Electromagnetic Scattering by Networks of High-Permittivity Thin Wires

The electromagnetic scattering from interconnections of high-permittivity dielectric thin wires with sizes smaller than (or almost equal to) the operating wavelength is investigated. A simple lumped element model for the polarization current intensities induced in the wires is proposed. The circuit elements are capacitances and inductances between the wires. An analytical expression for the induced polarization currents in terms of the magneto-quasistatic current modes 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 coupling to radiation is also included, and the radiative frequency shifts and the quality factors are derived. The introduced concept and methods may find applications both at the microwaves and in nanophotonics.