Observing localization and delocalization of the flat-band states in an acoustic cubic lattice

Abstract

Over the past decades, wave localization and a wide variety of related phenomena have come to the forefront of research. Here, we theoretically and experimentally investigate the localization and delocalization of the flat-band states in an acoustic cubic lattice. Under evanescent couplings, the band structure of the designed cubic lattice has two dispersive bands and two degenerate flat bands. According to the analyses, we find that the constructions of flat-band states only depend on the excitation pressures and the coupling coefficients, which are frequency independent. With the flat-band state excitation, the acoustic wave can be either localized or delocalized in the lattice, which is determined by the excitation frequency. When the excitation frequency is close to the flat-band frequency of the lattice, the flat-band state can spread into the whole cubic lattice due to the resonance energy transfer among primitive cells. On the other hand, when the excitation frequency deviates from the flat-band frequency, the flat-band state can be localized in any primitive cell of the designed lattice. This work lays the groundwork for exploring the high-dimensional bound states in acoustic systems and has potential impacts on the applications of acoustic sensing and sound energy harvesting.