Resonant metalenses for flexural waves in plates

Abstract

The dispersion curves of a cluster of closely spaced rods supported by a thin plate are characterised by subwavelength bandgaps and slow group velocities induced by local resonance effects. A recent analytical study [Williams, Roux, Rupin, and Kuperman (2015). Phys. Rev. B 91, 104307], has shown how the slow velocity branch depends, amongst other parameters, on the height of the rods that make up the cluster. Such metamaterial, offering easy-to-tune spatial velocity gradients, is a perfect candidate for building gradient index lenses such as Luneburg, Maxwell, and 90° rotating. Here theoretical results are combined with numerical simulations to design and test metalenses for flexural waves. The lenses are obtained by tuning the height of the cluster of rods such that they provide the required refractive index profile. Snapshots and videos from three-dimensional numerical simulations in a narrow band centered at ∼4 kHz are used to analyse the performances of three types of gradient index metalens (Luneburg, Maxwell, and 90° rotating).