The equivalent circuit imitating wave scattering by arrays of split-ring resonators

Abstract

The scattering of waves by a periodic chain of series resonant LC circuits in a two-dimensional lattice of lumped elements is considered, that imitates the scattering of electromagnetic waves by a periodic lattice of split-ring resonators. Using the translation symmetry of this chain we transformed the scattering problem into the problem of wave propagation along the strip with a single LC circuit. This problem was solved analytically presenting the transmittance as a sum of partial transmittances, corresponding to the frequency mini-bands of the strip. It is shown that the transmittance as a function of the incident wave frequency demonstrates two types of resonances with different resonant frequency dependence on the distance between neighbouring LC circuits.