Modeling of harmonic generation and shock formation in nonlinear surface acoustic waves in several real crystals

Abstract

Harmonic generation and shock formation in nonlinear surface acoustic waves that propagate in anisotropic crystals were studied numerically on the basis of a new theoretical model presented earlier [Hamilton et al., Nonlinear Acoustics in Perspective, edited by R. J. Wei (Nanjing University Press, Nanjing, 1996), pp. 64–69]. The theory applies for arbitrary elastic materials, surface cuts, and propagation directions. Numerical simulations were performed for initially sinusoidal signals propagating across the surface of KCl, Ni, and Si crystals for the (001), (110), and (111) cuts, and over the appropriate range of directions for each cut. Waveforms are shown to exhibit asymmetric distortion, well-defined shocks with cusped spikes in the horizontal waveform, and a phase shift in the zero crossings. Solutions for propagation in the (001) plane and in the 〈100〉 direction of KCl are shown to exhibit atypical trapping of energy in the lowest order harmonics. Analytical solutions derived for the fundamental and second-harmonic components for this particular case are in good agreement with the numerical solutions close to the source. Although the phenomenon resembles one observed in nonlinear optics resulting from dispersion, it is due instead to properties of the nonlinearity coefficient matrix. [Work supported by ONR.]