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.

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.

We discuss the simultaneous existence of phononic and photonic band gaps in a periodic array of holes drilled in a Si membrane. We investigate in detail both the centered square lattice and the boron nitride (BN) lattice with two atoms per unit cell which include the simple square, triangular and honeycomb lattices as particular cases. We show that complete phononic and photonic band gaps can be obtained from the honeycomb lattice as well as BN lattices close to honeycomb. Otherwise, all investigated structures present the possibility of a complete phononic gap together with a photonic band gap of a given symmetry, odd or even, depending on the geometrical parameters.

We present a theoretical analysis of the phonon transport and guiding of acoustic waves in a phononic crystal made up of a square array of cylindrical dots, which is deposited on a thin homogeneous plate. With appropriate choice of the geometrical parameters, this structure can display several gaps, one of them being well below the Bragg gap. With the help of the finite difference time domain method, we calculate the transmission coefficient vs the frequency and demonstrate a good agreement with the dispersion curves. We show the possibility of guided modes inside an extended linear defect created either by removing one row of cylinders or by changing the height or the materials constituting the dots in a row. The wavelengths of the waves transmitted in the low-frequency gap are about ten times larger than the width of the waveguide. We discuss the transmittivity of each confined mode appearing in the band gap as well as the conversion in the polarization of the transmitted waves which can occur more or less significantly.

We study theoretically the simultaneous existence of phononic and photonic band gaps in a periodic array of silicon pillars deposited on a homogeneous thin silica plate. Several lattices, namely, square, triangular, and honeycomb are investigated for a wide range of geometrical parameters. We discuss the most suitable cases for dual phononic-photonic band gaps, especially in comparison to the more conventional structures constituted by a periodic array of holes in a membrane.

We investigate theoretically the properties of phononic crystal plates with hollow pillars. Such crystals can exhibit confined whispering gallery modes around the hollow parts of the pillars whose localization can be increased by separating the pillar from the plate by a full cylinder. We discuss the behaviors of these modes and their potential applications in guiding and filtering. Filling the hollow parts with a fluid gives rise to new localized modes, which depend on the physical properties and height of the fluid. Thus, these modes can be actively controlled for the purpose of multichannel multiplexing. In particular, one can obtain localized modes associated with the compressional vibrations of the fluid along its height. They can be used for the purpose of sensing the acoustic properties of the fluid or their variations with temperature.