2D Periodic Structures Research Articles

A Generalized Polymer Precursor Ink Design for 3D Printing of Functional Metal Oxides

HighlightsA facile and generalized design strategy of polymer precursor inks was developed for direct ink writing of metal oxide into submicron 3D architectures.The Maillard reaction between polyethyleneimine and glucose endows the 3D-printed precursors with the excellent shape fidelity during high-temperature pyrolysis.As-printed 3D periodic dielectric structure with woodpile geometry shows a significant light-matter effect in mid-infrared region.

Meta-Material Layout for the Blast Protection of Above-Ground Steel Pipes

The current study investigates the capacity of the proposed meta-material layout for the blast protection of above-ground steel pipes against explosions. The philosophy of the meta-material layout’s design is described adequately, and the 1D periodic structures’ theory is adopted for the analytical prediction of the layout’s band-gaps. The special characteristics of the blast loading are explained, and specific time-related parameters are calculated. The layout is tested numerically for nine explosion scenarios of various magnitude via the finite element program ABAQUS, and the CONWEP model is selected for the simulation of the explosions. The results demonstrate a significant reduction in the maximum displacements developed on the pipe’s spring line and crown within a blast loading. This study composes an extension of the author’s previous research on buried steel pipes and surface explosion, advancing now the applicability of the meta-material layouts for the cases of above-ground steel pipes towards explosions and blast hazards. The outer goal is the investigation and the further spreading of the beneficial exploitation of meta-materials concepts for the scope of the pipelines’ effective blast protection, readdressing that this way is a major hazard for this type of structure and a gap in the current literature.

CIRCULAR POLARIZATION IN A $2\mathrm{D}$ PERIODIC ARTIFICIAL ANISOTROPIC DIELECTRIC MEDIUM

The phenomenon of polarization rotation in dielectric periodic structures is quite interesting. A similar structure was used in a sample with a 2D artificial periodic structure, where the plane wave propagation method was applied. Anisotropic dielectric constants were obtained, which were used for polarization rotation, and polarization rotation in an anisotropic medium was studied based on the dielectric permittivity of the effective medium. Those relationships, quantities, and parameters depending on the dielectric medium, dielectric permittivity, and 2D periodic structure have been studied and analyzed, which provide control of the degree of anisotropy, i.e. provide a distinction between fast and slow modes, which in turn provide the best polarization rotation per unit length.

Optimized geometric structure of Zn-BTC/POAP and Fe-BTC/POAP systems as electroactive materials in pseudocapacitors

In this work, Fe(II)-based metal organic framework (MOF), Zn-based MOF and hybrid poly orthoaminophenol/MOF composite were synthesized via a chemical method. Synthesized composite films have been characterized by conventional electrochemical methods and computational approach. The computational results show that both Zn-BTC and Fe-BTC interact well with 3POAP. Meanwhile, the adsorption energy of 3POAP on Fe-BTC is 2.03 eV higher than that of Zn-BTC. Therefore, it can be mentioned that the high adsorption energy of conductive polymer POAP on Fe-BTC compared to Zn-BTC has led to its better performance as the electrode of supercapacitors and these findings confirm the electrochemical results. It was found that in Zn-BTC/3POAP and Fe-BTC/3POAP systems the charge is transferred from the 3POAP to the MOFs. The results showed that the charge transfer from 3POAP to Fe-BTC is more than Zn-BTC which is a confirmation of the higher adsorption of 3POAP on Fe-BTC. The 3D periodic structure of Fe-BTC is generated by binuclear Fe(II) paddlewheel building units (PBUs) connected via the 1,3,5-benzenetricarboxylate organic ligands. Also, the adsorption energy of 3POAP on Fe2(PhCOO)4 and Zn2(PhCOO)4 was calculated using supermolecular approach. These results are compatible with the adsorption energy obtained from the periodic calculations, so that the adsorption of Fe structure was more than that of Zn. The Fe2(PhCOO)4…3POAP structure has the lowest band gap energy, so it can be concluded that the better adsorption of 3POAP on Fe-BTC not only results in higher adsorption energy, but also better electrical conductivity than the Zn-BTC. Computational results are in agreement with electrochemical results.

Transformation of Laguerre-Gaussian beams into 1D array of Hermite-Gaussian modes under the Talbot effect.

This work explains diffraction of Laguerre-Gaussian (LG) beams having non-zero radial indices from one dimensional (1D) periodic structures and their transformation into Hermite-Gaussian (HG) modes, theoretically, verifies using simulations and demonstrates the phenomenon experimentally. We first report a general theoretical formulation for such diffraction schemes, and then use it to investigate the near-field diffraction patterns from a binary grating having a small opening ratio (OR) by providing numerous examples. Results show that for OR≲ 0.1, at the Talbot planes, mainly at the first Talbot image, the images of individual lines of the grating obtain HG modes' intensity patterns. Therefore, the topological charge (TC) of the incident beam and its radial index can be determined from the observed HG mode. In this study, the effects of the OR of the grating and the number of Talbot plane on the quality of the generated 1D array of HG modes are also investigated. The optimum beam radius for a given grating is also determined. The theoretical predictions, are well confirmed by a number of simulations based on the free space transfer function and fast Fourier transform approach, and by experiments. The observed phenomenon, the transformation of LG beams into 1D array of HG modes under the Talbot effect, in addition of providing a way for characterization of LG beams with non-zero radial indices, itself is interesting and may be used in other fields of wave physics, especially for long-wavelength waves.

Leaky-Vivaldi antenna covered with metasurface with leaky wave radiation and aperture radiation.

A leaky-Vivaldi antenna covered with metasurface (LVAM) is proposed in this paper. The traditional Vivaldi antenna covered with metasurface realizes backward frequency beam-scanning from -41∘ to 0∘ in the high-frequency operating band (HFOB) and retains aperture radiation in the low-frequency operating band (LFOB). In the LFOB, the metasurface can be regarded as a transmission line to realize a slow-wave transmission. In the HFOB, the metasurface can be considered a 2D periodic leaky-wave structure to realize a fast-wave transmission. The simulated results show that LVAM has the -10 dB return loss bandwidths of 46.5% and 40.0%, and the realized gain of 8.8-9.6 dBi and 11.8-15.2 dBi cover the 5 G Sub-6 GHz band (3.3-5.3 GHz) and the X band (8.0-12.0 GHz), respectively. The test results are in good agreement with the simulated results. As a dual-band antenna covering the 5 G Sub-6 GHz communication band and military radar band, the proposed antenna can guide the future integrated design of communication and radar antenna systems.

Fully-Metallic 3-D Cells for Wideband Applications

This paper presents a novel full-metal 3D periodic structure that allows for the excitation of phase resonance. This phenomenon, thanks to the 3D geometry, enables the individual control of the phase response of each polarization along the frequency band. This structure is inspired on square waveguides that have open resonators slotted on the walls. An extended study has been carried out by modelling the unit cell via equivalent circuits with the goal of developing a powerful optimization tool instead of using more resource-consuming software. An ultra-wideband electric-field rotator covering a bandwidth of 141.8% has been designed with the aid of the circuit model and has been manufactured via 3D-printing laser powder bed fusion (LPBF). The experimental results have been validated with success.

Wave Propagation in Laminated Cylinders with Internal Fluid and Residual Stress

Numerical computation of wave propagation in laminated cylinders with internal fluid and residual stress is obtained using a Wave Finite Element formulation for 2D waveguides. Only a very small segment of the system is modelled, resulting in a very low-order finite element (FE) model to which the theory of wave propagation in 2D periodic structures is applied. The method uses standard FE formulations and exploits the capability of commercial FE software to model both fluid and structure and their interaction, resulting in a very large reduction in computational time. The presented approach is general, and can be applied without the need to make assumptions related to shell theory or low-frequency analysis. In particular, the laminated structure is discretised using 3D solid elements, thus representing the through-thickness dynamics with high accuracy. Residual radial and hoop stresses are included in the model by adding the FE pre-stress stiffness matrix to the original stiffness matrix of the system. The method provides simultaneously a very substantial reduction of computational cost, accurate solutions up to very high frequency and prediction of the dispersion curves for selected circumferential orders without the need for any further analysis. Here, the formulation of the method is introduced and its application to laminated cylinders filled with an acoustic fluid is presented. A composite, reinforced rubber cylinder, pre-stressed by a circumferential tension, is also shown as an example of a laminated pipe for high-pressure applications.

Plasmonic Photoresistor Based on Interconnected Metal‐Semiconductor Grating

AbstractMetal‐semiconductor nanostructures in various configurations are extensively used in photodetection, photocatalysis, and photovoltaics. For photodetection purposes, the working principle is straightforward; on illumination, generated charge carriers in excess lead to a decrease in resistance. Notably, using an interconnected metal‐semiconductor grating, it is observed and now reported an opposite response, an increase in the resistance. Such photoresistors are fabricated through wrinkle structuring and oblique angle material deposition methods. It is found that the controlled wrinkling leads to large‐area 1D periodic structures with coexisting cracking perpendicular to the grating direction—such cracks are used as connections between the two‐point contact measurement through the associated gold layer deposition. An enhanced current reduction is further observed on photoexcitation for an additional deposition of an amorphous titania layer. Subsequently, a discussion on the mechanisms and interaction between hot electron injection, charge carrier recombination, and thermalization is presented. Supported by numerical modeling, the angle‐resolved plasmonic modes with the photoresistance can be correlated. The ease of layered deposition of the materials allows one to extend the studies on cavity‐based structures with sandwiched titania layers as hotspots. This simple, scalable, and robust fabrication method thus promises an efficient routeway toward photosensor development in which plasmon‐mediated hot electrons play a crucial role.

Magnetically Tunable One-Dimensional Plasmonic Photonic Crystals.

Integrating plasmonic resonance into photonic bandgap nanostructures promises additional control over their optical properties. Here, one-dimensional (1D) plasmonic photonic crystals with angular-dependent structural colors are fabricated by assembling magnetoplasmonic colloidal nanoparticles under an external magnetic field. Unlike conventional 1D photonic crystals, the assembled 1D periodic structures show angular-dependent colors based on the selective activation of optical diffraction and plasmonic scattering. They can be further fixed in an elastic polymer matrix to produce a photonic film with angular-dependent and mechanically tunable optical properties. The magnetic assembly enables precise control over the orientation of the 1D assemblies within the polymer matrix, producing photonic films with designed patterns displaying versatile colors from the dominant backward optical diffraction and forward plasmonic scattering. The combination of optical diffraction and plasmonic properties within a single system holds the potential for developing programmable optical functionalities for applications in various optical devices, color displays, and information encryption systems.

Enhanced absorption in a 1D photonic crystal based on 3D Dirac semimetals

We theoretically reveal the absorption properties of a 1D periodic structure associated with alternating 3D Dirac semimetals and dielectric layers. The absorption spectra of this structure under both TM and TE polarized waves have been shown, where greatly enhanced absorption is achieved at a certain angle under the TM wave because of the zero effective perpendicular permittivity of the periodic structure. We also reveal that the absorption behavior in this structure can be engineered by the thicknesses of the 3D Dirac semimetal film and the dielectric layer in the unit cell of the periodic structure. In contrast to conventional absorbers made of the metals, the absorption in this periodic structure is highly controllable by the Fermi energy of 3D Dirac semimetals. Our results provide an alternative route to control absorption using 3D Dirac semimetals, which offers alternative options for possible device applications.

PEEC Model Based on a Novel Quasi-Static Green's Function for Two-Dimensional Periodic Structures

A quasi-static periodic Green's function (PGF) is proposed for modeling and designing metasurfaces in the form of two-dimensional (2D) periodic structures. By introducing a novel quasi-static approximation on the full-wave PGF in the spectrum domain, the quasi-static PGF is derived that can retain the contribution from propagating and evanescent modes below resonant frequency by a second-order polynomial of frequency. Unlike full-wave PGF, the proposed quasi-static PGF polynomial coefficients are frequency-invariant. Consequently, it can save the modeling time significantly by calculating the coefficients only once for a frequency band of interest. Moreover, a quasi-static PEEC model is developed from the proposed quasi-static PGF. It circumvents the breakdown problem around near-zero frequencies since the singularity in PGF is separated in the quasi-static PGF and eliminated analytically in model development. Therefore, both the time- and frequency-domain analysis can be conducted easily using a SPICE-like solver on the PEEC model. Two examples are given, one of which validates the accuracy of the proposed quasi-static PGF in a 2D periodic unit cell working at 0–12 GHz; the other demonstrates the superior performance in terms of model efficiency and stability by a Jerusalem-cross frequency selective surface (FSS) working at 0–20 GHz. The numerical results show that the proposed method is accurate and efficient in a wide band for metasurfaces made of two-dimensional periodic structures.

The Application of the Hybrid Projection Method for the Analysis

The problem of scattering of a plane electromagnetic wave by a 2D periodic structure formed by absorbing spherical radially inhomogeneous dielectric elements is considered. The elements have the type of electromagnetic black holes located on a semi-infinite substrate. The numerical algorithm of the solution is developed. The algorithm is based on the hybrid projection method and takes into account the peculiarities of the black hole construction. The algorithm is generalized to the case, when black holes are situated on aperfectly conducting screen. New expressions for calculating the power absorbed by the structure elements are derived. The numerical results characterizing the efficiency of the structure absorption are presented.

Meta-Kagome lattice structures for broadband vibration isolation

One-dimensional (1D) phononic crystal (PC) beams have been extensively studied due to their bandgap properties, but the idea of using this functional beam components to form three-dimensional (3D) periodic structures has rarely been mentioned. In this paper, the PC beam element is used to replace the ordinary member of the conventional Kagome lattice structures, thus, a meta-Kagome lattice (MKL) structure is innovatively constructed with broadband vibration isolation performance. The dispersion analysis is performed to reveal the mechanism of bandgap formation and the reason of getting broad bandgaps. Three kinds of MKL structures, namely, with triangular, rectangular and hexagonal pyramids are designed. The vibration transmission properties of the MKL columns with or without interfaces are studied to illustrate the isolation effect. Moreover, the vibration isolation performance of the sandwich structures composed of MKL cores is also studied, and the influence of the skin characteristics on the properties is discussed. Vibration transmission tests were conducted to verify the results. This work provides a new method to develop 3D multi-functional lattice structures, especially for load-bearing and vibration reduction.

Achiral Nanoparticle-Enhanced Chiral Twist and Thermal Stability of Blue Phase Liquid Crystals.

Blue phase liquid crystals (BPLCs) are chiral mesophases with 3D order, which makes them a promising template for doping nanoparticles (NPs), yielding tunable nanomaterials attractive for microlasers and numerous microsensor applications. However, doping NPs to BPLCs causes BP lattice extension, which translates to elongation of operating wavelengths of light reflection. Here, it is demonstrated that small (2.4 nm diameter) achiral gold (Au) NPs decorated with designed LC-like ligands can enhance the chiral twist of BPLCs (i.e., reduce cell size of the single BP unit up to ∼14% and ∼7% for BPI and BPII, respectively), translating to a blue-shift of Bragg reflection. Doping NPs also significantly increases the thermal stability of BPs from 5.5 °C (for undoped BPLC) up to 22.8 °C (for doped BPLC). In line with our expectations, both effects are saturated, and their magnitude depends on the concentration of investigated nanodopants as well the BP phase type. Our research highlights the critical role of functionalization of Au NPs on the phase sequence of BPLCs. We show that inappropriate selection of surface ligands can destabilize BPs. Our BPLC and Au NPs are photochemically stable and exhibit great miscibility, preventing NP aggregation in the BPLC matrix over the long term. We believe that our findings will improve the fabrication of advanced nanomaterials into 3D periodic soft photonic structures.

An Algebraic Wavenumber Identification (AWI) technique under stochastic conditions

This paper presents an inverse Algebraic Wavenumber Identification (AWI) technique for multi-modal 1D-periodic structures, which can extract complex wavenumbers from steady-state vibration measurements under stochastic conditions. These wave dispersion characteristics provide valuable vibroacoustic indicators for model updating, damage monitoring in operational conditions, or metamaterial design. Wavenumber extraction techniques are highly sensitive to noisy measurements, nonuniform sampling points, or geometrical uncertainties. The proposed formulation relies on algebraic parameters identification to enable the extraction of complex wavenumbers in four scenarios: (a) low Signal Noise Ratio; (b) small perturbation caused by uncertainties on sampling points’ coordinates; (c) unknown structural periodicity; (d) nonuniform sampling. This AWI is compared with Inhomogeneous Wave Correlation (IWC) method and INverse COnvolution MEthod (INCOME) to assess the robustness and accuracy of the method.

Multiscale Optimization of 3D‐Printed Beam‐Based Lattice Structures through Elastically Tailored Unit Cells

Herein, a numerical multiscale tool is developed to design 3D periodic lattice structures. The work is motivated by the high design freedom of additive manufacturing technologies, which enable complex multiscale lattice structures to be printed. A finite‐element‐based free‐material optimization method is used to determine the ideal orthotropic material properties of a 3D macrostructure space. Subsequently, a population‐based algorithm is established to design optimized microscopic lattice unit cells with the desired structural properties. The design variables are the coordinates of lattice skeleton nodes defined within the 3D lattice unit cell space, and the connectivities between them resulting in a truss skeleton. For the calculation of the mechanical properties of the individual lattice cells, an effective Timoshenko beam‐based finite element calculation method is developed. The macroscale structure can be constructed by periodically filling the domain with the customized unit cell representing a metamaterial. The method is demonstrated by 3D beam problems with compliance constraints. These macroscopic demonstrators of the developed lattice structures were also 3D‐printed. The benefit regarding the weight‐specific structural performance is validated through benchmarking with periodic lattice design solutions using well‐known standard lattice cells.

Seismic Composite Metamaterial: A Review

The modern construction revolution throughout the past two decades has brought the need for ground vibration mitigation, and this has been one of the major study areas. These studies were mainly focused on the effect of forestation on vibration reduction as the available natural metamaterial. Physical methods such as the finite element method and the boundary conditions of 2D and 3D applications in ground vibration reduction have been developed. Many researchers, scientists, and organizations in this field have emphasized the importance of these methods theoretically and numerically. This paper presents the historical context of resonant metamaterials (MMs), the current progress of periodic 2D and 3D structures, and the possible future outcomes from the seismic metamaterials (SMs), and it relates them with their elastic counterparts to the natural metamaterial (NMs). The idea of bandgaps (FBGs) in the frequency range of interest is reviewed and discussed in some detail. Moreover, the attenuation associated with ground vibrations, noise, seismology, and the like is explained by managing the peculiar mechanisms of ground vibrations. However, a comprehensive computational review focuses on shielding MMs for ground vibration mitigation in urban areas. This phenomenon led to unique features for various techniques to control the bandgap width for various construction applications. Ecological solutions involve the creation of an economic, environmentally based seismic shield for both the Bragg scattering and the local resonance bandgaps. Reportedly, additive studies based on numerical simulation and experiments have improved the functionality of the 2D and 3D periodic structures. It was found that the mechanical properties differ (i.e., stiffness, Poisson’s ratio, and bulk density) and that the geometrical parameters (i.e., lattice, model dimensions, distance from vibration sources, and number of periodic structures) exhibited strong effects on the width and location of the derived FBGs. The geometrical properties of the used unit cell have a strong effect on the attenuation mechanism. Although deep analysis was created in much of the previous research, it was revealed, based on that research, that the attenuation mechanism is still unclear. However, this review article presents a detailed exposition of the recent research progress of the seismic metamaterials, including 2D, 3D, and the main mechanisms of the theoretical backgrounds of energy attenuation. It also summarizes the effects of the factors on the width and location of the bandgaps at a low frequency. In addition, the natural metamaterials and the study of the urban environment are surveyed. The major findings of this review involve the effectiveness of NMs for different functionalities in ground vibration attenuation, which leads to diverse purposes and applications and proposes a roadmap for developing natural materials for clean and quiet environments.

High-Performance Directional Water Transport Using a Two-Dimensional Periodic Janus Gradient Structure.

Numerous materials in micro- or nanoscale hierarchical structures with surface gradients serve as the enablers in directional liquid transportation. However, concurrent high-speed and long-range liquid transport is yet to be fully realized so far. Here, an overall-improved approach is achieved in both water transport distance and velocity aspects using a 2D periodic Janus gradient structure, which is inspired by the Janus-wettable desert beetle back, tapered asymmetric cacti spine, and periodic Nepenthes alata microcavity. This 2D channel can efficiently regulate the kinetics of liquid transport within its confined structure, in which the terminal potential well and periodic Janus topological structure enable sustaining water propelling through a long distance. In addition, the rapidly formed aqueous film facilitates a high initial momentum and fast transport of liquid droplets along the channel, achieving an averaged velocity of over 400mm s-1 and a maximum normalized transport distance of 23.4 for a 3µL droplet, as well as an ultralow liquid volume loss of 6.02% upon high-flux water transport. This scalable, controllable, and easy-fabricable 2D water transport system provides an insightful pathway in realizing high-performance water manipulation and possibly facilitates substantial innovative applications in multidisciplinary fields.

Construction and Characterization of a Diphase Two-Dimensional Halogen-Bonded Organic Framework Based on a Pyrene Derivative

AbstractCrystalline porous materials have received extensive attention due to their fascinating structures and wide range of applications. We report a novel diphase two-dimensional (2D) halogen-bonded organic framework (XOF-TPP) based on 1,3,6,8-tetra(pyridin-4-yl)pyrene (TPP). XOF-TPP was constructed through [N···I+···N] interactions between the pyridyl groups of TPP and iodonium cations. The formation of XOF-TPP was monitored by X-ray photoelectron spectroscopy, IR spectroscopy, powder X-ray diffraction, scanning electron microscopy, and high-resolution transmission electron microscopy, and simulated theoretically. Small-angle X-ray scattering indicated that the XOF-TPP exists as a 2D periodic structure. This diphase 2D halogen-bonded organic framework has promise for practical applications in supramolecular functional materials.