Metadiffusers: Sound diffusers with deep-subwavelength dimensions

We present deep-subwavelength diffusing surfaces based on acoustic metamaterials, namely metadiffusers. Sound diffusers are surfaces whose acoustic scattering distribution is uniform. Here, we achieve sound diffusion by using acoustic metamaterials composed by rigidly backed slotted panels, each slit being loaded by an array of Helmholtz resonators. Both, strongly dispersive propagation and slow sound speed are observed inside the slits, shifting their quarter wavelength resonances to the deep-subwavelength regime. Thus, the reflection coefficient of each slit can be tailored to obtain either customized reflection phase, moderate or even perfect absorption. By using a set of different slits with tuned geometry we designed surfaces with spatially-dependent reflection coefficients having uniform magnitude Fourier transforms, presenting good diffusion performance. First, various sub-wavelength diffusers based on known number-theoretical sequences such as quadratic residue or primitive root sequences are presented. Second, accurate designs for binary, ternary and index sequence diffusers are presented making use of perfect acoustic absorption. Finally, a 3 cm thick metadiffuser (1/46 times smaller than the wavelength) was designed working efficiently for frequencies ranging from 250 Hz to 2 kHz, i.e., 3 octaves.