Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials

We study numerically the influence of the frequency dispersion of the dielectric function of metals on the physical properties of negative-refractive-index metamaterials. A numerical analysis is performed using the transfer matrix formalism in conjunction with the finite-difference time-domain method. We analyze the dependence of the transmission and absorption properties of a slab of split-ring-type resonators on the parameters characterizing the frequency dispersion of the metallic dielectric function: plasma frequency and damping frequency. Then, using these transmission and reflection coefficients, we show that the refractive index remains negative near the resonant frequency of the rings, despite the presence of frequency dispersion. We also determine the dependence of the position and width of the band gaps of a slab of such a metamaterial on the material dispersion. Finally, we also discuss the influence of the shape of the split-ring resonators on the transmission and reflection coefficients. The calculations are performed for both two- and three-dimensional structures.