  We measured and calculated transmission spectra of two-dimensional
quasiperiodic photonic crystals (PCs) based on a 5-fold (Penrose) or 8-fold
(octagonal) symmetric quasiperiodic pattern. The photonic crystal consisted of
dielectric cylindrical rods in air placed normal to the basal plane on vertices
of 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 as
2.4. An isotropic PBG-like dip was seen in tiny Penrose and octagonal PCs with
only 6 and 9 rods, respectively. These results indicate that local multiple
light scattering within the tiny PC plays an important role in the PBG
formation. Besides the isotropic PBG, we found dips depending on the incident
angle of the light. This is the first report of anisotropic structures clearly
observed in transmission spectra of quasiperiodic PCs. Based on rod-number and
rod-arrangement dependence, it is thought that the shapes and positions of the
anisotropic dips are determined by global multiple light scattering covering
the whole system. In contrast to the isotropic PBG due to local light
scattering, we could not find any PBGs due to global light scattering even
though we studied transmission spectra of a huge Penrose PC with 466 rods.
