Fundamental frequency degeneracy of standing surface acoustic waves under metallic gratings on piezoelectric...

The paper studies specific features of surface acoustic waves on piezoelectric substrates under infinite periodic grating arrays. The grating is made up of identical metallic electrodes of finite thickness and has one electrode per cell. It has been shown via the analysis of numerical algorithms and the coupling-of-modes equations that one of the fundamental frequencies of the standing wave under short-circuited grating necessarily coincides with one of the fundamental frequencies corresponding to the open-circuited grating if the substrate assumes particular orientations connected with its crystallographic symmetry. The existence of degeneracy does not depend on the material constants of the substrate and the electrode, the thickness of the electrode, and the specific electrode shape provided that the electrode is uniform along the wave normal and shaped symmetrically in the same direction. The proof applies both to ordinary and leaky surface waves.