Hexagonal structures for two-dimensional photonic crystals

Periodic dielectric structures have been recently proposed to inhibit spontaneous emission in semiconductors. From this suggestion, the new concepts of photonic band gap and photonic crystal have been developed. Zero-threshold lasers, waveguides, antenna substrates, filters and polarizers are promising applications. We propose a new class of two-dimensional periodic dielectric structures with hexagonal symmetry. We study the gap opening according to whether the dielectric constant of the cylinders is larger or smaller than that of the background. A potential application for the creation of photonic crystals in the optical domain is discussed.