  Localization of light is the photon analog of electron localization in
disordered lattices for whose discovery Anderson received the Nobel prize in
1977. The question about its existence in open three-dimensional materials has
eluded an experimental and full theoretical verification for decades. Here we
study numerically electromagnetic vector wave transmittance through realistic
digital representations of hyperuniform dielectric networks, a new class of
highly correlated but disordered photonic band gap materials. We identify the
evanescent decay of the transmitted power in the gap and diffusive transport
far from the gap. Near the gap, we find that transport sets off diffusive but,
with increasing slab thickness, crosses over gradually to a faster decay,
signaling localization. We show that we can describe the transition to
localization at the mobility edge using the self-consistent theory of
localization based on the concept of a position-dependent diffusion
coefficient.
