Two-dimensional time-domain Imaging of a Zero-Group-Velocity Lamb Mode

Abstract

Zero-group velocity (ZGV) modes are particular points in a dispersion relation where the group velocity tends toward 0 whereas the phase velocity remains finite. At this point the waves remain stationary, thus locally confining the energy. Despite many applications relying on them to provide a local measure of a given property (such as Poisson?s ratio, elastic constants or thickness), they have not previously been imaged, owing mainly to the dichotomy between the ZGV mode high quality factor and the frequency limitation of femtosecond pulsed laser techniques. In this talk, we image ZGV acoustic waves at ~1.7 GHz in a microscopic plate. Lamb waves in a bilayer consisting of a ~2 �m thickness silicon nitride plate coated with polycrystalline titanium are imaged in two dimensions by means of a time-resolved technique using an ultrashort-pulse laser. Arbitrary-frequency control is implemented to provide data at any desired frequency. In particular, we identify and isolate the first ZGV mode of our bilayer, its associated Q factor of 1150 and its lifetime of 0.22 �s. We also derive the experimental dispersion curves of the bilayer by means of spatio-temporal Fourier transforms, clearly revealing the location of the ZGV mode in frequency-wavevector space and its acoustic energy localization. Comparison with theoretical Lamb-wave dispersion curves gives good agreement. Applications of real-time imaging of ZGV Lamb modes include the possibility to perform local non- destructive evaluation of nanostructures, such as the detection of defects in adhesion or interfacial stiffnesses.