Abstract
We present a homogenization scheme for acoustic metamaterials that is based on reproducing the lowest orders of scattering amplitudes from a finite volume of metamaterials. This approach is noted to differ significantly from that of coherent potential approximation, which is based on adjusting the effective-medium parameters to minimizescatteringsinthelong-wavelengthlimit.Withtheaidofmetamaterials’eigenstates,theeffectiveparameters, such as mass density and elastic modulus can be obtained by matching the surface responses of a metamaterial’s structuralunitcellwithapieceofhomogenizedmaterial.FromtheGreen’stheoremappliedtotheexteriordomain problem, matching the surface responses is noted to be the same as reproducing the scattering amplitudes. We verifyourschemebyapplyingittothreedifferentexamples:alayeredlattice,atwo-dimensionalhexagonallattice, and a decorated-membrane system. It is shown that the predicted characteristics and wave fields agree almost exactly with numerical simulations and experiments and the scheme’s validity is constrained by the number of dominant surface multipoles instead of the usual long-wavelength assumption. In particular, the validity extends to the full band in one dimension and to regimes near the boundaries of the Brillouin zone in two dimensions.
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