Original basic properties of the Green's functions of a semi-infinite piezoelectric substrate

The Green's function formalism has been, and still is, widely used to analyze the electroacoustic interactions at the surface of a semi-infinite piezoelectric substrate. In fact, it is the spectral Green's functions, in the Fourier domain (frequency and wave number), which are actually calculated and used. In this paper, we show how the real domain (time and space) Green's function can be derived from the spectral Green's functions by only using the basic properties of the later. We find that the real domain Green's functions can be directly deduced, to within scale factors, from the imaginary parts of spectral Green's functions. In addition it has also been found that the contribution of a SAW to the spectral Green's function cannot be restricted to the classical, commonly accepted, pole-type characteristic. Details of some calculations will be given as well as results and discussion for the isotropic case.