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

TL;DR

This study demonstrates that a specially designed elastic plate with a radially varying thickness can mimic Maxwell's fish-eye lens in optics, showing similar imaging properties for flexural waves at specific frequencies.

Contribution

The paper experimentally shows that a piecewise constant thickness elastic plate can replicate Maxwell's fish-eye lens behavior for flexural waves, supported by FDTD simulations.

Findings

Imaging properties match ray trajectory predictions

Refocusing time varies with frequency due to dispersion

Experimental results agree with simulations

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.