Abstract
Three‐dimensional (3D) micro‐and nanostructures have played an important role in topological photonics, microfluidics, acoustic, and mechanical engineering. Incorporating biomimetic geometries into the design of metastructures has created low‐density metamaterials with extraordinary physical and photonic properties. However, the use of surface‐based biomimetic geometries restricts the freedom to tune the relative density, mechanical strength, and topological phase. The Steiner tree method inspired by the feature of the shortest connection distance in biological neural networks is applied, to create 3D metastructures and, through two‐photon nanolithography, neuron‐inspired 3D structures with nanoscale features are successfully achieved. Two solutions are presented to the 3D Steiner tree problem: the Steiner tree networks (STNs) and the twisted Steiner tree networks (T‐STNs). STNs and T‐STNs possess a lower density than surface‐based metamaterials and that T‐STNs have Young's modulus enhanced by 20% than the STNs. Through the analysis of the space groups and symmetries, a topological nontrivial Dirac‐like conical dispersion in the T‐STNs is predicted, and the results are based on calculations with true predictive power and readily realizable from microwave to optical frequencies. The neuron‐inspired 3D metastructures opens a new space for designing low‐density metamaterials and topological photonics with extraordinary properties triggered by a twisting degree‐of‐freedom.
Highlights
Kelvin foam from bubble systems,[7] into engineering
We have investigated a new family of low-density metamaterials inspired by the feature of the “shortest connection distance” in neurons: Steiner tree networks (STNs)
Using two-photon nanolithography (TPN), STNs nanostructures were fabricated with the lowest relative density compared to network structures designed from minimal surfaces, a property ensured by the use of the Steiner tree optimization approach
Summary
Neurons pursue the “shortest connection distance” for signal transmission and optimization.[38]. The 3D STNs we present here are 8-point Euclidean STNs achieved using a branching axon and dendrite optimization approach (Discussed in the Supporting information Section S1).[41] In this path-optimization approach, eight primary network sites (blue spheres shown in Figure 1a–c) starting from a primitive simple cubic Bravais lattice are allowed to connect to each other through dendritic connections at secondary networks sites (green spheres),[42] similar to dendritic synaptic connections of a biological neural network The solution of this optimization with the shortest path length and lowest symmetry is shown in Figure 1a (left). We refer to this second unique solution of equal lowest path length as a “twisted STNs (T-STNs)” which consists of the same six dendritic triple-junctions, three of which are rotated by 90° to form a structure in the tetragonal space group P4̄m2 Optimization on other 3D Bravais lattices or with more primary sites may give rise to more 3D STNs with unique properties and should be the subject of future investigations
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