Nonlinearly generated harmonics and attenuation of Rayleigh waves on crystalline quartz

Measurements have been made of the nonlinearly generated harmonics and attenuation of Rayleigh acoustic surface waves at microwave frequencies on crystalline quartz. The Rayleigh waves were generated using an interdigital transducer deposited on the x-z surface of the quartz crystal aligned so that the surface wave propagates in the pure-mode x direction. Attenuation coefficients α were measured using the laser diffraction technique at frequencies of ∼160, ∼280, and ∼492 MHz with resulting typical values of α=0.083 dB/μsec, α=0.206 dB/μsec, and α=0.812 dB/μsec, respectively. These results agree with previously reported values and with theoretical predictions. The growth and decay of nonlinearly generated harmonics of Rayleigh waves with a fundamental frequency of 281 MHz were observed also using the laser probe technique. A description of the variation of the Rayleigh waves' intensity for each of the three harmonics observed is provided by a set of coupled amplitude equations modified to include dispersion effects. It was not possible to describe the data using the coupled amplitude equations without including terms containing dispersion. Surface imperfections are assumed to be responsible for the dispersion as well as to contribute to the residual values for the attenuation coefficients. The small amount of dispersion needed for a good fit is determined. The nonlinearities are characterized by a set a nonlinear coefficients Γ. A computer program was written in order to solve the coupled amplitude equations and to determine a set of Γ values which provide a best description of the experimental data.