Dynamic behavior of mechanical cloaks designed by direct lattice transformation

Abstract: Steering waves in elastic solids is more demanding than steering waves in electromagnetism or acoustics. As a result, designing material distributions which are the counterpart of optical invisibility cloaks in elasticity poses a major challenge. Waves of all polarizations should be guided around an obstacle to emerge on the downstream side as though no obstacle were there. Recently, we have introduced the direct-lattice-transformation approach. This simple and explicit construction procedure led to extremely good cloaking results in the static case. Here, we transfer this approach to the dynamic case, i.e., to elastic waves or phonons. We demonstrate broadband reduction of scattering, with best suppressions exceeding a factor of five when using cubic coordinate transformations instead of linear ones. To reliably and quantitatively test these cloaks efficiency, we use an effective-medium approach.