Nonreciprocal Acoustic Devices with Asymmetric Peierls Phases.

Nonreciprocity in acoustics is of paramount importance in many practical applications and has been experimentally realized using nonlinear media, moving fluids, or time modulation, which regrettably suffer from large volumes and high-power consumption, difficulty in integration, and inevitable vibrations or phase noise. In modern Hamiltonian theory, the violation of system's reciprocity can be achieved via asymmetric Peierls phases, which typically involves with non-Hermiticity or time-reversal symmetry breaking. Here, we propose a framework for designing nonreciprocal acoustic devices based on the asymmetric Peierls phases that can be fully controlled via active acoustic components. The fully controlled Peierls phases enable various high-performance acoustic devices, including non-Hermitian extensions of isolators, gyrators, and circulators, which are otherwise impossible in previous approaches that are bound by Hermiticity or passivity. We reveal that the transmission phases in isolators are equivalent to the Peierls phase plus a constant. The nonreciprocal phase delay in gyrators and the unirotational transmission behavior in circulators result from the gauge-invariant Aharonov-Bohm phases determined by Peierls phases. Our work not only uncovers multiple intriguing physics related to Peierls phases but also provides a general approach to compact, integratable, nonreciprocal acoustic devices.

Refraction/reflection reversal in two-dimensional acoustic metagratingsa).

Unlike acoustic metasurfaces that rely solely on phase gradients, acoustic metagratings (AMs) operate based on both phase gradients and grating diffraction, thus further extending the generalized Snell's law (GSL). In particular, AMs can achieve reversal of refraction and reflection based on the parity of the number of wave propagations inside the AMs. So far, discussions of this GSL extension have largely been applied to one-dimensional periodic AMs, while the designs of two-dimensional (2D) periodic AMs and their performance in three-dimensional (3D) space have been quite limited. Here, we study the GSL extension in 3D space and experimentally demonstrate a series of functional 2D periodic AMs. The designed AMs can achieve sound refraction/reflection under any incidence angle in 3D space, without restrictions to certain critical ranges; adjusting incident angles only enables the reversal of refraction and reflection. Additionally, we demonstrate two types of dual-layer sound lenses based on two AMs, whose reversal of refraction and reflection can be realized by simply attaching or separating the two AMs. Our work paves the way to complex 3D wavefront manipulation of AMs, which may find potential use in practical acoustic devices.

Spinful Topological Phases in Acoustic Crystals with Projective PT Symmetry.

For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological phases. However, only recently has it been realized theoretically that in the presence of gauge symmetry, the algebraic structure of symmetries can be projectively represented, which possibly enables the switch between spinless and spinful topological phases. Here, we report the experimental demonstration of this idea by realizing spinful topological phases in "spinless" acoustic crystals with projective space-time inversion symmetry. In particular, we realize a one-dimensional topologically gapped phase characterized by a 2Z winding number, which features double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes. Our Letter thus overcomes a fundamental constraint on topological phases by spin classes.

Observation of Dirac Hierarchy in Three-Dimensional Acoustic Topological Insulators.

Dirac cones (DCs) play a pivotal role in various unique phenomena ranging from massless electrons in graphene to robust surface states in topological insulators (TIs). Recent studies have theoretically revealed a full Dirac hierarchy comprising an eightfold bulk DC, a fourfold surface DC, and a twofold hinge DC, associated with a hierarchy of topological phases including first-order to third-order three-dimensional (3D) topological insulators, using the same 3D base lattice. Here, we report the first experimental observation of the Dirac hierarchy in 3D acoustic TIs. Using acoustic measurements, we unambiguously reveal that lifting of multifold DCs in each hierarchy can induce two-dimensional topological surface states with a fourfold DC in a first-order 3D TI, one-dimensional topological hinge states with a twofold DC in a second-order 3D TI, and zero-dimensional topological corner states in a third-order 3D TI. Our Letter not only expands the fundamental research scope of Dirac physics, but also opens up a new route for multidimensional robust wave manipulation.

Observation of Dislocation-Induced Topological Modes in a Three-Dimensional Acoustic Topological Insulator.

The interplay between real-space topological lattice defects and the reciprocal-space topology of energy bands can give rise to novel phenomena, such as one-dimensional topological modes bound to screw dislocations in three-dimensional topological insulators. We obtain direct experimental observations of dislocation-induced helical modes in an acoustic analog of a weak three-dimensional topological insulator. The spatial distribution of the helical modes is found through spin-resolved field mapping, and verified numerically by tight-binding and finite-element calculations. These one-dimensional helical channels can serve as robust waveguides in three-dimensional media. Our experiment paves the way to studying novel physical modes and functionalities enabled by topological lattice defects in three-dimensional classical topological materials.

Three-dimensional flat Landau levels in an inhomogeneous acoustic crystal.

When electrons moving in two dimensions (2D) are subjected to a strong uniform magnetic field, they form flat bands called Landau levels (LLs). LLs can also arise from pseudomagnetic fields (PMFs) induced by lattice distortions. In three-dimensional (3D) systems, there has been no experimental demonstration of LLs  as a type of flat band thus far. Here, we report the experimental realization of a flat 3D LL in an acoustic crystal. Starting from a lattice whose bandstructure exhibits a nodal ring, we design an inhomogeneous distortion corresponding to a specific pseudomagnetic vector potential (PVP). This distortion causes the nodal ring states to break up into LLs, including a zeroth LL that is flat along all three directions. These findings suggest the possibility of using nodal ring materials to generate 3D flat bands, allowing access to strong interactions and other attractive physical regimes in 3D.

Observation of vortex-string chiral modes in metamaterials.

As hypothetical topological defects in the geometry of spacetime, vortex strings could have played many roles in cosmology, and their distinct features can provide observable clues about the early universe's evolution. A key feature of vortex strings is that they can interact with Weyl fermionic modes and support massless chiral-anomaly states along strings. To date, despite many attempts to detect vortex strings in astrophysics or to emulate them in artificially created systems, observation of these vortex-string chiral modes remains experimentally elusive. Here we report experimental observations of vortex-string chiral modes using a metamaterial system. This is implemented by inhomogeneous perturbation of Yang-monopole phononic metamaterials. The measured linear dispersion and modal profiles confirm the existence of topological modes bound to and propagating along the string with the chiral anomaly. Our work provides a platform for studying diverse cosmic topological defects in astrophysics and offers applications as topological fibres in communication techniques.

Acoustic Metagrating Holograms.

Metasurface holograms represent a common category of metasurface devices that utilize in-plane phase gradients to shape wavefronts, forming holographic images through the application of the generalized Snell's law (GSL). While conventional metasurfaces focus solely on phase gradients, metagratings, which incorporate higher-order wave diffraction, further expand the GSL's generality. Recent advances in certain acoustic metagratings demonstrate an updated GSL extension capable of reversing anomalous transmission and reflection, whose reversal is characterized by the parity of the number of wave propagation trips through the metagrating. However, the current extension of GSL remains limited to 1D metagratings, unable to access 2D holographic images in 3D spaces. Here, the GSL extension to 2D metagratings for manipulating waves within 3D spaces is investigated. Through this analysis, a series of acoustic metagrating holograms is experimentally demonstrated. These holographic images exhibit the unique ability to switch between transmission and reflection types independently. This study introduces an additional dimension to modern holography design and metasurface wavefront manipulation.

Three-dimensional valley-contrasting sound.

Spin and valley are two fundamental properties of electrons in crystals. The similarity between them is well understood in valley-contrasting physics established decades ago in two-dimensional (2D) materials like graphene-with broken inversion symmetry, the two valleys in graphene exhibit opposite orbital magnetic moments, similar to the spin-1/2 behaviors of electrons, and opposite Berry curvature that leads to a half topological charge. However, valley-contrasting physics has never been explored in 3D crystals. Here, we develop a 3D acoustic crystal exhibiting 3D valley-contrasting physics. Unlike spin that is fundamentally binary, valley in 3D can take six different values, each carrying a vortex in a distinct direction. The topological valley transport is generalized from the edge states of 2D materials to the surface states of 3D materials, with interesting features including robust propagation, topological refraction, and valley-cavity localization. Our results open a new route for wave manipulation in 3D space.

Low-Frequency, Open, Sound-Insulation Barrier by Two Oppositely Oriented Helmholtz Resonators.

In this work, a low-frequency, open, sound-insulation barrier, composed of a single layer of periodic subwavelength units (with a thickness of λ/28), is demonstrated both numerically and experimentally. Each unit was constructed using two identical, oppositely oriented Helmholtz resonators, which were composed of a central square cavity surrounded by a coiled channel. In the design of the open barrier, the distance between two adjacent units was twice the width of the unit, showing high-performance ventilation, and low-frequency sound insulation. A minimum transmittance of 0.06 could be observed around 121.5 Hz, which arose from both sound reflections and absorptions, created by the coupling of symmetric and asymmetric eigenmodes of the unit, and the absorbed sound energy propagating into the central cavity was greatly reduced by the viscous loss in the channel. Additionally, by introducing a multilayer open barrier, a broadband sound insulation was obtained, and the fractional bandwidth could reach approximately 0.19 with four layers. Finally, the application of the multilayer open barrier in designing a ventilated room was further discussed, and the results presented an omnidirectional, broadband, sound-insulation effect. The proposed open, sound-insulation barrier with the advantages of ultrathin thickness; omnidirectional, low-frequency sound insulation; broad bandwidth; and high-performance ventilation has great potential in architectural acoustics and noise control.

Vortex states in an acoustic Weyl crystal with a topological lattice defect.

Crystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

Acoustic Bessel Vortex Beam by Quasi-Three-Dimensional Reflected Metasurfaces.

Vortex beams have a typical characteristic of orbital angular momentum, which provides a new degree of freedom for information processing in remote communication and a form of non-contact manipulation for trapping particles. In acoustics, vortex beams are generally observed on the surface of a metamaterial structure or in a waveguide with a hard boundary owing to the characteristic of easy diffusion in free space. The realization of an acoustic vortex beam with a long-distance propagation in free space still remains a challenge. To overcome this, we report a type of acoustic Bessel vortex (ABV) beam created by a quasi-three-dimensional reflected metasurface in free space based on phase modulation. By using the Bessel and vortex phase profiles, we can realize an ABV beam with the high performances of both Bessel and vortex beams, and its effective propagation distance is larger than 9.2λ in free space. Beyond that, we discuss the bandwidth and topological charge of the ABV beam in detail, and the fractional bandwidth can reach about 0.28. The proposed ABV beam has the advantages of a high-performance vortex, long-distance propagation, and broad bandwidth, which provide a new pathway for designing multifunctional vortex devices with promising applications.

Demonstration of negative refraction induced by synthetic gauge fields.

Negative refraction is a counterintuitive wave phenomenon that has inspired the development of metamaterials and metasurfaces with negative refractive indices and surface phase discontinuities, respectively. Recent theories have proposed an alternative mechanism for negative refraction: Synthetic gauge fields, induced by either dynamical modulation or motion, can shift a material's dispersion in momentum space, forcing a positive refractive index medium to exhibit negative refraction above a certain threshold. However, this phenomenon has not previously been observed. Here, we report on the experimental demonstration of gauge field­induced negative refraction in a twisted bilayer acoustic metamaterial. The synthetic gauge fields arise in a projected two-dimensional geometry and can be continuously tuned by varying the wave number along the third dimension. Gauge field­induced waveguiding with backward-propagating modes is also demonstrated in a trilayer configuration. These results introduce a mechanism for performing wave manipulation in artificially engineered materials.

Acoustic non-Hermitian skin effect from twisted winding topology.

The recently discovered non-Hermitian skin effect (NHSE) manifests the breakdown of current classification of topological phases in energy-nonconservative systems, and necessitates the introduction of non-Hermitian band topology. So far, all NHSE observations are based on one type of non-Hermitian band topology, in which the complex energy spectrum winds along a closed loop. As recently characterized along a synthetic dimension on a photonic platform, non-Hermitian band topology can exhibit almost arbitrary windings in momentum space, but their actual phenomena in real physical systems remain unclear. Here, we report the experimental realization of NHSE in a one-dimensional (1D) non-reciprocal acoustic crystal. With direct acoustic measurement, we demonstrate that a twisted winding, whose topology consists of two oppositely oriented loops in contact rather than a single loop, will dramatically change the NHSE, following previous predictions of unique features such as the bipolar localization and the Bloch point for a Bloch-wave-like extended state. This work reveals previously unnoticed features of NHSE, and provides the observation of physical phenomena originating from complex non-Hermitian winding topology.

Observation of an acoustic octupole topological insulator.

Berry phase associated with energy bands in crystals can lead to quantised observables like quantised dipole polarizations in one-dimensional topological insulators. Recent theories have generalised the concept of quantised dipoles to multipoles, resulting in the discovery of multipole topological insulators which exhibit a hierarchy of multipole topology: a quantised octupole moment in a three-dimensional bulk induces quantised quadrupole moments on its two-dimensional surfaces, which in turn induce quantised dipole moments on one-dimensional hinges. Here, we report on the realisation of an octupole topological insulator in a three-dimensional acoustic metamaterial. We observe zero-dimensional topological corner states, one-dimensional gapped hinge states, two-dimensional gapped surface states, and three-dimensional gapped bulk states, representing the hierarchy of octupole, quadrupole and dipole moments. Conditions for forming a nontrivial octupole moment are demonstrated by comparisons with two different lattice configurations having trivial octupole moments. Our work establishes the multipole topology and its full hierarchy in three-dimensional geometries.

Binary-phase acoustic passive logic gates.

The recent rapid development of acoustic logic devices has opened up the possibilities of sound computing and information processing. However, simultaneous realization of acoustic logic devices with subwavelength size, broad bandwidth and passive structure still poses a great challenge. To overcome it, we propose a subwavelength acoustic logic gate which consists of binary-phase passive unit cells placed into a multi-port waveguide. Based on the phase manipulations of the unit cells, we experimentally and numerically realize three basic logic gates OR, NOT and AND, and a composite logic gate XOR with a uniform threshold of 0.4 Pa based on linear acoustic interferences. More importantly, We also design a composite logic gate XNOR by a four-port waveguide, and composite logic gates NOR and NAND and a logic operation A⊙(B+C) based on two logic gates. We demonstrate a 0.6λ-length, 0.3λ-width, and 0.2-fractional bandwidth acoustic logic gate constructed by passive structures, which may lead to important advances in various applications, such as acoustic computing, acoustic information processing and integrated acoustics.

Dual-Band Fano Resonance of Low-Frequency Sound Based on Artificial Mie Resonances.

It is reported both experimentally and numerically that dual-band acoustic Fano resonances (AFRs) of low-frequency sound are realized by a compound unit array composed of two types of multiple-cavity unit cells with different inner radii. Eigenmode analyses show that two types of monopolar Mie resonance (MMR) modes can be observed below 650 Hz, which arise from the coupling resonance of the overall structure and the Helmholtz resonance of each resonance cavity, respectively. Based on the MMRs with the out-of-phase characteristic induced by the mutual coupling of the two types of unit cells, the dual-band AFRs, in which the quality factor of the AFR II can exceed 600 when the ratio of the inner radii is closed to 1.0, can be observed. More interestingly, the application of the dual-band AFRs in sound encryption communication is further discussed. The proposed multiple-cavity unit cell and its associated dual-band AFRs provide diverse routes to design multiband sound devices with versatile applications, such as filtering, sensing, and communication.

Observation of a topological nodal surface and its surface-state arcs in an artificial acoustic crystal.

Three-dimensional (3D) gapless topological phases can be classified by the dimensionality of the band degeneracies, including zero-dimensional (0D) nodal points, one-dimensional (1D) nodal lines, and two-dimensional (2D) nodal surfaces. Both nodal points and nodal lines have been realized recently in photonics and acoustics. However, a nodal surface has never been observed in any classical-wave system. Here, we report on the experimental observation of a twofold symmetry-enforced nodal surface in a 3D chiral acoustic crystal. In particular, the demonstrated nodal surface carries a topological charge of 2, constituting the first realization of a higher-dimensional topologically-charged band degeneracy. Using direct acoustic field measurements, we observe the projected nodal surface and its Fermi-arc-like surface states and demonstrate topologically-induced robustness of the surface states against disorders. This discovery of a higher-dimensional topologically-charged band degeneracy paves the way toward further explorations of the physics and applications of new topological semimetal phases.

Programmable Coding Acoustic Topological Insulator.

Topological acoustics has recently revolutionized fundamental concepts of acoustic propagation, giving rise to strikingly unique acoustic edge modes immune to backscattering. Despite the rapid progress in this field, simultaneous realization of reconfigurability, intelligentization, and automatic control over acoustic propagation paths is posing a great challenge. This challenge is overcome by proposing the concept of a programmable acoustic topological insulator based on two digital elements "0" or "1," which consist of honeycomb-lattice sonic crystals made of cylindrical rods with different diameters. The acoustic propagation paths in the topological insulators can be controlled automatically by programming different coding sequences, which arises from efficient transformation of pseudospin-dependent edge modes on both interfaces of the digital elements. More importantly, a unique unit is experimentally fabricated that has either a "0" or "1" response automatically manipulated by an air cylinder, and design topological insulators with programmable functionality, to realize three digital acoustic devices, such as a single-pole double-throw switch, a single-pole single-throw switch, and a tunable logic gate. The proposed programmable topological insulators may enable future intelligent acoustic devices with exciting reconfigurable and programmable functionalities, which may lead to important advances in various applications, such as integrated acoustics, acoustic security, and information processing.

Modulating Sound with Acoustic Metafiber Bundles.

Acoustic metamaterials and metasurfaces provide great flexibility for manipulating sound waves and promise unprecedented functionality, ranging from transformation acoustics, acoustic cloaking, acoustic imaging to acoustic rerouting. However, the design of artificial structures with both broad bandwidth and multifunctionality remains challenging with traditional design approaches. Here we present a design and realization of a broadband acoustic metafiber bundle. Very different from previously reported acoustic metamaterials and metasurfaces, not only the metafiber structure is simple, flexible and tunable, but also the metafiber bundle has the advantages of broad bandwidth, high transmission, no resonance-induced energy loss and unchangeable output wavefront owing to eigenmodes in the passbands of the metafiber. Besides, it could also achieve arbitrary complex modulations of cylindrical and plane acoustic wavefronts. The metafiber bundles realize the exciting multifunctionality of both acoustic metamaterials and metasurfaces in a broad frequency range, which provides diverse routes to design novel acoustic devices with versatile applications.