Acoustic waves in the vicinity of the normal to the surface of piezoelectric crystals

The acoustic wave propagation in the vicinity of the normal to the plane surface confining a piezoelectric crystal of arbitrary symmetry is theoretically studied. An octet formalism arid a perturbation theory have been put forward to describe the wave fields in the region of concern. The developed mathematical approach has been applied to several problems. Specifically, the derivation of the transfer matrix for the normal direction to the surface has been discussed. Furthermore, we have discussed how to estimate the electric potential induced outside the piezoelectric material by a normally incident wave. In addition, an analytical expression has been derived for the numerical factor in the function describing the asymptotic behavior of quasielectrostatic Green's function for half-infinite piezoelectric substrates at small values of the wave vector