Directional Band Gap Research Articles

Vibration characteristics of innovative reentrant-chiral elastic metamaterials

In this work, an innovative two-dimensional (2D) hybrid auxetic elastic metamaterial (MODEL I) with reentrant triangular and chiral structures is proposed to open the broaden bandgap for vibration attenuation. Furthermore, the hybrid reentrant-chiral lattice with embedded resonators (MODEL II) shows multiple bandgaps at ultra-low frequency. Based on theoretical lumped mass-in-mass method and finite element method, the bandgap and longitudinal elastic wave attenuation are characterized. There is no complete bandgap in classical reentrant triangular lattice (MODEL 0), while the complete bandgaps width for MODEL I and II account for one forth of the concerned frequency range (0–4500 Hz). What more, the lower boundary of the first bandgap for MODEL II is 56% lower than that of MODEL I. The bandgap formation mechanisms are investigated by analyzing the mode shapes on the dispersion curves, and the frequency-dependent energy flow are studied through the iso-frequency contours, phase and group velocities. Finally, the longitudinal elastic wave attenuation of finite-size lattice of MODEL II illustrates ultra-wide vibration attenuation frequency range in the directional bandgaps. This research provides important clues and theoretical guidance for the design of vibration isolators, beam, plates and other renewed devices.

A hexagonal boron nitride super self-collimator for optical asymmetric transmission in the visible region

The two-dimensional (2D) hexagonal boron nitride (hBN) has been considered as a promising platform for quantum computing and information processing, due to the possibility in the generation of optically stable, ultra-bright quantum emitters in the visible region. In the meantime, integrable optical asymmetric transmission devices are necessary for functional quantum computing chips. In this study, we theoretically demonstrate an optical asymmetric transmission device working in the visible region based on a monolith 2D hBN super self-collimator. To maximize the self-collimation effect on improving the efficiency of the forward transmission, we not only design the photonic crystal structure with strong self-collimation characteristic, but also engineer the shape of the device. It is shown that by combining the two factors, the super self-collimation effect allows achieving a forward transmittance of up to 0.77. In the meantime, the structure effectively suppresses the backward transmission (down to 0.05) based on the directional bandgap, which results in a contrast ratio of up to 0.95 in the visible wavelength range of 590 nm–632 nm. More importantly, it is shown that by using the super self-collimation effect, the propagation efficiency inside the structure can be as high as 0.99 with minimum loss. Our results open up new possibilities in designing new nanophotonic devices based on 2D hBN for quantum computing and information processing.

High efficiency unidirectional optical transmission diode at 1550 nm based on H-PDLC Bragg grating-PC structure

In this paper, a method has been proposed for high efficiency unidirectional optical transmission diode at 1550 nm. We use a new composite structure, holographic polymer dispersed liquid crystal (H-PDLC) grating-photonic crystal (PC), to realize it. There exists the directional band gap for the PC structure in 1550 nm. Therefore, it is possible to use the H-PDLC Bragg grating to shift the incident angle to a particular value to satisfy the condition so that the PC energy band can be moved from the pseudo-band gap to the passband to achieve the purpose of unidirectional transmission optical diode with high-efficiency. So that when the 1550 nm beam diffracted from the H-PDLC grating to incident the PC structure, it will transmit the composite structure almost totally, but it will be completely none reflected from PC surface. The simulation results show that the forward transmittance is 94.1% and the backward transmittance is near 0. At the same time, H-PDLC grating provide a method to adjust the transmittance of the composite structure diode with its electrically-controlled characteristics. This composite structure design provides another efficient method for the realization of all-optical diodes in the field of optical communication.

Realization of full and directional band gap design by non-gradient topology optimization in acoustic metamaterials

Full and directional band gap acoustic metamaterials offer the promising ability of controlling and prohibiting propagation of acoustic/elastic waves in specified frequency ranges or directions. However, there is no guarantee that the optimization problem will be solved successfully with the existing gradient-based topology optimization methods because of the complexity of the problem and strong dependence on initial guesses. In this study, we developed a systematic topological optimization method based on material-field series expansion (MFSE) framework for full and directional band gap acoustic metamaterials design. Herein, the number of involved design variables of the MFSE method is greatly reduced to no more than 50, and an optimal band gap design of acoustic metamaterials is therefore able to be obtained with non-gradient optimization algorithms. Then, the Kriging-based optimization algorithm with a self-adaptive strategy is adopted for solving the optimization problem. The optimized designs finally converge to the orderly material distribution and numerical validations show improved full and directional propagation properties as expected. The realization of two-dimension acoustic metamaterials demonstrates that the proposed method can generate meaningful optimized topologies of PnCs for the full frequency band and directional propagation with a broad frequency range.

Nonlinear wave propagation and dynamic reconfiguration in two-dimensional lattices with bistable elements

This paper examines the propagation of elastic waves of large amplitudes in two-dimensional square lattices that include an alternating pattern of linear springs and nonlinear bistable springs. Because of the presence of bistable springs, these lattices have multiple stable configurations. In this paper, a theoretical model that takes into account the non-linearity of the bistable springs while neglecting geometric nonlinearities is used to study non-linear wave propagation in these lattices. Results from numerical simulations demonstrate that, for a lattice that is initially in a deformed stable equilibrium configuration, stimuli of large amplitudes are able to cause a reconfiguration of the lattice to a configuration of lower potential energy. Even for initial stable configurations that exhibit omnidirectional or directional bandgaps for infinitesimal wave propagation, waves of large amplitudes can propagate in the lattice due to its reconfiguration; however, due to the nonlinearity of bistable springs, the transmitted response tends to have multiple spectral peaks or be broadband for narrow-band stimuli of large amplitude. Simulations are used to study how the reconfiguration of the lattice depends on the amplitude and duration of the stimulus, on damping, and on the energy barrier between the two stable equilibria of the bistable springs. These numerical results suggest that these multistable lattices can serve as reconfigurable wave guides for which the amplitude of the stimulus offers opportunities for enhanced tunability.

Microparticle concentration and separation inside a droplet using phononic-crystal scattered standing surface acoustic waves

Rapid particle and biocell concentration and separation are important for the development of miniaturized physical, biological, and chemical systems. In this study, the scattering of standing surface acoustic waves (SSAWs) in an acoustofluidic phononic crystal (PnC) device is used to actuate spatial concentration and separation of suspended microparticles with two different sizes in a sessile droplet. The simulation design of the device and manipulation mechanisms of the two distinct particles are presented and discussed. A surface acoustic wave (SAW) acoustofluidic device with a nickel pillar-type PnC electroplated on a piezoelectric substrate, 128°YX LiNbO3, is designed and fabricated. A 30-MHz SSAW field is scattered within the directional phononic bandgap of the PnC to generate simultaneously acoustic radiation force and acoustic streaming flow to concentrate and separate 2- and 20-μm polystyrene microparticles. Experiments are conducted to verify the device functions on concentrating and separating microparticles. The results also suggest the possibilities of regarding phononic crystals as an effective element to tailor the SAW field for building other innovative acoustofluidic devices to achieve novel concentration, separation, and acoustic manipulation of biocells and biomolecules in discrete microfluidic systems.

Periodic plates with tunneled Acoustic-Black-Holes for directional band gap generation

Abstract Research in Acoustic Black Holes (ABHs) attracts increasing interests for its potential applications in vibration control. ABH effect features the energy focalization of flexural waves within a confined area inside a structure with a reducing power-law profiled thickness. With conventional design of ABH structures, however, systematic broadband ABH effects can only be achieved at relatively high frequencies while the mid-to-low frequency application can hardly be envisaged without prohibitively large ABH dimensions. We propose a kind of periodic plates carved inside with tunneled ABHs to achieve directional broad band gaps for flexural waves at mid-to-low frequencies. Analyses on the band structures and mode shapes show the generation of the band gaps through locally resonant effects of the ABH cells. With additional strengthening studs connecting the two ABH branches, Bragg scattering is produced due to its large impedance mismatch with the residual thickness of ABH profile. With the two effects combined, wide band gaps are achieved over a large frequency range for flexural waves travelling along the direction perpendicular to the tunneled ABHs. Both numerical and experimental results show significant attenuation gaps in finite plates with only three ABH cells. The proposed periodic plates with 1D tunneled ABHs and strengthening studs point at potential applications in wave filtering and vibration isolation applications.

Elastic waves propagation in thin plate metamaterials and evidence of low frequency pseudo and local resonance bandgaps

A comprehensive numerical simulation study on elastic wave propagation for a novel engineered thin plate metamaterial structural system is presented. To enhance the accuracy of model, a mesh convergence study is validated. The wave dispersion spectra with bandgaps for three types of structures are presented. Based on local resonance phenomena, the low frequency pseudo and local resonance bandgaps are reported. Highlights are also included for the Bragg scattering induced directional bandgaps. The effects of material and geometric parameters on bandgaps are discussed. The finite element based frequency response study further validates the reported bandgaps. The conclusions provide a new perspective for designs and applications of thin plate metamaterials for subwavelength wave manipulation including seismic shielding of civil infrastructures.

Asymmetric transmission of elastic shear vertical waves in solids

In this work, we propose an asymmetric transmission structure (ATS) for elastic shear vertical (SV) waves in solids, which has been relatively unexplored. The ATS is constituted by a metasurface and a phononic crystal (PC) possessing a directional band gap. While the metasurface aims to redirect the incident wave, the PC acts as a directional filter. The metasurface is composed of a stacked array of composite plates with two connecting parts made of different materials. To examine the performance of the designed ATS, full numerical simulations have been conducted. The numerical results indicate that the proposed ATS offered a relatively broad working frequency band and had a one order of magnitude difference in terms of transmission between the positive and negative incidences. Our study provides an alternative method to control elastic SV waves and could benefit applications in various fields, such as Micro-Electro-Mechanical System (MEMS), in which thin plates are frequently used components.

Flexural wave band gaps and vibration attenuation characteristics in periodic bi-directionally orthogonal stiffened plates

Vibrations in ship and offshore structures owing to various ocean environmental loads and excitations of power systems become increasingly serious. In this paper, the flexural wave propagation and vibration attenuation characteristics in periodic bi-directionally orthogonal stiffened plates are investigated. The dispersion relations and the displacement fields of the eigenmodes of infinite periodic bi-directionally orthogonal stiffened plates are calculated by using the finite element method in combination with Bloch periodic boundary conditions. Numerical results show that periodic bi-directionally orthogonal stiffened plates can yield complete and directional flexural wave band gaps, in which the propagation of flexural vibrational waves is prohibited and flexural vibration suppression is dramatically achieved. With the introduction of bi-directionally orthogonal stiffeners, the flexural wave and vibration energy is confined in the four corners of the plate owing to the scattering effect of the bi-directionally orthogonal stiffeners. The transmission spectra for a finite periodic stiffened plate are numerically and experimentally achieved to verify the existence of the flexural wave band gaps and vibration suppression characteristics. Furthermore, the effects of geometrical parameters on the flexural wave vibration band gaps are carried out. The flexural wave band gaps and vibration attenuation properties can be artificially modulated by changing the geometrical parameters of periodic bi-directionally orthogonal stiffened plates.

Dynamic reconfiguration of two-dimensional lattices with bistable springs

This study focuses on wave propagation and reconfiguration in two-dimensional square mass-spring lattices that include bistable springs. Due to the presence of directional and/or omnidirectional bandgaps in stable deformed configurations in which some of the bistable springs are in a deformed equilibrium, these lattices have the ability to serve as reconfigurable wave filters and wave guides. In this work, we study non-linear wave propagation in response to stimulus of large amplitude. Mechanical stimuli of large amplitudes have the capability of causing a dynamic reconfiguration of the lattice to a configuration of lower potential energy, which dramatically affect wave propagation. Using numerical simulations, the influence of the stimulus amplitude, duration, and location of the applied stimulus on the reconfiguration is analyzed. The ability to alter in a predictable manner wave propagation in these lattices offers new opportunities for tunable phononic crystals.

Two-dimensional silicon annular photonic crystals for realizing polarization-independent unidirectional transmission

Optical diode is a device that can realize unidirectional transmission of light. Its function is similar to that of an electronic diode. It has important applications in the field of optoelectronic integration and all-optical communications. Unidirectional wave transmission requires either time-reversal or spatial inversion symmetry breaking. The magneto-optical effect and optical nonlinearity are usually utilized to break the time-reversal symmetry and obtain the unidirectional transmission. However, these schemes all need high light intensity or magnetic field strength to be realized, and limit the usage. Therefore, spatial inversion symmetry breaking is highly desirable because of totally linear materials under low intensities. Quit a lot of researchers have designed optical diodes based on the photonic crystals and achieved unidirectional transmission for TE-like or TM-like light. The early design realized light unidirectional transmission by PC structures for only one polarization state (TE-like or TM-like incident light). It limits the application for the high integration and reconfigurable optical interconnection. The structure which can achieve unidirectional transmission for both TE and TM polarizations needs to be designed. The annular PCs have been verified to realize polarization-independent phenomena, such as beam splitting, self collimation and waveguide. In this paper, an annular PC is proposed. The plane wave expansion method is used to calculate band structures. The results show that it exhibits a significant directional band gap for both TE and TM mode. Then, the triangular annular PC is constructed, and its transmission spectra and field distributions are calculated by the finite-different time-domain method. It is found that the structure can realize the polarization-independent unidirectional transmission, but the forward transmissivity is too low (about 20%). Moreover, another smaller size annular PC is further introduced to form annular PC heterojunction, which effectively improves the polarization-independent unidirectional transmission performance and the forward transmissivity has doubled. Through the adjustment of the interface structure, the forward transmissivity is further increased. The optimized annular PC heterostructure can realize polarization-independent unidirectional transmission, and the forward transmissivity reaches 44%. The heterostructure can be used to fabricate polarization-independent optical diode, and may have potential applications in complex all-optical integrated circuits.

Observation of Nonreciprocal Wave Propagation in a Dynamic Phononic Lattice.

Acoustic waves in a linear time-invariant medium are generally reciprocal; however, reciprocity can break down in a time-variant system. In this Letter, we report on an experimental demonstration of nonreciprocity in a dynamic one-dimensional phononic crystal, where the local elastic properties are dependent on time. The system consists of an array of repelling magnets, and the on-site elastic potentials of the constitutive elements are modulated by an array of electromagnets. The modulation in time breaks time-reversal symmetry and opens a directional band gap in the dispersion relation. As shown by experimental and numerical results, nonreciprocal mechanical systems like the one presented here offer opportunities to create phononic diodes that can serve for rectification applications.

Robust edge states of planar phononic crystals beyond high-symmetry points of Brillouin zones

Robust edge states of the phononic crystals (PnCs) with the Dirac points fixed at corners or centers of the Brillouin zones (BZs) have received wide attentions. Here, we show that the Dirac points can degenerate at the high symmetrical boundaries of the first irreducible BZs. The mechanism of such Dirac dispersion is systematically discussed in the square lattice, the rectangular lattice, the centered rectangular lattice and the triangular lattice. These degenerated points, characterized by the vortex structure in a momentum space, are attributed to the band crossing in the presence of the crystalline mirror reflection symmetries. Variations of the geometric parameters can shift the positions of these Dirac points, but not lift them. By breaking the mirror reflection symmetries, the corresponding Dirac points will be lifted, yielding the directional or complete bandgaps. The phononic bandgaps efficiently block the propagation of the acoustic waves inside the bulks of the phononic systems, while their edge states localized at the domain walls between the PnCs with the distinct topological phases ensure the robust propagation of the sound energy flows. These results are unambiguously verified and determined by the experimental tests on the PnCs with the crystalline planar group P3m1.

Polarization-independent one-way transmission of silicon annular photonic crystal heterojunctions

To realize the one-way transmission is a key point in optical integration. As a step to this goal, heterojunctions composed of two 2D square-lattice silicon annular photonic crystals are constructed and expected to realize polarization-independent optical diodes. Band structures are calculated by the plane wave expansion method, and the transmission characteristics are analyzed using the finite-different time-domain method. The directional bandgap difference causes the one-way transmission behavior, and an overlapping one-way transmission frequency range for TE and TM modes is observed. Moreover, the transmission spectra, contrast ratio and field distributions for two polarizations demonstrate polarization-independent one-way transmission. The transmission performance is further enhanced and the equal forward transmittance for two polarizations reaches 45%.

Flexural wave band gaps in metamaterial plates: A numerical and experimental study from infinite to finite models

The proposed numerical design approach investigates both infinite and finite models and includes an experimental validation of elastic wave absorption and vibration suppression for flexural wave band gaps in metamaterial plates. The resonant metamaterial is obtained using a 2-dimensional periodic array of resonators (mass-screws) mounted to a thin homogeneous plate. The sensitivity analysis of the band gap frequency range takes into account the uncertainties of all the design parameters of the metamaterial plate. The theoretical approach uses the finite element method (FEM) to compare the predicted band gaps, which are derived from infinite and finite models of the metamaterial. An automatic method is proposed to detect the frequency ranges of band gaps in the finite metamaterial based on the behavior of the corresponding bare plate. Directional plane wave excitation and point force excitation are applied to evaluate the efficiency of the detection method. The results of these analyses are compared with experimental measurements. The frequency ranges of experimental vibration attenuation are in good agreement with the theoretically predicted complete and directional band gaps.

Multistable two-dimensional spring-mass lattices with tunable band gaps and wave directionality

In this paper, we consider elastic wave propagation in two dimensional periodic lattices that include an alternating pattern of linear springs and nonlinear bistable springs. Because of the bistable springs, these lattices have multiple stable equilibrium configurations. An analytical model that takes into account both nonlinear geometrical effects and nonlinearity of the springs is developed for the total potential energy of the system. After finding the stable equilibrium configurations of the unit cell by minimizing its potential energy, the propagation of waves of small amplitude is analyzed in each of these stable configurations using Bloch theorem. Examination of the band diagrams demonstrates that, depending on the model parameters, directional or complete band gaps can be observed in some of the deformed configurations, particularly for deformed configurations that are close to a critical point. Furthermore, analysis of the iso-frequency contours of the dispersion surfaces and of polar plots of the phase and group velocities indicates that the low frequency wave directionality of the lattice is tunable. For some designs, switching from one configuration to another configuration makes it possible to dramatically alter the preferred direction of wave propagation. Simulations of the response of lattices of finite size confirm that these lattices can be used as reconfigurable phononic crystals with tunable directivity, both in the low frequency range and within the directional band gaps.

Actively tunable transverse waves in soft membrane-type acoustic metamaterials

Membrane-type metamaterials have shown a fantastic capacity for manipulating acoustic waves in the low frequency range. They have the advantages of simple geometry, light weight, and active tunability. In general, these membrane-type metamaterials contain a rigid frame support, leading to a fixed configuration. However, in some instances, flexible and reconfigurable devices may be desirable. A soft membrane-type acoustic metamaterial that is highly flexible and controllable is designed here. Different from the previously designed membrane-type metamaterials, the stiff supporting frame is removed and the stiff mass at the center of each unit cell is replaced by the soft mass, realized by bonding fine metallic particles in the central region. In contrast to the previous studies, the propagation of elastic transverse waves in such a soft metamaterial is investigated by employing the plane wave expansion method. Both the Bragg scattering bandgaps and locally resonant bandgaps are found to coexist in the soft metamaterial. The influences of structural parameters and finite biaxial pre-stretch on the dynamic behavior of this soft metamaterial are carefully examined. It is shown that whether or not the wave propagation characteristics are sensitive to the finite deformation does not depend on the property and pre-stretch of the membrane. In addition, a broadband complete bandgap and a pseudo-gap formed by the combination of two extremely adjacent directional bandgaps are observed in the low-frequency range, and both can be controlled by the finite pre-stretch.

Polarization-independent one-way transmission by silicon annular photonic crystal antireflection structures

A triangular annular PC, which is a half of square-lattice silicon annular PC divided along diagonal line, is constructed. Band structures of the annular PC are investigated through the plane wave expansion method, and the directional bandgap mismatch for both TE modes and TM modes is presented. The finite-different time-domain simulations are used to calculate the TE-like and TM-like light transmission spectra, contrast ratio and field distributions. Though the triangular annular PC displays polarization-independent one-way transmission characteristic, the forward transmissivity (20%) is too low. Antireflection coating layer is introduced to increase forward transmissivity. Polarization-independent one-way transmission performance is improved by two antireflection coating layers added on the hypotenuse of the triangular annular PC, and the forward transmissivity for two polarizations increases to 46%.

Multi-channel unidirectional transmission of phononic crystal heterojunctions

Two square steel columns are arranged in air to form two-dimensional square lattice phononic crystals (PNCs). Two PNCs can be combined into a non-orthogonal 45[Formula: see text] heterojunction when the difference in the directional band gaps of the two PNC types is utilized. The finite element method is used to calculate the acoustic band structure, the heterogeneous junction transmission characteristics, acoustic field distribution, and many others. Results show that a non-orthogonal PNC heterojunction can produce a multi-channel unidirectional transmission of acoustic waves. With the square scatterer rotated, the heterojunction can select a frequency band for unidirectional transmission performance. This capability is particularly useful for constructing acoustic diodes with wide-bands and high-efficiency unidirectional transmission characteristics.