Impedance is an important issue in the design of acoustic lenses because mismatched impedance is detrimental to real focusing applications. Here, we report two designs of acoustic lenses that focus acoustic waves in water and air, respectively. They are tailored by acoustic meta-surfaces, which are rigid thin plates decorated with periodically distributed sub-wavelength slits. Their respective building blocks are constructed from the coiling-up spaces in water and the layered structures in air. Analytic analysis based on coupled-mode theory and transfer matrix reveals that the impedances of the lenses are matched to those of the background media. With these impedance-matched acoustic lenses, we demonstrate the acoustic focusing effect by finite-element simulations.

A second-order topological insulator is designed on a platform of a two-dimensional (2D) square lattice with all coupling coefficients having the same sign. Simulated results show the existence of two types of nontrivial corner states in this system, with one type being identified as bound states in the continuum (BIC). The non-BIC corner states are also found by surrounding a nontrivial sample by a trivial one, and interestingly, these perfectly confined corner states can be gradually delocalized and merge into edge states by tuning the intersystem coupling coefficient. Both BIC and non-BIC corner states originate from bulk dipole moments rather than quantized quadrupole moments, with the corresponding topological invariant being the 2D Zak phase. Full wave simulations based on realistic acoustic waveguide structures are demonstrated. Our proposal provides an experimentally feasible platform for the study of the interplay between BIC and a high-order topological insulator, and the evolution from corner states to edge states.

The leakage of sound waves in a resonance based rainbow trapping device prevents the sound wave being trapped in a specific location. In this study, we report a design of sound trapping device based on coupled Helmholtz resonators, loaded to an air waveguide, which can effectively tackle the wave leakage issue. We show that coupled resonators structure can generate dips in the transmission spectrum by an analytical model derived from Newton’s second law and numerical analysis based on finite-element method. An effective medium theory is derived, which shows that coupled resonators cause a negative effective bulk modulus near the resonance frequency and induce flat bands that give rise to the confinement of the incoming wave inside the resonators. We compute the transmission spectra and band diagram from the effective medium theory, which are consistent with the simulation results. Trapping and high absorption of sound wave energy are demonstrated with our designed device.

We propose to achieve efficient emission of highly directional sound beams from multiple monopole sources embedded in a subwavelength enclosure. Without the enclosure, the emitted sound fields have an indistinguishable or omnidirectional radiation directivity in far fields. The strong directivity formed in the presence of the enclosure is attributed to interference of sources under degenerate Mie resonances in the enclosure of anisotropic property. Our numerical simulations of sound emission from the sources demonstrate the radiation of a highly directed sound beam of unidirectional or bidirectional patterns, depending on how the sources are configured inside the enclosure. Our scheme, if achieved, can solve the challenging problem of poor directivity of a subwavelength sound system, and can guide beam forming and collimation by miniaturized devices.