Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral.

We present a numerical study on photonic bandgap and band edge 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 band edge 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 band edge modes that are absent in both photonic crystals and quasicrystals.