The plane-wave-expansion (PWE) approach dedicated to the simulation of periodic devices has been extended to 1-3 connectivity piezoelectric composite structures. The case of simple but actual piezoelectric composite structures is addressed, taking piezoelectricity, acoustic losses, and electrical excitation conditions rigorously into account. The material distribution is represented by using a bidimensional Fourier series and the electromechanical response is simulated using a Bloch-Floquet expansion together with the Fahmy-Adler formulation of the Christoffel problem. Application of the model to 1-3 connectivity piezoelectric composites is reported and compared to previously published analyses of this problem.

A scattering matrix approach is proposed to avoid numerical instabilities arising with the classical transfer matrix method when analyzing the propagation of plane surface acoustic waves in piezoelectric multilayers. The method is stable whatever the thickness of the layers, and the frequency or the slowness of the waves. The computation of the Green’s function and of the effective permittivity of the multilayer is outlined. In addition, the method can be easily extended to the case of interface acoustic waves.

Many ultrasonic devices, among which are surface and bulk acoustic wave devices and ultrasonic transducers, are based on multilayers of heterogeneous materials, i.e., piezoelectrics, dielectrics, metals, and conducting or insulating fluids. We introduce metal and fluid layers and half spaces into a numerically stable scattering matrix model originally proposed for solving the problem of plane wave propagation in piezoelectric and dielectric multilayers. The method is stable for arbitrary thicknesses of the layers. We discuss how the surface Green's functions can be computed for an arbitrary stack of homogeneous materials with plane interfaces. Aditionnally, we set up a backscattering algorithm to compute the distribution of electromechanical fields at any point in the stack. The model is assessed by considering some well-known examples.