Periodicity of linear and nonlinear surface acoustic wave parameters in the (111) plane of cubic crystals

Abstract

Previous numerical and experimental studies of surface acoustic waves (SAWs) in the (111) plane of cubic crystals have shown that linear properties, including the wave speed and the direction of power flow, exhibit sixfold symmetry. However, recent measurements by Lomonosov and Hess of finite-amplitude SAW pulses propagating in opposite directions in the (111) plane of crystalline silicon have demonstrated that the same periodicity does not hold for the nonlinear distortion. Calculations based on a model for nonlinear SAWs in anisotropic media [Hamilton et al., J. Acoust. Soc. Am. 105, 639–651 (1999)] indicate that complex-valued nonlinearity matrix elements, which describe the coupling between harmonics, have sixfold symmetry in magnitude but only threefold symmetry in phase. As a result, pulses traveling in opposite directions exhibit different nonlinear phase shifting between harmonics that give rise to the distinctly different types of observed distortion. Threefold symmetry of nonlinearity is also predicted for other cubic crystals besides silicon. Additional computations show that the complex-valued eigenvalues and eigenvectors of the linearized equations (physically corresponding to the depth decay coefficients and component amplitudes, respectively) also have sixfold symmetry in magnitude but only threefold symmetry in phase. [Discussions with A. P. Mayer are gratefully acknowledged.]