It is generally believed that long range periodic order is instrumenta
l in the formation of a photonic band gap, Using a spectral method tha
t scales linearly with the system size, we found that sizable spectral
gaps for each polarization in 2D can be found in aperiodic arrangemen
ts of dielectrics that resemble quasicrystalline tiling. Since the ape
riodic arrangement has many inequivalent sites, the defect properties
of these systems are more complex and interesting than conventional ph
otonic band gap systems. [S0031-9007(97)05157-0].