Abstract
Motivated by applications of recent interest related to propagation problems in the left-handed 2D inductor–capacitor metamaterial and standard 2D inductor–capacitor lattice with monochromatic inputs along the left and bottom boundary of a rectangular slab, we address the problem of wave diffraction on the 2D square lattice in a quadrant. The peculiar structure allows us to consider problems on half-plane, consequently, we study Dirichlet problems for the two-dimensional discrete Helmholtz equation in a half-plane and a quadrant. In view of the existence and uniqueness of solution, we provide new results for the real wave number k∈(0,22)∖{2} without passing to the complex wave number and derive an exact representation formula for solutions. For this purpose, we use the notion of the radiating solution and propose sufficient conditions for the given boundary data at infinity.
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