Doubly negative isotropic elastic metamaterial for sub-wavelength focusing: Design and realization

In spite of much progress in elastic metamaterials, tuning the effective density and stiffness to desired values ranging from negatives to large positives is still difficult. In particular, simultaneous realization of double negativity and isotropy, critical in sub-wavelength focusing, is very challenging since anisotropy is usually unavoidable in resonance-based metamaterials. The main difficulty is that there is no established systematic design method for simultaneous achieving of double negativity and isotropy. Thus, we propose a unique elastic metamaterial unit cell with which simultaneous realization can be achieved by an explicit step-by-step approach. The unit cell of the proposed metamaterial can be accurately modeled as an equivalent mass-spring system so that the effective properties can be easily controlled with the design parameters. The actual realization was carried out by acquiring the desired properties in sequential steps which is in detail. The specific application for this study is on sub-wavelength focusing, which will be demonstrated by waves from a single point source focused on a region smaller than half the wavelength. Actual experiments were performed on an aluminum plate where the designed metamaterial flat lens was imbedded. The results acquired through simulations and experiments suggest potential applications of the proposed metamaterial and the systematic design approach in advanced acoustic surgery or non-destructive testing.