Acoustic rainbow trapping by coiling up space

Coupled topological rainbow trapping of elastic waves in two-dimensional phononic crystals

Rainbow trapping, observed in elastic waves, has attracted considerable scientific interest owing to its potential applications in energy harvesting, buffering, and wavelength-division multiplexing devices. However, previous approaches have often necessitated complex geometric modifications to the scatterer, such as altering dimensions or shifting along diagonals to corners, limiting practical utility. Here, we realize the coupled topological edge states (CTESs) of elastic waves in a two-dimensional (2D) solid phononic crystal (PC) with inversion center changes. Changing the inversion center along the x or y directions by a specific distance can induce the topological phase transition. The topological edge states (TESs) arise at the interface by combining PCs with different topologies positioned adjacent to each other. Furthermore, it is demonstrated that TES exhibits topological robustness against defects. By introducing a gradient into the PC structure by altering the geometrical parameters of scatterers along the interface, the topological rainbow trapping of elastic waves is achieved. Finally, the CTES are generated by the interaction between TESs of different interfaces, which can lead to coupled topological rainbow trapping in phononic heterostructures with different displacement parameters along the multiple interface gradient. Our results pave the way for manipulating the symmetric and antisymmetric topological modes of elastic waves in topologically coupled waveguides, which offers potential applications in selective filtering and multiband waveguiding.

Experimental demonstration of rainbow trapping of elastic waves in two-dimensional axisymmetric phononic crystal platesa)

Structures with specific graded geometries or properties can cause spatial separation and local field enhancement of wave energy. This phenomenon is called rainbow trapping, which manifests itself as stopping the propagation of waves at different locations according to their frequencies. In acoustics, most research on rainbow trapping has focused on wave propagation in one dimension. This research examined the elastic wave trapping performance of a two-dimensional (2D) axisymmetric grooved phononic crystal plate structure. The performance of the proposed structure is validated using numerical simulations based on finite element analysis and experimental measurements using a laser Doppler vibrometer. It is found that rainbow trapping within the frequency range of 165-205 kHz is achieved, where elastic waves are trapped at different radial distances in the plate. The results demonstrate that the proposed design is capable of effectively capturing elastic waves across a broad frequency range of interest. This concept could be useful in applications such as filtering and energy harvesting by concentrating wave energy at different locations in the structure.

Design approach of perforated labyrinth-based acoustic metasurface for selective acoustic levitation manipulation

This paper proposes a metasurface design approach with perforated labyrinthine path coil structure to manipulate the acoustic transmission with inexpensive materials. The medium in the labyrinthine path coils in this design is air, but not limited to air. A systematic approach has been proposed for the unit cell design of acoustic metamaterials with adjustable resonance peak frequencies and bandgap width. The theory demonstrates that the length of pipe segments determines resonance peak frequencies and the cross-sectional area ratio adjusts the bandgap width. The proposed design approach uses an equivalent pipe circuit based analytical model to design the high transmission (high pass) and high reflection (low pass) unit cell. The simulation and experiment has been performed to evaluate the validity of the theory. Although there exists some assumptions in the theory, the theory still has enough accuracy to guide the metasurface design illustrated by the simulation and experiment results.

Engineering three-dimensional labyrinthine fractal acoustic metamaterials with low-frequency multi-band sound suppression

Acoustic metamaterials are a class of artificially periodic structures with extraordinary elastic properties that cannot be easily found in naturally occurring materials and can be applied to regulate the sound propagation behavior. The fractal configuration can be widely found in the acoustic system, like characterizing the broadband or multi-band sound propagation. This work will engineer three-dimensional (3D) labyrinthine fractal acoustic metamaterials (LFAMs) to regulate the sound propagation on subwavelength scales. The dispersion relations of LFAMs are systematically analyzed by the Bloch theory and the finite element method (FEM). The multi-bands, acoustic modes, and isotropic properties characterize their acoustic wave properties in the low-frequency regime. The effective bulk modulus and mass density of the LFAMs are numerically calculated to explain the low-frequency bandgap behaviors in specific frequencies. The transmissions and pressure field distributions of 3D LFAMs have been used to measure the ability for sound suppression. Furthermore, when considering the thermo-viscous loss on the transmission properties, the high absorptions occur within the multi-band range for low-frequency sound. Hence, this research contributes to potential applications on 3D LFAMs for multi-bands blocking and/or absorption on deep-subwavelength scales.

Cochlea-inspired design of an acoustic rainbow sensor with a smoothly varying frequency response

A number of physical arrangements for acoustic rainbow sensors have been suggested, where the aim is to separate different frequency components into different physical locations along the sensor. Although such spatial discrimination has been achieved with several designs of sensor, the resulting frequency responses at a given position along the sensor are generally not smoothly varying. In contrast, the cochlea provides an interesting natural example of a rainbow sensor, which has an exponential frequency distribution and whose response does vary smoothly with frequency. The design of a rainbow sensor is presented that has a number of discrete resonators and an exponential frequency distribution. We discuss the conditions for a smoothly varying frequency response in such a sensor, as part of a broader design strategy. It is shown that the damping within the resonators determines the trade-off between the frequency resolution and the number of elements required to achieve a smooth response. The connection is explained between this design and that of an effective acoustic absorber. The finite number of hair cells means that the cochlea itself can be thought of as being composed of discrete units and the conditions derived above are compared with those that are observed in the cochlea.

An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces

We consider a periodic array of resonators, formed from Euler-Bernoulli beams, attached to the surface of an elastic half-space. Earlier studies of such systems have concentrated on compressional resonators. In this paper, we consider the effect of the flexural motion of the resonators, adapting a recently established asymptotic methodology that leads to an explicit scalar hyperbolic equation governing the propagation of Rayleigh-like waves. Compared with classical approaches, the asymptotic model yields a significantly simpler dispersion relation, with closed-form solutions, shown to be accurate for surface wave-speeds close to that of the Rayleigh wave. Special attention is devoted to the effect of various junction conditions joining the beams to the elastic half-space which arise from considering flexural motion and are not present for the case of purely compressional resonators. Such effects are shown to provide significant and interesting features and, in particular, the choice of junction conditions dramatically changes the distribution and sizes of stop bands. Given that flexural vibrations in thin beams are excited more readily than compressional modes and the ability to model elastic surface waves using the scalar wave equation (i.e. waves on a membrane), the paper provides new pathways towards novel experimental set-ups for elastic metasurfaces.

Programmable Acoustic Metasurfaces

Metasurfaces open up unprecedented potential for wave engineering using subwavelength sheets. However, a severe limitation of current acoustic metasurfaces is their poor reconfigurability to achieve distinct functions on demand. Here a programmable acoustic metasurface that contains an array of tunable subwavelength unit cells to break the limitation and realize versatile two-dimensional wave manipulation functions is reported. Each unit cell of the metasurface is composed of a straight channel and five shunted Helmholtz resonators, whose effective mass can be tuned by a robust fluidic system. The phase and amplitude of acoustic waves transmitting through each unit cell can be modulated dynamically and continuously. Based on such mechanism, the metasurface is able to achieve versatile wave manipulation functions, by engineering the phase and amplitude of transmission waves in the subwavelength scale. Through acoustic field scanning experiments, multiple wave manipulation functions, including steering acoustic waves, engineering acoustic beams, and switching on/off acoustic energy flow by using one design of metasurface are visually demonstrated. This work extends the metasurface research and holds great potential for a wide range of applications including acoustic imaging, communication, levitation, and tweezers.

Compact Acoustic Rainbow Trapping in a Bioinspired Spiral Array of Graded Locally Resonant Metamaterials

Acoustic rainbow trappers, based on frequency selective structures with graded geometries and/or properties, can filter mechanical waves spectrally and spatially to reduce noise and interference in receivers. These structures are especially useful as passive, always-on sensors in applications such as structural health monitoring. For devices that face space and weight constraints, such as microelectromechanical systems (MEMS) transducers and artificial cochleae, the rainbow trapping structures must be compact as well. To address this requirement, we investigated the frequency selection properties of a space-saving design consisting of Helmholtz resonators arranged at sub-wavelength intervals along a cochlear-inspired spiral tube. The height of the Helmholtz resonators was varied gradually, which induced bandgap formation at different frequencies along the length of the spiral tube. Numerical simulations and experimental measurements of acoustic wave propagation through the structure showed that frequencies in the range of 1–10 kHz were transmitted to different extents along the spiral tube. These rainbow trapping results were achieved with a footprint that was up to 70 times smaller than the previous structures operating at similar bandwidths, and the channels are 2.5 times of the previous structures operating at similar bandwidths.

Experimental Evidence of Rainbow Trapping and Bloch Oscillations of Torsional Waves in Chirped Metallic Beams

The Bloch oscillations (BO) and the rainbow trapping (RT) are two apparently unrelated phenomena, the former arising in solid state physics and the latter in metamaterials. A Bloch oscillation, on the one hand, is a counter-intuitive effect in which electrons start to oscillate in a crystalline structure when a static electric field is applied. This effect has been observed not only in solid state physics but also in optical and acoustical structured systems since a static electric field can be mimicked by a chirped structure. The RT, on the other hand, is a phenomenon in which the speed of a wave packet is slowed down in a dielectric structure; different colors then arrive to different depths within the structure thus separating the colors also in time. Here we show experimentally the emergence of both phenomena studying the propagation of torsional waves in chirped metallic beams. Experiments are performed in three aluminum beams in which different structures were machined: one periodic and two chirped. For the smaller value of the chirping parameter the wave packets, with different central frequencies, are back-scattered at different positions inside the corrugated beam; the packets with higher central frequencies being the ones with larger penetration depths. This behavior represents the mechanical analogue of the rainbow trapping effect. This phenomenon is the precursor of the mechanical Bloch oscillations, which are here demonstrated for a larger value of the chirping parameter. It is observed that the oscillatory behavior observed at small values of the chirp parameter is rectified according to the penetration length of the wave packet.

Coupled Resonators for Sound Trapping and Absorption

The leakage of sound waves in a resonance based rainbow trapping device prevents the sound wave being trapped in a specific location. In this study, we report a design of sound trapping device based on coupled Helmholtz resonators, loaded to an air waveguide, which can effectively tackle the wave leakage issue. We show that coupled resonators structure can generate dips in the transmission spectrum by an analytical model derived from Newton's second law and numerical analysis based on finite-element method. An effective medium theory is derived, which shows that coupled resonators cause a negative effective bulk modulus near the resonance frequency and induce flat bands that give rise to the confinement of the incoming wave inside the resonators. We compute the transmission spectra and band diagram from the effective medium theory, which are consistent with the simulation results. Trapping and high absorption of sound wave energy are demonstrated with our designed device.

Acoustic Analogues of High-Index Optical Waveguide Devices

High index optical waveguide devices such as slab waveguides, strip waveguides and fibers play extremely important roles in a wide range of modern applications including telecommunications, sensing, lasing, interferometry, and resonant amplification. Yet, transposing these advantageous applications from optics to acoustics remains a fundamental practical challenge, since most materials exhibit refractive indices lower than that of air for sound waves. Here, we demonstrate the relevance of acoustic metamaterials for tackling this pivotal problem. More specifically, we consider a metamaterial built from subwavelength air-filled acoustic pipes engineered to effectively exhibit a higher refractive index than homogenous air. We show that such medium can be employed to realize acoustic equivalents of dielectric slab or strip waveguides, and optical fibers. Unlike conventional acoustic pipes, our guiding approach allows the waveguide to remain open to the external medium, which opens an abundance of new opportunities in noise management, medical imaging, underwater communication systems, and sensing.

Design of an underwater acoustic bend by pentamode metafluid

In this paper, an impedance matching underwater acoustic bend with pentamode microstructure is designed. The proposed bend is assembled by pentamode lattice. The effective density and compressive modulus of each unit cell can be tuned simultaneously, which are modulated to guarantee both the bending effect and high transmission. The standard deviations (SDs) of transmitted phase are calculated to quantitatively evaluate the degree of the distortion of the transmitted wavefront, while the transmission is calculated to appraise the degree of acoustic impedance matching. The low SDs and high transmission indicate that the designed bend has a nice broadband bending effect and is impedance-matched to water. This design has potential applications in underwater communication and underwater detection.

Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems

Perfect, broadband and asymmetric sound absorption is theoretically, numerically and experimentally reported by using subwavelength thickness panels in a transmission problem. The panels are composed of a periodic array of varying crosssection waveguides, each of them being loaded by Helmholtz resonators (HRs) with graded dimensions. The low cut-off frequency of the absorption band is fixed by the resonance frequency of the deepest HR, that reduces drastically the transmission. The preceding HR is designed with a slightly higher resonance frequency with a geometry that allows the impedance matching to the surrounding medium. Therefore, reflection vanishes and the structure is critically coupled. This results in perfect sound absorption at a single frequency. We report perfect absorption at 300 Hz for a structure whose thickness is 40 times smaller than the wavelength. Moreover, this process is repeated by adding HRs to the waveguide, each of them with a higher resonance frequency than the preceding one. Using this frequency cascade effect, we report quasi-perfect sound absorption over almost two frequency octaves ranging from 300 to 1000 Hz for a panel composed of 9 resonators with a total thickness of 11 cm, i.e., 10 times smaller than the wavelength at 300 Hz.

Magnetic-control multifunctional acoustic metasurface for reflected wave manipulation at deep subwavelength scale

Acoustic metasurfaces, exhibiting superior performance with subwavelength thickness, are ideal alternatives for functionalities such as wavefront modulation and acoustic energy trapping, etc. However, most of the reported acoustic metasurfaces were passive. Here a magnetically tuned mechanism is reported for membrane-type acoustic metamaterials. Harnessing the geometric nonlinearity of membrane structures, the transmission spectrum is both theoretically and experimentally tuned over broadband by an external static magnetic force. Simultaneously, the phase profiles can be readily tailored by the magnetic stimulus. Further, a magnetic-control multifunctional metasurface is proposed for low-frequency wave manipulation. By switching the magnetic force distribution, multi extraordinary phenomena, such as acoustic wave redirecting, focusing, bending, etc., are realized without changing the physical structure. Besides, it is demonstrated the proposed metasurface, at deep subwavelength scale (~1/85λ), supports anomalous reflected wave manipulation over a wide band. These results open up new degrees of freedom to steer acoustic wave and pave a way for designing active acoustic devices.

Rainbow trapping of ultrasonic guided waves in chirped phononic crystal plates

The rainbow trapping effect has been demonstrated in electromagnetic and acoustic waves. In this study, rainbow trapping of ultrasonic guided waves is achieved in chirped phononic crystal plates that spatially modulate the dispersion, group velocity, and stopband. The rainbow trapping is related to the progressively slowing group velocity, and the extremely low group velocity near the lower boundary of a stopband that gradually varies in chirped phononic crystal plates. As guided waves propagate along the phononic crystal plate, waves gradually slow down and finally stop forward propagating. The energy of guided waves is concentrated at the low velocity region near the stopband. Moreover, the guided wave energy of different frequencies is concentrated at different locations, which manifests as rainbow guided waves. We believe implementing the rainbow trapping will open new paradigms for guiding and focusing of guided waves. Moreover, the rainbow guided waves with energy concentration and spatial separation of frequencies may have potential applications in nondestructive evaluation, spatial wave filtering, energy harvesting, and acoustofluidics.

Implementation of dispersion-free slow acoustic wave propagation and phase engineering with helical-structured metamaterials

The ability to slow down wave propagation in materials has attracted significant research interest. A successful solution will give rise to manageable enhanced wave–matter interaction, freewheeling phase engineering and spatial compression of wave signals. The existing methods are typically associated with constructing dispersive materials or structures with local resonators, thus resulting in unavoidable distortion of waveforms. Here we show that, with helical-structured acoustic metamaterials, it is now possible to implement dispersion-free sound deceleration. The helical-structured metamaterials present a non-dispersive high effective refractive index that is tunable through adjusting the helicity of structures, while the wavefront revolution plays a dominant role in reducing the group velocity. Finally, we numerically and experimentally demonstrate that the helical-structured metamaterials with designed inhomogeneous unit cells can turn a normally incident plane wave into a self-accelerating beam on the prescribed parabolic trajectory. The helical-structured metamaterials will have profound impact to applications in explorations of slow wave physics.

There is great interest in slow wave propagation for a variety of applications. Here, Zhu et al. present a dispersion-free helical-structured metamaterial that implements acoustic wave deceleration at broad bandwidth and demonstrates specially designed phase modulation to incident sound through helicity tuning.

Acoustic dispersive prism

The optical dispersive prism is a well-studied element, which allows separating white light into its constituent spectral colors, and stands in nature as water droplets. In analogy to this definition, the acoustic dispersive prism should be an acoustic device with capability of splitting a broadband acoustic wave into its constituent Fourier components. However, due to the acoustical nature of materials as well as the design and fabrication difficulties, there is neither any natural acoustic counterpart of the optical prism, nor any artificial design reported so far exhibiting an equivalent acoustic behaviour. Here, based on exotic properties of the acoustic transmission-line metamaterials and exploiting unique physical behaviour of acoustic leaky-wave radiation, we report the first acoustic dispersive prism, effective within the audible frequency range 800 Hz–1300 Hz. The dispersive nature, and consequently the frequency-dependent refractive index of the metamaterial are exploited to split the sound waves towards different and frequency-dependent directions. Meanwhile, the leaky-wave nature of the structure facilitates the sound wave radiation into the ambient medium.