Focusing on Plates: Controlling Guided Waves using Negative Refraction

Elastic waves are guided along finite structures such as cylinders, plates, or rods through reflection, refraction, and mode conversion at the interfaces. Such wave propagation is ubiquitous in the world around us, and studies of elastic waveguides first emerged in the later part of the 19(th) century. Early work on elastic waveguides revealed the presence of backward propagating waves, in which the phase velocity and group velocity are anti-parallel. While backward wave propagation exists naturally in very simple finite elastic media, there has been remarkably little attention paid to this phenomenon. Here we report the development of a tunable acoustic lens in an isotropic elastic plate showing negative refraction over a finite acoustic frequency bandwidth. As compared to engineered acoustic materials such as phononic crystals and metamaterials, the design of the acoustic lens is very simple, with negative refraction obtained through thickness changes rather than internal periodicity or sub-wavelength resonant structures. A new class of acoustic devices, including resonators, filters, lenses, and cloaks, may be possible through topography optimization of elastic waveguide structures to exploit the unique properties of backward waves.