Piezoelectric Love waves on rotated Y-cut mm2 substrates

Abstract

Consider a layer consisting of a m3m dielectric crystal, with faces cut parallel to a symmetry plane. Then bond it onto a semi-infinite mm2 piezoelectric substrate. For an X- or Y-cut of the substrate, a Love wave can propagate in the resulting structure and the corresponding dispersion equation is derived analytically. It turns out that when the upper (free) face of the layer is metalized, a fully explicit treatment can also be conducted in the case of a Y-cut rotated about Z. In the case of a germanium layer over a potassium niobate substrate, the wave exists at any wavelength for X- and Y-cuts but this ceases to be the case for rotated cuts, with the appearance of forbidden ranges. By playing on the cut angle, the Love wave can be made to travel faster than, or slower than, or at the same speed as, the shear bulk wave of the layer. A by-product of the analysis is the derivation of the explicit secular equation for the Bleustein-Gulyaev wave in the substrate alone, which corresponds to an asymptotic behavior of the Love wave. The results are valid for other choices for the layer and for the substrate, provided they have the same, or more, symmetries.