The density of electromagnetic modes in photonic crystals based on the pyrochlore and kagomé lattices

We present a detailed analysis of the density of photonic states of an electromagnetic wave propagating through photonic crystals with the symmetry of the kagome and pyrochlore lattices. The evolution of this quantity with varying dielectric constant contrast is studied with the aim of identifying adequate ranges of this ratio for prospective applications. Some considerations about possible ways of facilitating fabrication of these structures in both two- and three-dimensions are also discussed.