Abstract
The method developed by Wiener and Hopf is applied to the problem of scattering of time-harmonic waves by the surface of a semi-infinite square lattice with mixed boundary condition. Three distinct configurations of the boundary are analyzed in the paper. The far-field approximation of the exact solution is provided along with some graphical illustrations and numerical calculations. Potential applications of the analysis include the scattering of elastic, phononic, photonic and electronic waves by surfaces which are exposed, in patches, simultaneously to different kinds of environmental conditions.
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