An investigation of surface acoustic waves in an anisotropic crystal

A substrate of a surface acoustic waves (SAW) device is usually treated as a semi-infinite elastic body though it is virtually a finite elastic solid. With the two-dimensional theory, a new method is developed for the analysis of SAW propagating under periodic metal grating on a finite anisotropic solid, resembling Chen and Haus´s theory. We use the two-dimensional solutions of the mechanical displacements to derive the expression of the reflection coefficient dominated by the mechanical loading effect and achieve the value for Al grating on Y-cut quartz substrate. In addition, we find that the reflection coefficients are different when the length of the solid respectively equals odd and even times as long as the wavelength. Our theory also shows that when the length of the elastic solid is odd times as long as the wavelength the reflection coefficient is positive, whereas when the length of the elastic solid is even times the reflection coefficient is negative.