Acoustic nonlinearity of a piezoelectric crystal surface

A general approach to acoustic nonlinear problems using partial-mode field decomposition at the piezoelectric crystal surface has been developed in terms of a nonlinear reflection method. A quadratic approximation solution of the reflection problem for a free boundary of a nonlinear piezocrystal shows that the second harmonic field is determined by numerous cross and self-interactions of four fundamental reflected waves. These interactions produce 2ω elastic and electrical sources both in the bulk and at the surface of the crystal because of the second- and third-order elastic, piezoelectric, dielectric, etc., material parameters. Phase matching of the harmonics produced by self-mode interactions is a cause of surface acoustic wave (SAW) second harmonic generation, with the amplitude growing along the boundary. The analytical expression for the SAW second harmonic in a piezocrystal was derived by solving the nonlinear reflection problem. The efficiency of SAW second harmonic generation is determined by the contribution of all four of the partial waves of the fundamental SAW and is proportional to the material acoustic nonlinear parameter values, mode slowness, and their respective amplitudes and phases. Nonlinear SAW steady-state wave patterns in piezocrystals are predicted to be different from conventional N- or ‘‘sawtooth’’ types.