A perturbation analysis of the attenuation and dispersion of surface waves

Abstract

A perturbation formulation of the equations of linear piezoelectricity is obtained using a Green’s function approach. Although the resulting equation for the first perturbation of the eigenvalue strictly holds for real perturbations of real eigenvalues only, it is formally extended to the case of purely imaginary perturbations of real eigenvalues. The extended equation is applied in the calculation of the attenuation of surface waves due to the finite electrical conductivity of thin metal films plated on the surface and air loading. The influence of the viscosity of the air is included in the air-loading analysis, and the calculated attenuation increases accordingly. Since the metal films are thin compared with a wavelength, an approximate thin-plate conductivity equation is employed in the determination of the attenuation due to the electrical conductivity of the films. The resulting attenuation is obtained over a very large range of values of sheet conductivity. This is accomplished by using the equation for the first perturbation of the eigenvalue iteratively to determine the solution and attendant attenuation to any desired degree of accuracy. The phase velocity dispersion curve due to the mechanical effect of a thin film plated on a substrate is determined for relatively large wavelengths by employing the perturbation equation iteratively, and excellent agreement is obtained with the results of other more direct approaches. The calculations have been performed for an aluminum film on either ST-cut quartz or Y-Z lithium niobate.