Elastic wave manipulation in geodesic lenses

TL;DR

This paper explores how curvature in elastic waveguides can be used to control wave propagation, combining theoretical modeling with experimental validation to demonstrate curvature-based wave manipulation techniques.

Contribution

It introduces a theoretical framework linking curvature to refractive index modulation in elastic waveguides and validates it through experiments on 3D printed membranes.

Findings

Curved profiles can effectively manipulate elastic wave trajectories.

Theoretical predictions match experimental results.

Curvature enables guiding, focusing, and steering of elastic waves.

Abstract

We investigate wave propagation in curved, thin elastic waveguides, where curvature is shown to be equivalent to a spatially modulated refractive index. We establish this relationship within a theoretical framework that leverages non-Euclidean transformations. Theoretical predictions illustrate how curved profiles can be designed to manipulate wave trajectories in analogy with geometrical optics principles. Experiments on 3D printed curved membranes confirm the theoretical predictions, and suggest curvature as a viable approach for guiding, focusing and steering of elastic waves.