FDTD study of resonance processes in metamaterials

The finite-difference time-domain simulations in the frequency domain are used to study resonance phenomena in left-handed metamaterials consisting of the arrays of split-ring resonators (SRRs) and metal rods. It is demonstrated that, at frequencies corresponding to the band of enhanced transmission of the metamaterial, the half-wavelength resonances occur in both the SRRs and rods. The observed resonances in rods make questionable the applicability of the plasma concept to the analysis of the metamaterial performance. We also show that overlapping of electric or magnetic fields at resonance causes coupling between resonators and assembling them in three-dimensional groups, which rearrange in dependence on frequency inside the transmission band. As the result, the resonance phenomena in the metamaterial proceed essentially nonuniform, although the size of the metamaterial units is less than the wavelength. We suggest that coupling between resonators is capable of providing the electromagnetic response, similar to that observed at the backward-wave propagation in double-negative media. The latter is demonstrated on the example of the all-dielectric metamaterial composed from an array of dielectric resonators.