Hexagonal photonic-band-gap structures

We investigate a class of two-dimensional hexagonal structures that possess photonic band gaps. This class includes the previously studied triangular structure as a particular case. By symmetry analysis, we obtain a clear insight into the gap opening and we show how the photonic band gaps are affected by the characteristics of materials, according to whether the dielectric constant of the cylinders is larger or smaller than the background one. The photonic band structures present numerous gaps, and we study the evolution of these gaps as functions of the diameter and nature of cylinders. Our results demonstrate the existence of absolute band gaps for many configurations, largest gaps being obtained for triangular and graphite structures.