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 (LSU) as a 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 bandgap structures possess substantial LSU and validate LSU’s importance in gap formation through design of amorphous gyroid structures. Amorphous gyroid samples are fabricated via three-dimensional ceramic printing and the bandgaps 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 optimization and the possibility of an amorphous gyroid’s self-assembly.
Highlights
The interaction of a material with light is intimately related to its wavelength-scale structure
We demonstrate the connection between local self-uniformity (LSU) and photonic bandgap (PBG) forming ability by designing novel amorphous gyroid connected networks
With the aim of clarifying these PBG forming characteristics, here we develop LSU a general measure of structural order in connected networks
Summary
The interaction of a material with light is intimately related to its wavelength-scale structure. The formation of PBGs is conventionally interpreted as a result of coherent scattering by a PhC’s lattice planes[7,8] In this picture, a plane wave may be scattered onto its counter-propagating equivalent when the wavevector of the initial state lies on the edge of the PhC’s Brillouin zone (BZ). In spite of the many PhC designs that have since been discovered, those based on the diamond network remain the champion, possessing the largest complete PBGs13,14. PhCs derived from the body-centred cubic singlenetwork gyroid (SNG) structure (triamond) and low-symmetry diamond embeddings all possess near-champion PBGs in spite of their less spherical BZs13. A glassy 3D network—dubbed photonic amorphous diamond (PAD)—exhibits a sizeable complete PBG4 This gap exists despite PAD’s diffuse primary diffraction maximum which spreads the structure’s coherent scattering power of a range of wavevectors[5]
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