Measurement of the electric permittivity using Bleustein–Gulyaev wave sensor

We present a novel compact electric permittivity sensor that exploits Bleustein–Gulyaev waves propagating along the surface of shear-poled piezoelectrics. We formulate the dynamic nonlinear electromechanical partial differential equations of motion governing wave propagation under electromagnetically quasistatic conditions. The permittivity of the medium-under-test was found to influence the sensor eigenvalues, enabling the implementation of a frequency-shift permittivity sensor. Solution of the equations of motion demonstrates resonance of the first and third modes when excited using an interdigitated transducer. We fabricated two sensor prototypes on shear-poled PZT4 and LiNbO3 substrates and used a Vector Network Analyzer to observe the shift in their fundamental natural frequency in the presence of various media-under-test. S11 measurements show deterministic and repeatable shifts in the resonant frequency of the first mode of the LiNbO3 sensor measured at $\Delta f_1 = 3.51$ MHz for ethanol and $\Delta f_1 = 7.49$ MHz for deionized water where the bare surface frequency was initially at $f_1 = 25.27$ MHz.