Imaging gigahertz zero-group-velocity Lamb waves

Qingnan Xie,Oliver B Wright,Paul H Otsuka,Sylvain Mezil,Motonobu Tomoda,Zhonghua Shen,Jérôme Laurent,Osamu Matsuda

doi:10.1038/s41467-019-10085-4

Abstract

Zero-group-velocity (ZGV) waves have the peculiarity of being stationary, and thus locally confining energy. Although they are particularly useful in evaluation applications, they have not yet been tracked in two dimensions. Here we image gigahertz zero-group-velocity Lamb waves in the time domain by means of an ultrafast optical technique, revealing their stationary nature and their acoustic energy localization. The acoustic field is imaged to micron resolution on a nanoscale bilayer consisting of a silicon-nitride plate coated with a titanium film. Temporal and spatiotemporal Fourier transforms combined with a technique involving the intensity modulation of the optical pump and probe beams gives access to arbitrary acoustic frequencies, allowing ZGV modes to be isolated. The dispersion curves of the bilayer system are extracted together with the quality factor Q and lifetime of the first ZGV mode. Applications include the testing of bonded nanostructures.

Highlights

Zero-group-velocity (ZGV) waves have the peculiarity of being stationary, and locally confining energy
ZGV Lamb waves with pulsed lasers has, not proved possible owing to the extremely sharp resonances associated with ZGV modes—exhibiting Q factors up to 14,70018, for example— whereas acoustic frequencies are usually limited to integral multiples of the laser repetition rate
Because of the symmetry of the excitation with respect to coordinate x, acoustic waves with positive and negative k should be generated with equal amplitude and initially form a single wave packet located at the excitation point

Summary

Introduction

Zero-group-velocity (ZGV) waves have the peculiarity of being stationary, and locally confining energy. 1234567890():,; Waveguides channel propagating waves with reduced losses thanks to the confined dimensions, and are widely used in optics and acoustics They are dispersive, i.e., the phase and the group velocities differ. Zero-groupvelocity (ZGV) modes are particular points in a dispersion relation where the group velocity vanishes whereas the phase velocity remains finite These modes can be found in most waveguide geometries (e.g., fibres and cylinders[1,2], plates[3,4], etc.) and have the advantages of combining reduced losses and high Q factor. We image a GHz ZGV Lamb mode in a bilayer consisting of a silicon-nitride plate coated with polycrystalline titanium by means of a time-resolved two-dimensional (2D) imaging technique incorporating an ultrashort-pulse laser[19]. The experimental dispersion curves of the bilayer are obtained, clearly showing the location of the ZGV mode in frequency-wavevector space and its acoustic energy localization

Methods

Results

Conclusion