3D Printing of Periodic Porous Metamaterials for Tunable Electromagnetic Shielding Across Broad Frequencies.

The new-generation electronic components require a balance between electromagnetic interference shielding efficiency and open structure factors such as ventilation and heat dissipation. In addition, realizing the tunable shielding of porous shields over a wide range of wavelengths is even more challenging. In this study, the well-prepared thermoplastic polyurethane/carbon nanotubes composites were used to fabricate the novel periodic porous flexible metamaterials using fused deposition modeling 3D printing. Particularly, the investigation focuses on optimization of pore geometry, size, dislocation configuration and material thickness, thus establishing a clear correlation between structural parameters and shielding property. Both experimental and simulation results have validated the superior shielding performance of hexagon derived honeycomb structure over other designs, and proposed the failure shielding size (Df ≈λ/8 - λ/5) and critical inclined angle (θf ≈43° - 48°), which could be used as new benchmarks for tunable electromagnetic shielding. In addition, the proper regulation of the material thickness could remarkably enhance the maximum shielding capability (85 - 95 dB) and absorption coefficient A (over 0.83). The final innovative design of the porous shielding box also exhibits good shielding effectiveness across a broad frequency range (over 2.4 GHz), opening up novel pathways for individualized and diversified shielding solutions.

Thermal Metamaterials with Configurable Mechanical Properties.

Thermal metamaterials are typically achieved by mixing different natural materials to realize effective thermal conductivities (ETCs) that conventional materials do not possess. However, the necessity for multifunctional design of metamaterials, encompassing both thermal and mechanical functionalities, is somewhat overlooked, resulting in the fixation of mechanical properties in thermal metamaterials designed within current research endeavors. Thus far, conventional methods have faced challenges in designing thermal metamaterials with configurable mechanical properties because of intricate inherent relationships among the structural configuration, thermal and mechanical properties in metamaterials. Here, a data-driven approach is proposed to design a thermal metamaterial capable of seamlessly achieving thermal functionalities and harnessing the advantages of microstructural diversity to configure its mechanical properties. The designed metamaterial possesses thermal cloaking functionality while exhibiting exceptional mechanical properties, such as load-bearing capacity, shearing strength, and tensile resistance, thereby affording mechanical protection for the thermal metadevice. The proposed approach can generate numerous distinct inverse design candidate topological functional cells (TFCs), designing thermal metamaterials with dramatic improvements in mechanical properties compared to traditional ones, which sets up a novel paradigm for discovering thermal metamaterials with extraordinary mechanical structures. Furthermore, this approach also paves the way for investigating thermal metamaterials with additional physical properties.

Wafer-Scale Replication of Plasmonic Nanostructures via Microbubbles for Nanophotonics.

Quasi-3D plasmonic nanostructures are in high demand for their ability to manipulate and enhance light-matter interactions at subwavelength scales, making them promising building blocks for diverse nanophotonic devices. Despite their potential, the integration of these nanostructures with optical sensors and imaging systems on a large scale poses challenges. Here, a robust technique for the rapid, scalable, and seamless replication of quasi-3D plasmonic nanostructures is presented straight from their production wafers using a microbubble process. This approach not only simplifies the integration of quasi-3D plasmonic nanostructures into a wide range of standard and custom optical imaging devices and sensors but also significantly enhances their imaging and sensing performance beyond the limits of conventional methods. This study encompasses experimental, computational, and theoretical investigations, and it fully elucidates the operational mechanism. Additionally, it explores a versatile set of options for outfitting nanophotonic devices with custom-designed plasmonic nanostructures, thereby fulfilling specific operational criteria.

Metamaterial design for aortic aneurysm simulation using 3D printing.

INTRODUCTION: The use of three-dimensional (3D) printed anatomic models is steadily increasing in research and as a tool for clinical decision-making. The mechanical properties of polymers and metamaterials were investigated to evaluate their application in mimicking the biomechanics of the aortic vessel wall. METHODOLOGY: Uniaxial tensile tests were performed to determine the elastic modulus, mechanical stress, and strain of 3D printed samples. We used a combination of materials, designed to mimic biological tissues' properties, the rigid VeroTM family, and the flexible Agilus30™. Metamaterials were designed by tessellating unit cells that were used as lattice-reinforcement to tune their mechanical properties. The lattice-reinforcements were based on two groups of patterns, mainly responding to the movement between links/threads (chain and knitted) or to deformation (origami and diamond crystal). The mechanical properties of the printed materials were compared with the characteristics of healthy and aneurysmal aortas. RESULTS: Uniaxial tensile tests showed that the use of a lattice-reinforcement increased rigidity and may increase the maximum stress generated. The pattern and material of the lattice-reinforcement may increase or reduce the strain at maximum stress, which is also affected by the base material used. Printed samples showed max stress ranging from 0.39 ± 0.01 MPa to 0.88 ± 0.02 MPa, and strain at max stress ranging from 70.44 ± 0.86% to 158.21 ± 8.99%. An example of an application was created by inserting a metamaterial designed as a lattice-reinforcement on a model of the aorta to simulate an abdominal aortic aneurysm. CONCLUSION: The maximum stresses obtained with the printed models were similar to those of aortic tissue reported in the literature, despite the fact that the models did not perfectly reproduce the biological tissue behavior.

Metamaterial-Assisted Illumination Nanoscopy with Exceptional Axial Resolution.

Recent advancements in optical metamaterials have opened new possibilities in the exciting field of super-resolution microscopies. The far-field metamaterial-assisted illumination nanoscopies (MAINs) have, very recently, enhanced the lateral resolution to one-fifteenth of the optical wavelength. However, the axial localization accuracy of fluorophores in the MAINs remains rarely explored. Here, a MAIN with a nanometer-scale axial localization accuracy is demonstrated by monitoring the distance-dependent photobleaching dynamics of the fluorophores on top of an organic hyperbolic metamaterial (OHM) substrate under a wide-field single-objective microscope. With such a regular experimental configuration, 3D imaging of various biological samples with the resolution of ≈40 nm in the lateral dimensions and ≈5 nm in the axial dimension is realized. The demonstrated imaging modality enables the resolution of the 3D morphology of nanoscopic cellular structures with a significantly simplified experimental setup.

Local-to-non-local transition laws for stiffness-tuneable monoatomic chains preserving springs mass.

Recently, non-local configurations have been proposed by adding beyond nearest neighbour couplings among elements in lattices to obtain roton-like dispersion relations and phase and group velocities with opposite signs. Even though the introduction of non-local elastic links in metamaterials has unlocked unprecedented possibilities, literature models and prototypes seem neither to provide criteria to compare local and non-local lattices nor to discuss any related rules governing the transition between the two configurations. A physically reasonable principle that monoatomic one-dimensional chains must obey to pass from single- to multi-connected systems is here proposed through a mass conservation law for elastic springs thereby introducing a suitable real dimensionless parameter [Formula: see text] to tune stiffness distribution. Therefore, the dispersion relations as a function of [Formula: see text] and of the degree of non-locality [Formula: see text] are derived analytically, demonstrating that the proposed principle can be rather interpreted as a general mechanical consistency condition to preserve proper dynamics, involving the spring-to-bead mass ratio. Finally, after discussing qualitative results and deriving some useful inequalities, numerical simulations and two-dimensional FFTs are performed for some paradigmatic examples to highlight key dynamics features exhibited by chains with finite length as the parameters [Formula: see text] and [Formula: see text] vary.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Investigating and exploiting the impact of variability in resonator parameters on the vibration attenuation in locally resonant metamaterials.

Locally resonant metamaterials (LRMs) have recently emerged in the search for lightweight noise and vibration solutions. These materials have the ability to create stop bands, which arise from the sub-wavelength addition of identical resonators to a host structure and result in strong vibration attenuation. However, their manufacturing inevitably introduces variability such that the system as-manufactured often deviates significantly from the original as-designed. This can reduce attenuation performance, but may also broaden the attenuation band. This work focuses on the impact of variability within tolerance ranges in resonator properties on the vibration attenuation in metamaterial beams. Following a qualitative pre-study, two non-intrusive uncertainty propagation approaches are applied to find the upper and lower bounds of three performance metrics, by evaluating deterministic metamaterial models with uncertain parameters defined as interval variables. A global search approach is used and compared with a machine learning (ML)-based uncertainty propagation approach which significantly reduces the required number of simulations. Variability in resonator stiffnesses and masses is found to have the highest impact. Variability in the resonator positions only has a comparable impact for less deep sub-wavelength designs. The broadening potential of varying resonator properties is exploited in broadband optimization and the robustness of the optimized metamaterial is assessed.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Wave propagation in tailored metastructures consisting of elastic beams and rigid bodies.

This paper presents a study of wave propagation through an infinite periodic structure that consists of elastic Timoshenko beams interconnected with rigid bodies. This is a generalized approach in which the beams are not coaxial and the centre of mass of each rigid body is placed away from the intersection of their neutral axes. An analytical approach is used by applying the transfer matrix method (TMM), along with the Floquet-Bloch theorem for elastic wave propagation. Subsequent parametric analysis is performed with visualization of resulting band diagrams of a representative structure. These results are verified through comparison with solutions obtained using the finite-element method (FEM). In this manner, a comprehensive dynamical analysis of tailored metastructures is provided.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

On the role of geometric phase in the dynamics of elastic waveguides.

The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of geometric phase, which is an additional phase factor occurring in dynamical systems, holds the same meaning across different fields of application, its use and interpretation can acquire important nuances specific to the system of interest. In recent years, the development of quantum topological materials and its extension to classical mechanical systems have renewed the interest in the concept of geometric phase. This review revisits the concept of geometric phase and discusses, by means of either established or original results, its critical role in the design and dynamic behaviour of elastic waveguides. Concepts of differential geometry and topology are put forward to provide a theoretical understanding of the geometric phase and its connection to the physical properties of the system. Then, the concept of geometric phase is applied to different types of elastic waveguides to explain how either topologically trivial or non-trivial behaviour can emerge based on the geometric features of the waveguide. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Selective dynamic band gap tuning in metamaterials using graded photoresponsive resonator arrays.

The introduction of metamaterials has provided new possibilities to manipulate the propagation of waves in different fields of physics, ranging from electromagnetism to acoustics. However, despite the variety of configurations proposed so far, most solutions lack dynamic tunability, i.e. their functionality cannot be altered post-fabrication. Our work overcomes this limitation by employing a photo-responsive polymer to fabricate a simple metamaterial structure and enable tuning of its elastic properties using visible light. The structure of the metamaterial consists of graded resonators in the form of an array of pillars, each giving rise to different resonances and transmission band gaps. Selective laser illumination can then tune the resonances and their frequencies individually or collectively, thus yielding many degrees of freedom in the tunability of the filtered or transmitted wave frequencies, similar to playing a keyboard, where illuminating each pillar corresponds to playing a different note. This concept can be used to realize low-power active devices for elastic wave control, including beam splitters, switches and filters.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

THz Metamaterial Sensitivity Enhancement by Reduction of Substrate's Fabry-Pérot Oscillations Using Back Plates as an Optical De-Coupler.

This work presents a new method for the enhancement of sensitivity in Terahertz (THz) spectroscopy on metamaterial (MM) in terms of its resonance frequency shift (ΔF), by attaching the dielectric back plate to the MM's silicon (Si) wafer. The dielectric back plates are designed to minimize the Fresnel reflections at the backside of the substrate, identical to a broadband antireflective (AR) plate tailored for THz. Utilizing broadband AR technology, we demonstrate the concept of decoupling MM resonance from the substrate's Fabry-Pérot (FP) oscillations. This is done by effectively coupling the THz light out of the high-permittivity substrate, resulting in the improved quality factor of the MM resonance and overall plasmonic enhancement on the metasurface. The back plate acts as a surface plasmonic enhancer to the THz MM by increasing the field intensity on the front metasurface, leading to enhancement of dielectric response (MM's ΔF). This makes the MM resonance ultrasensitive to the minor changes of particle size/concentration under test spread on the metasurface, contributing to enhanced resonance ΔF. The plate also makes the Si substrate optically lossless, enabling the full effect of MM resonance shift and increasing the resonance ΔF by 8-fold compared with MM's fabricated on conventional Si substrates. This research is backed-up with system-level CST simulations and experimental THz impedance spectroscopy of the MM. This method and chip structure is CMOS compatible having potential applications for any resonant MM fabricated on a substrate aimed to maximize dielectric sensitivity for biosensing and nanoparticle THz spectroscopy.

An efficient multiscale method for subwavelength transient analysis of acoustic metamaterials.

A reduced-order homogenization framework is proposed, providing a macro-scale-enriched continuum model for locally resonant acoustic metamaterials operating in the subwavelength regime, for both time and frequency domain analyses. The homogenized continuum has a non-standard constitutive model, capturing a metamaterial behaviour such as negative effective bulk modulus, negative effective density and Willis coupling. A suitable reduced space is constructed based on the unit cell response in a steady-state regime and the local resonance regime. A frequency domain numerical example demonstrates the efficiency and suitability of the proposed framework.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Well-Ordered Bicontinuous Nanohybrids from a Bottom-Up Approach for Enhanced Strength and Toughness.

Biomimicking natural structures to create structural materials with superior mechanical performance is an area of extensive attention, yet achieving both high strength and toughness remains challenging. This study presents a novel bottom-up approach using self-assembled block copolymer templating to synthesize bicontinuous nanohybrids composed of well-ordered nanonetwork hydroxyapatite (HAp) embedded in poly(methyl methacrylate) (PMMA). This structuring transforms intrinsically brittle HAp into a ductile material, while hybridization with PMMA alleviates the strength reduction caused by porosity. The resultant bicontinuous PMMA/HAp nanohybrids, reinforced at the interface, exhibit high strength and toughness due to the combined effects of topology, nanosize, and hybridization. This work suggests a conceptual framework for fabricating flexible thin films with mechanical properties significantly surpassing those of traditional composites and top-down approaches.

Stress guides in generic static mechanical metamaterials.

The confinement of waves within a waveguide can enable directional transmission of signals, which has found wide applications in communication, imaging, and signal isolation. Extending this concept to static systems, where material deformation is piled up along a spatial trajectory, remains elusive due to the sensitivity of localized deformation to structural defects and impurities. Here, we propose a general framework to characterize localized static deformation responses in two-dimensional generic static mechanical metamaterials, by exploiting the duality between space in static systems and time in one-dimensional non-reciprocal wave systems. An internal time-reverse symmetry is developed by the space-time duality. Upon breaking this symmetry, quasi-static load-induced deformation can be guided to travel along a designated path, thereby realizing a stress guide. A combination of time-reverse and inversion symmetries discloses the parity-time symmetry inherent in static systems, which can be leveraged to achieve directional deformation shielding. The tailorable stress guides can find applications in various scenarios, ranging from stress shielding and energy harvesting in structural tasks to information processing in mechanical computing devices.

Proximal High-Index Metamaterials based on a Superlattice of Gold Nanohexagons Targeting the Near-Infrared Band.

Plasmonic nanoparticles can be assembled into a superlattice, to form optical metamaterials, particularly targeting precise control of optical properties such as refractive index (RI). The superlattices exhibit enhanced near-field, given the sufficiently narrow gap between nanoparticles supporting multiple plasmonic resonance modes only realized in proximal environments. Herein, the planar superlattice of plasmonic Au nanohexagons (AuNHs) with precisely controlled geometries such as size, shape, and edge-gaps is reported. The proximal AuNHs superlattice realized over a large area with selective edge-to-edge assembly exhibited the highest-ever-recorded RI values in the near-infrared (NIR) band, surpassing the upper limit of the RI of the natural intrinsic materials (up to 10.04 at λ = 1.5 µm). The exceptionally enhanced RI is derived from intensified in-plane surface plasmon coupling across the superlattices. Precise control of the edge-gap of neighboring AuNHs systematically tuned the RI as confirmed by numerical analysis based on the plasmonic percolation model. Furthermore, a 1D photonic crystal, composed of alternating layers of AuNHs superlattices and low-index polymers, is constructed to enhance the selectivity of the reflectivity operating in the NIR band. It is expected that the proximal AuNHs superlattices can be used as new optical metamaterials that can be extended to the NIR range.

Generative models struggle with kirigami metamaterials.

Generative machine learning models have shown notable success in identifying architectures for metamaterials-materials whose behavior is determined primarily by their internal organization-that match specific target properties. By examining kirigami metamaterials, in which dependencies between cuts yield complex design restrictions, we demonstrate that this perceived success in the employment of generative models for metamaterials might be akin to survivorship bias. We assess the performance of the four most popular generative models-the Variational Autoencoder (VAE), the Generative Adversarial Network (GAN), the Wasserstein GAN (WGAN), and the Denoising Diffusion Probabilistic Model (DDPM)-in generating kirigami structures. Prohibiting cut intersections can prevent the identification of an appropriate similarity measure for kirigami metamaterials, significantly impacting the effectiveness of VAE and WGAN, which rely on the Euclidean distance-a metric shown to be unsuitable for considered geometries. This imposes significant limitations on employing modern generative models for the creation of diverse metamaterials.

Improved performance of temperature sensors based on the one-dimensional topological photonic crystals comprising hyperbolic metamaterials.

This paper seeks to progress the field of topological photonic crystals (TPC) as a promising tool in face of construction flaws. In particular, the structure can be used as a novel temperature sensor. In this regard, the considered TPC structure comprising two different PC designs named PC1 and PC2. PC1 is designed from a stack of multilayers containing Silicon (Si) and Silicon dioxide (SiO2), while layers of SiO2 and composite layer named hyperbolic metamaterial (HMM) are considered in designing PC2. The HMM layer is engineered using subwavelength layers of Si and Bismuth Germinate, or BGO ( Bi 4 Ge 3 O 12 ). The mainstay of our suggested temperature sensor is mainly based on the emergence of some resonant modes inside the transmittance spectrum that provide the stability in the presence of the geometrical changes. Meanwhile, our theoretical framework has been introduced in the vicinity of transfer matrix method (TMM), effective medium theory (EMT) and the thermo-optic characteristics of the considered materials. The numerical findings have extensively introduced the role of some topological parameters such as layers' thicknesses, filling ratio through HMM layers and the periodicity of HMM on the stability or the topological features of the introduced sensor. Meanwhile, the numerical results reveal that the considered design provides some topological edge states (TESs) of a promising robustness and stability against certain disturbances or geometrical changes in the constituent materials. In addition, our sensing tool offers a relatively high sensitivity of 0.27 nm/°C.

Machine-Learning-Based Characterization and Inverse Design of Metamaterials.

Metamaterials, characterized by unique structures, exhibit exceptional properties applicable across various domains. Traditional methods like experiments and finite-element methods (FEM) have been extensively utilized to characterize these properties. However, exploring an extensive range of structures using these methods for designing desired structures with excellent properties can be time-intensive. This paper formulates a machine-learning-based approach to expedite predicting effective metamaterial properties, leading to the discovery of microstructures with diverse and outstanding characteristics. The process involves constructing 2D and 3D microstructures, encompassing porous materials, solid-solid-based materials, and fluid-solid-based materials. Finite-element methods are then employed to determine the effective properties of metamaterials. Subsequently, the Random Forest (RF) algorithm is applied for training and predicting effective properties. Additionally, the Aquila Optimizer (AO) method is employed for a multiple optimization task in inverse design. The regression model generates accurate estimation with a coefficient of determination higher than 0.98, a mean absolute percentage error lower than 0.088, and a root mean square error lower than 0.03, indicating that the machine-learning-based method can accurately characterize the metamaterial properties. An optimized structure with a high Young's modulus and low thermal conductivity is designed by AO within the first 30 iterations. This approach accelerates simulating the effective properties of metamaterials and can design microstructures with multiple excellent performances. The work offers guidance to design microstructures in various practical applications such as vibration energy absorbers.

Design of Locally Resonant Acoustic Metamaterials with Specified Band Gaps Using Multi-Material Topology Optimization.

Locally Resonant Acoustic Metamaterials (LRAMs) have significant application potential because they can form subwavelength band gaps. However, most current research does not involve obtaining LRAMs with specified band gaps, even though such LRAMs are significant for practical applications. To address this, we propose a parameterized level-set-based topology optimization method that can use multiple materials to design LRAMs that meet specified frequency constraints. In this method, a simplified band-gap calculation approach based on the homogenization framework is introduced, establishing a restricted subsystem and an unrestricted subsystem to determine band gaps without relying on the Brillouin zone. These subsystems are specifically tailored to model the phenomena involved in band gaps in LRAMs, facilitating the opening of band gaps during optimization. In the multi-material representation model used in this method, each material, except for the matrix material, is depicted using a similar combinatorial formulation of level-set functions. This model reduces direct conversion between materials other than the matrix material, thereby enhancing the band-gap optimization of LRAMs. Two problems are investigated to test the method's ability to use multiple materials to solve band-gap optimization problems with specified frequency constraints. The first involves maximizing the band-gap width while ensuring it encompasses a specified frequency range, and the second focuses on obtaining light LRAMs with a specified band gap. LRAMs with specified band gaps obtained in three-material or four-material numerical examples demonstrate the effectiveness of the proposed method. The method shows great promise for designing metamaterials to attenuate specified frequency spectra as required, such as mechanical vibrations or environmental noise.

Structure-Property Relationships in Auxetic Liquid Crystal Elastomers-The Effect of Spacer Length.

Auxetics are materials displaying a negative Poisson's ratio, i.e., getting thicker in one or both transverse axes when subject to strain. In 2018, liquid crystal elastomers (LCEs) displaying auxetic behaviour, achieved via a biaxial reorientation, were first reported. Studies have since focused on determining the physics underpinning the auxetic response, with investigations into structure-property relationships within these systems so far overlooked. Herein, we report the first structure-property relationships in auxetic LCEs, examining the effect of changes to the length of the spacer chain. We demonstrate that for LCEs with between six and four carbons in the spacer, an auxetic response is observed, with the threshold strain required to achieve this response varying from 56% (six carbon spacers) to 81% (four carbon spacers). We also demonstrate that Poisson's ratios as low as -1.3 can be achieved. Further, we report that the LCEs display smectic phases with spacers of seven or more carbons; the resulting internal constraints cause low strains at failure, preventing an auxetic response. We also investigate the dependence of the auxetic threshold on the dynamics of the samples, finding that when accounting for the glass transition temperature of the LCEs, the auxetic thresholds converge around 56%, regardless of spacer length.