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When electric and acoustic waves simultaneously pass through a piezoelectric material, nonlinearities can arise. The electric and acoustic waves can mix, generating a signal consisting of both sum and difference spectral components. Here we present a method of directly measuring the nonlinearly mixed electric-acoustic signal using a vector network analyzer (VNA). In normal VNA operation, sources and receivers operate at the same frequency. In our measurements, we employ a frequency offset mode, where receivers in the VNA can be tuned to a frequency different from the source frequency. Here, we measure at the expected mixing product frequency of the electrical and acoustic signals we introduce into the measurement to capture nonlinear electric-acoustic mixing. We present measurements of electric-acoustic mixing in a block of lead zirconium titanate (PZT) mounted on top of an electric co-planar waveguide connected to the VNA. The results show the presence of many coupled electric-acoustic modes. To interpret these modes, we characterized the PZT block with modal analysis and finite element simulations. Some of the observed nonlinear electric-acoustic modes directly correlated with the mechanical modes of the block, while others did not. Overall, this method allows for direct probing of non-linear electric-acoustic mixing in materials and devices.
Lirette et al. (Fri,) studied this question.