Photonic-band-gap effects in two-dimensional polycrystalline and amorphous structures

Abstract

We study numerically the density of optical states (DOS) in two-dimensional photonic structures with short-range positional order and observe a transition from polycrystalline to amorphous photonic systems. In polycrystals, photonic band gaps (PBGs) are formed within individual domains, which leads to a depletion of the DOS similar to that in periodic structures. In amorphous photonic media, the domain sizes are too small to form PBGs, thus the depletion of the DOS is weakened significantly. The critical domain size that separates the polycrystalline and amorphous regimes is determined by the attenuation length of Bragg scattering, which depends not only on the degree of positional order but also the refractive-index contrast of the photonic material. Even with relatively low-refractive-index contrast, we find that modest short-range positional order in photonic structures enhances light confinement via collective scattering and interference.