Acoustic lattice resonances and generalised Rayleigh–Bloch waves

Abstract

The intrigue of waves on periodic lattices and gratings has resonated with physicists and mathematicians alike for decades. In-depth analysis has been devoted to the seemingly simplest array system: a one-dimensionally periodic lattice of two-dimensional scatterers embedded in a dispersionless medium governed by the Helmholtz equation. We investigate such a system and experimentally confirm the existence of a new class of generalised Rayleigh–Bloch waves that have been recently theorised to exist in classical wave regimes, without the need for resonant scatterers. Airborne acoustics serves as such a regime and we experimentally observe the first generalised Rayleigh–Bloch waves above the first cut-off, i.e., in the radiative regime. We consider radiative acoustic lattice resonances along a diffraction grating and connect them to generalised Rayleigh–Bloch waves by considering both short and long arrays of non-resonant 2D cylindrical Neumann scatterers embedded in air. On short arrays, we observe finite lattice resonances under continuous wave excitation, and on long arrays, we observe propagating Rayleigh–Bloch waves under pulsed excitation. We interpret their existence by considering multiple wave scattering theory and, in doing so, unify differing nomenclatures used to describe waves on infinite periodic and finite arrays and the interpretation of their dispersive properties.

The interaction of waves with periodic structures is a feature central to many areas of physics from quantum mechanics to acoustics. Here, the authors numerically and experimentally demonstrate the presence of Rayleigh-Bloch waves in the regime above the first cut-off using acoustic gratings.