WAVE PROPAGATION THROUGH A SQUARE LATTICE WITH SOURCES ON LINE SEGMENTS

We study the problems related to the propagation of time harmonic waves through a two-dimensional square lattice with sources on line segments. The discrete Helmholtz equation with the wave number k is an element of (0,2 root 2 \ {2} and input data prescribed on finite rows/columns of lattice sites is investigated without passing to the complex wave number. Similarly to the continuum theory, we use the notion of radiating solution. The unique solvability result and the Green's representation formula are obtained with the help of difference potentials. Finally, we propose a method for numerical calculation. Efficiency of our approach is demonstrated in examples related to the propagation problems in the left-handed 2D inductor-capacitor metamaterial.