On the determination of the effective permittivity of metamaterials: a spectral FDTD approach

A new modified FDTD referred to spectral FDTD is introduced to calculate the effective permittivity of metamaterials. An array of periodic spheres and an array of periodic cubes are analyzed by the technique, and the effective permittivities for both structures are calculated. It is observed that the cubical inclusions have a larger effective permittivity than the spherical inclusions for the same volume and dielectric constant of each inclusion. Because of the versatility of the spectral FDTD technique, the technique introduced here provides an efficient tool to calculate the effective permittivity of metamaterials with the arbitrary shaped inclusion.