Wave scattering on lattice structures involving an array of cracks

Abstract

Scattering of waves as a result of a vertical array of equally spaced cracks on a square lattice is studied. The convenience of Floquet periodicity reduces the study to that of scattering of a specific wave-mode from a single crack in a waveguide. The discrete Green’s function, for the waveguide, is used to obtain the semi-analytical solution for the scattering problem in the case of finite cracks whereas the limiting case of semi-infinite cracks is tackled by an application of the Wiener–Hopf technique. Reflectance and transmittance of such an array of cracks, in terms of incident wave parameters, is analysed. Potential applications include construction of tunable atomic-scale interfaces to control energy transmission at different frequencies.