Singularities of the planar Green function in the spectral domain

Abstract

The electro-acoustic field amplitudes at the boundary of a piezoelectric half-space satisfy a matrix relation which is characteristic of the medium. The elements of the matrix are functions of slowness. In the paper, the singularities of the matrix are investigated at cutoff points of bulk waves. An approximated formula is derived for the matrix in the neighborhood of the greatest cutoff point, which takes into account also the singularity related to the Rayleigh wave. The results of numerical calculations are presented for several piezoelectrics.