Dyadic Green's functions for multi-layer SAW substrates

Recent formulations of the dyadic (or generalized) Green's function describ e the relationship between sources (both mechanical stresses and electrical charge) and waves (both mechanical displacements and acoustic potential) o n the surface of a substrate. The 16 elements of the function intrinsically describe all propagation modes, whether Rayleigh or leaky, and are, theref ore, extremely useful in the design of surface acoustic wave devices. In ad dition to requiring little computational effort, the dyadic Green's functio n provides much more information than the traditional effective permittivit y 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 contai ns the substrate characteristics and, once obtained, can be used to describ e the surface behavior with no further regard to the substrate's compositio n.