Photonic Band Gap Effects in Two-dimensional Polycrystalline and Amorphous Structures

TL;DR

This study numerically investigates how short-range positional order in two-dimensional photonic structures influences the formation of photonic band gaps, revealing a transition from polycrystalline to amorphous regimes and the role of domain size and refractive index contrast.

Contribution

It identifies the critical domain size for PBG formation and demonstrates how modest positional order enhances light confinement even at low refractive index contrast.

Findings

Polycrystalline structures exhibit PBGs within individual domains.

Amorphous structures show significantly weakened DOS depletion.

Short-range order improves light confinement at low index contrast.

Abstract

We study numerically the density of optical states (DOS) in two-dimensional photonic structures with short-range positional order, and observe a clear transition from polycrystalline to amorphous photonic systems. In polycrystals, photonic band gaps (PBGs) are formed within individual do- mains, 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.