3D Metamaterials Research Articles

Optical Metasurfaces: Evolving from Passive to Adaptive

AbstractOptical metasurfaces are nanoengineered architectures aiming at the functional control of light propagation. In recent years, the performance of metasurfaces has been significantly improved and with the availability of such 2D metamaterials, different optical elements, such as flat achromatic lenses or compact spectrometers have been demonstrated. However, to a large extent, such demonstrations have focused on the realization of entirely passive (nonadaptive) metasurface properties. Adaptivity and active tuning of the optical function of a metasurface after fabrication is highly desirable, because it enables a host of more advanced applications such as beam scanning and dynamic holographic displays. Here, the evolution of the state of the art of metasurfaces toward attaining the adaptivity property and the resulting active control over the wavefront of light is reviewed. Starting from an overview of passive metasurfaces, the different approaches targeting adaptive metasurfaces are discussed, concluding with identifying crucial challenges and opportunities in this future‐oriented field.

Elastodynamic response of three-dimensional phononic crystals using laser Doppler vibrometry

The elastodynamic response of finite 3D phononic structures is analyzed by means of comparing experimental findings obtained through a laser Doppler vibrometry-based methodology and theoretical computations performed with the layer-multiple-scattering method. The recorded frequency-gap spectrum of the phononic slabs exhibited a good agreement of theory to experiment. Along these lines, a newly developed technique, based on laser Doppler vibrometry, has been proposed and validated for the dispersion efficiency in 3D phononic metamaterials.

Magnetic permeability in Fresnel’s equation

Magnetic permeabilities derived for infinite, periodic media are used in the Fresnel equation to calculate the reflection from corresponding semi-infinite media. By comparison to finite-difference time-domain (FDTD) simulations, we find that the Fresnel equation gives accurate results for 2D metamaterials which mimic natural magnetism, in a frequency range where the magnetic moment density dominates the O(k2) part of the total Landau–Lifshitz permittivity. For a 1D layered structure, or for large frequencies, the correspondence is poor. We also demonstrate that even if a medium is described accurately by a local permittivity and permeability, the Fresnel equation is not necessarily valid.

Topology optimization for auxetic metamaterials based on isogeometric analysis

In this paper, an effective and efficient topology optimization method, termed as Isogeometric Topology Optimization (ITO), is proposed for systematic design of both 2D and 3D auxetic metamaterials based on isogeometric analysis (IGA). Firstly, a density distribution function (DDF) with the desired smoothness and continuity, to represent the topological changes of structures, is constructed using the Shepard function and non-uniform rational B-splines (NURBS) basis functions. Secondly, an energy-based homogenization method (EBHM) to evaluate material effective properties is numerically implemented by IGA, with the imposing of the periodic boundary formulation on material microstructure. Thirdly, a topology optimization formulation for 2D and 3D auxetic metamaterials is developed based on the DDF, where the objective function is defined as a combination of the homogenized elastic tensor and the IGA is applied to solve the structural responses. A relaxed optimality criteria (OC) method is used to update the design variables, due to the non-monotonic property of the problem. Finally, several numerical examples are used to demonstrate the effectiveness and efficiency of the proposed method. A series of auxetic microstructures with different deformation mechanisms (e.g. the re-entrant and chiral) can be obtained. The auxetic behavior of material microstructures are numerically validated using ANSYS, and the optimized designs are prototyped using the Selective Laser Sintering (SLS) technique.

Design 3D metamaterials with compression-induced-twisting characteristics using shear–compression coupling effects

Metamaterials with compression-induced-twisting (CIT) features shows great potential applications in sensors and actuators. In this paper, a series of 3D metamaterials are developed with the inspiration of the shear–compression coupling effect of the 2D materials, which exhibits twisting behavior when subjected to uniaxial loading. Analytical solutions and numerical simulations are both carried out to demonstrate the possible CIT performance of the proposed 3D metamaterial models, with good agreement obtained. A linear relationship between the 2D shear–compression coupling effect and the twist angle per axial strain of the 3D structures is also deduced. In addition, the twist angle per axial strain can be designed to be infinite. This concept of CIT metamaterials in this paper might shed light on the design and optimization of 3D architectures with multifunctional applications.

Hyperbolic Metamaterials and Metasurfaces: Fundamentals and Applications

AbstractRecent advances in nanofabrication and characterization technologies have spurred many breakthroughs in the field of optical metamaterials and metasurfaces that provide novel ways of manipulating light interaction in a well controllable manner. Among these artificial nanostructured materials, 3D bulk hyperbolic metamaterials and 2D planar hyperbolic metasurfaces exhibit ultra‐anisotropic electromagnetic responses and lead to dramatic changes for the light propagation behaviors. Here, the dispersions and realizations of hyperbolic media are first briefly discussed. Then, the recent achievements of various optical applications based on hyperbolic metamaterials and metasurfaces, including beam manipulation, super‐resolution imaging, spontaneous and thermal emission engineering, ultrasensitive optical sensing, and broadband optical absorption are reviewed. This review provides an overview and vision for the future of hyperbolic media and their potential impact on the development of novel nanophotonic devices and systems.

Rapid multi-material 3D printing with projection micro-stereolithography using dynamic fluidic control

Mask projection stereolithography is a digital light processing-based additive manufacturing technique that has various advantages, such as high-resolution, scanning-free parallel process, wide material sets available, and support-structure-free three-dimensional (3D) printing. However, multi-material 3D printing with mask projection stereolithography has been challenging due to difficulties of exchanging a liquid-state material in a vat. In this work, we report a rapid multi-material projection micro-stereolithography using dynamic fluidic control of multiple liquid photopolymers within an integrated fluidic cell. Highly complex multi-material 3D micro-structures are rapidly fabricated through an active material exchange process. Material flow rate in the fluidic cell, material exchange efficiency, and the effects of energy dosage on curing depth are studied for various photopolymers. In addition, the degree of cross-contamination between different materials in a 3D printed multi-material structure is evaluated to assess the quality of multi-material printing. The pressure-tight and leak-free fluidic cell enables active and fast switch between liquid photopolymers, even including micro-/nano-particle suspensions, which could potentially lead to facile 3D printing of multi-material metallic/ceramic structures or heterogeneous biomaterials. In addition, a multi-responsive hydrogel micro-structure is printed using a thermo-responsive hydrogel and an electroactive hydrogel, showing various modes of swelling actuation in response to multiple external stimuli. This new ability to rapidly and heterogeneously integrate multiple functional materials in three-dimension at micro-scale has potential to accelerate advances in many emerging areas including 3D metamaterials, tissue engineering, and soft robotics.

3D Hilbert fractal acoustic metamaterials: low-frequency and multi-band sound insulation

In this work, we present a class of three-dimensional (3D) labyrinthine acoustic metamaterials with self-similar fractal technique, which can produce multiple frequency-band sound insulation in deep-subwavelength scale. By simultaneously exploiting the multi-frequency bandgaps and the low-frequency characteristics, the Hilbert cubes are explored to design the 3D Hilbert fractal acoustic metamaterials (HFAMs). The multiple-band features of the HFAMs are examined by the finite element method and the effective medium theory, in which the negative bulk modulus and the mass density are responsible for the formation of the multi-bandgaps. These multi-frequency properties are induced by the Fabry–Perot multi-resonance of 3D HFAMs, which possess an ultra-high refractive index. Hence, the multi-band sound insulations of 3D HFAMs with the negative effective property are achieved below 500 Hz. These properties of the designed 3D HFAMs provide an effective way for acoustic metamaterials to achieve multi-band filtering and noise attenuation in the low-frequency regime.

Zero chiral bulk modes in 3D Weyl metamaterials

Zero chiral bulk modes in 3D Weyl metamaterials

Designing hierarchical metamaterials by topology analysis with tailored Poisson’s ratio and Young’s modulus

In this work, we present an innovative three-dimensional (3D) hierarchical design strategy to systematically summarize the configuration characteristics of existing cellular structures and propose a novel class of mechanical metamaterials based on topology analysis, which have tailored Poisson’s ratio and Young’s modulus. Theoretical, numerical and experimental analyses were conducted to reveal the basic mechanical properties of the metamaterials. And these results agree very well which validate the correctness of the theories. Samples of the proposed structures made of Nylon were fabricated through 3D printing technology to carry out compression tests and finite element analysis (FEA) were performed to give an insight into the mechanical response. Experimental and numerical results revealed that the proposed 3D second-order hierarchical metamaterials can achieve a series of special combinations of Poisson’s ratio in three perpendicular directions. The sign and magnitude of Poisson’s ratio can be tailored by appropriately adjusting the first and second order configurations and their geometrical parameters. Meanwhile, systemic analysis and comparison reveal that relative Young’s modulus is contingent on deformation pattern, i.e., axial-deformation dominated stiffness is much higher than bending-dominated stiffness. Similar to Poisson’s ratio, the magnitude of Young’s modulus can be tailored by geometrical parameters and first and second order configurations in a relative large range in the case of given Poisson's ratio (sign and magnitude). This work can provide useful reference for the design, fabrication and analysis of 3D metamaterials with novel properties and functions, particularly with auxetic behavior, which are promising in some technical applications.

Three-dimensional metamaterial Hall-bar devices

We realize classical Hall bars, made of chain-mail-inspired cubic-symmetry 3D metamaterials composed of interlinked hollow tori, contacted to printed circuit boards. This step is a prerequisite for refined experiments compared to our previous probe-station based measurements as well as for potential applications of 3D Hall-effect metamaterials in general. On this basis, we systematically study the dependence of the Hall voltage on the relative orientation of the 3D metamaterial crystallographic axes with respect to the applied static magnetic field vector and the imposed current flow direction. Our findings are consistent with an isotropic sign-reversed Hall coefficient, which has been predicted by homogenization theory.

Nanoplumbing with 2D Metamaterials.

Complex manipulations of DNA in a nanofluidic device require channels with branches and junctions. However, the dynamic response of DNA in such nanofluidic networks is relatively unexplored. Here, the transport of DNA in a 2D metamaterial made by arrays of nanochannel junctions is investigated. The mechanism of transport is explained as Brownian motion through an energy landscape formed by the combination of the confinement free energy of DNA and the effective potential of hydrodynamic flow, which both can be tuned independently within the device. For the quantitative understanding of DNA transport, a dynamic mean-field model of DNA at a nanochannel junction is proposed. It is shown that the dynamics of DNA in a nanofluidic device with branched channels and junctions is well described by the model.

3D‐Printed Mechanical Metamaterials with High Energy Absorption

AbstractRecently, 3D metamaterials have been achieved with inaccessible mechanical properties in natural materials such as negative Poisson's ratio, stiffness, and thermal expansion coefficient. While most of the developed metamaterials are with engineerable deformation evolution of structures, few studies have revealed their potential in energy absorption due to the limited mechanical properties of 3D‐printed constituent materials and inevitable structural defects induced by the manufacturing process. Herein, an approach is proposed for creating 3D metamaterials of auxetic composite lattices via laser‐sintering of carbon nanotubes reinforced nanocomposites, which provide a platform for the design and manufacturing of systems with programmable energy absorption capability. The optimization of constituent material and structural design enables the improvement of energy absorption performance across multiple scales. The energy absorption capacity of auxetic metamaterials was exponentially scaled with the relative density with the order of 2.5–3. The rationally topologized auxetic metamaterials exhibit a combination of high specific densification strength (0.0195 MPa kg−1 m−3), ultrahigh energy absorption capacity (6.29 MJ m−3), and excellent specific energy absorption (20.42 J g−1). Impressively, this group of auxetic metamaterials possesses the advantageous specific energy absorption approaching that of titanium alloy foams as well as over a broad range of materials including plastic foams, aluminum alloy foams, and other 3D‐printed lightweight structures.

Self-faceting of emulsion droplets as a route to solid icosahedra and other polyhedra

HypothesisTemperature-controlled self-faceting of liquid droplets has been recently discovered in surfactant-stabilized alkane-in-water emulsions. We hypothesize that similar self-faceting may occur in emulsion droplets of UV-polymerizable linear hydrocarbons. We further hypothesize that the faceted droplet shapes can be fixed by UV-initiated polymerization, thus providing a new route towards the production of solid polyhedra. ExperimentsTemperature-induced shape variations were studied by optical microscopy in micron-size emulsion droplets of UV-polymerizable alkyl acrylate. When polymerized, the resultant solid particles’ 3D shape and internal structure were determined by combined scanning electron microscopy (SEM) and focused ion beam (FIB) slicing. The SEM and FIB nanoscale resolution provided a far greater detail imaging than that achievable for the liquid droplets, which could only be studied by optical microscopy, severely limiting their 3D shape determination. FindingsWe demonstrate the formation of solid icosahedra, polyhedral platelets, and rods of hitherto-unreported sizes, well below the 3D-printing resolution (∼20μm). The presence of icosahedral shapes and the absence of any resolvable internal structure at sub-μm length scales, are in line with the surface-freezing-driven mechanism proposed for the faceting phenomenon. Further development of the method presented here may allow large-quantity production of shaped micron- to nano- sized colloidal building blocks for 3D metamaterials and other applications.

Realization of complex curved waveguide based on local resonant 3D metamaterial

To overcome the negative impact of diffraction effect on the transmission wave front at the bend and to improve the transmission efficiency of acoustic wave in the bend waveguide, the finite element method by COMSOL was used to simulate the propagation characteristics of acoustic wave in the structure of bending acoustic waveguide, based on local resonance acoustic metamaterials. Specifically, the vibration mechanism of three-dimensional (3D) component locally resonant phononic crystals was presented, and the acoustic metamaterial models of M-shaped, L-shaped and S-shaped bent waveguides were constructed on the basis of the protocells. The local resonance between the acoustic wave and the protocells in the waveguide model was investigated, in order to produce the nondestructive bending propagation effect of the acoustic wave. The results of finite element analysis show that the plane acoustic waves incident from the M-shaped, L-shaped and S-shaped bending waveguide model will propagate directionally along the model structure after being controlled at the resonance frequency. These results confirm the flexibility and feasibility of the bending acoustic waveguide model designed by the local resonance acoustic metamaterials. In addition, the acoustic waveguide model in long-distance special environment was designed and the low loss transmission of acoustic signal was implemented. This study provides a new solution for engineering applications, such as ultrasonic signal detection and underwater acoustic communication transmission.

Vacancies for controlling the behavior of microstructured three-dimensional mechanical metamaterials

Mechanical metamaterials are designed to exhibit enhanced properties not found in natural materials or to bolster the properties of existing materials. The theoretical foundations for tuning the mechanical properties have been established, including topological states, controllable buckling behavior, and quasi-two-dimensional mechanical metamaterials with structures containing vacancies. However, the fabrication and experimental procedures to study these structures at the microscale have not been developed yet and the three-dimensional (3D) architectures examined to date are fairly limited. In this study, 3D mechanical metamaterial structures with select unit cells designed to have vacancies were fabricated by multi-photon lithography, having as the principal objective to control (localize) failure and increase the strain energy capacity of the structure. The metamaterial structure from which all the current designs originate is the octet-truss structure, one of the most widely studied 3D metamaterials. The design of the structures was inspired by the role of vacancies in crystal lattices. Vacancies were introduced in the metamaterial structures to allow localized buckling of lattice members to occur in specific unit cells. The significant increase of the strain energy dissipated in these metamaterials is demonstrated by nanoindentation experiments and finite element results. Vacancy effects on the dynamic response of metamaterial structures are also examined in the light of modal analysis simulations. The findings of this study illustrate the importance of strategically placing vacancies in the microlattices of metamaterial structures to control the overall mechanical behavior and greatly increase strain energy dissipation.

Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures

Straight beams, rods and trusses are common elements in structural and mechanical engineering, but recent advances in additive manufacturing now also enable efficient freeform fabrication of curved, deformable beams and beam structures, such as microstructures, metamaterials and conformal lattices. To exploit this new design freedom for applications with nonlinear mechanical behavior, we introduce an isogeometric method for shape optimization of curved 3D beams and beam structures. The geometrically exact Cosserat rod theory is used to model nonlinear 3D beams subject to large deformations and rotations. The initial and current geometry are parameterized in terms of NURBS curves describing the beam centerline and an isogeometric collocation approach is used to discretize the strong form of the balance equations. Then, a nonlinear optimization problem is formulated in order to optimize the positions of the control points of the NURBS curve that describes the beam centerline, i.e., the geometry or shape of the beam. To solve the design problem using gradient-based algorithms, we introduce semi-analytical, inconsistent analytical and fully analytical approaches for calculation of design sensitivities. The methods are numerically validated and their performance is investigated, before the applicability and versatility of our 3D beam shape optimization method is illustrated in various numerical applications, including optimization of an auxetic 3D metamaterial.

Metasurfaces Atop Metamaterials: Surface Morphology Induces Linear Dichroism in Gyroid Optical Metamaterials

Optical metamaterials offer the tantalizing possibility of creating extraordinary optical properties through the careful design and arrangement of subwavelength structural units. Gyroid-structured optical metamaterials possess a chiral, cubic, and triply periodic bulk morphology that exhibits a redshifted effective plasma frequency. They also exhibit a strong linear dichroism, the origin of which is not yet understood. Here, the interaction of light with gold gyroid optical metamaterials is studied and a strong correlation between the surface morphology and its linear dichroism is found. The termination of the gyroid surface breaks the cubic symmetry of the bulk lattice and gives rise to the observed wavelength- and polarization-dependent reflection. The results show that light couples into both localized and propagating plasmon modes associated with anisotropic surface protrusions and the gaps between such protrusions. The localized surface modes give rise to the anisotropic optical response, creating the linear dichroism. Simulated reflection spectra are highly sensitive to minute details of these surface terminations, down to the nanometer level, and can be understood with analogy to the optical properties of a 2D anisotropic metasurface atop a 3D isotropic metamaterial. This pronounced sensitivity to the subwavelength surface morphology has significant consequences for both the design and application of optical metamaterials.

Multi-stable mechanical metamaterials by elastic buckling instability

The mechanical responses of two novel kinds of two-dimensional (2D) mechanical metamaterials containing opposite or parallel snapping curved (U-shaped) segments with elastic snap-through instability mechanism are systematically investigated. Under uniaxial loading, the metamaterials undergo a large deformation caused by stiffness mismatch between snapping (buckling instabilities) and supporting (relative stiffer/thicker) components, exhibiting very small transverse deformation after every snapping. Based on the multi-stable mechanism, phase transformation/shape-reconfiguration and zero Poisson’s ratio are achieved up to large morphological change. Nonlinear mechanical responses including self-recovering snapping and multi-stability enabling snapping behaviors can be generated by tuning the geometric parameters (the relative thickness of the snapping and supporting segments as well as the amplitude of the snapping curved segments). Then topology analysis is carried out to develop the 2D structures to a series of 3D hierarchical configurations from which can be chosen for various engineering conditions with enhanced snapping mechanism. Specifically, multi-stable/shape-reconfigurable tubes and cylinders are designed using the 3D configurations. Besides, one of the 3D metamaterials is developed for functional applications as shock absorber and damper, i.e., the process from fully stretched state to fully compacted state is used to absorb energy and reduce incoming pressure with small stiffness and strength; then the fully compacted metamaterials are used to carry load and attenuate vibration with relative bigger stiffness and strength. This work gives advance to the design, analysis and manufacture of functionally reconfigurable mechanical metamaterials.

Ion-Induced Localized Nanoscale Polymer Reflow for Three-Dimensional Self-Assembly.

Thermal reflow of polymers is a well-established phenomenon that has been used in various microfabrication processes. However, present techniques have critical limitations in controlling the various attributes of polymer reflow, such as the position and extent of reflow, especially at the nanoscale. These challenges primarily result from the reflow heat source supplying heat energy to the entire substrate rather than a specific area. In this work, a focused ion beam (FIB) microscope is used to achieve controllable localized heat generation, leading to precise control over the nanoscale polymer reflow. Through the use of the patterning capability of FIB microscopy, dramatically different reflow performances within nanoscale distances of each other are demonstrated in both discrete periodic and continuous polymer structures. Further, we utilize a self-assembly process induced by nanoscale polymer reflow to realize 3D optical devices, specifically, vertically aligned nanoresonators and graphene-based nanocubes. HFSS and Comsol simulations have been carried out to analyze the advantages of the polymer-based 3D metamaterials as opposed to those fabricated with a metallic hinge. The simulation results clearly demonstrate that the polymer hinges have a dual advantage; first, the removal of any interference from the transmission spectrum leading to strong and distinct resonance peaks and, second, the elimination of parasitic leeching of the enhanced field by the metallic hinge resulting in stronger volumetric enhancement. Thus, the 2-fold advantages existing in 3D polymer-hinge optical metamaterials can open pathways for applications in 3D optoelectronic devices and sensors, vibrational molecular spectroscopy, and other nanoscale 3D plasmonic devices.