Three-dimensional photonic quasicrystal with a complete band gap

The band structure of three-dimensional cubic approximants of a photonic quasicrystal has been determined by numerical calculation. The approximants of different orders appear to have large, almost isotropic, band gaps in a wide range of relative permittivity values. The existence of the complete band gap in the photonic quasicrystal with the six-dimensional bcc lattice is shown.