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

Victor Y. Zhang (1) , Vincent Laude (2)

1 IEMN - Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

This paper presents a unified and full scattering matrix (s-matrix) formalism. A stable recursive algorithm is derived for computation of the total s-matrix of a multilayered stack in terms of the interface s-matrix, both referring to the eigen-modes amplitudes. The derivation is direct and succinct, the derived expressions of the s-matrix are terse and concise, and the recursion is efficient and convenient for implementation. By combining the s-matrix formalism and the surface impedance matrix of the external media, various terminations of the stack can be easily handled. Numerical examples are given to show its numerical superiority over other currently used matrix formalisms: including unconditional stability throughout large and small thicknesses and pole-free feature.

Domaines: Acoustique [physics.class-ph]

Victor Y. Zhang, Vincent Laude. Unified and stable scattering matrix formalism for acoustic waves in piezoelectric stacks. Second ASA-EAA Joint Conference, ACOUSTICS'08, Jul 2008, Paris, France. pp.5957-5962, ⟨10.1121/1.2935657⟩. ⟨hal-00343688⟩