An analysis of transverse modes in acoustic surface wave resonators

Abstract

A system of approximate surface wave equations employed in an earlier treatment of the reflection of straight-crested surface waves by arrays of reflecting strips is extended to the case of variable-crested surface waves. Although the basic straight-crested surface wave velocities are determined as in the previous treatment, in the present case a reduction in straight-crested surface wave velocity in the unplated region due to the adjacent plated regions, which is essential for the existence of the guided transverse modes, is determined by means of a perturbation procedure. The attendant depth dependence for each region is employed in the variational principle as in the earlier treatment, but now the variable cresting relation for the isotropic substrate is incorporated in the description. The resulting equations are applied in the determination of both the transverse modes in each region and the transmission line representation of each mode. The transverse wave numbers in a given mode are taken to be the same in the plated and unplated regions in order that the interior edge conditions be satisfied pointwise. The system of parallel transmission lines is applied in the analysis of the reflection of variable-crested surface waves by uniformly spaced arrays. The response to a rectangular input of a particular reflecting array consisting of aluminum reflecting strips on ST-cut quartz is calculated and compared with measurements.