An analytical solution is presented for the electromagnetic scattering from an infinite-length metallic carbon nanotube and a carbon nanotube bundle. The scattering field and scattering cross section are predicted using a modal technique based on a Bessel and Hankel function for the electric line source and a quantum conductance function for the carbon nanotube. For the particular case of an isolated armchair （10, 10） carbon nanotube, the scattered field predicted from this technique is in excellent agreement with the measured result. Furthermore, the analysis indicates that the scattering pattern of an isolated carbon nanotube differs from that of the carbon nanotube bundle of identical index （m, n） metallic carbon nanotubes.
We propose a bulk negative refractive index （NRI） metamaterial composed of periodic array of tightly coupled metallic cross-pairs printed oR the six sides of a cube for applications of superlenses. The structural characteristics of the three-dimensional （3D） metamaterial consist in the high symmetry and the superposition of metallic cross-pairs, which can increase the magnetic inductive coupling between adjacent cross-pairs and realize a broadband and isotropic NRI. The proposed 3D structure is simulated using the CS~ Microwave Studio 2006 to verify the design validity. The simulation results show that the proposed structure can not only realize simultaneously an electric and magnetic response to an incident electromagnetic （EM） wave, but also exhibit a broadband NRI whose relative bandwidth can reach up to 56.7%. In addition, the NRI band is insensitive to tile polarization and the incident angle of the incident EM wave. Therefore, the proposed metamaterial is a good candidate material as three-dimensional broadband isotropic NRI metamaterial.
