Periodic Structures Research Articles

Theoretical analysis of a refractive index sensor based on optical Tamm state of graphene metastructure under arbitrary polarization deflection angle

In this paper, a refractive index sensor based on a metastructure (MS) is proposed, which achieves sensing through the sharp valleys formed in the reflection spectrum by the excitation of optical Tamm states (OTS) by gyroidal graphene. Differences in the refractive index of the filling medium in the pores of gyroidal graphene will cause shifts in the reflection valleys. The graphene layer is followed by a periodic structure consisting of alternating zirconium dioxide (ZrO2) and α-molybdenum trioxide (α-MoO3). The 4 × 4 transfer matrix method (TMM) is used for the calculation of the results, which allows the case of arbitrary polarization deflection angles ϕ to be considered in the discussion. Different values of ϕ can lead to a switch in the dominance of the sensor, specifically, the structure has a larger linear interval but lower sensitivity at ϕ = 0°, which is the opposite of the situation at ϕ = 90°. The sensor can be used in a variety of scenarios such as biochemical sensing, gas detection, etc, and brings the polarization deflection angle of the incident wave into the discussion.

Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

AbstractThe suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch’s theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169.57 Hz to 216.42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure’s two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i.e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure’s excellent low-frequency vibration suppression capability.

Features of Earth’s lower ionosphere during solar eclipse and sunset and sunrise hours according to measurements by the API method near Nizhny Novgorod

We present the results of experimental studies into the response of Earth’s lower ionosphere to a partial solar eclipse. The studies have been carried out using the method of resonant scattering of radio waves by artificial periodic irregularities (APIs) in ionospheric plasma. The irregularities were created in the field of a standing wave when a powerful radio wave, generated by radiation to the zenith by transmitters of the mid-latitude heating facility SURA, was reflected from the ionosphere. During location of a periodic structure by probe radio waves when the Wolf—Bragg backscattering condition was met, a scattered signal was received and its amplitude and phase were measured. After the end of the impact on the ionosphere, the irregularities gradually disappeared (relaxed). We have examined variations in characteristics of scattered signals. During the eclipse, the scattered signal amplitude increased by 30–40 dB, and the relaxation time increased 1.5–2.0 times. In some cases, stratification of the signal amplitude in the D-region was observed due to stratification of the electron density profile. By analyzing altitude profiles of relaxation time, we obtained neutral component temperature and density, height of the turbopause, and turbulent velocity. The velocity of vertical regular motion of plasma at each height was measured from the time variation in the scattered signal phase. From the results of measurements of scattered signal characteristics during four partial eclipses, we have obtained that the neutral component temperature decreases, on average, 50–70 K. Variations in the temperature, vertical plasma velocity, and turbopause level exhibited deep quasi-periodic variations with periods from 15 min to several hours, typical of internal gravity wave propagation. The vertical temperature and velocity profiles showed changes with altitude on scales ranging from 5 to 30 km. Comparison between the results of studies of the lower ionosphere during sunrise-sunset hours has revealed that its response during a partial eclipse and the transition to the night regime is identical. According to the measurements by the partial reflection method, during the August 01, 2008 eclipse there was a decrease in the electron density in the D-region 3–5 times. We have concluded that during an eclipse there was a significant change in both the ionized and neutral components of the atmosphere in the lower ionosphere.

Fast and Robust Modeling of Lanthanide and Actinide Complexes, Biomolecules, and Molecular Crystals with the Extended GFN-FF Model.

Lanthanides (Ln) and actinides (An) have recently become important tools in biomedical and materials science. However, the development of computational methods able to describe such elements in various environments has not kept up with the pace of the field. Addressing this challenge, this work introduces and showcases an extension of the GFN-FF to An alongside a reparameterization for Ln. This development fills a gap for fast computational methods that are out-of-the-box applicable to large f-element-containing systems with thousands of atoms. We discuss the reparameterization of the charge model and the covalent topology setup and showcase the model through various applications: Molecular dynamics simulations, optimization of Ln-containing biomolecules, and optimizations of several periodic structures. With the presented improvements, GFN-FF is a powerful method that routinely delivers robust and accurate geometries for large Ln/An systems with thousands of atoms.

Simultaneous low-frequency vibration isolation and energy harvesting via attachable metamaterials

In this study, we achieved energy localization and amplification of flexural vibrations by utilizing the defect mode of plate-attachable locally resonant metamaterials, thereby realizing compact and low-frequency vibration energy suppression and energy harvesting with enhanced output performance. We designed a cantilever-based metamaterial unit cell to induce local resonance inside a periodic supercell structure and form a bandgap within the targeted low-frequency range of 300–450 Hz. Subsequently, a defect area was created by removing some unit cells to break the periodicity inside the metamaterial, which led to the isolation and localization of the vibration energy. This localized vibration energy was simultaneously converted into electrical energy by a piezoelectric energy harvester coupled with a metamaterial inside the defect area. Consequently, a substantially enhanced energy harvesting output power was achieved at 360 Hz, which was 43-times higher than that of a bare plate without metamaterials. The proposed local resonant metamaterial offers a useful and multifunctional platform with the capability of vibration energy isolation and harvesting, while exhibiting easy handling via attachable designs that can be tailored in the low-frequency regime.

Tunable Plasmon Resonance in Silver Nanodisk-on-Mirror Structures and Scattering Enhancement by Annealing.

In this study, we evaluated the surface plasmon characteristics of periodic silver nanodisk structures fabricated on a dielectric thin-film spacer layer on a Ag mirror substrate (NanoDisk on Mirror: NDoM) through finite difference time domain (FDTD) simulations and experiments involving actual sample fabrication. Through FDTD simulations, it was confirmed that the NDoM structure exhibits two sharp peaks in the visible range, and by adjusting the thickness of the spacer layer and the size of the nanodisk structure, sharp peaks can be obtained across the entire visible range. Additionally, we fabricated the NDoM structure using electron beam lithography (EBL) and experimentally confirmed that the obtained peaks matched the simulation results. Furthermore, we discovered that applying annealing at an appropriate temperature to the fabricated structure enables the adjustment of the resonance peak wavelength and enhances the scattering intensity by approximately five times. This enhancement is believed to result from changes in the shape and size of the nanodisk structure, as well as a reduction in grain boundaries in the metal crystal due to annealing. These results have the potential to contribute to technological advancements in various application fields, such as optical sensing and emission enhancement.

Optimized graphene metamaterial for dual plasmon-induced transparency in terahertz band with multifunctional applications

Abstract This paper proposes a patterned graphene periodic metamaterial structure, optimized using an improved genetic algorithm to adjust the position and size of each graphene strip, thereby achieving dual plasmon-induced transparency (PIT) effects in the terahertz band, resulting in extraordinary multifunctionality. The finite difference time domain method is employed to obtain the transmission spectrum, and coupled mode theory is used for theoretical analysis and verification of the dual-PIT effect. The structure exhibits multifunctionality: when used as a photoelectric switch, it achieves a modulation depth of up to 99.04% with an insertion loss as low as 0.16 dB by tuning the Fermi level. Additionally, the structure demonstrates excellent sensing performance, with a maximum sensitivity and figure of merit reaching 0.84 THz/RIU and 88.55, respectively. Furthermore, the slow light performance of the structure is investigated, showing a group delay of up to 0.5 picoseconds.

Periodic INAR(1) model with Bell innovations distribution

Abstract In this paper, we introduce a class of periodic integer-valued autoregressive BL-PINAR(1) models with Bell innovations distribution based on the binomial thinning operator. The basic probabilistic and statistical properties of this class are studied. Indeed, the first and the second moment periodically stationary conditions are established. The closed forms of these moments are, under the obtained conditions, derived. Furthermore, the periodic autocovariance structure is also considered while providing the closed form of the periodic autocorrelation function. The conditional least squares (CLS), Yule–Walker (YW), weighted conditional least squares (WCLS), and conditional maximum likelihood (CML) methods are applied to estimate the underlying parameters. The asymptotic properties of the CLS and the YW estimators are obtained. The performances of these methods are compared through a simulation study. An application on a real data set is provided.

Crisis-induced vibrational resonance in a phase-modulated periodic structure.

Double vibrational resonance is reported for a driven oscillator in a periodic structure of the Josephson junction type with high-frequency phase modulation. We identify two distinct phase modulation effects, namely, resonant induction and resonant amplification, leading to the appearance of a double resonance. We analyze these vibrational resonance phenomena theoretically and numerically, and we show that the origin of the induced resonance is traceable to a transition from periodicity to quasiperiodicity associated with an attractor-merging crisis.

Outer Zone Relativistic Electron Response to Mesoscale Periodic Density Structures in the Solar Wind: Van Allen Probes Measurements

AbstractWe investigate the relativistic and the ultra‐relativistic outer radiation belt electron response to the Periodic Density Structures (PDS) in the solar wind. We have studied four intervals between 0000 UT and 1500 UT during 17 January 2013 interplanetary coronal mass ejection (ICME) sheath event following the passage of an interplanetary shock (IP) on 16 January, at 2240 UT. Earlier studies limited to geosynchronous orbit have shown that PDS induce Ultra‐Low‐Frequency (ULF) oscillations in the magnetosphere and modulate energetic electron intensities. Our study shows for the first time, using pitch angle resolved electron intensity measurements, that PDS modulate relativistic and ultra‐relativistic electron intensities in the heart of the radiation belts (L ≈ 4). We find that the modulation of electron intensities occur at frequencies close to those of interplanetary PDS. Furthermore, electron intensity modulations occur over a wide range of energy (≈200 keV to 4 MeV) and pitch angles (≈20–120°). This event study suggests that relativistic and ultra‐relativistic electron intensity modulations driven by PDS may be largely energy and pitch angle independent.

Preparation and optical characterization of 3D-TiO2 thin films with brilliant colors

In this paper, three-dimensional titanium dioxide (3D-TiO2) thin films with periodic structure were obtained by periodic pulse anodization of high-purity titanium wafers under specific alternating voltage (AV) using asymmetric sawtooth waveforms. The effect of voltage amplitude and electrolyte concentration on the structural color of the 3D-TiO2 thin films were investigated. It is shown that the nanotubes grown by asymmetric sawtooth wave at a specific AV have a “bamboo” shape, and the cycle length, as well as the inner and outer tube diameters of the nanotubes are closely related to the AV. The structural color of the samples was different at varying voltages and electrolyte concentrations for the same oxidation cycle time. The structural color of films grown under low voltage is analyzed to be related to the scattering and absorption of light on their surfaces. The thickness of the film grown under high voltage satisfies the conditions for light interference. The maximum reflected wavelength is red-shifted and then blue-shifted as the electrolyte concentration decreases. The study shows that the microstructure is the main influence on the color change of 3D-TiO2 thin films.

Manipulate dynamic chemical interactions in renewable polymers for 3D printing tunable, healable, and recyclable metamaterials

Mechanical metamaterials have garnered significant interests due to their unique properties, which arise from the periodic structures of their constituent units. However, traditional mechanical metamaterials suffer from limitations of fixed properties of the constituent units or irreversibility if they are damaged or little-to-no recyclability. Addressing this challenge, herein, a photoresin consisting of a monomer synthesized from a renewable biomass—epoxidized soybean oil (ESO)—citric acid (CA) and other components was developed for light-based 3D printing. It is discovered that the UV irradiation initiates photopolymerized of the highly photoactive epoxidized soybean oil-ethyl acrylamide (ESO-EA) monomer while enabling the epoxy-acid reaction (EAR) of the epoxy groups in ESO-EA with carboxyl groups in CA to create dynamic chemical bonds (DCBs). This formed dynamic crosslinking network endows the printed material with tunable tensile strengths (0.3–10.4 MPa) and shape memory behaviors (transition temperature: 22–48 °C) while maintaining high stretchability (fractural strain: 81 %–205 %). Thermal annealing facilitates dynamic transesterification reactions (DTER) to further improve the mechanical properties while making the printed materials healable and recyclable. By integrating these innovations into liquid crystal display (LCD) based 3D printing, we demonstrate origami metamaterials with tunable, multi-stable mechanical behaviors as well as property recovery after self-healing of the damaged structures by both simulations and experiments. Finally, the printed metamaterials can be recycled with the well-preserved properties.

A new periodic shaft model for broadband ultra-low-frequency vibration reduction in spinning shafts

Vibration isolation is found in periodic structures having a special feature known as vibration band gap. A periodic shaft model is proposed and analyzed in this study. This model is composed of a spinning solid shaft carrying periodic arrays of outer cantilever hollow shafts. The generalized differential quadrature rule (GDQR) method combined with the Bloch theorem is used to calculate the vibration band gaps of this periodic shaft. Results are verified by the forced vibration responses obtained using the GDQR method. Results indicate that for each length of the hollow shafts, there is a spinning velocity range for which the first band gap starts from zero frequency. In other words, each model of this periodic shaft can be used for vibration reduction over an ultra-low-frequency band gap at different spinning velocities. Results also indicate that there is a model with specific value of the hollow shafts length for which the second band gap is very close to the first band. For this model, the width of the ultra-low-frequency band gap is much greater than other models. Finally, verification of the GDQR method shows that it can be used as a precise numerical method for free and forced vibration analysis of the spinning shafts.

Laser engineered architectures for magnetic flux manipulation on superconducting Nb thin films

Custom shaped magnetic flux guiding channels have been fabricated on superconducting Nb thin films by laser nanopatterning of their surface. Preferential pathways are defined by suitable combination of imprinted anisotropic pinning domains through laser-induced periodic surface structures (LIPSS). Generated by the selective energy deposition of femtosecond UV laser pulses, quasi-parallel ripple structures are formed under optimized irradiation conditions. On average, each domain is formed by grooves with a lateral period of 260–270 nm and a depth about 80 nm. By combination of scanning and transmission electron microscopy, magneto-optical imaging, and conductive atomic force microscopy techniques, we conclude that the boundaries of the LIPSS-covered domains play a prominent role in the magnetic flux diversion process within the film. This is confirmed by dedicated modeling of the flux dynamics, combined with the inversion of the magneto-optical signal. The created metasurfaces enable control of the flux penetration process at the microscale.

Compressive Properties and Fracture Behaviours of Ti/Al Interpenetrating Phase Composites with Additive-Manufactured Triply Periodic Minimal Surface Porous Structures

Compressive Properties and Fracture Behaviours of Ti/Al Interpenetrating Phase Composites with Additive-Manufactured Triply Periodic Minimal Surface Porous Structures

The influence of ultrafast laser processing on morphology and optical properties of Au-GaAs composite structure

The results of direct femtosecond laser structuring of GaAs wafer coated with continuous semitransparent gold (Au) film are presented. The obtained structures demonstrate a combination of different features, namely laser-induced periodic surface structures (LIPSS) on semiconductor and metal film, nanoparticles, Au islands, and fragments of exfoliated Au film. The properties of Au-GaAs samples are studied with scanning electron microscopy (SEM), Raman scattering, and photoluminescence (PL) spectroscopy. The behaviour of phonon modes and enhancement of band-edge PL of Au-GaAs composite sample are discussed. The Raman spectra of Au-GaAs sample processed at different levels of irradiation pulse energy reveal forbidden TO and allowed LO phonon modes for selected geometry of experiment, as well as the manifestation of GaAs surface oxidation and amorphization. A 12-fold increase of PL intensity for Au-GaAs sample with LIPSS compared to initial GaAs surface is observed. The detected PL enhancement is caused by an increase of absorption in GaAs due to the light field enhancement near the Au nanoislands and a decrease of nonradiative surface recombination. The blue shift of PL band is caused by the quantum size effect in GaAs nano-sized features at laser processed surface. The combination of GaAs substrate with surface micro- and nanostructures with Au nanoparticles can be useful for photovoltaic and sensorics applications.

Enhanced osteointegration and osteogenesis of osteoblast cells by laser-induced surface modification of Ti implants

Dental and orthopedic implants have become routine medical technologies for tooth replacement and bone fixation. Despite significant progress in implantology, achieving sufficient osseointegration remains a challenge, often leading to implant failure over the long term. Nanotechnology offers the potential to mimic the natural patterns of living tissues, providing a promising platform for tissue engineering and implant surface design. Among the various methods for developing nanostructures, High-Regular Laser-Induced Periodic Surface Structures (HR-LIPSS) techniques stand out for their ability to fabricate highly ordered nanostructures with excellent long-range repeatability and production efficiency. In this study, we utilized an innovative technical approach to generate traditional laser-induced superficial LIPSS nanostructures, followed by detailed surface analysis using classical microscopy and physicochemical methods. Our findings demonstrate for the first time that nanostructured LIPSS surfaces can significantly enhance cell adhesion and proliferation while providing an optimal environment for cell metabolism. Given the high reproducibility, low cost, and potential of HR-LIPSS techniques to support cell growth and differentiation, this novel technology has the potential to impact both the industrial development of new implants and clinical outcomes after implantation.

Tailoring elastic bandgaps and moduli of triply periodic minimal surface structures by a hybrid technique

This work aimed to investigate elastic dispersion behaviors of triply periodic minimal surface (TPMS) lattice structures. The dispersion curves were established using the finite element (FE) Bloch reduction method, in which the Bloch periodic boundary condition was implied via the Bloch transform matrix. Four different types of both surface- and solid-based TPMS lattices with varying relative densities were considered. It was found that only the solid-based Neovius and Schwarz structures provided complete elastic bandgaps. Then, elastic stiffnesses of the structures obtained by representative volume element (RVE) models were evaluated with regard to their achieved band gaps. Reducing the volume fraction of lattices obviously enhanced the bandgap behaviors, while decreasing the specific moduli. Moreover, new hybrid phononic lattices were introduced for tailoring the elastic bandgap and mechanical properties. The results showed that incorporating the strut-based face-centered cubic (FCC) lattice in the TPMS structures could obviously improve the bandgap characteristics and simultaneously maintain reasonable specific elastic properties. Finally, wave suppression structure by using the dispersion curves was demonstrated by examining a simple beam infilled with the periodic lattices under excited loads. It was shown that the TPMS structures could be well applied as an effective wave suppression feature in load-bearing structures.

Representing crystal potential energy surfaces via a stationary-point network

A cornerstone of materials physics is the principle that all properties of crystalline systems are fundamentally determined based on the underlying potential energy surface (PES), which affects the structural stability and structure–property relations. Finding a proper representation of the PES is essential for the implementation of this principle, which has attracted considerable interest over the past decades; however, progress has been impeded by the lack of a firm theoretical basis for effectively exploring the vast configurational space. Here, we introduce a new method for constructing a crystal PES by using a solution landscape with an improved high-index saddle dynamic scheme, in which generalized coordinates are introduced to encode crystals that satisfy translational and rotational invariance. To represent the PES of periodic crystalline structures, we devise an advanced graph-based stationary-point network to visualize and analyze complex PES terrains, with nodes and edges representing stationary points and their connections, respectively. Crystalline GaN and Si are considered as exemplary case studies, and our newly devised approach leads to the discovery of several hidden transition paths with low enthalpy barriers associated with multistep processes; thus, the effectiveness of the approach is validated. Our method combined with the first-principles calculations offers a viable solution to long-standing problems associated with crystal PESs, such as the kinetics of activated processes, materials stability and synthesizability. These findings represent a notable advancement and offer a basis for future research.

The dynamic behaviour of a finite periodic structure comprising either symmetric or asymmetric exponential- and conical-shaped rods

Periodic structure research is driven by the aim of incorporating them into modern engineering systems to address specific challenges, such as vibration reduction within defined frequency ranges. This paper explores the dynamic behaviour of a periodic structure comprising rods with varying cross-sectional areas. Two specific cases are considered, one in which the unit cell consists of two rods where the cross-sectional area varies exponentially and one where the cross-sectional areas vary conically. The structures are modelled using receptance matrices of a single cell, which are then transformed into transfer matrices. This facilitates a comparison of the two structures and helps to relate the results between finite and infinite structures. An experimental study to validate the approach and some of the results is also presented. It is shown that the structures composed of rods with exponentially or conically varying cross-section areas have similar behaviour. Reasonably good correspondence between the predictions and the experimental results were found. However, some additional features were found in the measured receptances due to bending vibration that was not considered in the theoretical model. Asymmetric cells are found to perform better and have a wider attenuation band when compared to symmetrical cells.