EXPERIMENTAL EVIDENCE OF DISTORTED RIPPLING PROFILES OF FINITE AMPLITUDE ACOUSTIC SUFACE-WAVES

Abstract

Waveform distortion of acoustic surface waves is experimentally analyzed through testing the modification of rippling profiles. An optical probing method has been used, which allows one to measure the phase shift between fundamental and second harmonic through the asymmetries of the light diffracted in second orders by the distorted waves. Several configurations of the rippling profiles have been investigated of surface waves propagating on LiNbOo, LiTa03, Bii2Ge020 a SiOg. Cases have been found where phase relation between fundamental and second harmonic waves is such as to produce straight forward or backward sloping profiles. 1.INTRODUCTION. It is well known that the growing of harmonic along the propagation path of finite amplitude acoustic bulk waves in condensed media produces characteristic sawtooth distortions of the velocity profiles. The waveforms develop along the propagation direction into forward or backward sloping waves. These most stable configurations correspond to the two allowed phase relations between fundamental and second harmonic waves, which differ by a IT angle one with respect to the other. In case of surface waves, the inhomogeneous nature causes various waveform distortion to be expected. The final configuration of the wave, indeed, depends upon the relative amplitudes and phases with which nonlinear partial waves grow along the propagation direction. In the present work, waveform distortion of acoustic surface waves is experimentally analyzed through testing the modification of the rippling profiles along the propagation path. An optical method has been used, which allows one to measure the phase shift between fundamental and second harmonic through the asymmetries of the light diffracted into second orders by the distorted waves. 2. THE NON-LINEAR PROBLEM. The analytical approacn to tne problem of nonlinear propagation of acoustic surface waves has been variously attempted in recent times, through either some kind of phenomenological approach /1,2/ or simplifying assumptions /3,4/. A number of papers by Stegeman et al. /5/ recently obtained valuable theoretical results which match very closely the experimental date available. The analytical problem is to solve the nonlinear equation of motion : subjected to the stress-free boundary condition on the propagation surface. Here, p is the density of the medium, u the 'Hsplacer'ent vector and a., = ' ' Tk = 3U/3(3ui/axk), with U density of the internal energy. To our purpose, we presently discuss the problem in a very simplified qualitative way, by referring to the characteristics approach proper to a wide range of problems dealing with wave propagation. According to it, and limiting our attention first to the case of bulk waves in isotropic media, a family of curves can be traced on the plane (x,t) which are called characteristic curves and have the property that the acoustic perturbation is constant along anyone of them /6/. The slope of the curves gives the velocity with which the perturbation propagates at any point in space and instant of time. The curves run as parallel straight lines in case of linear propagation and may have different inclinations otherwise. In the former case, one obtains the well known result JOURNAL DE PHYSIQUE Colloque CQ, supplement au n° 11, tome 40, novembre 1979, page C8-249 Resume. La distorsion des ondes acoustiques de Rayleigh a ete experimentalement etudiee en analysant l'asymetrie du spectre de la lumiere diffractee produit par les changements du profil de deformation de la surface sur laquelle se propagent les ondes. On presente ici une methode optique qui a permis la determination experiementale de la relation de phase existant entre l'onde a presuence fondamentale et l'onde a la frequence de l'harmonique 2 pour plusieurs echantillons de cristaux piezo-electriques (LiNb03, LiTa03, Bi'i2Ge020 et Si02)• Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979843