Band structure of comb-like photonic crystals containing meta-materials

We study the transmission properties and band structure of comb-like photonic crystals (PC) with backbones constructed of meta-materials (negative-index materials) within the frame of the interface response theory. The result shows the existence of a special band gap at low frequency. This gap differs from the Bragg gaps in that it is insensitive to the geometrical scaling and disorder. In comparison with the zero-average-index gap in one-dimensional PC made of alternating positive- and negative-index materials, the gap is obviously deeper and broader, given the same system parameters. In addition, the behavior of its gap-edges is also different. One gap-edge is decided by the average permittivity whereas the other is only subject to the changing of the permeability of the backbone. Due to this asymmetry of the two gap-edges, the broadening of the gap could be realized with much freedom and facility.