Creating compact localized modes for robust sound transport via singular flat band engineering

Extreme localization in engineered lattices is paramount for wave manipulation and robust signal guidance. Yet, an experimental demonstration of flat-band-induced compact localized states (CLS) and boundary modes in acoustic Kagome lattices has remained elusive, a gap we address herein. Compact localized states populate singular dispersion bands characterized by band crossing, where a quadratic and a flat dispersion coalesce into a singularity. The strength of this singularity is quantified using the Hilbert-Schmidt quantum distance, providing a bulk-boundary correspondence. This condition gives rise to states extremely localized in the plane and protected by dispersion flatness, characterized by broadband and sustained confinement over time. The analysis is extended to a system of coupled acoustic waveguides, where sound propagates out-of-plane within tightly localized in-plane sites, either at the boundaries or within the interior of the lattice. This framework opens avenues for the manipulation and transport of sound waves, with potential applications in communication, signal processing, and sound isolation, expanding the reach of flat-band lattice physics within acoustics.