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

The interesting photonic band gap maps of two- and three-dimensional photonic crystals with the symmetry of the kagome and pyrochlore lattices 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 lattices amenable to fabrication, the results described below make this family of photonic crystals very promising for potential applications and very interesting from the fundamental point of view.