Artificial Periodic Structures Research Articles

Reverse design and application of phononic crystals based on deep learning

Abstract This paper reverse-design phononic crystals with band gaps within a targeted frequency band using the trained conditional variational autoencoder (CVAE) and further studies the vibro-acoustic characteristics of a composite sandwich plate with a phononic crystal panel as the core layer. Firstly, a matrix composed of 0 s and 1 s, representing scatterers and substrates, is randomly generated by MATLAB to represent two-dimensional phononic crystals. The three-dimensional phononic crystals are obtained by stretching the two-dimensional phononic crystals along the average direction, and COMSOL Multiphysics is used to calculate the band gap. In order to maximize the production of phononic crystals with a band gap distribution, the convolutional neural network is trained to predict whether the generated phononic crystals have band gaps. Finally, using data on the structures of phononic crystals and their band gap distributions, the CVAE is trained to achieve the reverse design of artificial periodic structures based on the target band gap. To verify the effectiveness of the structures obtained through the reverse design method on vibration and noise reduction, the submerged vibro-acoustic characteristics of a composite sandwich plate are studied. The plate consists of a phononic crystal panel and carbon fiber panels. The model of the composite sandwich plate is fabricated, and its submerged vibro-acoustic characteristics are tested and compared with numerical results. Finally, the submerged vibro-acoustic response levels of composite sandwich plates with phononic crystal panels and honeycomb panels as core layers are compared using numerical methods. This comparison assesses the phononic crystal panel’s vibration and noise reduction effects.

Atomically precise vacancy-assembled quantum antidots.

Patterning antidots, which are regions of potential hills that repel electrons, into well-defined antidot lattices creates fascinating artificial periodic structures, leading to anomalous transport properties and exotic quantum phenomena in two-dimensional systems. Although nanolithography has brought conventional antidots from the semiclassical regime to the quantum regime, achieving precise control over the size of each antidot and its spatial period at the atomic scale has remained challenging. However, attaining such control opens the door to a new paradigm, enabling the creation of quantum antidots with discrete quantum hole states, which, in turn, offer a fertile platform to explore novel quantum phenomena and hot electron dynamics in previously inaccessible regimes. Here we report an atomically precise bottom-up fabrication of a series of atomic-scale quantum antidots through a thermal-induced assembly of a chalcogenide single vacancy in PtTe2. Such quantum antidots consist of highly ordered single-vacancy lattices, spaced by a single Te atom, reaching the ultimate downscaling limit of antidot lattices. Increasing the number of single vacancies in quantum antidots strengthens the cumulative repulsive potential and consequently enhances the collective interference of multiple-pocket scattered quasiparticles inside quantum antidots, creating multilevel quantum hole states with a tunable gap from the telecom to far-infrared regime. Moreover, precisely engineered quantum hole states of quantum antidots are geometry protected and thus survive on oxygen substitutional doping. Therefore, single-vacancy-assembled quantum antidots exhibit unprecedented robustness and property tunability, positioning them as highly promising candidates for advancing quantum information and photocatalysis technologies.

Kinking prohibition enhancement of interface crack in artificial periodic structures with local resonators

In this study, the propagation and kinking of an interface crack between two dissimilar artificial periodic structures with local resonators is investigated. By Fourier transform, the dynamic fracture problem is derived as an equation with Wiener–Hopf type. An additional band gap can be created by local resonators. During the dynamic failure, elastic waves will be excited continuously from the crack tip and result in the energy dissipation. Moreover, the energy release ratio which characterizes the fracture resistance is obtained. The meta-arrest property of the artificial periodic structure with local resonators is illustrated. Based on inverse Fourier transform, the displacement field is given to further understand the deformation and oscillation of crack faces. Based on the crack-tip field, the maximum energy release rate criterion is presented to discuss about whether the crack can propagate through kinking out of the interface. Comparing with the model without local resonators, we find that crack kinking can be prohibited in the proposed artificial periodic structures. Finally, finite element simulation and experiment are performed to show the good agreement with the theoretical predictions.

Triply degenerate nodal line and tunable contracted-drumhead surface state in a tight-binding model

The study of topological semimetals has been extended to more general topological nodal systems such as metamaterials and artificial periodic structures. Among various nodal structures, triply degenerate nodal line (TDNL) is rare and, hence, has received little attention. In this work, we have proposed a simple tight-binding (TB) model, which hosts a topological non-trivial TDNL. This TDNL not only has the drumhead surface states (DSSs) as usual nodal line systems but also has surface states that form a contracted-drumhead shape. The shape and area of this contracted drumhead can be tuned by the hopping parameters of the model. This provides an effective way to modulate surface states and their density of states, which can be important in future applications of topological nodal systems.

Terahertz resonance frequency through ethylene glycol phononic multichannel sensing via 2D MoS2/PtSe2 structure

Artificial periodic structures drew a lot of attention because of their ability to be built with novel acoustic features. A novel nanostructured phononic superlattice (NPhS) based two-dimensional multilayer structure as a high-sensitive multichannel liquid sensor that provided bright multichannel band gap windows has been introduced. Theoretically, the designed structure is composed of [(MoS2/PtSe2)4] NPhS with a cavity filled with different concentrations of Ethylene Glycol at room temperature toward acoustic bandgap engineering multichannel sensor. We examined the interaction of acoustic waves with nano and bulk phononic superlattice (PhS) structures. In addition, we studied the effect of using different analyte layer thicknesses on the resonance peaks that appeared inside the band gaps. Many sharp resonance peaks appeared in multi-band gaps, which introduced high sensitivity, Q-factor, and figure of merit (FOM) values for each concentration of Ethylene Glycol. Furthermore, the effect of resonance peaks' full width at half maximum (FWHM) on the Q-factor of the NPhS multichannel sensor has been studied. From our results, the relation between the sensitivity of our multichannel sensor and the resonance frequency of each concentration shows a linear behavior. The highest sensitivity was obtained for a 1.00 m% concentration of 0.21 (GHz/(kg/m3)) at a resonance frequency value of 0.21 THz. In addition, the NPhS multichannel sensor recorded the highest Q-factor for 0.8069 m% with a value of 1744 and the highest FOM for 0.3819 m% with a value of 0.05988 (m3/kg). Moreover, we studied the effect of temperature on the sensitivity of the NPhS multichannel sensor. We showed the highest sensitivity value of 1.79 (GHz/o C) at 10 °C towards Ethylene Glycol. Further, the dispersion relation of an acoustic wave propagating inside perfect and defected nano and bulk PhS structures has been introduced. Our proposed multichannel liquid sensor can introduce a novel sensitivity at Terahertz frequency ranges.

Periodic in-filled pipes embedded in semi-infinite space as seismic metamaterials for filtering ultra-low-frequency surface waves

The use of artificial periodic structures such as periodic wave barriers and seismic metamaterials has attracted attention as an effective approach to reduce the impact of ambient vibrations or earthquakes. In previous research, a large amount of steel was usually used in the design of seismic metamaterials to achieve ultra-low surface wave band gaps (BGs). However, the use of such large amounts of steel is inconvenient and expensive in practical engineering applications. To address this issue, this study considered the use of common building materials, namely, concrete, rubber, and soil, for the preparation of seismic metamaterials. Using these three materials, a one-dimensional (1D) seismic metamaterial composed of periodic in-filled pipes and a substrate was proposed. Ultra-low surface wave BGs (0–10 Hz) of the seismic metamaterial were identified using the sound cone method. Several important geometrical and material parameters that could influence the BGs were studied. Based on the 1D metamaterial, a 2D seismic metamaterial with a complete ultra-low BG was proposed to filter Rayleigh waves at any angle in the surface plane. The screening effectiveness of the 1D and 2D seismic metamaterials was evaluated using 2D and 3D numerical models, respectively. The results show that the ultra-low BG width decreases with an increase in the distance between two adjacent in-filled pipes. The small height of the in-filled pipe is beneficial for achieving a large ultra-low BG. A high elastic modulus and a low mass density of the soft filling material correspond to a large ultra-low BG width. The generation of ultra-low BGs in both 1D and 2D seismic metamaterials is attributed to the torsional resonance of the filling soft material. This study can serve as a reference for the design of new seismic metamaterials with practical value in engineering.

Interface State in One-dimensional Acoustic Resonator System with Inversion Symmetry Breaking

Topological sonic crystals are artificial periodic structures that support robust edge or interface state. Most previous studies on interface state in one-dimensional system heavily rely on Su-Schrieffer-Heeger (SSH) model, which modulates inter and intra hopping strength to yield a nontrivial topological phase. Whether it is possible to achieve interface states by connecting two trivial phases remains a question. To this point, in this paper, we propose a novel method of breaking the inversion symmetry of diatomic and elaborate the underlying mechanism using a spring-mass model. Instead of modulating spring stiffness corresponding to hopping strength which is intrinsically requested in the SSH model, we perturb the masses to break inversion symmetry while springs remain unchanged. Although breaking inversion symmetry in diatomic does not lead to a nontrivial phase, it is found that the interface state would still emerge within the chain formed by connecting two different configurations. Subsequently, this mechanism is applied to a one-dimensional acoustic resonator system connecting two different configurations to realize interface state. Simulation results reveal that acoustic wave has strongly localized at predicted interface frequency. Our study provides a novel approach of producing interface states in the one-dimensional acoustic system.

Metasurfaces with Bound States in the Continuum Enabled by Eliminating First Fourier Harmonic Component in Lattice Parameters.

Conventional photonic lattices, such as metamaterials and photonic crystals, exhibit various interesting physical properties that are attributed to periodic modulations in lattice parameters. In this study, we introduce novel types of photonic lattices, namely Fourier-component-engineered metasurfaces, that do not possess the first Fourier harmonic component in the lattice parameters. We demonstrate that these metasurfaces support the continuous high-Q bound states near second stop bands. The concept of engineering Fourier harmonic components in periodic modulations provides a new method to manipulate electromagnetic waves in artificial periodic structures.

Tunability and Fano Resonance Properties in Different Types of One-Dimensional Superconductor Photonic Crystals

The Fano resonance and EIR properties in different topological one-dimensional superconductor photonic crystals has been investigated theoretically using the Transfer Matrix Method (TMM). Different types of periodic heterostructures are studied and they are designed by alternating pairs of superconductor materials such (Nb/BSCCO), (Rb3C60/ YBa2Cu3O7) and (K3C60/(BiPb)2Sr2Ca2Cu3Oy). All artificial periodic structures are sacked by dielectric cap layer at different induced fields. To exam the efficiency of the reported structures, different parameters are used for analysis such as layers thicknesses, temperature, angle of incidence, the kind of superconductor materials and the dielectric constant of the cap layer. The investigation results exhibit the presence of tunable Fano resonances and EIR resonance peak accompanied by asymmetrical line shape and they are very sensitive to the dielectric cap layer, the superconductor materials and the wave incidence angle.

Acoustic energy transport characteristics based on amplitude and phase modulation using waveguide array

To realize the multi-functional manipulation of the acoustic field with a simple artificial structure, a waveguide array based on resonant units was proposed in this work. Based on the transmission spectrum and zero-like refractive index of the waveguide unit, the amplitude of the transmitted wave can be manipulated. By changing the size of the waveguide unit flexibly, the phase of the transmitted wave can be manipulated. In addition, by extending the waveguide array to the sub-wavelength scale, an acoustic metasurface with both amplitude and phase modulation functions can be implemented, which provides new ways for the design of lightweight artificial periodic structures.

4D printed zero Poisson's ratio metamaterial with switching function of mechanical and vibration isolation performance

The unusual properties of mechanical metamaterials are determined by the configuration of artificial periodic structures. However, the mechanical performance of conventional metamaterials is irreversible and cannot perceive and respond to the changes in the environment. In present study, a zero Poisson's ratio metamaterial with intelligent switching mechanical properties and vibration isolation effect is proposed. Based on a 4D printing method of shape memory polymer, this metamaterial is created that can sense temperature changes and switch mechanical properties. The macroscopic deformation and the morphology change of the metamaterial during compression tests are analyzed using experimental and finite element methods. The irregular buckling distortion of the metamaterial is eliminated by cylindrical design, and controllable and adjustable local deformation and stress-strain curve are achieved based on microstructure gradient design. Subsequently, this work focused on the vibration isolation performance of metamaterials, and found fascinating shock absorption performance. Compared with traditional linear spring, this metamaterial spring can effectively reduce the vibration amplitude of certain frequency bands before reaching the resonance peak, which provides a new realization method for low-frequency vibration isolation design.

Topology optimization of periodic barriers for surface waves

Dispersion engineering is always the important topic in the field of artificial periodic structures. In particular, topology optimization of composite structures with expected bandgaps plays a key role. However, most reported studies focused on topology optimization for bulk waves, and the optimization for surface wave bandgaps (SWBGs) is still missing. In this paper, we develop a topology optimization framework based on the genetic algorithm and finite element method to design periodic barriers embedded in semi-infinite space for reducing surface waves on demand. The objective functions for SWBGs are proposed based on the energy distribution properties of surface waves. The numerical results show that the optimization framework has stable convergence for this problem and is effective to optimize SWBGs. Considering large SWBGs and low filling fraction of solids, we investigate single- and multi-objective optimizations, respectively, and obtain novel wave barriers with good performance. The beneficial configuration features and mechanism of broadband SWBGs from the optimized results are explored. The results indicate that for the first-order SWBG, most optimized structures consist of a main scatterer at the center and some subsidiary scatterers near the surface. The rigid body resonance of the main scatterer determines the lower edge of SWBG, and the subsidiary scatterers can regulate the upper edge. Higher-order SWBGs are generated from the interaction of multiple scatterers, whose relative distance has a great influence on the position of SWBGs. The optimized structures can make the surface waves propagate far away from the surface within the frequencies of bandgaps, leading to a strong attenuation of surface vibration. In practice, our topological optimization framework is promising in designing high-performance surface wave devices and novel isolating structures for earthquake or environmental vibration in civil engineering.

Compact Hexagonal Ultra Wide Band Fractal Antenna for Wireless Body Area Networks

A Hexagonal Microstrip Ultra Wide Band Fractal Antenna for wireless body area network applications is proposed. The Hexagonal antenna is powered through co-planar waveguide (CPW) feed structure. The proposed antenna uses a hexagonal fractal structures to achieve its Ultra Wide Band characterization. The addition of fractal elements introduces multi-resonance at different frequencies and covers a large bandwidth of 3.8GHz–10.1GHz respectively. This antenna creates a Fractal geometry inside the patch with similar in shape but difference in sizes. Electromagnetic Band Gap structures are introduced in order to improve gain and directivity of the antenna. Electromagnetic Bandgap Structure (EBG) is mainly focused on overcoming the limitation of Microstrip Patch antenna parameters such as low gain, excitation of surface waves. Electromagnetic Band Gap structures are defined as artificial periodic structures that exhibit unique electromagnetic features, such as frequency band gap for surface waves and in-phase reflection coefficient for incident plane waves, which makes them desirable for low-profile antenna designs. The Electromagnetic Band Gap structure is placed behind the antenna to suppress the propagation of surface wave and to improve gain, directivity and to reduce the side lobes of the radiation pattern. The effect of surface currents in the ground plane reduces the antennas operating bandwidth which is reduced by introducing defective ground structure. The size of the antenna is 25×25×1.588 . The proposed antenna has an average gain of 3.8dB. The radiation pattern obtained is unidirectional.

Nonreciprocal transmission for the SH wave in a nonlinear elastic wave metamaterial with imperfect interfaces

During the past decades, phononic crystals and elastic wave metamaterials as the artificial periodic structures have received considerable attention. Due to their distinguishing properties, these structures can be used for the wave energy manipulation, e.g., band gaps, elastic wave cloaking and topological state, etc. A well-known characteristic is the band gap which means that the elastic wave cannot propagate in some certain frequency regions. Based on this property, many engineering applications can be achieved, e.g., filtering and wave isolation, etc. The investigations mentioned above are mainly focused on the linear elastic problems which cannot present the nonlinear wave properties. However, the nonlinearity appearing in the materials and structures can bring new and interesting wave phenomena. One of the nonlinear characteristics is the generation of the higher order harmonics. It can be applied to the nonlinear nondestructive testing. Recently, increasing attention has been focused on the nonlinear wave motion, which can result in the nonlinear band gap and acoustic diode. The new concept named as the acoustic diode has been presented by the combination of the band gap and material nonlinearity, which permits the wave propagation in only one direction. It can be achieved when the fundamental wave sits in the stop band but the second harmonic belongs to the pass band. However, the acoustic wave has one direction displacement component and usually propagates in the air or liquid. Thus we wonder whether the nonreciprocal phenomenon of the elastic wave can be achieved in the solid materials. The problem will become more interesting and necessary because of the coupling displacements with the vector characteristic in solids. In our previous work, we have discussed the nonreciprocal transmission for the incident SH and in-plane elastic waves in a nonlinear elastic wave metamaterial. The interface in the consecutive layers is always assumed as perfect, which means that the displacement and stress components are continuous across the interface. But perfect interfaces may become imperfect in practice during the manufacture, which indicates that the interfacial property on the band gaps is obvious. Then the imperfect interface can offer a new opportunity to tune the nonreciprocal transmission of the elastic wave which depends on the band gap property. In this work, the nonreciprocal transmission for the SH wave in a layered nonlinear elastic wave metamaterial with the imperfect interfaces is investigated. The combination of the structural asymmetry and material nonlinearity breaks the inherent reciprocity of the classic wave system. The second harmonic can be generated by the interaction between the incident SH wave and material nonlinearity. Based on the Bloch’s law and stiffness matrix method, the band gaps and transmission coefficients of both the fundamental and second harmonic waves are obtained. The effects of the interfacial properties on the nonlinear phononic crystal and elastic wave metamaterial are discussed. We find that comparing with the perfect interface system, the central frequency of the nonreciprocal regions shifts towards the low frequency region by the effects of imperfect interfaces. This present work is expected to be helpful to design the practical devices with the tuning nonreciprocal transmission of the elastic wave.

Realization of Multi-Modulation Schemes for Wireless Communication by Time-Domain Digital Coding Metasurface

Metasurfaces are well-designed artificial periodic or quasiperiodic structures to achieve customized electromagnetic responses. Based on the time-domain digital coding metasurface (TDCM) with dynamic reflection or transmission characteristics, one can realize direct information modulation on the metasurface, which has been used in wireless communications. In comparison with the classical architectures of wireless communication systems, the TDCM has advantages for simple architecture, easy manufacture, and low cost. However, the wireless communication systems based on the TDCM are still limited by low conversion efficiency, spectrum pollution, and hard to implement high-order modulation schemes. To solve these limitations, we propose a new route to achieve multi-modulation schemes in wireless communications by regulating the reflection phases of the TDCM in a nonlinear way. By carefully designing the regulation voltages applied to the diodes on TDCM, arbitrary constellation diagrams are successfully synthesized. The novel systems can implement various modulation schemes such as quadrature phase shift keying (QPSK), 8PSK, and 16QAM with good communication quality, high stability, and free scheme switching. The presented method may find important applications in modern wireless communication technologies.

Highly Confined Surface Plasmon Polaritons from Graphene Quantum Cherenkov Effect

Highly confined surface plasmon polaritons (HC-SPPs) can significantly enhance light-matter interaction and dramatically shrink electronic or photonic systems, including x-ray sources. However, due to the short wavelength and low phase velocity of HC-SPPs, traditional approaches have a hard time exciting them. Here electron-beam excitation of hot carriers plus the quantum Cherenkov effect in graphene are predicted to yield monochromatic HC-SPPs at 1/300 of the vacuum wavelength, with the Fermi energy of graphene dynamically tuning the frequency. Thus one can realize a compact x-ray source without artificial periodic structures, pointing ultimately to tabletop x-ray systems.

Analysis of an Ultra-Low Frequency and Ultra-Broadband Phononic Crystals Silencer with Small Size

Existing research shows that acoustic BG in a certain frequency range can be realized by installing an expansion chamber on duct system, but the problems of broadband and size limitations at low frequencies remain to be researched. The study of acoustic and elastic wave propagation in artificial periodic structures has received increasing attention for many decades, and the presence of bandgap (BG) in phononic crystals (PCs), which inhibits elastic/acoustic wave propagation within the BG’ frequency range, supplies a new way to control noise and vibrations in duct system. Based on PC theory, a duct silencer backed with a gas–liquid expansion chamber is proposed to enhance the acoustic performance of low-frequency noise attenuation. The transfer matrix method (TMM) is used to investigate the acoustic BG properties. The influences on the BG properties of some key parameters are analyzed, and the band formation mechanism is revealed by the law of energy conservation. The results show that silencers with a small size can effectively attenuate ultra-low frequencies and ultra-broad bands.

Directional Transmission Characteristics of Acoustic Waves Based on Artificial Periodic Structures

Acoustic artificial periodic structures, also known as phononic crystal, have been widely used in special acoustic problems such as low-frequency vibration reduction and noise reduction due to their bandgap characteristics. Different from previous researches, which focus on the bandgap characteristics, we designed a locally resonant artificial periodic structure, which can not only use the bandgap characteristics to design a directional transmission channel of acoustic waves, but also use its bandpass characteristics to generate multidirectional transmission of acoustic waves. The vibration mechanism of two-dimensional, three-components phononic crystal lattice structures was given, and a variety of directional transmission models of acoustic waves were constructed based on the unit cell. The simulation results showed that acoustic directional transmission characteristics were produced by the locally periodic resonance structure, and the transmission direction depends on the design of the structure. By taking advantage of the superposition properties of acoustic waves, the incident acoustic wave in the horizontal direction can be converted into the outgoing acoustic wave in the vertical direction without changing the position of the model, and this capability greatly expands the application range of the artificial periodic structure. In addition, the transmission characteristics of the directional transmission effect have a strong correlation with the frequency; that is, limited by the wavelength, the acoustic pressure distribution mode at different frequencies will be different. At the resonant frequency of the structure, the transmission efficiency of the acoustic wave will be highest. Moreover, similar to the traditional artificial periodic structure, the acoustic model proposed in this paper also has bandgap characteristics. Using bandgap characteristics, we designed an acoustic directional transmission channel to achieve uniform directional transmission of acoustic waves. These results greatly enrich the application space of artificial acoustic structures and provide new ideas for acoustic communication, acoustic detection, and acoustic stealth.

Acoustic Focusing Imaging Characteristics Based on Double Negative Locally Resonant Phononic Crystal

To achieve high-efficiency and high-resolution acoustic focusing, we used artificial periodic acoustic structures composed of cell arrays to manipulate the acoustic transmission wave front, and used finite element software to simulate the acoustic field characteristics. We found that when focuses generated by arc-shaped acoustic excitation sources are incident on one side of the model, the energy will be localized within the structure to reduce its transmission loss, and then the high-resolution emission focus will be generated on the other side of the model. The magnitude of the acoustic pressure at the focus point will change with the frequency of the incident acoustic wave and will reach an extreme value at the resonant frequency. In addition, we explored the acoustic transmission characteristics of structures at different widths and found that it is only necessary to increase the width of the model by an integer multiple of half a wavelength to achieve low loss focusing effects at various distances. The acoustic phenomena studied in this paper may provide new methods for the application of photoacoustic signal detection, ultrasound medical imaging and ultrasonic nondestructive testing.

Modulating Band Gap Structure by Parametric Excitations

Artificial periodic structures are used to control spatial and spectral properties of acoustic or elastic waves. The ability to exploit band gap structure creatively develops a new route to achieve excellently manipulated wave properties. In this study, we introduce a paradigm for a type of real-time band gap modulation technique based on parametric excitations. The longitudinal wave of one-dimensional (1D) spring-mass systems that undergo transverse periodic vibrations is investigated, in which the high-frequency vibration modes are considered as parametric excitation to provide pseudo-stiffness to the longitudinal elastic wave in the propagating direction. Both analytical and numerical methods are used to elucidate the versatility and efficiency of the proposed real-time dynamic modulating technique.