Complete Band Gap Research Articles

Investigation on tailoring the width and central frequency of bandgaps of TPMS structures

AbstractTriply periodic minimal surfaces (TPMS) lattice structures present outstanding properties such as lightweight, high strength, energy absorption, and wave propagation control, which are extensively investigated in recent years. However, one of the main challenges when designing TPMS is the proper selection of cell type and volume ratio in order to obtain the desired properties for specific applications. To this aim, this work provides a comprehensive numerical study of bandgap’s formation in the sub-2 kHz frequency range for the seven major cell type TPMS structures, including Primitive, Gyroid, Neovius, IWP, Diamond, Fischer–Koch S, and FRD, for a comprehensive range of volume ratios. Results show that these seven TPMS structures present a complete bandgap between the 3rd and 4th dispersion curves. The width of the bandgap is strongly dependent of the TPMS lattice and the widest bandgaps are seen on the Neovius and Primitive-based lattice (reaching a maximum width of 0.458 kHz and 0.483 kHz, respectively) for volume ratios over 0.3. Below this volume ratio, the bandgap of the Primitive structure becomes negligible, and the Neovius and IWP structures are the best candidates among the 7 tested TPMS cases. The central frequency of the bandgaps is less sensitive to the lattice and are predominantly tailored by the volume ratio. With this study, we demonstrate that the proper selection of the periodic cell type and volume ratio can tailor the bandwidth of complete bandgaps from a tens of Hz up to 0.48 kHz, while the central frequency can be selected from 0.72 to 1.81 kHz according to the volume ratio. The goal of this study is to serve as a database for the Primitive, Gyroid, Neovius, IWP, Diamond, Fischer–Koch S, and FRD TPMS structures for metamaterial designers.

Disentangled Higher‐Orbital Bands and Chiral Symmetric Topology in Confined Mie Resonance Photonic Crystals

AbstractTopological phases based on tight‐binding models have been extensively studied in recent decades. By mimicking the linear combination of atomic orbitals in tight‐binding models based on the evanescent couplings between resonators in classical waves, numerous experimental demonstrations of topological phases have been successfully conducted. However, in dielectric photonic crystals, the Mie resonances' states decay too slowly as , leading to intrinsically different physics between tight‐binding models and dielectric photonic crystals. Here, a confined Mie resonance photonic crystal is proposed by embedding perfect electric conductors between dielectric rods, creating the chiral symmetric band structure which ideally matches tight‐binding models with nearest‐neighbour couplings. As a consequence, disentangled band structure spanned by higher atomic orbitals is observed. Moreover, the result provides an effective route to achieve a 3D photonic crystal with a complete photonic bandgap and third‐order topology. The implementation offers a versatile platform for studying exotic higher‐orbital bands and achieving tight‐binding‐like 3D topological photonic crystals.

Pushing the limits of complete omnidirectional bandgaps in 2D nonsymmorphic single-phase phononic crystals

We expand the limits of complete omnidirectional bandgaps (neither P- nor S-waves can propagate) for high symmetry two-dimensional phononic crystal (PnC) designs. We reveal an extremely large 124% complete omnidirectional bandgap and demonstrate the possibility of creating custom, mechanically robust PnCs with improved characteristics via simple geometric changes to known PnC designs. The findings are experimentally validated, proving that it is feasible to achieve extreme ultrasonic attenuation using the nonsymmorphic p4gm symmetry group design, for both P- and S-waves, which significantly outperforms symmorphic p4mm-group PnC designs. We shed light on the high attenuation properties of the p4gm PnC for S-waves (which is rarely explored experimentally), revealing differences between the mode types. Practical insight into the design of PnCs with improved acoustic properties for potential applications in the field of vibration isolation, most notably when S-wave elimination is vital, is discussed.

A surface-wave seismic metamaterial filled with auxetic foam

Auxetic materials with negative Poisson's ratio (PR) exhibit superior mechanical properties with regard to energy absorption, while their potential for surface wave shielding is only in its beginnings. To attenuate surface waves in ultra-low frequencies (the starting frequency close to 0 Hz), which is the main scope of concern in seismic protection, this paper presents a novel type of seismic metamaterial (SM) with square pillars embedded as vibrators that is filled by auxetic foam. The designed SM is comprised of three commonly used construction materials, i.e., soil, concrete and auxetic foam. Combining the dispersive analysis and sound cone method, an ultra-low-frequency bandgap from 0 to 16.42 Hz is opened via the tensile resonance of the auxetic foam and the inverse dispersion effect. Furthermore, the parametric analysis further shows that filling material with a low Poisson ratio and low mass density is more favorable to widening the first complete bandgap (FCB), which means that foam is the ideal filling material for SM. The transmission spectra of the corresponding finite samples coincide well with the bandgap calculations. And the dynamic response of a scaled-down setup with a characteristic size of 1/10 of the original metamaterial is experimentally tested to validate the effectiveness of our study. We expect that this study prompts the engineering application of auxetic materials and ordinary building materials in seismic wave shielding at deep sub-wavelength frequencies.

Insights into acoustic properties of seven selected triply periodic minimal surfaces-based structures: A numerical study

Poly(methyl methacrylate)-based triply periodic minimal surfaces (TPMS) structures promise great potential in phononic applications, but the complicated TPMS structure induces a design challenge for controlling their properties. Numerical acoustic simulations of seven major PMMA-based TPMS lattice structures are presented for low-frequency sound attenuation applications while varying their relative density. Except for the local resonances in primitive and Neovius-based lattice structures, the acoustic properties of other TPMS structures show a common Bragg bandgap with a central frequency of around 435 Hz and a bandwidth of around 286 Hz, which results from multiple scattering of periodic unit cells. In contrast, the acoustic bandgaps of primitive and Neovius-based lattices have much smaller and larger complete bandgaps, respectively, which are mainly attributed to the local resonances in their geometric cavities with different sizes. Thus, by taking the mechanism of generated bandgaps in the TPMS-based lattice structures into consideration, we can design suitable bandgaps for acoustic applications in the specific frequency range.

Lever-type inertial amplification plates for low-frequency vibration reduction

In this work, a lever-type inertial amplification (LIA) metastructure is proposed to enhance the vibration reduction capability of thin plates in the low-frequency range. The mechanism consists of a rigid lever hinged on the host plate at two separate locations and a small mass mounted at the end of the lever. Band-structures of the unit cell and vibration transmissibility of the finite LIA plate are computed by using the combination of analytical method and finite element method. Numerical results show that compared with the local resonant (LR) plates with the same added mass, the proposed LIA plates generate wider and deeper complete bandgaps at the same target frequency. The Bragg bandgaps occurring at higher frequencies are also broader compared with those of the LR plates due to a stronger impedance mismatch between the host plate and the attachments. Moreover, the vibration reduction performance of the LIA plate presents unique direction-dependent characteristics: maximum vibration attenuation is achieved when the LIA mechanisms are installed parallel to the wave propagation direction. To address the issue that single-level LIA takes up too much space to install, a multi-level LIA design is proposed. On one hand, the multi-level design makes the LIA mechanisms much more compact without hampering their vibration reduction performance; on the other hand, the combination of sub-levels greatly enhances the design flexibility of LIA mechanisms. Finally, experiments are performed to further confirm the vibration reduction performance of the proposed LIA plates.

Attenuation analysis of low-frequency surface waves in the ultra-low-frequency bandgap of embedded seismic metamaterials

Seismic metamaterials (SMs) have potential applications in the protection of buildings from earthquake hazards, while research on the attenuation of low-frequency seismic waves is still limited. In this paper, an embedded seismic metamaterial with an ultra-low-frequency bandgap is proposed as a research object to analyze the attenuation of low-frequency seismic surface waves. The band structure of the proposed SM has the absence of surface wave solutions and has an ultra-low-frequency complete bandgap with a range of 0–16.3 Hz. Subsequently, the vibration modes and strain energy distribution of the SMs lattice, especially at low frequencies, are analyzed. The results show that there are vibration modes with energy concentrated in the SM and near the surface in the range of 0–1.3 Hz. According to the amplitude reduction analysis, the surface wave has no attenuation in the range of 0–1.3 Hz, and the attenuation zone is 1.3–20 Hz. Two types of actual seismic records are used as input signals to validate the attenuation zone. This indicates that some of the low-frequency surface waves in the ultra-low frequency-bandgap could not be attenuated. It is necessary to analyze the low-frequency band with large strain energy in conjunction with vibration modes and amplitude reduction when designing SMs with the ultra-low-frequency bandgap. Moreover, the effects of parameters and gradient arrangement on proposed SM attenuated low-frequency surface waves are analyzed, where the soil Young’s modulus is the key factor affecting the SM attenuated low-frequency surface waves.

Analysis of the band gap characteristics of a new type of three-dimensional single phase phononic crystal

A novel three-dimensional single-phase phononic crystal is proposed. Compared with the traditional multi-component three-dimensional phononic crystal, the single-phase phononic crystal has a low broadband gap, a single structure material, and a stable and portable structure. COMSOL software was used to calculate the band structure, vibration mode and transmission characteristics of single cell. Change the material parameters and structural parameters of the structure to study the change of energy band. The results show that there are five complete band gaps in the frequency range of 0–2400 Hz, and the low frequency range forms a broadband gap with a relative bandwidth of more than 0.7. The low band gap is mainly caused by the coupled vibration of scatterers, while the high band gap is mainly affected by the matrix frame. The thicker the scatterer, the lower the overall band gap, the easier to form a low broadband gap; By changing the material parameters, the normalized frequency of the first complete band gap of the structure remains within 0.1. The range and width of the band gap can be controlled by adjusting the scatterer. The designed structure is suitable for low frequency vibration and noise reduction.

Edge and corner states in two-dimensional finite phononic crystals: Simulation and experimental study

We investigate the mechanical vibration transmission in two-dimensional infinite and finite phononic crystals (PCs). The infinite PC consists of a periodic structure formed by square plates connected to the center of each of their nearest neighbors through a tiny beam. Numerical simulations using finite elements show a wide full bandgap for frequencies between 27 kHz and 32 kHz, approximately. Acoustic resonant spectroscopy was used to measure the PC frequency spectra for the different vibrations, using a finite PC consisting of 8 by 8 cells, which was designed with the same configuration as the infinite one. Experimental results corroborate the existence of a full complete bandgap predicted by the numerical method. However, the width was significantly reduced due to the appearance of edge and corner states. The border states were obtained numerically using a supercell. The measured wave amplitudes and the simulated ones present a great similarity. Some states appear located at the corners of the finite PC demonstrating that zero-dimensional states can also appear in two-dimensional phononic crystals.

Design of a Functionally Graded Material Phonon Crystal Plate and Its Application in a Bridge

In order to alleviate the structural vibrations induced by traffic loads, in this paper, a phonon crystal plate with functionally graded materials is designed based on local resonance theory. The vibration damping performance of the phonon crystal plate is studied via finite element numerical simulation and the band gap is verified via vibration transmission response analysis. Finally, the engineering application mode is simulated to make it have practical engineering application value. The results show that the phonon crystal plate has two complete bandgaps within 0~150 Hz, the initial bandgap frequency is 0.00 Hz, the cut-off frequency is 128.32 Hz, and the internal ratio of 0~100 Hz is 94.13%, which can effectively reduce the structural vibration caused by traffic loads. Finally, stress analysis of the phonon crystal plate is carried out. The results show that phonon crystals of functionally graded materials can reduce stress concentration through adjusting the band gap. The phonon crystal plate designed in this paper can effectively suppress the structural vibration caused by traffic loads, provides a new method for the vibration reduction of traffic infrastructure, and can be applied to the vibration reduction of bridges and their auxiliary facilities.

Bandgap and wave attenuation optimization of tetra-chiral metamaterial using PSO algorithm

The development of vibration suppression systems with desired efficiency and low cost is one of the significant challenges in engineering. In this study, a parametric lattice model is considered to analyze the wave mitigation features in the metamaterial based on a tetra-chiral topology of the periodic cell equipped with internal resonators. Bloch wave theorem and finite element method are employed to explore the bandgap of the structure and its wave mitigation features. Since the unit cell geometry can be designed to open and shift bandgaps, particle swarm optimization algorithm is used to find the largest possible gap in the desired frequency range. The optimization method is programmed using MATLAB combined with an in-house finite element solver, considering the parameters' ranges to ensure geometric compatibility. In all studied cases, the optimized geometry leads to superior vibration suppression and larger complete bandgaps.

Programmed Self‐Assembly of Single Colloidal Gyroids for Chiral Photonic Crystals (Adv. Mater. 23/2023)

Colloidal Self Assembly In article number 2211197, Dwaipayan Chakrabarti and co-workers report on the self-assembly of enantiomorphic single colloidal gyroid crystals in silico from designer chiral patchy spheres. Each of these crystals is shown to support a complete photonic bandgap, whilst also exhibiting rich chiroptical properties. This computational study introduces single colloidal gyroids as attractive targets for chiral photonic crystals operating at optical frequencies. Image credit: Wesley Flavell.

Low Frequency Attenuation Characteristics of Two-Dimensional Hollow Scatterer Locally Resonant Phonon Crystals.

The finite element method (FEM) was applied to study the low frequency band gap characteristics of a designed phonon crystal plate formed by embedding a hollow lead cylinder coated with silicone rubber into four epoxy resin short connecting plates. The energy band structure, transmission loss and displacement field were analyzed. Compared to the band gap characteristics of three traditional phonon crystal plates, namely, the square connecting plate adhesive structure, embedded structure and fine short connecting plate adhesive structure, the phonon crystal plate of the short connecting plate structure with a wrapping layer was more likely to generate low frequency broadband. The vibration mode of the displacement vector field was observed, and the mechanism of band gap formation was explained based on the spring mass model. By discussing the effects of the width of the connecting plate, the inner and outer radii and height of the scatterer on the first complete band gap, it indicated that the narrower the width of the connecting plate, the smaller the thickness; the smaller the inner radius of the scatterer, the larger the outer radius; and the higher the height, the more conducive it is to the expansion of the band gap.

Waveguides induced by replacing defects in phononic crystal

Phononic crystal, the artificial material, has shown the ability to guide the waves. In this paper, we theoretically and experimentally realize interface transports by doping replacing defects in the acoustic valley insulators. Each cell of the valley insulators has a large resonator and a small resonator. The valley insulators exhibit a complete band gap. The bands are divided into two groups respectively below and above the gap. If the small resonators are replaced by the large resonators, the bands above the gap, will move down and submerge into the valley band gap. If the large resonators are replaced by the small resonator, the bands below the gap, will move up and submerge into the valley band gap. The eigenmodes of the evolving bands show that the acoustic pressure energy is concentrated on the interfaces formed by the replacing defects. The frequency-selective transports can be induced by the band evolution. The replacing defects can be doped everywhere in the bulk, forming various waveguides completely wrapped by the valley insulators. Our works reveal the mechanism of guiding waves by the replacing defects in the acoustic valley insulator. The replacing defects can be doped conveniently and can manipulate the waves flexibly.

DNA origami-designed 3D phononic crystals

Abstract Moulding the flow of phononic waves in three-dimensional (3D) space plays a critical role in controlling the sound and thermal properties of matter. To this end, 3D phononic crystals (PnCs) have been considered the gold standard because their complete phononic bandgap (PnBG) enables omnidirectional inhibition of phononic wave propagation. Nevertheless, achieving a complete PnBG in the high-frequency regime is still challenging, as attaining the correspondingly demanded mesoscale 3D crystals consisting of continuous frame networks with conventional fabrications is difficult. Here, we report that a DNA origami-designed-3D crystal can serve as a hypersonic 3D PnC exhibiting the widest complete PnBG. DNA origami crystallization can unprecedentedly provide 3D crystals such that continuous frame 3D crystals at the mesoscale are realizable. Furthermore, their lattice symmetry can be molecularly programmed to be at the highest level in a hierarchy of symmetry groups and numbers, which can facilitate the widening of the PnBG. More importantly, conformal silicification can render DNA origami-3D crystals rigid. Overall, we predict that the widest hypersonic PnBG can be achieved with DNA origami-designed 3D crystals with optimal lattice geometry and silica fraction; our work can provide a blueprint for the design and fabrication of mesoscale 3D PnCs with a champion PnBG.

Transverse Magnetic Mode Laser in Photonic Crystal Nanobeam Cavity

We experimentally demonstrate a transverse magnetic (TM) mode laser in a photonic crystal (PhC) slab structure at room temperature. This study proposes a PhC nanobeam (NB) cavity to support a high-quality-factor ($Q$-factor) TM mode. For a large and complete photonic band gap, the PhC NB structures consist of large air holes in a thick dielectric slab. The PhC NB cavity is optimized numerically for a high-$Q$-factor TM mode of over 1 000 000 by reducing the radii of the air holes quadratically from the center to the edge of the PhC NB. A single-TM-mode lasing action is observed in an In-Ga-As-P quantum well (QW)-embedded optimized PhC NB cavity structure at room temperature via optical pulse pumping, where the QW layer is lightly etched. We believe that the TM mode lasers in PhC NB cavities with a lightly etched QW can be good candidates for a surface plasmon excitation source or a highly sensitive optical sensor.

Deep Learning-based Inverse Design of the Complete Photonic Band Gap in Two-Dimensional Photonic Crystals

Background: With the continuous development of computer science, data-driven computing methods have shown their advantages in various fields. In the field of photonics, deep learning (DL) can be used to inversely design the structure of optical devices. Objective: The two-dimensional (2D) photonic crystal (PCs) with adjustable structural parameters and a large complete photonic band gap (CPBG) are inversely designed in terms of DL neural network (NN) tagged to obtain a specified width of CPBG. Methods: The new PCs structure is designed by combining multiple factors that produce a CPBG. Tandem networks are used to speed up the training of the NN and tackle the problem of nonuniqueness that arises in inverse design. Results: After various attempts and improvements, the ideal PCs structure was obtained. It is found that the connecting channel between the primitives in the PCs unit cell has a dominate effect on the CPBG. The use of a tandem network enables better convergence of the network. Finally, suitable NN can be obtained, which can realize the forward prediction of the CPBG and the inverse design of the structure. Conclusion: DL can realize forward prediction and inverse design of 2D PCs targeting the width of the CPBG, which broadens the application scope of DL in the field of PCs.

Topological band gaps and edge modes materialized by symmetric silicon-on-insulator photonic crystal slabs in the mid-IR range

We successfully fabricated silicon-on-insulator (SOI) photonic crystal (PhC) slabs in which electromagnetic topological band gaps and edge modes were materialized for symmetric transverse-electric-like modes. Because the structure of our specimens can be regarded as symmetric about the horizontal middle plane of the PhC slab, their symmetric and antisymmetric eigenmodes were rigorously separated, so we could achieve genuine photonic band gaps for the former. We fabricated those specimens by electron beam lithography of the top Si layer of SOI wafers and successive plasma-enhanced chemical vapor deposition of a ${\mathrm{SiO}}_{2}$ capping layer. We confirmed the complete common band gap of topologically trivial and nontrivial PhCs and the topological edge modes on the boundary between them by angle-resolved reflection spectroscopy in the mid-infrared range. This is an observation of the common band gap and edge modes that materialized in symmetric PhC slabs without a membrane structure, that is, without the etching of a sacrificial layer under the PhC to increase the refractive-index contrast and the width of the common band gap.

Achieving Complete Band Gaps of Water Waves with Shallow-Draft Cylinder Arrays

Conventionally, band gaps of water waves can be obtained with periodic arrays of bottom-mounted obstacles or vertical cylinders. However, such structures need to possess a large ratio of volume in water, and may not be easy to build and move in practical ocean engineering. Here, we theoretically propose and experimentally demonstrate that when the water surface is pierced by a fixed, rigid cylinder array, a complete band gap of water waves can be achieved, in which the propagation of water waves is forbidden in all the directions. Such a band gap can exist even when the cylinders have a draft much smaller than the water depth ($d\ensuremath{\ll}h$). Based on the complete band gap, a semicircular shape of the fixed-surface disk array is further constructed, which can block omnidirectional water waves generated by a point source.

Programmed Self-Assembly of Single Colloidal Gyroids for Chiral Photonic Crystals.

Gyroid structures are of extensive interest because they provide a rich platform for chiroptics as well as topological photonics. While the double-gyroid morphology as a bicontinuous structure is not uncommon in self-assembled soft materials, direct self-assembly of single-network gyroids has proven elusive. Here, an enantiomorphic pair of single-gyroid crystals comprising colloidal spheres is presented, and two distinct routes are demonstrated for programmed self-assembly of each single colloidal gyroid enantiomorph from rationally designed patchy spheres. The designer colloidal patchy spheres, which closely hew to their synthetic feasibility, are chiral, having either two staggered rectangular patches at opposite poles or four circular patches arranged in a well-defined geometry. The single colloidal gyroid, as well as its inverse structure, is shown to support a wide complete photonic bandgap in addition to exhibiting rich chiroptical properties, making them attractive chiral photonic crystals. The versatility of this single colloidal gyroid, the bottom-up routes devised here in silico, and the robustness of the design space for the chiral colloidal patchy spheres together make a strong case for single colloidal gyroids to supersede colloidal diamond, as a target for programmed self-assembly, in the quest for a photonic crystals operating at opticalfrequencies.