Unified and stable scattering matrix formalism for acoustic waves in piezoelectric stacks

Abstract

This paper presents a unified and full scattering matrix (s-matrix) formalism for modeling of acoustic waves in piezoelectric multilayered structures. A stable recursive algorithm is derived for computation of the total s-matrix of a stack in terms of the interface s-matrix, both referring to the eigenmode amplitudes. The derivation is direct and succinct, the deduced expressions of the s-matrix are terse and concise, and the recursion algorithm is efficient and convenient for implementation. The total s-matrix recursion scheme differs from the previously published partial matrix algorithms in that the recursions are conducted once for all independent of the stack boundary conditions and so the same results apply for any post-specified boundary condition. Numerical examples are given to show its numerical features that are superior to other currently used matrix formalisms, such as unconditional stability for both large and small thicknesses, being pole-free and branch point-sensitive, constant mean magnitude with stable phase, involving only dimensionless elements.