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Traditional sound diffusers are quasi-random phase gratings attached toreflecting surfaces whose purpose is to augment the spatiotemporal incoherenceof the acoustic field scattered from reflective surfaces. This configurationallows one to cover a large reflecting surface by periodically tiling thediffuser unit cells to cover a large area while reducing undesirable specularreflection for incident plane waves. However, the periodic arrangement of theunit cells leads to coherent constructive and destructive interference in thescattered field in some directions which is undesirable for achieving acousticdiffusivity. The spatial uniformity of acoustic energy scattered fromconventional diffusers constructed in this way is a fundamental limitation ofthe traditional approach which is not easily overcome when one wishes to coverlarge reflecting surfaces. In this work, we investigate spatiotemporalmodulation of the surface acoustic admittance of an acoustic diffuser as a newapproach to improve the sound diffusion. We develop a semi-analytical modelthat employs Fourier series expansion to determine the scattered sound fieldfrom a surface admittance consisting of a quadratic residue diffuser (QRD)design whose individual well admittances are modulated with a traveling wavewith modulation frequency, $\omega_{\mrm{m}}$, amplitude, $Y_\mrm{m}$, and awavenumber that matches the unit cell length, $\Lambda$. We observe significantimprovement in diffusion performance due to the fact that the spatiotemporalmodulation scatters sound into additional frequency--wavenumber pairsassociated with harmonics of the modulation frequency and their diffractionorders. The semi-analytical model results are verified using time-domain finiteelement model.

Sound diffusion with spatiotemporally modulated acoustic metasurfaces