A theory as the basis for solving nonlinear boundary value problems is described. A new analysis is presented for nonlinear reflection, which reveals that there is a two-dimensional spatial increase of the second-harmonic wave. The accretion along the propagation direction is the result of the self-interaction of the primary wave; the one in the wave front is due to the boundary restriction.
Bulk wave reflection formulas are extended to the surface-wave case, considering Rayleigh and Stoneley waves in terms of refracted inhomogeneous longitudinal and transversal waves, linked by the surface coupling. In this manner, a physical mechanism of second-harmonic generation process is clearly shown. The analytical expressions and physical pictures of Rayleigh- and Stoneley-wave harmonic generation have been derived in a second-order approximation. The solution shows that the second-harmonic surface waves have a field structure different from the fundamental ones and varying with the propagation distance. Some parameters were defined to characterize the elastic surface-wave second-harmonic generation efficiency. Numerical data for some isotropic materials are present. The steady-state form of finite amplitude surface wave is described and explained by a clear physical model.
Surface acoustic waves (SAW’s) have been optically generated and detected on metallic spheres. The source was a focused yttrium aluminum garnet (YAG) laser operated in the Q-switched mode and the probe was a sensitive optical heterodyne interferometer. The curvature of the surface gives rise to dispersive effects. The variation of the SAW group velocity is deduced from the evolving waveforms of pulses detected after propagating a few turns around the sphere. The observation of SAW pulse waveforms at positions away from the pole (a point diametrically opposite to the source) reveals that the spectral components undergo a π-phase shift when passing through the pole.
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