Electromagnetic localized modes of linear periodic arrays of thin metallic wires

Electromagnetic wave modes localized along 1D periodic finite array of thin metallic parallel cylindrical wires are studied. The array is embedded into free space and excited by normally incident plane wave. We apply analysis based on the Pocklington system of integral equations to compute resonance frequencies and construct excited wave modes above the array. This approach is based on the long-wave approximation of thin wires. The description of the wave modes is directly connected with another problem of guided localized electromagnetic waves propagating along 1D periodic infinite array of thin metallic wires. For the second problem, the quasi-periodic wave field is constructed as a superposition of vector wave fields irradiated by linear electric currents. The approach is also based on the method of integral equations of Pocklington type. Dispersion curves are presented for the first lowest complex half-wave resonance of a single thin vibrator, well-known in radiophysics. An approximate quantization condition is being discussed that helps to compute resonance frequencies of the excited wave modes for the finite array. The data of the dispersion dependencies are incorporated into this quantization condition.