Scattering and Transmission of Elastic Waves from an Interface Between Two Planar Waveguides

Abstract

The scattering and transmission properties of elastic waves in a two-dimensional waveguide constructed from two dissimilar square lattices which exhibit a strain field at the interface, have been theoretically studied. The strain field is described by the existence of the local forces at an interface different to those occurring outside the surrounding interface. The theoretical approach using the matching procedure for calculating phonon scattering at the interface domain boundary is also presented. The reflection and transmission probabilities in the scattering region are calculated and illustrated for the longitudinal and transversal propagating modes in the normal incidence of the elastic wave. The conductance properties in full accordance with the Landauer–Büttiker description of electron transport are also calculated. The asymmetric Fano resonance type may appear in the phonon transmission spectra due to the coherent coupling between the two-dimensional crystal phonons and the localized vibration modes on the interface boundary. A discussion on the vibrational waves in the scattering region is given. We also show how even a simple interface in a two-dimensional situation can be used as a phonon filter, and how phonons can be used to probe an interface.