Mechanical metamaterials.

Mechanical metamaterials, also known as architected materials, are rationally designed composites, aiming at elastic behaviors and effective mechanical properties beyond ('meta') those of their individual ingredients-qualitatively and/or quantitatively. Due to advances in computational science and manufacturing, this field has progressed considerably throughout the last decade. Here, we review its mathematical basis in the spirit of a tutorial, and summarize the conceptual as well as experimental state-of-the-art. This summary comprises disordered, periodic, quasi-periodic, and graded anisotropic functional architectures, in one, two, and three dimensions, covering length scales ranging from below one micrometer to tens of meters. Examples include extreme ordinary linear elastic behavior from artificial crystals, e.g. auxetics and pentamodes, 'negative' effective properties, behavior beyond classical linear elasticity, e.g. arising from local resonances, chirality, beyond-nearest-neighbor interactions, quasi-crystalline mechanical metamaterials, topological band gaps, cloaking based on coordinate transformations and on scattering cancelation, seismic protection, nonlinear and programmable metamaterials, as well as space-time-periodic architectures.

(3+1)D printed adiabatic 1-to-M broadband couplers and fractal splitter networks.

We experimentally demonstrate, based on a generic concept for creating 1-to-M couplers, single-mode 3D optical splitters leveraging adiabatic power transfer towards up to 4 output ports. We use the CMOS compatible additive (3+1)D flash-two-photon polymerization (TPP) printing for fast and scalable fabrication. Optical coupling losses of our splitters are reduced below our measurement sensitivity of 0.06 dB by tailoring the coupling and waveguides geometry, and we demonstrate almost octave-spanning broadband functionality from 520 nm to 980 nm during which losses remain below 2 dB. Finally, based on a fractal, hence self-similar topology of cascaded splitters, we show the efficient scalability of optical interconnects up to 16 single-mode outputs with optical coupling losses of only 1 dB.

Additive 3D photonic integration that is CMOS compatible.

Today, continued miniaturization in electronic integrated circuits (ICs) appears to have reached its fundamental limit at ∼2 nm feature-sizes, from originally ∼1 cm. At the same time, energy consumption due to communication becomes the dominant limitation in high performance electronic ICs for computing, and modern computing concepts such neural networks further amplify the challenge. Communication based on co-integrated photonic circuits is a promising strategy to address the second. As feature size has leveled out, adding a third dimension to the predominantly two-dimensional ICs appears a promising future strategy for further IC architecture improvement. Crucial for efficient electronic-photonic co-integration is complementary metal-oxide-semiconductor (CMOS) compatibility of the associated photonic integration fabrication process. Here, we review our latest results obtained in the FEMTO-ST RENATECH facilities on using additive photo-induced polymerization of a standard photo-resin for truly three-dimensional (3D) photonic integration according to these principles. Based on one- and two-photon polymerization (TPP) and combined with direct-laser writing, we 3D-printed air- and polymer-cladded photonic waveguides. An important application of such circuits are the interconnects of optical neural networks, where 3D integration enables scalability in terms of network size versus its geometric dimensions. In particular viaflash-TPP, a fabrication process combining blanket one- and high-resolution TPP, we demonstrated polymer-cladded step-index waveguides with up to 6 mm length, low insertion (∼0.26 dB) and propagation (∼1.3 dB mm-1) losses, realized broadband and low loss (∼0.06 dB splitting losses) adiabatic 1 to M couplers as well as tightly confining air-cladded waveguides for denser integration. By stably printing such integrated photonic circuits on standard semiconductor samples, we show the concept's CMOS compatibility. With this, we lay out a promising, future avenue for scalable integration of hybrid photonic and electronic components.

Single-Step-Lithography Micro-Stepper Based on Frictional Contact and Chiral Metamaterial.

Stepper motors and actuators are among the main constituents of control motion devices. They are complex multibody systems with rather large overall volume due to their multifunctional parts and elaborate technological assembly processes. Miniaturization of individual parts is still posing assembly problems. In this paper, a single-step lithography process to fabricate a micro-stepper engine with an accurate micrometric rotation axis and an overall sub-millimeter size is demonstrated. The device is based on the frictional contacts and chiral metamaterials to get rid of the dependence on the accuracy of parts. The functional aspects of fabricated samples are discussed for many rotation cycles and for different frictional surfaces.

Isotropic Chiral Acoustic Phonons in 3D Quasicrystalline Metamaterials.

The elastic properties of three-dimensional (3D) crystalline mechanical metamaterials, unlike those of amorphous structures, are generally strongly anisotropic-even in the long-wavelength limit and for highly symmetric crystals. Aiming at isotropic linear elastic wave propagation, we therefore study 3D periodic approximants of 3D icosahedral quasicrystalline mechanical metamaterials consisting of uniaxial chiral metarods. Considering the increasing order of the approximants, we approach nearly isotropic effective speeds of sound and isotropic acoustical activity. The latter is directly connected to circularly polarized 3D metamaterial chiral acoustic phonons-for all propagation directions in three dimensions.

Mechanical cloak design by direct lattice transformation.

Spatial coordinate transformations have helped simplifying mathematical issues and solving complex boundary-value problems in physics for decades already. More recently, material-parameter transformations have also become an intuitive and powerful engineering tool for designing inhomogeneous and anisotropic material distributions that perform wanted functions, e.g., invisibility cloaking. A necessary mathematical prerequisite for this approach to work is that the underlying equations are form invariant with respect to general coordinate transformations. Unfortunately, this condition is not fulfilled in elastic-solid mechanics for materials that can be described by ordinary elasticity tensors. Here, we introduce a different and simpler approach. We directly transform the lattice points of a 2D discrete lattice composed of a single constituent material, while keeping the properties of the elements connecting the lattice points the same. After showing that the approach works in various areas, we focus on elastic-solid mechanics. As a demanding example, we cloak a void in an effective elastic material with respect to static uniaxial compression. Corresponding numerical calculations and experiments on polymer structures made by 3D printing are presented. The cloaking quality is quantified by comparing the average relative SD of the strain vectors outside of the cloaked void with respect to the homogeneous reference lattice. Theory and experiment agree and exhibit very good cloaking performance.

Experimental Evidence for Sign Reversal of the Hall Coefficient in Three-Dimensional Metamaterials.

Effectively inverting the sign of material parameters is a striking possibility arising from the concept of metamaterials. Here, we show that the electrical properties of a p-type semiconductor can be mimicked by a metamaterial solely made of an n-type semiconductor. By fabricating and characterizing three-dimensional simple-cubic microlattices composed of interlocked hollow semiconducting tori, we demonstrate that sign and magnitude of the effective metamaterial Hall coefficient can be adjusted via a tori separation parameter-in agreement with previous theoretical and numerical predictions.

Diffuse-light all-solid-state invisibility cloak.

An ideal invisibility cloak makes arbitrary macroscopic objects within the cloak indistinguishable from its surrounding­for all directions, illumination patterns, polarizations, and colors of visible light. Recently, we have approached such an ideal cloak for the diffusive regime of light propagation using a core-shell geometry and a mixture of water and white wall paint as the surrounding. Here, we present an all-solid-state version based on polydimethylsiloxane doped with titania nanoparticles for the surrounding/shell and on a high-reflectivity microporous ceramic for the core. By virtue of reduced effects of absorption, especially from the core, the cloaking performance and the overall light throughput are improved significantly.

Experiments on cloaking in optics, thermodynamics and mechanics.

Spatial coordinate transformations can be used to transform boundaries, material parameters or discrete lattices. We discuss fundamental constraints in regard to cloaking and review our corresponding experiments in optics, thermodynamics and mechanics. For example, we emphasize three-dimensional broadband visible-frequency carpet cloaking, transient thermal cloaking, three-dimensional omnidirectional macroscopic broadband cloaking for diffuse light throughout the entire visible range, cloaking for flexural waves in thin plates and three-dimensional elasto-static core-shell cloaking using pentamode mechanical metamaterials.

Thermal conductivity of wrinkled graphene ring with defects.

Graphene rings have great prospects in the fields of biological modulators, electrochemical biosensors, and resonators, but are prone to wrinkling which can affect their physical properties. This work establishes a theoretical model predicting the torsional wrinkling behavior of defective monolayer graphene rings, which provides direct understanding and reliable accuracy of the wrinkle levels. Then the thermal conductivity of wrinkled graphene rings is studied considering different wrinkle levels, defect concentrations and radii. It is found that with increased radius, defect concentration and torsional angle, the ratio of wrinkle amplitude to wavelength increases gradually. Vacancy defects and radii have more significant influences on the thermal conductivity than torsional wrinkles. The main influence mechanism of wrinkles and defects on thermal conductivity is revealed by phonon density of state. This work provides theoretical guidance for thermal manipulation based on the wrinkle-tuning approach.

Dispersion Engineering by Hybridizing the Back-Folded Soft Mode of Monomode Elastic Metamaterials with Stiff Acoustic Modes.

In many cases, the hybridization of two or more excitation modes in solids has led to new and useful dispersion relations of waves. Well-studied examples are phonon polaritons, plasmon polaritons, particle-plasmon polaritons, cavity polaritons, and magnetic resonances at optical frequencies. In all of these cases, the lowest propagating mode couples to a finite-frequency localized resonance. Herein, the unusual metamaterial phonon dispersion relations arising from the hybridization of an ordinary acoustical phonon mode with a back-folded soft or easy phonon mode of a monomode elastic metamaterial are discussed. Conceptually, the single easy mode can have strictly zero wave velocity. In reality, its wave velocity is very much smaller than that of all other modes. Considering polymeric three-dimensional printed elastic monomode metamaterials at ultrasound frequencies, it is shown theoretically and experimentally that the resulting pronounced avoided crossing, with a frequency splitting comparable to the mid-frequency, leads to backward-wave behavior for the lowest band over a broad frequency range, conceptually at zero loss.

Metamaterials beyond electromagnetism.

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.

Experiments on transformation thermodynamics: molding the flow of heat.

It was recently shown theoretically that the time-dependent heat conduction equation is form invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped onto (meta)materials with spatially inhomogeneous and anisotropic heat-conductivity tensors in the laboratory space. On this basis, we design, fabricate, and characterize a microstructured thermal cloak that molds the flow of heat around an object in a metal plate. This allows for transient protection of the object from heating while maintaining the same downstream heat flow as without object and cloak.

Nonlocal Cable-Network Metamaterials.

Metamaterials are artificial materials in which the atoms of ordinary solids are replaced by tailored functional building blocks. Therefore, previous work has emphasized tailoring the inside of the building blocks, for example, by exploiting local resonances, to realize unusual effective metamaterial properties. However, the wave properties of a metamaterial are not only determined by its building blocks but also by the interactions between these building blocks. Here, reconfigurable "plug-and-play" electromagnetic metamaterials are introduced for which the building blocks are essentially trivial standard bayonet Neill-Concelman (BNC) connectors and the effective metamaterial properties are solely achieved by tailoring the local and especially the nonlocal interactions mediated by standard coaxial cables. Unprecedented dispersion relations of the lowest band with multiple regions of slow waves and backward waves are demonstrated. Importantly, the dispersion relation of such metamaterials dominated by nonlocal interactions is not limited by the principle of causality in the same way as for metamaterials designed by local resonances of building blocks.

Controlled Dispersion and Transmission-Absorption of Optical Energy through Scaled Metallic Plate Structures.

The dispersive feature of metals at higher frequencies has opened up a plethora of applications in plasmonics. Besides, Extraordinary Optical Transmission (EOT) reported by Ebbesen et al. in the late 90's has sparked particular interest among the scientific community through the unprecedented and singular way to steer and enhance optical energies. The purpose of the present paper is to shed light on the effect of the scaling parameter over the whole structure, to cover the range from the near-infrared to the visible, on the transmission and the absorption properties. We further bring specific attention to the dispersive properties, easily extractable from the resonance frequency of the drilled tiny slits within the structure. A perfect matching between the analytical Rigorous Coupled Wave Analysis (RCWA), and the numerical Finite Elements Method (FEM) to describe the underlying mechanisms is obtained.

Non-reciprocal and non-Newtonian mechanical metamaterials.

Non-Newtonian liquids are characterized by stress and velocity-dependent dynamical response. In elasticity, and in particular, in the field of phononics, reciprocity in the equations acts against obtaining a directional response for passive media. Active stimuli-responsive materials have been conceived to overcome it. Significantly, Milton and Willis have shown theoretically in 2007 that quasi-rigid bodies containing masses at resonance can display a very rich dynamical behavior, hence opening a route toward the design of non-reciprocal and non-Newtonian metamaterials. In this paper, we design a solid structure that displays unidirectional shock resistance, thus going beyond Newton's second law in analogy to non-Newtonian fluids. We design the mechanical metamaterial with finite element analysis and fabricate it using three-dimensional printing at the centimetric scale (with fused deposition modeling) and at the micrometric scale (with two-photon lithography). The non-Newtonian elastic response is measured via dynamical velocity-dependent experiments. Reversing the direction of the impact, we further highlight the intrinsic non-reciprocal response.

Fano Resonances in Metal Gratings with Sub-Wavelength Slits on High Refractive Index Silicon.

The enhancement of optical waves through perforated plates has received particular attention over the past two decades. This phenomenon can occur due to two distinct and independent mechanisms, namely, nanoscale enhanced optical transmission and micron-scale Fabry-Perot resonance. The aim of the present paper is to shed light on the coupling potential between two neighboring slots filled with two different materials with contrasting physical properties (air and silicon, for example). Using theoretical predictions and numerical simulations, we highlight the role of each constituent material; the low-index material (air) acts as a continuum, while the higher-index material (silicon) exhibits discrete states. This combination gives rise to the so-called Fano resonance, well known since the early 1960s. In particular, it has been demonstrated that optimized geometrical parameters can create sustainable and robust band gaps at will, which provides the scientific community with a further genuine alternative to control optical waves.

Tetramode Metamaterials as Phonon Polarizers.

In classical Cauchy elasticity, 3D materials exhibit six eigenmodes of deformation. Following the 1995 work of Milton and Cherkaev, extremal elastic materials can be classified by the number of eigenmodes, N, out of these six that are "easy". Using Greek number words, this leads to hexamode (N = 6), pentamode (N = 5), tetramode (N = 4), trimode (N = 3), dimode (N = 2), and monomode (N = 1) materials. While hexamode materials are unstable in all regards, the possibility of pentamode metamaterials ("meta-fluids") has attracted considerable attention throughout the last decade. Here, inspired by the 2021 theoretical work of Wei, Liu, and Hu, microstructured 3D polymer-based tetramode metamaterials are designed and characterized by numerical band-structure calculations, fabricated by laser printing, characterized by ultrasound experiments, and compared to the theoretical ideal. An application in terms of a compact and broadband polarizer for acoustical phonons at ultrasound frequencies is demonstrated.

Micro-Scale Mechanical Metamaterial with a Controllable Transition in the Poisson's Ratio and Band Gap Formation.

The ability to significantly change the mechanical and wave propagation properties of a structure without rebuilding it is currently one of the main challenges in the field of mechanical metamaterials. This stems from the enormous appeal that such tunable behavior may offer from the perspective of applications ranging from biomedical to protective devices, particularly in the case of micro-scale systems. In this work, a novel micro-scale mechanical metamaterial is proposed that can undergo a transition from one type of configuration to another, with one configuration having a very negative Poisson's ratio, corresponding to strong auxeticity, and the other having a highly positive Poisson's ratio. The formation of phononic band gaps can also be controlled concurrently which can be very useful for the design of vibration dampers and sensors. Finally, it is experimentally shown that the reconfiguration process can be induced and controlled remotely through application of a magnetic field by using appropriately distributed magnetic inclusions.