Zero permittivity materials: Band gaps at the visible

We theoretically discuss the possibility of having materials with zero effective permittivity that would create band gaps in a wide range of frequencies up to the visible. The physical realization of these materials is also discussed in terms of embedding metallic nanoparticles and nanowires in a dielectric medium. In the limit of long wavelengths, these composites will behave like a homogeneous medium with zero permittivity that will completely reflect electromagnetic waves. We present transmittivity calculations by using finite-difference time domain for periodic structures that proves the concept and shows the validity of the long wavelength approximation. The striking result is that the cutoff frequency ωc is determined by the lattice parameter of the composite. By properly choosing the lattice constant of the composite and permittivity of metal and dielectric constituents, we can have full band gaps at any frequency range but especially in the visible.