Piezoelectric Love waves on rotated Y-cut mm2 substrates

TL;DR

This paper analytically derives dispersion relations for Love waves on rotated Y-cut mm2 piezoelectric substrates, revealing how cut angles influence wave speed and existence, with implications for wave control.

Contribution

It provides explicit analytical solutions for Love wave propagation on rotated Y-cut mm2 substrates, including the secular equation for Bleustein-Gulyaev waves, advancing understanding of wave behavior in anisotropic piezoelectric layers.

Findings

Love wave existence depends on cut angle and wavelength.

Wave speed can be tuned by adjusting the cut angle.

Forbidden ranges of propagation appear for rotated cuts.

Abstract

Consider a layer made of a m3m insulator crystal, with faces cut parallel to a symmetry plane. Then bond it onto a semi-infinite mm2 piezoelectric substrate. For a 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 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.