Designing Perturbative Metamaterials from Discrete Models: From Veselago lenses to topological insulators

Abstract

Discrete models provide concise descriptions of complex physical phenomena, such as negative refraction, topological insulators, and Anderson localization. While there are multiple tools to obtain discrete models that demonstrate particular phenomena, it remains a challenge to find metamaterial designs that replicate the behavior of desired nontrivial discrete models. Here we solve this problem by introducing a new class of metamaterial, which we term 'perturbative metamaterial', consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model (individual masses and springs) to individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing 2D mechanical metamaterials that realize Veselago lenses, zero-dispersion bands, and topological insulators. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal, and photonic metamaterials composed of weakly interacting unit cells.

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Cited by in corpus (51)

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• Observation of nonreciprocal wave propagation in a dynamic phononic lattice
• Observation of Quadrupole Transitions and Edge Mode Topology in an LC network
• Tailoring Structure-borne Sound Through Bandgap Engineering in Phononic Crystals and Metamaterials: A Comprehensive Review
• Observation of an acoustic octupole topological insulator
• Systematic design and realization of double-negative acoustic metamaterials by topology optimization
• Shapely Atoms
• Unsupervised Manifold Clustering of Topological Phononics
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• A Universal Mirror-stacking Approach for Constructing Topological Bound States in the Continuum
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• Nonlinear dispersion relation in anharmonic periodic mass-spring and mass-in-mass systems
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• Topological materials for full-vector elastic waves
• Closed-form existence conditions for band-gap resonances in a finite periodic chain under general boundary conditions
• Rapid Exploration of Topological Band Structures using Deep Learning
• Effective Phononic Crystals for Non-Cartesian Elastic Wave Propagation
• Topological Toda lattice and nonlinear bulk-edge correspondence
• Turing complete mechanical processor via automated nonlinear system design
• Omnidirectional flexural invisibility of multiple interacting voids in vibrating elastic plates
• Stopping and reversing sound via dynamic dispersion tuning in a phononic metamaterial
• Efficient Design of Helical Higher-Order Topological Insulators in 3D Elastic Medium
• Quench dynamics and bulk-edge correspondence in nonlinear mechanical systems
• Theoretical band-gap bounds and coupling sensitivity for a periodic medium with branching resonators
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• Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems
• Asymptotically exact photonic analogues of chiral symmetric topological tight-binding models
• Selectable diffusion direction with topologically protected edge modes
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• Designing nanophotonic structures using conditional-deep convolutional generative adversarial networks
• Nonlinear topological phase diagram in dimerized sine-Gordon model
• Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators
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• Edge States with Hidden Topology in Spinner Lattices
• Topological Micro-Electro-Mechanical Systems
• Classifying topological floppy modes in the continuum
• Phase-preserving nonreciprocal dynamics in coupled nonlinear oscillators
• Acoustic waveguide filters made up of rigid stacked materials with elastic joints
• Dynamics of 2D topological quadrupole insulator and Chern insulator induced by real-space topological changes