Abstract
Metamaterials are rationally designed composites aiming at effective material parameters that go beyond those of the ingredient materials. For example, negative metamaterial properties, such as the refractive index, thermal expansion coefficient or Hall coefficient, can be engineered from constituents with positive parameters. Likewise, large metamaterial parameter values can arise from all-zero constituents, such as magnetic from non-magnetic, chiral from achiral and anisotropic from isotropic. The field of metamaterials emerged from linear electromagnetism two decades ago and today addresses nearly all conceivable aspects of solids, ranging from electromagnetic and optical, and mechanical and acoustic to transport properties — linear and nonlinear, reciprocal and non-reciprocal, monostable and multistable (programmable), active and passive, and static and dynamic. In this Review, we focus on the general case of 3D periodic metamaterials, with electromagnetic or optical, acoustic or mechanical, transport or stimuli-responsive properties. We outline the fundamental bounds of these composites and summarize the state of the art in theoretical design and experimental realization.
Key points
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Metamaterials are rationally designed composites made of tailored building blocks, which are composed of one or more constituent bulk materials, leading to effective medium properties beyond those of their ingredients.
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Metamaterials thereby fulfil a long-standing dream of condensed matter physics to design materials on the computer to avoid tedious trial-and-error procedures and excessive experimentation.
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Although many 1D and 2D model architectures have been considered because of their ease of fabrication and reduced design complexity, the full potential of the metamaterial concept is opened up for 3D microstructures and nanostructures.
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In electromagnetism and optics, examples are effective diamagnetism and paramagnetism up to optical frequencies, impedance matching and duality, negative refractive indices, maximum electromagnetic chirality, perfect optical absorption and non-reciprocal propagation of electromagnetic waves without static magnetic fields.
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In acoustics and mechanics, examples are the complete flexibility in tailoring elastic parameters, chiral mechanical behaviour, sign reversal of the static effective compressibility, negative dynamic mass density, non-reciprocal sound propagation, broadband perfect sound absorption at the fundamental limit imposed by causality and highly nonlinear, multistable and programmable properties from linear elastic constituents.
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In transport, examples are highly anisotropic thermal conductance, sign reversal of the absolute mobility and the Hall coefficient, highly anisotropic Hall tensors, giant magnetoresistances and thermoelectric power factors that are enhanced by orders of magnitude.
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Future 3D material printers may achieve thousands of different effective metamaterial properties from only a small number of input material cartridges — in analogy to today’s 2D graphical printers that mix thousands of colours from just three colour cartridges.
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Acknowledgements
The authors acknowledge stimulating discussions with C. Rockstuhl and C. Kern (Karlsruhe Institute of Technology (KIT)). M.K. acknowledges support by the Engineering and Innovation through Physical Sciences, High-technologies and Cross-disciplinary Research (EIPHI) Graduate School (contract ANR-17-EURE-0002) and the French Investissements d’Avenir program, the I-SITE Bourgogne Franche-Comté (BFC) project (contract ANR-15-IDEX-03). G.W.M. thanks the National Science Foundation for support via grant DMS-1211359 and DMS-1814854. M.W. acknowledges support by the Excellence Cluster '3D Matter Made to Order', the Helmholtz program 'Science and Technology of Nanosystems' (STN), the Karlsruhe School of Optics & Photonics (KSOP) and the 'Virtual Materials Design' (VIRTMAT) project of KIT.
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Glossary
- Inverse design
-
A design approach that defines the desired properties and searches for a microstructure exhibiting them; the inverse of taking a microstructure and calculating its properties.
- Topology optimization
-
A mathematical method that finds a microstructure that optimizes a set of parameters within a given design space and for given constraints.
- Auxetic
-
An auxetic material shrinks laterally when being contracted axially. This behaviour corresponds to a negative Poisson ratio ν.
- Pentamode
-
A pentamode material is a linear elastic 3D material for which five of the six possible modes of deformation cost no energy. Such materials behave approximately as a liquid.
- 2D Huygens metasurfaces
-
2D arrangements of electric and magnetic polarizable elements that modify the transmitted light yet lead to zero reflections.
- Faraday active
-
Refers to media that rotate the polarization axis of linearly polarized light in the presence of a static magnetic field but that do not change the sense of rotation upon back-reflection of light.
- Cauchy elasticity tensor
-
This tensor is the generalization of Hooke’s spring constant. It connects the stress and the strain tensors.
- Lamé parameters
-
A possible pair of parameters that characterize the Cauchy elasticity tensor in an isotropic homogeneous medium. The second Lamé parameter is identical to the shear modulus.
- Eringen micropolar continuum mechanics
-
A generalization of Cauchy continuum mechanics, in which four rank-4 tensors are required to describe the connection between strain and microrotation tensors and between stress and torque tensors.
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Kadic, M., Milton, G.W., van Hecke, M. et al. 3D metamaterials. Nat Rev Phys 1, 198–210 (2019). https://doi.org/10.1038/s42254-018-0018-y
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DOI: https://doi.org/10.1038/s42254-018-0018-y
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