  We study photonic band gap formation in two-dimensional high refractive index
disordered materials where the dielectric structure is derived from packing
disks in real and reciprocal space. Numerical calculations of the photonic
density of states demonstrate the presence of a band gap for all polarizations
in both cases. We find that the band gap width is controlled by the increase in
positional correlation inducing short-range order and hyperuniformity
concurrently. Our findings suggest that the optimization of short-range order,
in particular the tailoring of Bragg scattering at the isotropic Brillouin
zone, are of key importance for designing disordered PBG materials.
