  We present a numerical study on photonic bandgap and bandedge modes in the
golden-angle spiral array of air cylinders in dielectric media. Despite the
lack of long-range translational and rotational order, there is a large PBG for
the TE polarized light. Due to spatial inhomogeneity in the air hole spacing,
the bandedge modes are spatially localized by Bragg scattering from the
parastichies in the spiral structure. They have discrete angular momenta that
originate from different families of the parastichies whose numbers correspond
to the Fibonacci numbers. The unique structural characteristics of the
golden-angle spiral lead to distinctive features of the bandedge modes that are
absent in both photonic crystals and quasicrystals.
