Dyadic Green's functions for multi-layer 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 sixteen 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. While requiring little additional computational effort, the dyadic Green's function thus 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. The dyadic Green's function for a sample multi-layer substrate is presented.