Control of Love waves by resonant metasurfaces

Antonio Palermo,Alessandro Marzani

doi:10.1038/s41598-018-25503-8

Abstract

Metasurfaces of mechanical resonators have been successfully used to control in-plane polarized surface waves for filtering, waveguiding and lensing applications across different length scales. In this work, we extend the concept of metasurfaces to anti-plane surface waves existing in semi-infinite layered media, generally known as Love waves. By means of an effective medium approach, we derive an original closed-form dispersion relation for the metasurface. This relation reveals the possibility to control the Love waves dispersive properties by varying the resonators mechanical parameters. We exploit this capability to manipulate the metasurface refractive index and design two gradient index (GRIN) metalenses, i.e. a Luneburg lens and a Maxwell lens. We confirm the performance of the designed lenses using full 3D finite element simulations. Our work demonstrates the possibility of realizing wave control devices for anti-plane waves.

Highlights

The study of surface waves in solid materials is a classical topic of elastodynamics which still attracts the interest of numerous researchers from different disciplines such as geophysics, geotechnical engineering, solid-state physics, material science, electronic engineering, among the others
We consider an elastic medium composed of a soft isotropic elastic layer of depth H, shear velocity cT,[1] and density ρ, welded to a stiffer elastic isotropic half-space, of shear velocity cT,2 > cT,[1] and density ρ
We analyze the interaction of plane harmonic Love waves of angular frequency ω and wavenumber k, polarized along the y-axis, with an array of horizontal mechanical resonators of resonance frequency ωr of

Summary

Introduction

The study of surface waves in solid materials is a classical topic of elastodynamics which still attracts the interest of numerous researchers from different disciplines such as geophysics, geotechnical engineering, solid-state physics, material science, electronic engineering, among the others. Love waves, which are the most known type of anti-plane waves, are guided modes traveling at the free surface of a soft elastic layer “welded” to a more rigid substrate. Their dispersive properties have been originally formalized by A. Metasurfaces of resonant rods at the free surface of an elastic plate have been designed to control the dispersive properties of flexural waves for waveguiding, cloaking and lensing[18,19,20]. To the best of our knowledge, the interaction between anti-plane waves in layered media, e.g. Love waves, and metasurfaces of resonators has not been investigated yet. Correspondence and requests for materials should be addressed to A.M. (email: alessandro.marzani@ unibo.it) www.nature.com/scientificreports/

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