  Starting from the general modal solutions for a homogeneous layer of
arbitrary material and crystalline symmetry, a matrix formalism is developed to
establish the semi analytical expressions of the surface impedance matrices
(SIM) for a single piezo-electric layer. By applying the electrical boundary
conditions, the layer impedance matrix is reduced to a unified elastic form
whether the material is piezoelectric or not. The characteristic equation for
the dispersion curves is derived in both forms of a 3-dimentional acoustic SIM
and of an electrical scalar function. The same approach is extended to
multilayered structures such as a piezoelectric layer sandwiched in between two
metallic electrodes, a Bragg coupler, and a semi-infinite substrate as well.
The effectiveness of the approach is numerically demonstrated by its ability to
determine the full spectra of guided modes, even at extremely high frequencies,
in layered plates comprising of up to four layers and three materials. Negative
slope in f-k curve for some modes, asymptotic behavior at short wavelength
regime, as well as wave confinement phenomena made evident by the numerical
results are analyzed and interpreted in terms of the surface acoustic waves and
of the interfacial waves in connection with the bulk waves in massive
materials.
