Explicit secular equations for piezoacoustic surface waves: Shear-Horizontal modes

TL;DR

This paper derives explicit secular equations for shear-horizontal surface waves in certain piezoelectric crystals, enabling precise analysis of wave behavior under various boundary conditions and crystal orientations.

Contribution

It provides explicit polynomial secular equations for shear-horizontal surface waves in $ar{4}$ symmetry piezoelectric crystals for multiple boundary conditions, extending previous work.

Findings

Explicit secular equations for different boundary conditions.

Numerical analysis of wave properties in specific crystals.

Method applicability to crystals with 222 symmetry.

Abstract

Attention is given to surface waves of shear-horizontal modes in piezoelectric crystals permitting the decoupling between an elastic in-plane Rayleigh wave and a piezoacoustic anti-plane Bleustein-Gulyaev wave. Specifically, the crystals possess $\bar{4}$ symmetry (inclusive of $\bar{4}2$m, $\bar{4}3$m, and 23 classes) and the boundary is any plane containing the normal to a symmetry plane (rotated $Y$-cuts about the $Z$ axis). The secular equation is obtained explicitly as a polynomial not only for the metallized boundary condition but, in contrast to previous studies on the subject, also for other types of boundary conditions. For the metallized surface problem, the secular equation is a quadratic in the squared wave speed; for the un-metallized surface problem, it is a sextic in the squared wave speed; for the thin conducting boundary problem, it is of degree 16 in the speed. The relevant root of the secular equation can be identified and the complete solution is then found (attenuation factors, field profiles, etc.). The influences of the cut angle and of the conductance of the adjoining medium are illustrated numerically for GaAs ($\bar{4}3$m), BaLaGa$_3$O$_7$ ($\bar{4}2$m) and Bi$_{12}$GeO$_{20}$ (23). Indications are given on how to apply the method to crystals with 222 symmetry.