Dyadic Green's functions for multi-layer SAW substrates

Recent formulations of the dyadic (or generalized) Green's function describe the relationship between sources (both mechanical stresses and electrical charge) and waves (both mechanical displacements and acoustic potential) on the surface of a substrate. The 16 elements of the function intrinsically describe all propagation modes, whether Rayleigh or leaky, and are, therefore, extremely useful in the design of surface acoustic wave devices. In addition to requiring little computational effort, the dyadic Green's function provides much more information than the traditional effective permittivity function. In this paper, we extend the calculation of the dyadic Green's function to multi-layer substrates. We show that its computation involves a simple cascaded matrix multiplication. The resulting function fully contains the substrate characteristics and, once obtained, can be used to describe the surface behavior with no further regard to the substrate's composition.