Dispersion spectrum of acoustoelectric waves in 1D piezoelectric crystal coupled with 2D infinite network of capacitors

A one-dimensional piezoelectric crystal coupled through periodically embedded electrodes with a two-dimensional semi-infinite periodic network of capacitors is considered. The unit cell of the network contains two capacitors with capacitances C-1 and C-2 which are in parallel and in series, respectively, with the electrodes. The dispersion spectrum of the longitudinal acoustoelectric wave in the piezoelectric crystal coupled with the electric wave of potentials and charges in the network of capacitors is investigated. It is shown that when C-1 and C-2 are of the same sign, the dispersion spectrum consists of a discrete set of curves, for which the electric wave exponentially decays into the depth of the network of capacitors. In contrast, if C-1 and C-2 are of the opposite sign and vertical bar C-1/C-2 vertical bar < 1, then the spectrum simultaneously includes the discrete set of dispersion curves, corresponding to the localized waves, and the continuous band, which admits a finite but not localized (not decaying into the depth) wave field at any frequency and wavenumber within the band. Finally, when C-1 and C-2 are of the opposite sign and vertical bar C-1/C-2 vertical bar >= 1, the whole dispersion spectrum is a continuous band. The width of the continuous band and the equation describing the dispersion curves are found explicitly; the equation for the wave field is also obtained. Another interesting spectral feature is the unusual non-monotonic shape of the dispersion curves for a certain range of C-1(< 0), C-2. This shape is due to the hybridization of the individual spectra of the crystal and of the network of capacitors. Published by AIP Publishing.