Complete Band Gap Research Articles

Complex band structure of two-dimensional thermal wave crystals

We investigate the complex band structure of temperature oscillations in a two-dimensional thermal wave crystal. We use the Cattaneo-Vernotte heat model to describe the thermal properties. We apply the plane wave method to calculate the complex band structure of a square lattice composed of an infinite array of square bars. We find that a complete band gap exists across the whole Brillouin zone, where temperature oscillations are forbidden. This has potential applications in thermal management, thermal cloaking, and other areas.

Bandgap characteristics of four component periodic pile barriers in passive vibration isolation

Based on the local resonance theory, the vibration isolation performance of four-component periodic pile barriers consisting of a matrix, an outer pipe, an inner pipe, and a pile core was investigated using the finite element method (FEM). This configuration is contrasted with traditional three-component periodic pile barriers, which are composed of a matrix, a pipe, and a pile core. The four-component systems demonstrate significantly broader bandgaps compared to three-component systems. To validate the efficiency of the FEM, model test on pile barriers were conducted, facilitating a comparison between the FEM and experimental observations of bandgap characteristics. Additionally, the effects of the outer pipe’s density, elastic modulus, and thickness on the complete bandgap characteristics were comprehensively studied within the four-component structure. It is found that the broadest vibration isolation band gaps occur under hexagonal arrangement pattern. In square and hexagonal lattice configurations, the density, elastic modulus, and thickness of the outer pipe pile’s pile have predominantly influenced the upper bound frequency (UBF). There has been a positive correlation between the elastic modulus and the UBF, while the density and thickness have shown inverse relationships. Moreover, there exists a elastic modulus threshold, marking a transition in the displacement mode of the UBF, from the outer irreducible Brillouin zone (M or X) to the inner zone (Γ). Once the threshold is exceeded, both the vibration displacement mode and the width of bandgap remain substantially unchanged. The results obtained in the present paper are very useful for the design and application of periodic pile barriers in ambient vibration reduction.

Composite metastructure with tunable ultra-wide low-frequency three-dimensional band gaps for vibration and noise control

Low-frequency vibration and noise control present enduring engineering challenges that garner extensive research attention. Despite numerous active and passive control solutions, achieving multiple ultra-wide attenuation regions remains elusive. Addressing vibration and noise control across a multidirectional broad low-frequency spectrum, three-dimensional metastructures have emerged as innovative solutions. This study introduces a novel three-dimensional composite metastructure featuring multiple ultra-wide three-dimensional complete band gaps. The research emphasizes the design strategy of elastic ligaments to achieve multiple ultra-wide attenuation regions spanning from 0.7 to 40 kHz. The band structures are elucidated through modal analysis and further substantiated by an analytical model based on a spring-mass chain with an additional resonator. The underlying physical mechanism for the formation of multiple ultra-wide band gaps is revealed through novel vibration modes from finite element analyses. Furthermore, we demonstrate that the distribution and the relative width of the ultra-wide band gaps can be tuned by modifying the geometric parameters of the metastructure. Utilizing additive manufacturing, prototypes are fabricated, and low-amplitude vibration tests are conducted to evaluate real-time vibration attenuation properties. Consistency is observed among theoretical, numerical, and experimental results. The proposed structure shows significant potential for high-performance meta-devices aimed at controlling noise and vibration across an extremely wide low-frequency spectrum.

Longitudinal wave propagation in a practical metamaterial lattice

A practical metamaterial lattice is constructed by integrating curved beams, four-link mechanisms, and cantilever beams with lumped masses. It can generate two complete low-frequency bandgaps due to the lateral local resonance, inertia mass, and the main chain. The effective mass density and stiffness are obtained using different effective models, which show negative within the bandgaps. The analysis of the energy distribution and the space wave attenuation reveals that the metamaterial can attenuate the elastic waves in an exponential form within the bandgaps along the lattice. The finite element model is established to show the dynamic behaviour of the elastic wave propagation in the frequency domain and transient domain. Both results show that waves can be efficiently blocked within the bandgaps, while outside the bandgaps, waves can propagate without any attenuation. Finally, the experimental model of practical metamaterial is constructed, and the test piece is excited by a force hammer. Experimental results verify that the practical metamaterial can efficiently suppress the vibration within the bandgap frequency and validate the accuracy of the theoretical prediction.

Local resonance metamaterial-based integrated design for suppressing longitudinal and transverse waves in fluid-conveying pipes

To solve the problem of low broadband multi-directional vibration control of fluid-conveying pipes, a novel metamaterial periodic structure with multi-directional wide bandgaps is proposed. First, an integrated design method is proposed for the longitudinal and transverse wave control of fluid-conveying pipes, and a novel periodic structure unit model is constructed for vibration reduction. Based on the bandgap vibration reduction mechanism of the acoustic metamaterial periodic structure, the material parameters, structural parameters, and the arrangement interval of the periodic structure unit are optimized. The finite element method (FEM) is used to predict the vibration transmission characteristics of the fluid-conveying pipe installed with the vibration reduction periodic structure. Then, the wave/spectrum element method (WSEM) and experimental test are used to verify the calculated results above. Lastly, the vibration attenuation characteristics of the structure under different conditions, such as rubber material parameters, mass ring material, and fluid-structure coupling effect, are analyzed. The results show that the structure can produce a complete bandgap of 46 Hz–75 Hz in the low-frequency band below 100 Hz, which can effectively suppress the low broadband vibration of the fluid-conveying pipe. In addition, a high damping rubber material is used in the design of the periodic structure unit, which realizes the effective suppression of each formant peak of the pipe, and improves the vibration reduction effect of the fluid-conveying pipe. Meanwhile, the structure has the effect of suppressing both bending vibration and longitudinal vibration, and effectively inhibits the transmission of transverse waves and longitudinal waves in the pipe. The research results provide a reference for the application of acoustic metamaterials in the multi-directional vibration control of fluid-conveying pipes.

3D printed photonic crystals with a complete bandgap in the visible range

3D printed photonic crystals with a complete bandgap in the visible range

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.

Printing of 3D photonic crystals in titania with complete bandgap across the visible spectrum.

A photonic bandgap is a range of wavelengths wherein light is forbidden from entering a photonic crystal, similar to the electronic bandgap in semiconductors. Fabricating photonic crystals with a complete photonic bandgap in the visible spectrum presents at least two important challenges: achieving a material refractive index > ~2 and a three-dimensional patterning resolution better than ~280 nm (lattice constant of 400 nm). Here we show an approach to overcome such limitations using additive manufacturing, thus realizing high-quality, high-refractive index photonic crystals with size-tunable bandgaps across the visible spectrum. We develop a titanium ion-doped resin (Ti-Nano) for high-resolution printing by two-photon polymerization lithography. After printing, the structures are heat-treated in air to induce lattice shrinkage and produce titania nanostructures. We attain three-dimensional photonic crystals with patterning resolution as high as 180 nm and refractive index of 2.4-2.6. Optical characterization reveals ~100% reflectance within the photonic crystal bandgap in the visible range. Finally, we show capabilities in defining local defects and demonstrate proof-of-principle applications in spectrally selective perfect reflectors and chiral light discriminators.

A new seismic metamaterial design with ultra-wide low-frequency wave suppression band utilizing negative Poisson's ratio material

In this paper, we present a new seismic metamaterial (SM) for the suppression of Lamb waves and surface waves utilizing the negative Poisson's ratio (NPR) foam. The periodic cell of the metamaterial is composed of a square cylinder made of steel in the center and NPR foam connecters at the corners. Utilizing the unique resonance properties of the NPR material, an ultra-low-frequency broadband wave suppression is achieved. First, the characteristics of bandgaps (BGs) of the proposed structure with different materials were analyzed using the finite element (FE) method. It shows that the application of the NPR foam can significantly broaden the BGs compared with the case using traditional rubber. The vibration modes were analyzed to investigate the mechanism of BG generation, and the results show that the broad BG is achieved via the unique local resonance mechanism of the NPR foam. Subsequently, the frequency-domain analysis was carried out to verify the shielding effect of the designed SM on Lamb waves, using a periodic structure consisting of 10 × 6 unit cells. It shows that the designed SM can effectively attenuate Lamb waves in the range of 3–44 Hz with attenuation up to −590 dB at 32 Hz. A parametric analysis shows that the NPR foam with small thickness, high modulus, low mass density, and low Poisson's ratio can broaden the first complete BG. In addition, the acoustic cone method was combined with the frequency-domain analysis to calculate the BGs of the proposed structure against the surface wave, using a periodic structure consisting of 20 unit cells. It shows that the surface wave can be significantly attenuated within the BG. Finally, real seismic excitations were applied for time-domain analyses, and the simulation results show that the proposed structure can effectively shield the low-frequency seismic surface waves in the range of 0.1–20 Hz. The design scheme proposed in this paper is simple in structure and easy to implement, and is believed to possess bright application potentials in seismic protection.

Data-driven inverse design of the perforated auxetic phononic crystals for elastic wave manipulation

Abstract In addition to the distinctive features of tunable Poisson’s ratio from positive to negative and low stress concentration, the perforated auxetic metamaterials by peanut-shaped cuts have exhibited excellent phononic crystal (PNC) behavior as well for elastic wave manipulation. Thus they have attracted much attention in vibration suppression for dynamic applications. However, traditional structural designs of the auxetic PNCs considerably depend on designers’ experience or inspiration to fulfill the desired multi-objective bandgap properties through extensive trial and error. Hence, developing a more efficient and robust inverse design method remains challenging to accelerate the creation of auxetic PNCs and improve their performance. To shorten this gap, a new machine learning (ML) framework consisting of double back propagation neural network (BPNN) modules is developed in this work to produce desired configurations of the auxetic PNCs matching the customized bandgap. The first inverse BPNN module is trained to establish a logical mapping from the bandgap properties to the structural parameters, and then the second forward BPNN module is introduced to give the new property prediction by using the design configurations generated from the former. The error between the new predictions and the desired target properties is minimized through a limited number of iterations to produce the final optimal objective configurations. The results indicate that the perforated auxetic metamaterials behave relatively wide complete bandgap and the present ML model is effective in designing them with specific bandgaps within or beyond the given dataset. The study provides a powerful tool for designing and optimizing the perforated auxetic metamaterials in dynamic environment.

Frequency-selective valley-edge transmission and channeling in phononic-crystal plates with dual topological modulations

In this numerical study, we propose dual-modulated topological pillared phononic crystal (PnC) plates and demonstrate their application in achieving frequency-selective waveguiding of Lamb-wave valley-edge states. We show that both the radius and the height of the pillars in the honeycomb unit cell can be varied, allowing a generalized parameter space to obtain the complete topological bandgaps and two groups of distinct valley Hall phases for designing topological waveguides operating in different frequency ranges. Accordingly, we construct different types of phase domain walls to support valley-edge states using the dual-modulated PnC plates with a lattice constant of 2000 μm and with topological bandgaps opened around the Dirac cone frequency of 426 kHz. The numerical results show that the valley-edge states emerge to cover different frequency ranges and exhibit robust backscattering immunity when propagating along zigzag paths with sharp corners. Furthermore, the transport path of the valley-edge states can be designed to be highly dependent on the operating frequency in different domain walls. Consequently, we design a straight waveguide and three multichannel waveguides to demonstrate frequency-dependent switchable transmission and selective channeling of valley-edge states, respectively. The results of this study pave the way for the development and optimization of topological acoustic circuits using the generalized parameter space approaches and are expected to find promising applications in frequency-controlled and signal-division devices.

Reconfigurable frequency demultiplexer using coupled-resonator elastic waveguides

Reconfigurable coupled-resonator elastic waveguides are formed using defects composed of threaded rods, fixed with nuts and attached to a perforated two-dimensional phononic crystal slab. The resonant frequency of the defect can be tuned continuously within a complete phononic bandgap by adjusting the length of the threaded rod. Straight waveguides are formed from a line of defects. Phononic circuits are created by coupling three parallel straight waveguides. Through precise manipulation of the length of the threaded rod assembly, frequency demultiplexing of Lamb waves is achieved. Numerical and experimental results are found to be in good agreement. This work is of significance for the practical design of phononic devices including reconfigurable circuits.

A low-frequency and broadband wave-insulating vibration isolator based on plate-shaped metastructures

A metamaterial vibration isolator, termed as wave-insulating isolator, is proposed, which preserves enough load-bearing capability and offers ultra-low and broad bandgaps for greatly enhanced wave insulation. It consists of plate-shaped metacells, whose symmetric and antisymmetric local resonant modes offer several low and broad mode bandgaps although the complete bandgap remains high and narrow. The bandgap mechanisms, vibration isolation properties, effects of key parameters, and robustness to complex conditions are clarified. As experimentally demonstrated, the wave-insulating isolator can improve the vibration insulation in the ranges of [50 Hz, 180 Hz] and [260 Hz, 400 Hz] by 15 dB and 25 dB, respectively, in contrast to the conventional isolator with the same first resonant frequency.

Complete photonic bandgap in a low-index two-dimensional quasicrystalline structure.

A bandgap in the continuum spectrum of photons in addition to its basic physical significance has strong potential for applications. Analogous to semiconductor crystals for electrons, periodic dielectric structures named photonic crystals were proposed to control photon flux propagation. In our search for low refractive index (RI) structures with a photonic bandgap, initial research efforts were focused on photonic crystal design, while aperiodic structures allow lower values of refractive index contrast to sustain a photonic bandgap. Here, we report on a two-dimensional quasicrystalline structure designed as a set of one-dimensional lattices merged into a single binary structure made of two materials with refractive index contrast 2|n1 - n2|/(n1 + n2) = 0.16 and even less in theory. We confirmed the theoretical prediction of bandgap exciting by measuring the radiation suppression of a dipole source placed in the center of the quasicrystalline structure. The full-wave numerical simulations and the experimental study appear to be in good agreement with the theoretical model.

Three-dimensional photonic crystal optical gas sensor for trace detection and ultrafast response of chemical warfare agent in atmospheric humidity

Chemical warfare agents (CWAs) are toxic that pose a threat to the environment and human health, even trace amounts of CWAs can be fatal. In view of this, there is an urgent need to develop gas sensors for trace detection and ultrafast response of CWAs. Herein, an optical gas sensor has been proposed based on metal−organic frameworks (MOFs) three−dimensional (3D) photonic crystal to detect trace CWAs’ simulant (dimethyl methylphosphonate, DMMP) in different atmospheric humidity (RH 20 %, RH 40 %, RH 60 %, RH 80 %). At relative humidity (RH) of 20 %, the sensor shows excellent selectivity of DMMP due to the specific interactions of van der Waals force between UiO−67 and phosphoryl oxygen (OP) group of DMMP (C3H9O3P), the ultrahigh sensitivity (42.7 ppb), ultrafast response (0.5 s) are profit from the ordered superstructure of 3D photonic crystal and its complete photonic bandgap. At higher humidity (RH 40%–80 %), the sensor shows excellent stability, long–term repeatability, and it still keeps ultrahigh sensitivity (12.1 ppb), ultrafast response (0.49 s) for DMMP at RH 80 %. Moreover, an optical gas sensor array has been prepared to solve the problem of cross−sensitive between DMMP and other CWAs at highest humidity (RH ≥ 80 %), the average classification accuracy can reach 98.6 %.

Design of tunable pneumatic metamaterials for low-frequency vibration control

For addressing the limitations of traditional elastic metamaterials in opening wide bandgaps below 100 Hz, a tunable pneumatic metamaterial plate with airbag local resonators is proposed. Utilizing the characteristics of airbags, such as small volume, large load-bearing capacity, easy stiffness adjustment, and the ability to provide multi-directional restoring forces, a structured low-stiffness local resonator with a certain load-bearing capacity is designed. By varying the gauge pressure of the airbag, the bandgap can be moved toward lower frequencies, thereby achieving a broad low-frequency vibration suppression capability for various wave propagations. The low-frequency vibration bandgap characteristics of the tunable pneumatic metamaterial are analyzed and verified by applying the finite element method. The results illustrate that this tunable pneumatic metamaterial can attenuate bending waves in the range of 22–121 Hz by adjusting the air pressure. Moreover, increasing the gauge pressure will not only shift the complete bandgap toward lower frequencies but also significantly expand the bandwidth of the complete bandgap. For instance, increasing the gauge pressure from 0 to 50 kPa reduces the opening frequency of the complete bandgap from 36 to 22 Hz while enhancing the relative bandwidth from 0.52 to 0.85. Extending from this, a parametric study was conducted to examine the impact of the structural parameters of airbag-type resonant units on bandgap evolution, summarizing the general principles for achieving wide low-frequency bandgaps. Finally, the bandgap characteristics of the tunable pneumatic metamaterial are confirmed through the frequency response function of a finite periodic structure.

Observation of photonic chiral edge states in penrose quasicrystals

Photonic chiral edge states with one-way propagation and robust topological protection are hallmark features of photonic Chern insulators. To date, photonic chiral edge states have been observed in two-dimensional (2D) periodic and amorphous gyromagnetic photonic crystals. Recent theoretical studies reveal that photonic chiral edge states can also exist in 2D Penrose quasicrystals with long-range order but lack translational symmetry. Here, we report the first experimental observation of photonic chiral edge states in a 2D Penrose-tiled gyromagnetic photonic quasicrystal. By using microwave measurements, we observe a complete photonic band gap in the Penrose photonic quasicrystal despite the absence of bulk Bloch bands in momentum space. Moreover, we directly observe unidirectional backscattering-immune photonic chiral edge states within the photonic bandgap of the 2D Penrose quasicrystal. These results broaden our understanding of photonic chiral edge states and provide a new platform for exploring the intriguing properties of topological photonic quasicrystals.

Diamond-lattice photonic crystals assembled from DNA origami.

Colloidal self-assembly allows rational design of structures on the micrometer and submicrometer scale. One architecture that can generate complete three-dimensional photonic bandgaps is the diamond cubic lattice, which has remained difficult to realize at length scales comparable with the wavelength of visible or ultraviolet light. In this work, we demonstrate three-dimensional photonic crystals self-assembled from DNA origami that act as precisely programmable patchy colloids. Our DNA-based nanoscale tetrapods crystallize into a rod-connected diamond cubic lattice with a periodicity of 170 nanometers. This structure serves as a scaffold for atomic-layer deposition of high-refractive index materials such as titanium dioxide, yielding a tunable photonic bandgap in the near-ultraviolet.

Dynamic bandgap responsiveness of modified re-entrant metamaterials in thermal-mechanical field

This paper introduces a nested sinusoidal re-entrant (NSR) metamaterial characterized by tunable complete bandgaps (CBGs) and dynamic responsiveness in thermal-mechanical dual fields. NSR comprises shape memory polymer and features a sinusoidal modification with nested re-entrant hexagonal and star-shape re-entrant structure. Dynamic response of NSR is studied using the representative volume element method, specifically focusing on the effective modulus and Poisson's ratio and CBGs under varying average strains. The findings indicate that both the mechanical properties and CBGs exhibit dynamic responses to mechanical field, demonstrating interrelation between mechanical adjustments and functional performance. Moreover, the study examines how temperature fluctuations influence the NSR's elastic modulus, thereby altering its CBGs. Hence, manipulating both compression and temperature variations presents a viable approach to control and adjust the CBGs of NSR effectively. These results are validated by computations of the frequency response function under various average strains. Overall, this design presents a promising approach for developing mechanical metamaterials with tunable functionality.

Elastoacoustic wave propagation in a biphasic mechanical metamateriala).

Humans are sensitive to air-borne sound as well as to mechanical vibrations propagating in solids in the frequency range below 20 kHz. Therefore, the development of multifunctional filters for both vibration reduction and sound insulation within the frequency range of human sensitivity is a research topic of primary interest. In this paper, a high-contrast biphasic mechanical metamaterial, composed of periodic elastic solid cells with air-filled voids, is presented. By opening intercellular air-communicating channels and introducing channel-bridging solid-solid couplings, the frequency dispersion spectrum of the metamaterial can be modified to achieve complete and large bandgaps for acoustic and elastic waves. From a methodological viewpoint, the eigenproblem governing the free wave propagation is solved using a hybrid analytical-computational technique, while the waveform classification is based on polarization factors expressing the fraction of kinetic and elastic energies stored in the solid and fluid phases. Based on these theoretical results, a mechanical metafilter consisting of an array of a finite number of metamaterial cells is conceived to provide a technical solution for engineering applications. The forced response of the metafilter is virtually tested in a computational framework to assess its performance in passively controlling the propagation of broadband sound and vibration signals within solid and fluid environments. Quantitative results synthesized by transmission coefficients demonstrate that the metafilter can remarkably reduce the transmitted response in the frequency band of human sensitivity.