Homogenization of acoustic metamaterials of Helmholtz resonators in fluid

By using a two-step homogenization approach, we derive analytical formulas of effective mass density rho(e) and effective bulk modulus B-e for two- and three-dimensional acoustic metamaterials of Helmholtz resonators (HRs) in fluid. A negative B-e is found at certain frequencies due to the monopolar resonance, leading to a low-frequency acoustic band gap. A unified picture is presented for metamaterials of HRs and three-component metamaterials of negative rho(e). Our work supports recent observations in a one-dimensional array of HRs [N. Fang et al., Nat. Mater. 5, 452 (2006)] and presents important high-dimensional extensions for exploring more fascinating phenomena.