Designing Hyper-Thin Acoustic Metasurfaces with Membrane Resonators

Abstract: We design extremely-thin acoustic metasurfaces, providing a versatile platform for the manipulation of reflected pressure fields, that are constructed from mass loads and stretched membranes fixed to a periodic rigid framework. These metasurfaces demonstrate deeply subwavelength control and can have thicknesses an order of magnitude less than those based around Helmholtz resonators. Each sub-unit of the metasurface is resonant at a frequency tuned geometrically, this tunability provides phase control and using a set of finely tuned membrane resonators we create a phase-grating metasurface. This surface is designed to exhibit all-angle negative reflections with the ratio of wavelength, $\lambda$, to thickness, $h$, of $\lambda/h\approx 23.1$, and to create a flat mirror using the phase profile of an elliptic reflecting mirror. A further important acoustic application is to sound diffusers and we proceed to design a deeply subwavelength membrane-based meta-diffuser that can be two orders of magnitude thinner than the operating wavelength, i.e. thickness $\approx\lambda/102$. This paves the way for developing advanced acoustic metasurfaces with applicability to functional acoustic devices in sound-related industries.