New classes of non-crystalline photonic band gap materials

Due to their ability to control the most fundamental properties of light, photonic band gap (PBG) materials open a new frontier in both basic science and technology [1,2]. Until now, the only materials known to have complete photonic band gaps were photonic crystals, periodic structures. We show that there exists a more general class of systems, called hyperuniform photonic structures, which exhibit large and complete photonic band gaps. The common feature of hyperuniform photonic structures considered here is that they are derived from hyperuniform point patterns [3]. Hyperuniform point patterns are those whose number variance within a spherical sampling window of radius R (in d dimensions) grows more slowly than the window volume for large R, i.e., 〈N R 2〉 − 〈N R 〉2 ∼ Rp, where p ≪ d. This classification includes all crystals and quasicrystals [4], as well as a special subset of disordered structures.