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We measured and calculated transmission spectra of two-dimensionalquasiperiodic photonic crystals (PCs) based on a 5-fold (Penrose) or 8-fold(octagonal) symmetric quasiperiodic pattern. The photonic crystal consisted ofdielectric cylindrical rods in air placed normal to the basal plane on verticesof tiles composing the quasiperiodic pattern. An isotropic photonic band gap(PBG) appeared in the TM mode, where electric fields were parallel to the rods,even when the real part of a dielectric constant of the rod was as small as2.4. An isotropic PBG-like dip was seen in tiny Penrose and octagonal PCs withonly 6 and 9 rods, respectively. These results indicate that local multiplelight scattering within the tiny PC plays an important role in the PBGformation. Besides the isotropic PBG, we found dips depending on the incidentangle of the light. This is the first report of anisotropic structures clearlyobserved in transmission spectra of quasiperiodic PCs. Based on rod-number androd-arrangement dependence, it is thought that the shapes and positions of theanisotropic dips are determined by global multiple light scattering coveringthe whole system. In contrast to the isotropic PBG due to local lightscattering, we could not find any PBGs due to global light scattering eventhough we studied transmission spectra of a huge Penrose PC with 466 rods.Comment: One tex file for manuscript and 12 PNG files for figures consisting  of Fig.1a-d, 2,3, ...

physical review. b, condensed matter

Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals