The central correlations between the geometrical and topological characteristics of structured photonic materials and the photonic functionality they enable is of fundamental importance. Here, we introduce a new metric, local self-uniformity (LSU) as a measure of the structural order of photonic network structures. The LSU characterizes the intimate connection between uniformity of the local environments and the overall photonic band gap properties and provides a new design strategy for non-periodic materials. LSU can be employed to rank photonic networks with the SRS-gyroid and diamond networks reaching a maximal unity value of LSU. We then explore the connection between the LSU concept and the photonic band gap formation and introduce a novel architecture, the amorphous gyroid network or triamond. Moreover, we demonstrate all architectures displaying large photonic band gaps, be they periodic or disordered, are characterized by large values of the LSU metric. We also show that LSU is significant metric beyond the formation of photonic band gaps and apply it to characterise the wing-scale structuring in the butterfly Pseudolycaena marsyas. We fabricate the first prototypes of amorphous gyroid at a centimetre length scale in high index alumina ceramic. To achieve this, we employ a novel lithography-based ceramic manufacturing (LCM) process which can and achieve sub-millimetre feature resolution with a minimum of post-processing steps. Microwave transmission measurements are in good agreement with FDTD simulations and confirm the existence of large and robust band gaps.
Marian Florescu and Steven Sellers, "Local self-uniformity and photonic bandgaps in amorphous gyroid structures (Conference Presentation)," Proc. SPIE 10541, Photonic and Phononic Properties of Engineered Nanostructures VIII, 105410O (Presented at SPIE OPTO: January 30, 2018; Published: 14 March 2018); https://doi.org/10.1117/12.2290116.5751531106001.
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