Demonstration of Acoustic Higher-Order Topological Stiefel-Whitney Semimetal.

The higher-order topological phases have attracted intense attention in the past years, which reveals various intriguing topological properties. Meanwhile, the enrichment of group symmetries with projective symmetry algebras redefines the fundamentals of topological matter and makes Stiefel-Whitney (SW) classes in classical wave systems possible. Here, we report the experimental realization of higher-order topological nodal loop semimetal in an acoustic system and obtain the inherent SW topological invariants. In stark contrast to higher-order topological semimetals relating to complex vector bundles, the hinge and surface states in the SW topological phase are protected by two distinctive SW topological charges relevant to real vector bundles. Our findings push forward the studies of SW class topology in classical wave systems, which also show possibilities in robust high-Q-resonance-based sensing and energy harvesting.

Thermal meta-device in analogue of zero-index photonics.

Inspired by the developments in photonic metamaterials, the concept of thermal metamaterials has promised new avenues for manipulating the flow of heat. In photonics, the existence of natural materials with both positive and negative permittivities has enabled the creation of metamaterials with a very wide range of effective parameters. In contrast, in conductive heat transfer, the available range of thermal conductivities in natural materials is far narrower, strongly restricting the effective parameters of thermal metamaterials and limiting possible applications in extreme environments. Here, we identify a rigorous correspondence between zero index in Maxwell's equations and infinite thermal conductivity in Fourier's law. We also propose a conductive system with an integrated convective element that creates an extreme effective thermal conductivity, and hence by correspondence a thermal analogue of photonic near-zero-index metamaterials, a class of metamaterials with crucial importance in controlling light. Synergizing the general properties of zero-index metamaterials and the specific diffusive nature of thermal conduction, we theoretically and experimentally demonstrate a thermal zero-index cloak. In contrast with conventional thermal cloaks, this meta-device can operate in a highly conductive background and the cloaked object preserves great sensitivity to external temperature changes. Our work demonstrates a thermal metamaterial which greatly enhances the capability for molding the flow of heat.

One-Way Localized Adiabatic Passage in an Acoustic System.

Stimulated adiabatic passage utilizes radiation pulses to efficiently and selectively transfer population between quantum states, via an intermediate state that is normally decaying. In this Letter, we propose the analog of stimulated adiabatic passage in an acoustic system. It is realized with cavities that correlate through adiabatically time-varying couplings, where the cavities and time-varying couplings mimic discrete states and radiation pulses, respectively. With appropriate arrangements of coupling actions, an acoustic wave can be efficiently transferred from the initial excited cavity to the target cavity in the forward direction, immune to the intermediate dark cavity. On the other hand, for the backward propagation, the acoustic energy is perfectly localized in the intermediate dark cavity and completely dissipated. We analytically, numerically, and experimentally demonstrate such unidirectional sound localization and unveil the essential role of zero-eigenvalue eigenstates in the adiabatic passage process.

Experimental Demonstration of Acoustic Chern Insulators.

We report the experimental realization of an acoustic Chern insulator (ACI), by using an angular-momentum-biased resonator array with the broken Lorentz reciprocity. High Q-factor resonance of the constituent rotors is leveraged to reduce the required rotation speed. ACI is a new topological acoustic system analogous to the electronic quantum Hall insulator, based on an effective magnetic field. Experimental results show that the ACI featured with a stable and uniform metafluid flow bias supports one-way nonreciprocal transport of sound at its edges, which is topologically immune to various types of defects. Our work opens up opportunities for exploring unique observable topological phases and developing topological-insulator-based nonreciprocal devices in acoustics.

Spectrum Control through Discrete Frequency Diffraction in the Presence of Photonic Gauge Potentials.

By using optical phase modulators in a fiber-optical circuit, we theoretically and experimentally demonstrate large control over the spectrum of an impinging signal, which may evolve analogously to discrete diffraction in spatial waveguide arrays. The modulation phase acts as a photonic gauge potential in the frequency dimension, realizing efficient control of the central frequency and bandwidth of frequency combs. We experimentally achieve a 50 GHz frequency shift and threefold bandwidth expansion of an impinging comb, as well as the frequency analogue of various refraction phenomena, including negative refraction and perfect focusing in the frequency domain, both for discrete and continuous incident spectra. Our study paves a promising way towards versatile frequency management for optical communications and signal processing using time modulation schemes.

Anisotropic reflection oscillation in periodic multilayer structures of parity-time symmetry.

We show that periodic multilayer structures with parity-time (PT) symmetries imposed by a balanced arrangement of gain and loss can exhibit anisotropic reflection oscillation patterns as the number of unit-cells is increasing. At the minima of reflection oscillation patterns, the PT symmetric medium exhibits bidirectional transparency with the eigenvalues of the scattering matrix degenerated, where the PT symmetric set-up can still render directional responses due to the one-way field localization inside the system. With certain number of unit-cells, the PT symmetric crystal is unidirectionally invisible. More complicated reflection/transmission oscillations can be observed by segregating neighboring unit-cells with a uniform dielectric layer. Our results may pave the way towards a new class of functional optical devices with intriguing and unexpected directional responses.

Experimental investigation of acoustic moiré effect controlled by twisted bilayer gratings.

Recently, the moiré pattern has attracted lots of attention by superimposing two planar structures of regular geometries, such as two sets of metasurfaces or gratings. Here, we show the experimental investigation of acoustic moiré effect by using twisted bilayer gratings (i.e., one grating twisted with respect to the other). We observed the guided resonance that occurred when the incident ultrasound beam was coupled with the guiding modes in a meta-grating, significantly influencing the reflection and transmission. Tunable guided resonances from the moiré effect with complete ultrasound reflection at different frequencies were further demonstrated in experiments. Combining the measurements of transmission spectra and the Fast Fourier Transform analyses, we reveal the guided resonance frequencies of moiré ultrasonic metasurface can be effectively controlled by adjusting the twisting angle of the bilayer gratings. Our results can be explained in a simplified model based on the band folding theory, providing a reliable prediction on the precise control of ultrasound reflection via the twisting angle adjustment. Our work extends the moiré metasurface from optics into acoustics, which shows more possibilities for the ultrasound beam engineering from the moiré effect and enables the exploration of functional acoustic devices for ultrasound imaging, treatment and diagnosis.

Observation of non-Hermitian skin effect in thermal diffusion.

The paradigm shift of Hermitian systems into the non-Hermitian regime profoundly modifies inherent property of the topological systems, leading to various unprecedented effects such as the non-Hermitian skin effect (NHSE). In the past decade, the NHSE has been demonstrated in quantum, optical and acoustic systems. Beside those wave systems, the NHSE in diffusive systems has not yet been observed, despite recent abundant advances in the study of topological thermal diffusion. In this work, we design a thermal diffusion lattice based on a modified Su-Schrieffer-Heeger model and demonstrate the diffusive NHSE. In the proposed model, the asymmetric temperature field coupling inside each unit cell can be judiciously realized by appropriate configurations of structural parameters. We find that the temperature fields trend to concentrate toward the target boundary which is robust against initial excitation conditions. We thus experimentally demonstrated the NHSE in thermal diffusion and verified its robustness against various defects. Our work provides a platform for exploration of non-Hermitian physics in the diffusive systems, which has important applications in efficient heat collection, highly sensitive thermal sensing and others.

Acoustic Higher-Order Topological Insulators Induced by Orbital-Interactions.

The discovery of higher-order topological insulator metamaterials, in analogy with their condensed-matter counterparts, has enabled various breakthroughs in photonics, mechanics, and acoustics. A common way of inducing higher-order topological wave phenomena is through pseudo-spins, which mimic the electron spins as a symmetry-breaking degree of freedom. Here, this work exploits degenerate orbitals in acoustic resonant cavities to demonstrate versatile, orbital-selective, higher-order topological corner states. Type-II corner states are theoretically investigated and experimentally demonstrated based on tailored orbital interactions, without the need for long-range hoppings that has so far served as a key ingredient for Type-II corner states in single-orbital systems. Due to the orthogonal nature of the degenerate p orbitals, this work also introduces a universal strategy to realize orbital-dependent edge modes, featuring high-Q edge states identified in bulk bands. These findings provide an understanding of the interplay between acoustic orbitals and topology, shedding light on orbital-related topological wave physics, as well as its applications for acoustic sensing and trapping.

Robust temporal adiabatic passage with perfect frequency conversion between detuned acoustic cavities.

For classical waves, phase matching is vital for enabling efficient energy transfer in many scenarios, such as waveguide coupling and nonlinear optical frequency conversion. Here, we propose a temporal quasi-phase matching method and realize robust and complete acoustical energy transfer between arbitrarily detuned cavities. In a set of three cavities, A, B, and C, the time-varying coupling is established between adjacent elements. Analogy to the concept of stimulated Raman adiabatic passage, amplitudes of the two couplings are modulated as time-delayed Gaussian functions, and the couplings' signs are periodically flipped to eliminate temporal phase mismatching. As a result, robust and complete acoustic energy transfer from A to C is achieved. The non-reciprocal frequency conversion properties of our design are demonstrated. Our research takes a pivotal step towards expanding wave steering through time-dependent modulations and is promising to extend the frequency conversion based on state evolution in various linear Hermitian systems to nonlinear and non-Hermitian regimes.

Observation of parity-time symmetry in diffusive systems.

Phase modulation has scarcely been mentioned in diffusive physical systems because the diffusion process does not carry the momentum like waves. Recently, non-Hermitian physics provides a unique perspective for understanding diffusion and shows prospects in thermal phase regulation, exemplified by the discovery of anti-parity-time (APT) symmetry in diffusive systems. However, precise control of thermal phase remains elusive hitherto and can hardly be realized, due to the phase oscillations. Here we construct the PT-symmetric diffusive systems to achieve the complete suppression of thermal phase oscillation. The real coupling of diffusive fields is readily established through a strong convective background, and the decay-rate detuning is enabled by thermal metamaterial design. We observe the phase transition of PT symmetry breaking with the symmetry-determined amplitude and phase regulation of coupled temperature fields. Our work shows the existence of PT symmetry in dissipative energy exchanges and provides unique approaches for harnessing the mass transfer of particles, wave dynamics in strongly scattering systems, and thermal conduction.

Orbital topological edge states and phase transitions in one-dimensional acoustic resonator chains.

Topological phases of matter have attracted significant attention in recent years, due to the unusual robustness of their response to defects and disorder. Various research efforts have been exploring classical and quantum topological wave phenomena in engineered materials, in which different degrees of freedom (DoFs) - for the most part based on broken crystal symmetries associated with pseudo-spins - induce synthetic gauge fields that support topological phases and unveil distinct forms of wave propagation. However, spin is not the only viable option to induce topological effects. Intrinsic orbital DoFs in spinless systems may offer a powerful alternative platform, mostly unexplored to date. Here we reveal orbital-selective wave-matter interactions in acoustic systems supporting multiple orbital DoFs, and report the experimental demonstration of disorder-immune orbital-induced topological edge states in a zigzag acoustic 1D spinless lattice. This work expands the study of topological phases based on orbitals, paving the way to explore other orbital-dependent phenomena in spinless systems.

Decorated bacteria-cellulose ultrasonic metasurface.

Cellulose, as a component of green plants, becomes attractive for fabricating biocompatible flexible functional devices but is plagued by hydrophilic properties, which make it easily break down in water by poor mechanical stability. Here we report a class of SiO2-nanoparticle-decorated bacteria-cellulose meta-skin with superior stability in water, excellent machining property, ultrathin thickness, and active bacteria-repairing capacity. We further develop functional ultrasonic metasurfaces based on meta-skin paper-cutting that can generate intricate patterns of ~10 µm precision. Benefited from the perfect ultrasound insulation of surface Cassie-Baxter states, we utilize meta-skin paper-cutting to design and fabricate ultrathin (~20 µm) and super-light (<20 mg) chip-scale devices, such as nonlocal holographic meta-lens and the 3D imaging meta-lens, realizing complicated acoustic holograms and high-resolution 3D ultrasound imaging in far fields. The decorated bacteria-cellulose ultrasonic metasurface opens the way for exploiting flexible and biologically degradable metamaterial devices with functionality customization and key applications in advanced biomedical engineering technologies.

Reciprocity of thermal diffusion in time-modulated systems.

The reciprocity principle governs the symmetry in transmission of electromagnetic and acoustic waves, as well as the diffusion of heat between two points in space, with important consequences for thermal management and energy harvesting. There has been significant recent interest in materials with time-modulated properties, which have been shown to efficiently break reciprocity for light, sound, and even charge diffusion. However, time modulation may not be a plausible approach to break thermal reciprocity, in contrast to the usual perception. We establish a theoretical framework to accurately describe the behavior of diffusive processes under time modulation, and prove that thermal reciprocity in dynamic materials is generally preserved by the continuity equation, unless some external bias or special material is considered. We then experimentally demonstrate reciprocal heat transfer in a time-modulated device. Our findings correct previous misconceptions regarding reciprocity breaking for thermal diffusion, revealing the generality of symmetry constraints in heat transfer, and clarifying its differences from other transport processes in what concerns the principles of reciprocity and microscopic reversibility.

Odd Willis coupling induced by broken time-reversal symmetry.

When sound interacts with geometrically asymmetric structures, it experiences coupling between pressure and particle velocity, known as Willis coupling. While in most instances this phenomenon is perturbative in nature, tailored asymmetries combined with resonances can largely enhance it, enabling exotic acoustic phenomena. In these systems, Willis coupling obeys reciprocity, imposing an even symmetry of the Willis coefficients with respect to time reversal and the impinging wave vector, which translates into stringent constraints on the overall scattering response. In this work, we introduce and experimentally observe a dual form of acoustic Willis coupling, arising in geometrically symmetric structures when time-reversal symmetry is broken, for which the pressure-velocity coupling is purely odd-symmetric. We derive the conditions to maximize this effect, we experimentally verify it in a symmetric subwavelength scatterer biased by angular momentum, and we demonstrate the opportunities for sound scattering enabled by odd Willis coupling. Our study opens directions for acoustic metamaterials, with direct implications for sound control, non-reciprocal scattering, wavefront shaping and signal routing, of broad interest also for nano-optics, photonics, elasto-dynamics, and mechanics.

Square-root-like higher-order topological states in three-dimensional sonic crystals.

The square-root descendants of higher-order topological insulators were proposed recently, whose topological property is inherited from the squared Hamiltonian. Here we present a three-dimensional (3D) square-root-like sonic crystal by stacking the 2D square-root lattice in the normal (z) direction. With the nontrivial intralayer couplings, the opened degeneracy at theK-Hdirection induces the emergence of multiple acoustic localized modes, i.e., the extended 2D surface states and 1D hinge states, which originate from the square-root nature of the system. The square-root-like higher order topological states can be tunable and designed by optionally removing the cavities at the boundaries. We further propose a third-order topological corner state in the 3D sonic crystal by introducing the staggered interlayer couplings on each square-root layer, which leads to a nontrivial bulk polarization in thezdirection. Our work sheds light on the high-dimensional square-root topological materials, and have the potentials in designing advanced functional devices with sound trapping and acoustic sensing.

Efficient nonreciprocal mode transitions in spatiotemporally modulated acoustic metamaterials.

In linear, lossless, time-invariant, and nonbiased acoustic systems, mode transitions are time reversible, consistent with Lorentz reciprocity and implying a strict symmetry in space-time for sound manipulation. Here, we overcome this fundamental limitation by implementing spatiotemporally modulated acoustic metamaterials that support nonreciprocal sound steering. Our mechanism relies on the coupling between an ultrathin membrane and external biasing electromagnetic fields, realizing programmable dynamic control of the acoustic impedance over a motionless and noiseless platform. The fast and flexible impedance modulation of our metamaterial imparts an effective unidirectional momentum in space-time to realize nonreciprocal transitions in k-ω space between different diffraction modes. On the basis of these principles, we demonstrate efficient nonreciprocal sound steering, showcasing unidirectional evanescent wave conversion and nonreciprocal upconversion focusing. More generally, our metamaterial platform offers opportunities for generation of nonreciprocal Bloch waves and extension to other domains, such as non-Hermitian topological and parity-time symmetric acoustics.

Super-resolution acoustic image montage via a biaxial metamaterial lens.

Ever since the Victorian era, montage, the process of pictorial composition made by juxtaposing or superimposing photographs, has been a very popular post-editing imaging technique. Despite showing a strong power in demonstrating complex wave field effects, this technique has neither been fully explored in acoustic imaging nor been realized in real-time systems with the capability beyond diffraction limits. On the other hand, the recent prospect of metamaterials has shown their great potentials in super-resolution acoustic imaging. However, the miracle jigsaw of more advanced functional modulation of acoustic wave fields at deep subwavelength scale still remains elusive. Here we report the experimental implementation of super-resolution acoustic image montage through a judiciously designed biaxial metamaterial lens. Based on the non-diffraction birefringence in the biaxial metamaterials, we realized various montage functionalities such as duplication, composition, and decomposition of sound images with distinctive deep subwavelength features. Our work represents an important step in developing versatile functional acoustic metamaterial devices for imaging purposes, as it provides on-demand editing of sound field patterns beyond diffraction limits.

An Acoustic Meta-Skin Insulator.

Acoustic metamaterials with artificial microstructures are attractive to realize intriguing functions, including efficient waveguiding, which requires large impedance mismatches to realize total side reflection with negligible transmission and absorption. While large impedance mismatch can be readily realized in an air environment, acoustic waveguiding in an underwater environment remains elusive due to insufficient impedance mismatch of state-of-the-art metamaterials. Here, a superhydrophobic acoustic metasurface of microstructured poly(vinylidene fluoride) membrane, referred to as a "meta-skin" insulator, which is able to confine acoustic waves in an all-angle and wide spectrum range due to tremendous impedance mismatch at stable air/water interfaces, viz., the Cassie-Baxter state is demonstrated. By utilizing the meta-skin insulator with broadband and high throughput, orbital-angular-momentum multiplexing at a high spectral efficiency and binary coding along large-angle bending channels for bit-error-free acoustic data transmission in an underwater environment are demonstrated. Very different from optical and/or electrical cable communications, acoustic waves can be simply and effectively coupled into remote meta-skin acoustic fibers from free space, which is technologically significant for long-haul and anti-interference communication. This work can enlighten many fluidic applications based on efficient waveguiding, such as in vivo ultrasound medical treatment and imaging.

Probability-Density-Based Deep Learning Paradigm for the Fuzzy Design of Functional Metastructures.

In quantum mechanics, a norm-squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the fuzzy structure of microcosmos. Recently, hybrid neural structures raised intense attention, resulting in various intelligent systems with far-reaching influence. Here, we propose a probability-density-based deep learning paradigm for the fuzzy design of functional metastructures. In contrast to other inverse design methods, our probability-density-based neural network can efficiently evaluate and accurately capture all plausible metastructures in a high-dimensional parameter space. Local maxima in probability density distribution correspond to the most likely candidates to meet the desired performances. We verify this universally adaptive approach in but not limited to acoustics by designing multiple metastructures for each targeted transmission spectrum, with experiments unequivocally demonstrating the effectiveness and generalization of the inverse design.