The introduction of engineered resonance phenomena on surfaces has opened a new frontier in surface science and technology. Pillared phononic crystals, metamaterials, and metasurfaces are an emerging class of artificial structured media, featuring surfaces that consist of pillars—or branching substructures—standing on a plate or a substrate. A pillared phononic crystal exhibits Bragg band gaps, while a pillared metamaterial may feature both Bragg band gaps and local resonance hybridization band gaps. These two band-gap phenomena, along with other unique wave dispersion characteristics, have been exploited for a variety of applications spanning a range of length scales and covering multiple disciplines in applied physics and engineering, particularly in elastodynamics and acoustics. The intrinsic placement of pillars on a semi-infinite surface—yielding a metasurface—has similarly provided new avenues for the control and manipulation of wave propagation. Classical waves are admitted in pillared media, including Lamb waves in plates and Rayleigh and Love waves along the surfaces of substrates, ranging in frequency from hertz to several gigahertz. With the presence of the pillars, these waves couple with surface resonances richly creating new phenomena and properties in the subwavelength regime and in some applications at higher frequencies as well. At the nanoscale, it was shown that atomic-scale resonances—stemming from nanopillars—alter the fundamental nature of conductive thermal transport by reducing the group velocities and generating mode localizations across the entire spectrum of the constituent material well into the terahertz regime. In this article, we first overview the history and development of pillared materials, then provide a detailed synopsis of a selection of key research topics that involve the utilization of pillars or similar branching substructures in different contexts. Finally, we conclude by providing a short summary and some perspectives on the state of the field and its promise for further future development.

With the growing interest in the field of artificial materials, more advanced and sophisticated functionalities are required from phononic crystals and acoustic metamaterials. This implies a high computational effort and cost, and still the efficiency of the designs may be not sufficient. With the help of third‐wave artificial intelligence technologies, the design schemes of these materials are undergoing a new revolution. As an important branch of artificial intelligence, machine learning paves the way to new technological innovations by stimulating the exploration of structural design. Machine learning provides a powerful means of achieving an efficient and accurate design process by exploring nonlinear physical patterns in high‐dimensional space, based on data sets of candidate structures. Many advanced machine learning algorithms, such as deep neural networks, unsupervised manifold clustering, reinforcement learning and so forth, have been widely and deeply investigated for structural design. In this review, we summarize the recent works on the combination of phononic metamaterials and machine learning. We provide an overview of machine learning on structural design. Then discuss machine learning driven on‐demand design of phononic metamaterials for acoustic and elastic waves functions, topological phases and atomic‐scale phonon properties. Finally, we summarize the current state of the art and provide a prospective of the future development directions.

Phononic crystals and acoustic metamaterials are periodic structures whose effective properties can be tailored at will to achieve extreme control on wave propagation. Their refractive index is obtained from the homogenization of the infinite periodic system, but it is possible to locally change the properties of a finite crystal in such a way that it results in an effective gradient of the refractive index. In such case the propagation of waves can be accurately described by means of ray theory, and different refractive devices can be designed in the framework of wave propagation in inhomogeneous media. In this paper we review the different devices that have been studied for the control of both bulk and guided acoustic waves based on graded phononic crystals.

We investigate the properties of a phononic crystal plate with hollow pillars and introduce the existence of whispering-gallery modes (WGMs). We show that by tuning the inner radius of the hollow pillar, these modes can merge inside both Bragg and low frequency band gaps, deserving phononic crystal and acoustic metamaterial applications. These modes can be used as narrow pass bands for which the quality factor can be greatly enhanced by the introduction of an additional cylinder between the hollow cylinder and the plate. We discuss some functionalities of these confined WGM in both Bragg and low frequency gaps for wavelength division in multiplexer devices using heteroradii pillars introduced into waveguide and cavity structures.

Metasurfaces are planar metamaterials with a flat surface and a subwavelength thickness that are able to shape arbitrary wave fronts such as focusing or imaging. There is a broad interest in the literature about subwavelength focusing and imaging based on bulk metamaterials while the utilization of metasurfaces for elastic waves has rarely been reported. Here, we present a type of elastic metasurface consisting of a line of gradient resonant pillars for robust deep subwavelength focusing and imaging of elastic waves in a plate. Numerical approaches supported by analytic Huygens-Fresnel demonstrations show that the subwavelength full width at half maximum (FWHM) behaves linearly as a function of the ratio F/D where F is the measured focal length and D the metasurface length. We discuss the range of F/D where FWHM remains smaller than half a wavelength in the near field. The focal length F and the FWHM exhibit stable performances when submitted to disorder perturbations in the geometrical parameters and to frequency fluctuations. We show that the enhanced focusing resolution with smaller FWHM can be very beneficial for energy harvesting since the output electric power can be increased by more than one order of magnitude. The proposed elastic metasurfaces bring a way for high resolution focusing and imaging which is useful for applications in various domains such as energy harvesting, wave sensing, communication, nondestructive evaluation.

Many efforts have been devoted to studying the robustness of topologically protected edge states in acoustics; however, the robustness of conventional edge states is rarely reported. In this work we theoretically study interface acoustic states appearing in finite arrays of resonators on a thin plate with topologically protected and conventional designs. Topologically protected interface states are first analyzed by employing the concept of breaking inversion symmetry within the unit cell of a honeycomb lattice for cylindrical and spherical resonators; we further demonstrate the robustness of the wave propagation along a zigzag path containing sharp corners and defects. In parallel, a conventional interface state is also designed and compared to the same situations. We found that the conventional interface state suffers backscattering in the zigzag path while it can show a more confined wave transport in some cases. The presence of a defect along the propagation path scatters the conventional interface wave and in particular can prohibit full propagation in the presence of a localized state at the defect. Then, we show that the immunity of the topologically protected design needs the interface to be surrounded by at least two hexagons of the phononic crystals on both sides, especially at the sharp corners in the zigzag path, while the conventional design only needs one hexagon of bulk media with the advantage of compact wave transport. Position and height disorders are further introduced to the interface pillars for both designs. It is revealed that in both designs, the transmission decreases quasilinearly with position disorder while it exhibits an abrupt drop with height disorder showing a transition threshold. With high disorder perturbation, waves can hardly enter the interface for the topologically protected design, while waves are trapped at the interface for the conventional design. A certain robustness against disorder is exhibited for conventional edge states. This work provides insight into the interface states in micro- and nanoscale characterization and figures out the behaviors for both topologically protected and conventional interface states.