Electromagnetic Scattering by Networks of High-Permittivity Thin Wires

The electromagnetic scattering from a network of high-permittivity dielectric thin wires with the network's size smaller than or almost equal to the operating wavelength is investigated. A simple lumped-element theory for the polarization current intensities induced in the wires is developed. The network elements are capacitances and inductances between the wires. An analytical expression for the induced polarization currents is obtained. The connection between the spectral properties of the loop inductance matrix and the network's resonances is established. The number of the allowed current modes and resonances is deduced from the topology of the circuit's digraph. The radiative coupling is also included, and the radiative frequency shifts and the quality factors are derived. The introduced concept and methods may find applications both at radio frequencies and in nanophotonics.