Abstract
The interaction of a material with light is intimately related to its wavelength-scale structure. Simple connections between structure and optical response empower us with essential intuition to engineer complex optical functionalities. Here we develop local self-uniformity as a novel measure of a random network’s internal structural similarity, ranking networks on a continuous scale from crystalline, through glassy intermediate states, to chaotic configurations. We demonstrate that complete photonic band gap structures possess substantial local selfuniformity and validate local self-uniformity’s importance in gap formation through design of novel amorphous gyroid structures. Amorphous gyroid samples are fabricated via 3D ceramic printing and the band gaps experimentally verified. We explore also the wing-scale structuring in the butterfly Pseudolycaena marsyas and show that it possesses substantial amorphous gyroid character, demonstrating the subtle order achieved by evolutionary optimisation and the possibility of an amorphous gyroid’s self-assembly.