Nonlinear surface acoustic waves in cubic crystals
R. E. Kumon (National Institute of Standards and Technology, 325 Broadway, Mail Stop 853, Boulder, CO 80305-3328 USA) and M. F. Hamilton (Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712-1063 USA)
Both the linear and nonlinear properties of surface waves in crystals are significantly different from those in isotropic media. Recently developed model equations are employed to perform theoretical and numerical studies of nonlinear surface acoustic waves in nonpiezoelectric, cubic crystals. The model possess a nonlinearity matrix that describes the coupling of the harmonic interactions. This matrix is shown to provide a useful tool for characterizing waveform distortion. Selected numerical results are presented for propagation of initially monofrequency surface waves in various surface cuts and directions. When the nonlinearity matrix is real-valued, compression shocks form in some directions, whereas rarefaction shocks form in others. In certain directions, generation of one or more harmonics may be suppressed, and shock formation postponed. In still other cases, energy may be rapidly transferred to the highest harmonics, and sharply cusped shocks are formed. When the nonlinearity matrix is complex-valued, the velocity waveforms may exhibit asymmetric distortion and low frequency oscillations near peaks and shocks. Measurements of pulsed waveforms in crystalline silicon obtained by collaborators at the University of Heidelberg are shown to be quantitatively reproduced by the calculated results.