Experiments on Maxwell's Fish-eye dynamics in elastic plates

Abstract

We experimentally demonstrate that a Duraluminium thin plate with a thickness profile varying radially in a piecewise constant fashion as h(r)=h(0)(1+(r/Rmax)), with h(0)=0.5 mm, h(Rmax)=2 mm and Rmax=10 cm behaves in many ways as Maxwell's fish-eye lens in optics, since its imaging properties for a Gaussian pulse with central frequencies 30~kHz and 60~kHz are very similar to those predicted by ray trajectories (great circles) on a virtual sphere (rays emanating from the North pole meet at the South pole). However, refocusing time depends on the carrier frequency as a direct consequence of the dispersive nature of flexural waves in thin plates. Importantly, experimental results are in good agreement with Finite-Difference-Time-Domain simulations.