Wave scattering on lattice structures involving array of cracks

TL;DR

This paper investigates wave scattering caused by an array of cracks on a lattice, using advanced mathematical techniques to analyze energy transmission, with potential applications in designing tunable atomic-scale interfaces.

Contribution

It introduces a semi-analytical method combining Green's functions and Wiener--Hopf techniques for wave scattering on lattice structures with cracks.

Findings

Derived expressions for reflectance and transmittance of crack arrays.

Analyzed wave behavior for finite and semi-infinite cracks.

Potential to control energy transmission at various frequencies.

Abstract

Scattering of waves due to 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 specific wave-mode from single crack in a waveguide. The discrete Green's function, for the waveguide, is used to obtain semi-analytical solution for scattering problem in case of finite cracks whereas the limiting case of semi-infinite cracks is tackled by an application of Wiener--Hopf technique. Reflectance and transmittance of such an array of cracks, in terms of incident wave parameters, is analyzed. Potential applications include construction of tunable atomic scale interfaces to control energy transmission at different frequencies.