Surface Green´s function of a piezoelectric half-space

The computation of the two-dimensional harmonic spatial-domain Green´s function at the surface of a piezoelectric half-space is discussed. Starting from the known form of the Green´s function expressed in the spectral domain, the singular contributions are isolated and treated separately. It is found that the surface acoustic wave contributions (i.e., poles in the spectral Green´s function) give rise to an anisotropic generalization of the Hankel function H₀⁽²⁾, the spatial Green´s function for the scalar two-dimensional wave equation. The asymptotic behavior at infinity and at the origin (for the electrostatic contribution) also are explicitly treated. The remaining nonsingular part of the spectral Green´s function is obtained numerically by a combination of fast Fourier transform and quadrature. Illustrations are given in the case of a substrate of Y-cut lithium niobate.