title: Local self-uniformity in photonic networks.
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.
authors.affiliation: Advanced Technology Institute and Department of Physics, University of Surrey, Guildford GU2 7XH, UK.
authors.forename: Steven R
authors.initials: SR
authors.lastname: Sellers
authors.affiliation: Department of Physics and Astronomy, San Francisco State University, 1600 Holloway Avenue, San Francisco, California 94132, USA.
authors.forename: Weining
authors.initials: W
authors.lastname: Man
authors.affiliation: Department of Physics and Astronomy, San Francisco State University, 1600 Holloway Avenue, San Francisco, California 94132, USA.
authors.forename: Shervin
authors.initials: S
authors.lastname: Sahba
authors.affiliation: Advanced Technology Institute and Department of Physics, University of Surrey, Guildford GU2 7XH, UK.
authors.forename: Marian
authors.initials: M
authors.lastname: Florescu