Surface Acoustic Waves Propagation at Lossy Metasurfaces: Experimental and Theoretical Characterization of Complex Dispersion Relations

While metasurfaces properties are known to govern the dispersion relation of Surface Acoustic Wave (SAW) that mimics surface plasmon phenomena, little attention has been paid to the effects of micro-structural dissipation on that dispersion relation. Here we report the experimental and theoretical characterization of both SAW propagation and attenuation in the presence of a lossy metasurface. The latter consists of quarter-wavelength resonators embedded in a rigid board and arranged periodically in a square lattice. Complex SAW wavenumbers are retrieved experimentally using a spatial Laplace Transform, and experimental results are compared with those from an analytical model using Plane Wave Expansions. Both real and imaginary parts of the SAW wavenumber are presented and results bears testament to the hybridisation of the metasurface-induced dispersion relation with periodicity-induced Bragg interferences. The accuracy of homogenization approaches is estimated and the possibility of slow sound applications using such a metasurface is discussed in regard to SAW attenuation.