Band gaps atlas for photonic crystals having the symmetry of the pyrochlore and kagome lattices

A new family of two- and three-dimensional photonic crystals with the symmetry of the kagome and pyrochlore lattices that exhibit interesting photonic band structures are reported. From large complete photonic band gaps in three dimensions to enormous partial gaps in two dimensions for certain polarizations occurring at feature sizes that make these lattice amenable of fabrication, the results described below sure make this new family of photonic crystals very promising for potential applications and very interesting from the fundamental point of view.