Nonlinear surface-wave interactions: Parametric mixing and harmonic generation

The nonlinear interaction of surface acoustic waves propagating in the same direction has been treated from the rigorous theory of thermoelasticity. Exact expressions were derived for the nonlinear volume forces and surface stresses, and the nonlinear cross sections were calculated under two separate assumptions. First, the work done by the nonlinear forces and surface stresses on a normal-mode surface wave was evaluated and assumed to be totally converted into surface-wave energy. In the second approach, a linear analytic solution was formulated which simultaneously satisfies the nonlinear wave equation and maintains a stress-free boundary condition. Numerical values for the strength of second-harmonic generation were calculated for 24 materials. The characteristics of nonlinear surface-wave generation were compared with those of nonlinear bulk-wave generation and significant differences were found. Coupled amplitude equations were derived to treat the case of multiharmonic generation. Finally, a characteristic power parameter which describes energy conversion from the fundamental into the second harmonic was derived for surface waves and evaluated for 24 materials.