New hexagonal structures for two-dimensional photonic band gap materials.

Recently, periodic dielectric structures have been 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, wave guides and polarizers are promising applications. A new class of two-dimensional periodic structures with hexagonal symmetry is investigated in order to obtain photonic band gap materials. This set has the hexagonal symmetry and contains, in particular, several structures previously discussed. The photonic band gap structure is related to the basic properties of the materials and some features of the opening of the gaps are explained. By varying the crystal pattern, we show how band gaps common to E and H polarizations appear for a new design of two-dimensional periodic dielectric structures. The dependence of the widths of these gaps on the filling patterns is studied and potential application for the creation of photonic crystals in the optical domain is discussed.