Numerical study of two-dimensional metamaterial composites: the existence of a stop band

Two-dimensional metamaterial photonic crystals composed of dispersive left-handed materials and a right-handed medium were investigated. The existence of a stop band was studied by finite-difference time-domain calculations incorporated into an auxiliary differential equation (FDTD-ADE) method. The existence of a stop band was studied in the case of Drude-type dispersion responses for the dielectric permittivity and magnetic permeability of the metamaterial. A distinct stop band appears when the dispersive left-handed metamaterials are embedded in a positive-refractive-index medium and spatially isolated from each other. In contrast, the stop band is absent when the metamaterials span the entire photonic crystal.