We study the scattering of an electromagnetic wave from a cylinder of infinite length fabricated from a combined split-ring resonator (SRR) and thin metal wire medium that is characterized by an effective frequency-dependent permittivity ${\epsilon }_{\mathrm{eff}}\left(\omega \right)$ and permeability ${\mu }_{\mathrm{eff}}\left(\omega \right)$ that can both be negative in a certain frequency region, and thus constitutes a left-handed (LH) metamaterial. We evaluate the scattering width of the cylinder in terms of the most general form of the Mie coefficients $a_n{,b}_n$ that takes into account the magnetic effects through the effective refractive index $n_{\mathrm{eff}}\left(\omega \right)=\sqrt{{\epsilon }_{\mathrm{eff}}\left(\omega \right)}\sqrt{{\mu }_{\mathrm{eff}}\left(\omega \right)}.$ Incident waves of both E polarization (where the electric field is parallel to the axis of the cylinder) and H polarization (where the magnetic field is parallel to the axis of the cylinder) are considered. We find that in the case when the magnetic field is perpendicular to the plane of the SRR, the scattering width as a function of the frequency of the incident wave reveals the resonances of the Mie coefficients $a_n$ and $b_n,$ for both E- and H-polarized incident waves. These peaks occur in the frequency range where the effective refractive index is negative, and they arise from modes that propagate with a negative group velocity. This behavior is consistent with the results of transfer-matrix calculations and transmission experiments on two-dimensional LH metamaterials, which show that the medium becomes transparent to the electromagnetic radiation in this frequency region.

• Received 30 March 2001

DOI:https://doi.org/10.1103/PhysRevB.66.045116