Imaginary branches of surface acoustic wave slowness curves
Résumé
The imaginary branches of surface acoustic wave slowness curves are needed in many modal or spectral models that account for waveguides or diffraction based on the angular spectrum of waves approach. Their determination for an arbitrary anisotropic piezoelectric substrate considering either free or shorted surface boundary conditions is discussed. In the case of true, i.e., lossless, surface acoustic wave, the imaginary branches are obtained by a search in the complex transverse slowness plane as a function of the propagation slowness. As a side result, the parabolic approximation is compared with the exact solution and it turns out that its quality depends dramatically on the particular material cut considered. The case of pseudo- or leaky surface acoustic waves is also analyzed and it is found that difficulties arise in connection with the partial-wave selection rule for semi-infinite substrates.