Directional dependence of nonlinear surface acoustic waves in the (001) plane of cubic crystals

Spectral evolution equations are used to perform analytical and numerical studies of nonlinear surface acoustic waves in the (001) plane of a variety of nonpiezoelectric cubic crystals. The basic theory underlying the model equations is outlined, and quasilinear solutions of the equations are presented. Expressions are also developed for a characteristic length scale for nonlinear distortion and a nonlinearity coefficient. A time-domain equation corresponding to the spectral equations is derived. Numerical calculations based on measured second- and third-order elastic constants taken from the literature are performed to predict the evolution of initially monofrequency surface waves. Nonlinearity matrix elements that indicate the coupling strength of harmonic interactions are shown to provide a useful tool for characterizing waveform distortion. The formation of compression or rarefaction shocks can be strongly dependent on the direction of propagation, and harmonic generation is suppressed or increased in certain directions.