrate symmetric reflection and absorption behavior. The scattering coefficients are different at non-zero frequencies but still in the metamaterial limit and are correct when the Willis coupling is included. They showed that asymmetry in poroelastic layers results in direction-dependent absorption coefficients. To validate these scattering coefficients, the frequency range is wider when the Willis coupling matrix is accounted for than in its absence.19
Advanced sensing and detection are also important applicable functions of acoustic and elastic metamaterials that can overcome some pending limits in current technologies.
Dai et al. presented an acoustic meta-stethoscope consisting of multilayered perforated round plate units and a cylindrical shell with subwavelength size, simple fabrication, and easy assembly for high-sensitivity cardiac auscultation. They proved that the equivalent acoustic propagation path is substantially increased by the metamaterial with a high refractive index, enabling downscaling the device to a subwavelength footprint. The auscultation performance of the meta-stethoscope is experimentally characterized by detecting the cardiac sound signal from the human heart through different types of clothing, showing an expected sensitivity enhancement exceeding 10 dB within the predicted working frequency regardless of the type of clothing.20
Liu et al. proposed a seashell-inspired metasensor that can simultaneously perform spatial frequency mapping and act as a polarizer. The structure emerges from a universal parametric design that encompasses diverse spiral geometries with varying circular cross sections and curvature radii, all leading to tonotopic behavior. Adoption of an optimization process leads to a planar geometry that enables us to simultaneously achieve tonotopy for orthogonally polarized modes, leading to the possibility to control polarization as well as the spatial distribution of frequency maxima along the spiral axis.21
Aslam et al. proposed a metallic ring-shaped metafilter designed to explore high-order bandgaps to enhance the detection of material microstructural changes in high-frequency, nonlinear, guided wave-based techniques. They underscored the significance of parameters such as the number of rings employed in the filter, signal duration, and bandgap width in optimizing its performance. The defect localization technique, based on the time difference of arrival of second-order wave modes, accurately predicts the defect location.22
Kim et al. studied an advanced photocatalyst model characterized by high efficiency and ease in dispersion and retrieval processes. The fabrication of the specimens was achieved through a combined approach of additive manufacturing and chemical synthesis. The open-cell structure, composed of photopolymerized polymers and synthesized nanocrystals, displays a notable aspect ratio, an extensive surface area, and a significant porosity. These features facilitate the concurrent entry of fluid and light into the core of the framework, leading to enhanced light scattering and activation of photoinduced redox reactions on organic contaminants adhered to the anatase TiO2 surface. The photocatalytic performance was quantified through a spectroscopic analysis, monitoring the absorbance changes associated with organic pollutant degradation.23
Acoustic metamaterials and phononic crystals are excellent platforms to realize various topological states and other abnormal properties.
Geng et al. described the acoustic realization of third-order quartic-root topological insulators based on the original 3D square-root sonic crystals. By inserting extra sites into the 3D square-root lattice, they renormalized the coupling parameters and obtained multiple topological boundary states in different bulk gaps with distinct phase profiles. They further validated the robustness of the corner states under random bulk disorder and showed the diversified localizations of topological edge states at distinct frequencies on different-shaped 3D sonic crystals.24
Xu et al. explored the distinctive properties associated with a type-II Dirac point in a simply structured phononic crystal with a lattice deformation. A practical implementation of such a phononic crystal is achieved with LEGO bricks. Upon introducing a periodic parity–time (PT) symmetric non-Hermitian perturbation, the phononic crystal undergoes a transition from PT-symmetric phase to PT-broken phase, causing the deformation of type-II Dirac point into an oval of exceptional points in the band structure. They analyzed the symmetric and broken phases and demonstrated that broadband unidirectional transparency and a coherent perfect absorber and laser can be realized.25
Willey et al. reported that the coiled phononic crystal exhibits duality of its dispersion curves relative to its coiling/twist angle, meaning that the dispersion curves are symmetric about a particular coiling/twist angle defined configuration. The ability to link unit cells with different wave propagation orientations, but the same dispersion/dynamic stiffness, is used to create an elastic hierarchically coiled phononic crystal based on a fractal space-filling curve design. They numerically demonstrated reflectionless wave propagation in large fractal architectures such that regular phononic properties, such as passbands and bandgaps, are preserved, allowing for propagation of broadband signals and filtering.26
Ellouzi et al. numerically and experimentally studied a 3D printed acoustic lens capable of generating a double vortex pattern with a topological charge of 1 and an optional focusing profile in water. The results indicated that by altering the positioning of the vortices’ axes, it is possible to control both the intensity and the location of the pressurized zone. The proposed approach showed promise for enhancing the effectiveness and versatility of various applications by generating a larger number of vortices and freely tailoring the focal profile with a single lens.27
Khalil et al. provided a detailed explanation of the design, simulation, and experiment of quad-square metamaterial-based negative-index unit cells for S-band applications. A series of systematic parametric studies were conducted to optimize the quad square metamaterial structure. Key parameters, such as substrate types, unit cell arrays, thicknesses of substrate, and split gaps, were varied to determine their impact on the structure. The validated equivalent circuit result was compared to the simulated results, showing a significant agreement.28
In conclusion, this Special Topic on new frontiers in acoustic and elastic metamaterials and metasurfaces collects 28 published papers from international experts in this community for the following five main areas: (i) sound absorbers and insulators; (ii) various functions for guided waves; (iii) new effects in 1D structures; (iv) advanced sensing and detection; and (v) topological insulators and other abnormal properties. We hope that the advances in this collection will call for new efforts in addressing the challenges to discover more properties in fundamental aspects and develop new technologies in application aspects.
We acknowledge all the authors who have contributed to this Special Topic and the journal editors and staff who helped to manage this collection. We also acknowledge support by the National Natural Science Foundation of China (Grant No. 12272267), the Young Elite Scientists Sponsorship Program by CAST (Grant No. 2021QNRC001), the Shanghai Science and Technology Commission (Grant No. 22JC1404100), Shanghai Gaofeng Project for University Academic Program Development, the NAP award (Grant No. 020482) from Nanyang Technological University, Singapore, the Project No. PID2021-124814NBC22, funded by MCIN/AEI/10.13039/501100011033/“FEDER A way of making Europe,” and the Project No. CNS2023-145510 funded by MCIN/AEI/10.13039/501100011033, “European Union NextGenerationEU/PRTR.”
AUTHOR DECLARATIONS
Author Contributions
Yabin Jin: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Yifan Wang: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Daniel Torrent: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Abdelkrim Khelif: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal).