A perturbative analysis of surface acoustic wave propagation and reflection in interdigital transducers

The coupling of stress and strain fields to electric fields present in anisotropic piezoelectric crystals makes them ideal for use as electromechanical transducers in a wide variety of applications. In recent years such crystals have been utilized to produce surface acoustic wave devices for signal processing applications, in which an applied metallic grating both transmits and receives, through the piezoelectric effect, electromechanical surface waves. The design of such interdigital transducers requires an accurate knowledge of wave propagation and reflection. The presence of the metal grating in addition to its ideal transduction function, by means of electrical and mechanical loading, also introduces a velocity shift as well as reflection into substrate surface waves. We seek to obtain a consistent formulation of the wave behavior due to the electrical and mechanical loading of the substrate crystal by the metallic grating. A perturbative solution up to second order in $h/\lambda$ is developed, where h is the maximum grating height and $\lambda$ the acoustic wavelength. For the operating frequencies and physical parameters of modern surface acoustic wave devices such an analysis will provide an adequate description of device behavior in many cases, thereby circumventing the need for more computationally laborious methods. Numerical calculations are presented and compared with available experimental data.