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.