Unveiling Extreme Anisotropy in Elastic Structured Media

Abstract

Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones, and saddle points; identifying these and the nature of the associated modes from a direct reading of the dispersion surfaces is not straightforward, especially in three dimensions or at high frequencies when several dispersion surfaces fold back in the Brillouin zone. A recently proposed asymptotic high-frequency homogenization theory is applied to a challenging time-domain experiment with elastic waves in a pinned metallic plate. The prediction of a narrow high-frequency spectral region where the effective medium tensor dramatically switches from positive definite to indefinite is confirmed experimentally; a small frequency shift of the pulse carrier results in two distinct types of highly anisotropic modes. The underlying effective equation mirrors this behavior with a change in form from elliptic to hyperbolic exemplifying the high degree of wave control available and the importance of a simple and effective predictive model.