Abstract
It is generally believed that long range periodic order is instrumental for the formation of a photonic band gap (PBG). Using a time domain spectral method that scales linearly with the system size, we found that sizable spectral gaps for each polarization in 2D can be found in aperiodic arrangements of dielectrics that resemble quasi-crystalline tiling in 2D. The effect of defects, randomness and disorder on the photonic band gap are studied for this class of systems. The properties of defects state of with in PBG of photonic crystals with square lattice structure are also studied. The states are localized in nature so that the PBG systems with defects behave like metallic micro-cavities with resonating frequencies being governed by the dimensions of the defects.