Modeling of multilayered acoustic wave devices with the method of reverberation-ray matrix

The method of reverberation-ray matrix (MRRM) are modified and extended to the analysis of wave propagation in multilayered acoustic wave devices based on three-dimensional linear piezoelectricity. By the plane wave solution assumption, state equations are established whose solutions are expressed with unknown wave amplitudes. Within the framework of MRRM, the phase and scattering relations are properly set up to determine the unknowns without involving exponentially growing functions and matrix inversion operations in an easy and uniform way. Thus the present MRRM is unconditionally stable and free from limitations to the frequency, the thickness of individual layers and the total number of layers. The surface waves, the interface waves and the bulk waves are all included in the formulation. Therefore, the present formulation applies to SAW devices as well as BAW devices. Numerical examples are given to illustrate the well performance of the proposed formulation of MRRM for the analysis of free waves in multilayered acoustic wave devices.