Classical Wave Systems Research Articles

Boundary-localized many-body bound states in the continuum

Bound states in the continuum (BICs), referring to spatially localized bound states with energies falling within the range of extended modes, have been extensively investigated in single-particle systems, leading to diverse applications in photonics, acoustics, and other classical-wave systems. Recently, there has been theoretical interest in exploring many-body BICs in interacting quantum systems, which necessitate the careful design of impurity potentials or spatial profiles of interaction. Here, we propose a type of many-body BICs localized at boundaries, which can be purely induced by the uniform onsite interaction without requiring any specific design of impurity potential or nonlocal interaction. We numerically show that three or more interacting bosons can concentrate on the boundary of a homogeneous one-dimensional lattice, which is absent at single- and two-particle counterparts. Moreover, the eigenenergy of multi-boson bound states can embed within the continuous energy spectra of extended scattering states, thereby giving rise to interaction-induced boundary many-body BICs. Furthermore, by mapping Fock states of three and four bosons to nonlinear circuit networks, we experimentally simulate boundary many-body BICs. Our findings enrich the comprehension of correlated BICs beyond the single-particle level, and have the potential to inspire future investigations on exploring many-body BICs.

Progress on the morphing of topological modes by non-Hermitian skin effect in classical wave systems

Progress on the morphing of topological modes by non-Hermitian skin effect in classical wave systems

Pseudomagnetic fields in bilayer phononic crystals

Pseudomagnetic field (PMF), as an artificial gauge field, has attracted widespread attention in the exploration of magnetic-like effects in artificial structural materials. It offers a novel mechanism for manipulating wave fields in classical wave systems where there is no or weak response to actual magnetic fields. In this work, we construct acoustic PMFs in bilayer phononic crystals by imposing uniaxial linear gradient strain on the scatterers of both layers. Under the PMFs, the linear nodal rings, occurring at around the K and points of the bilayer phononic crystals, split into acoustics Landau levels (LLs). Specifically, the n = 0 plateau of the LLs splits into two discrete ones due to the interlayer coupling. Furthermore, we construct two heterostructures by splicing two phononic crystals with opposite PMFs and observe unique in-plane snake-like propagations of the edge state as well as oscillations between the upper and lower layers. Bilayer structure provides additional degree of freedom to generate PMFs in various types of semimetals and enriches the manipulation of acoustic wave propagations. In addition, it can be extended to other classical wave systems, such as electromagnetic wave and mechanical systems.

Numerical Studies on the Classical Long Wave System Describing Shallow Water Waves With Dispersion

In this study, a reliable and efficient local discontinuous Galerkin scheme for numerically solving the classical long wave system is proposed. This scheme approximates the temporal derivatives using the explicit strong-stability-preserving higher-order Runge-Kutta method, while the space derivatives are approximated using the local discontinuous Galerkin method, yielding an ordinary differential equation system. Numerical examples for various test problems are presented to offer a comprehensive understanding of the accuracy and reliability of the proposed method. The results obtained, which confirm the sub-optimal order of accuracy, are displayed in multiple tables. Additionally, several two-dimensional and three-dimensional graphical depictions of the problem have been provided to illustrate the behavior of the solution.

Topological valley mode separation of elastic waves and potential applications

Topological metamaterials in condensed matter systems have shown significant potential for information and energy applications due to their novel wave propagation behaviors. Recently, there has been an increasing focus on studying topological metamaterials in classical wave systems. Elastic waves, as full-vector classical waves, possess more intricate mechanical characteristics compared to sound waves and electromagnetic waves. This complexity not only offers diverse practical application possibilities but also presents notable research challenges in the field of topological metamaterials. In this study, our main objective is to achieve the ideal mode separation of elastic waves, specifically separated into the in-plane and out-of-plane components, and explore its potential applications. Firstly, we design phononic crystals with dual Dirac cones. Through geometric perturbation, we successfully separate the valley Hall phases of in-plane and out-of-plane modes. By superimposing different topological phases, we achieve three types of topological edge states: in-plane waves, out-of-plane waves, and hybrid waves. Combining these different topological edge states enables us to effectively separate the elastic waves into in-plane and out-of-plane components. Furthermore, we investigate the potential application of mode separation in energy harvesting. We achieve the energy localization of different wave modes based on the topological whispering-gallery mode. Additionally, by utilizing piezoelectric materials, we realize the subregional energy harvesting of in-plane and out-of-plane modes. The mechanical properties resulting from mode separation and topological whispering-gallery mode hold great potential for signal filtering and energy storage, thereby opening up new possibilities for controlling and utilizing elastic waves in various engineering scenarios.

Hermitian and non-hermitian higher-order topological states in mechanical metamaterials

Higher-order topological insulators exhibit clear hierarchical boundary states, providing an amazing platform for robust wave manipulations in mechanical or acoustic systems. Recently, this theory has been extended to non-Hermiticity-induced higher-order topology, which enables actively controllable topological transport. Nevertheless, most related studies focus on the non-Hermitian quadrupole topology, associated with the coexistence of negative and positive couplings to constitute a π-flux lattice, which hindered the realizations in classical wave systems. Here, we propose a novel tight-binding model without negative couplings, which supports non-Hermiticity-induced higher-order topological states. In the Hermitian case, the middle band gaps host the vanishing bulk polarization and the associated topology is dependent only upon the associated edge polarization. By introducing the external loss as non-Hermitian components, we reveal that therein the trivial structures can also host topological corner states, featured by the quantized nonzero edge polarizations in the biorthogonal basis. Furthermore, such a topological phase transition induced by non-Hermiticity can be realized for almost all of our lattices, except for the isotropic case where the middle band gaps never open. Basing on the theoretical design, we map the lattice models into the mechanical metamaterials to access the analogous higher-order topology in the elastic wave systems for both Hermitian and non-Hermitian physics. The simulated band structures match well with theoretical solutions. And the robust higher-order topological states are also identified. Our work paves the way to implement the non-Hermitian higher-order topology and offers the possibility for wave manipulations in non-Hermitian systems.

Corner states and particle trapping in waterborne acoustic crystals

Higher-order topological insulators exhibit intriguing capacity to confine energy on lower-dimensional boundaries owing to the unique bulk-boundary correspondence. Many potential practical applications of the higher-order states in classical wave systems have been proposed and achieved. In this work, we implement a second-order topological insulator in a waterborne acoustic crystal by drilling and grooving a copper plate based on a two-dimensional Su–Schrieffer–Heeger lattice with different intracell and intercell couplings. The far-field transmission spectrum and near-field pressure field distributions verify the existence of the one-dimensional edge states and zero-dimensional corner states in the bulk bandgap. Due to the highly localized edge and corner states, the polystyrene particles are trapped at the edges and corners by the acoustic gradient force. Our findings provide a good platform to manipulate underwater acoustic wave and may inspire topological acoustic applications.

Higher-order Non-Hermitian skin effect in an acoustic lattice

Non-Hermitian physical systems offer a distinct band topology that gives rise to the interesting phenomenon known as the non-Hermitian skin effect (NHSE). However, the exploration of higher-order NHSE in classical wave systems by leveraging non-reciprocity has been largely unexplored. In this study, we introduce a novel approach to experimentally realize the higher-order NHSE in a two-dimensional non-reciprocal breathing acoustic Kagome lattice. This lattice is composed of acoustic cavities with non-reciprocal coupling achieved through electrically controlled active acoustic elements. We successfully observed second-order corner modes using a 3 × 3 lattice, which manifest as localized pressure distributions at specific frequencies in both parallelogram and triangular topological acoustic lattices. We delve into the underlying mechanisms and their implications, thereby paving the way for a deeper understanding of higher-order NHSE and potentially innovative applications rooted in the acoustic non-reciprocity.

Topological phase-dependent thermalization dynamics in radiative heat transfer: insights from a one-dimensional Su-Schrieffer-Heeger model.

Various unusual behavior of artificial materials is governed by their topological properties, among these, the edge state in classical and quantum wave systems has captured significant attention due to its widespread relevance and applications across various fields of study. Observation of such topological features has led researchers to extend the idea of band theory to diffusive systems. Inspired by the well-known Su-Schriefer-Heegar (SSH) model we employed the concept of band topology to explore the topological characteristics of radiative heat transfer in a one-dimensional chain consisting of an odd number of nanoparticles. We demonstrate the topological phase transition, and topological modes with edge as well as bulk states in an array of nanoparticles exchanging heat via radiation. The demonstrated topological features of radiative systems can find important applications in the future studies of heat transfer at the nanoscale.

Acoustic real second-order nodal-loop semimetal and non-Hermitian modulation

The unique features of spinless time-reversal symmetry and tunable ℤ2 gauge fields in artificial systems facilitate the emergence of topological properties in the landscape, such as the recently explored Möbius-twisted phase and real second-order nodal-loop semimetals. However, these properties have predominantly been proposed only in theoretical frameworks. In this study, we present a cunningly designed blueprint for realizing an acoustic real second-order nodal-loop semimetal through the incorporation of projective translation symmetry into a three-dimensional stacked acoustic graphitic lattice. Additionally, we introduce non-Hermitian modulation to the topologically protected propagation of degenerate drumhead surface and hinge states, which depend on the specific on-site gain and loss textures. It should be emphasized that this demonstration can be extended to other classical wave systems, thereby potentially opening up opportunities for the design of functional topological devices.

Landscape of wave focusing and localization at low frequencies

AbstractHigh‐contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localization at low frequencies. We use an asymptotic framework to develop a landscape theory for high‐contrast systems that resonate in a subwavelength regime. Our from‐first‐principles asymptotic analysis yields a characterization in terms of the generalized capacitance matrix, giving a discrete approximation of the three‐dimensional scattering problem. We develop landscape theory for the generalized capacitance matrix and use it to predict the positions of three‐dimensional wave focusing and localization in random and non‐periodic systems of subwavelength resonators.

Topological Plasma Transport from a Diffusion View

Recent studies have identified plasma as a topological material. Yet, these researches often depict plasma as a fluid governed by electromagnetic fields, i.e., a classical wave system. Indeed, plasma transport can be characterized by a unique diffusion process distinguished by its collective behaviors. We adopt a simplified diffusion-migration method to elucidate the topological plasma transport. Drawing parallels to the thermal conduction-convection system, we introduce a double-ring model to investigate the plasma density behaviors in the anti-parity-time reversal (APT) unbroken and broken phases. Subsequently, by augmenting the number of rings, we have established a coupled ring chain structure. This structure serves as a medium for realizing the APT symmetric one-dimensional (1D) reciprocal model, representing the simplest tight-binding model with a trivial topology. To develop a model featuring topological properties, we should modify the APT symmetric 1D reciprocal model from the following two aspects: hopping amplitude and onsite potential. From the hopping amplitude, we incorporate the non-reciprocity to facilitate the non-Hermitian skin effect, an intrinsic non-Hermitian topology. Meanwhile, from the onsite potential, the quasiperiodic modulation has been adopted onto the APT symmetric 1D reciprocal model. This APT symmetric 1D Aubry–André–Harper model is of topological nature. Additionally, we suggest the potential applications for these diffusive plasma topological states. This study establishes a diffusion-based approach to realize topological states in plasma, potentially inspiring further advancements in plasma physics.

Higher-order elastic topological insulators with reconfigurable route and tunable corner states

In recent years, topological insulators (TIs) have been introduced in classical wave systems as a new type of quantum material, opening up new ways and approaches for manipulating the propagation of acoustic/elastic waves. The excellent topological protection characteristics of the edge states and corner states in TIs have the potential to significantly impact various scientific and technological advancements, which has attracted widespread attention from the academic community. However, in the case of the majority of elastic TIs, the application is significantly restricted by the fixed interface path and corner state frequency once the structural materials are prepared. To overcome this limitation, this paper presents an elastic TI with reconfigurable topological paths. By manipulating the rotation angle of each unit cell's eccentric cylinder, it becomes feasible to achieve interface paths of any desired shape. Numerical simulation and experimental results indicate that elastic waves exclusively propagate along topological interface paths of different configurations, demonstrating excellent robustness to defects. Furthermore, by incorporating magnetorheological elastomers into the structure, it becomes possible to generate higher-order corner states by adjusting the width of the connected narrow bands. For a structure composed of nontrivial unit cells, it is possible to generate edge states as well as two distinct types of corner states. Elastic waves exhibit strong confinement to edges or corner points and have topological protection properties. By harnessing the magnetorheological effect, it becomes possible to overcome the limitations of traditional higher-order topological insulators, where the corner state frequency is fixed. This approach allows for active manipulation of the working frequency by applying different magnetic fields. Consequently, this research provides valuable insights and serves as a reference for designing intelligent elastic waveguide devices and energy harvesting devices.

Geometric Phase in Twisted Topological Complementary Pair.

Geometric phase enabled by spin-orbit coupling has attracted enormous interest in optics over the past few decades. However, it is only applicable to circularly-polarized light and encounters substantial challenges when applied to wave fields lacking the intrinsic spin degree of freedom. Here, a new paradigm is presented for achieving geometric phase by elucidating the concept of topological complementary pair (TCP), which arises from the combination of two compact phase elements possessing opposite intrinsic topological charge. Twisting the TCP leads to the generation of a linearly-varying geometric phase of arbitrary order, which is quantified by the intrinsic topological charge. Notably distinct from the conventional spin-orbit coupling-based theories, the proposed geometric phase is the direct result of the cyclic evolution of orbital-angular-momentum transformation in mode space, thereby exhibiting universality across classical wave systems. As a proof of concept, the existence of this geometric phase is experimentally demonstrated using scalar acoustic waves, showcasing the remarkable ability in the precise manipulation of acoustic waves at subwavelength scales. These findings engender a fresh understanding of wave-matter interaction in compact structures and establish a promising platform for exploring geometric phase, offering significant opportunities for diverse applications in wave systems.

High-order mode interface states of surface water waves based on non-Bragg resonances

In this paper, we connect two periodic channels with bandgaps of different physical properties to form a heterojunction of surface water waves, which realize a high-order mode water wave interface state and concentrate the water wave energy near the heterojunction interface. By introducing a spatial symmetry breaking mechanism, we obtain a periodic channel with non-Bragg bandgaps due to different mode resonances. At a similar central frequency of the gap, another periodic channel is designed to generate Bragg bandgaps of the same mode resonances. The results of the mode analysis indicate that the localized region of the interface state in the frequency range of the non-Bragg bandgap contains a high-order mode component, which is dominant. The interface states induced by the high-order modes are much more efficient in wave accumulation. By introducing defect structures with different lengths, the frequency tuning of the high-order mode interface states is also achieved. The high-order mode interface state provides a different way for wave aggregation, and its implementation is also applicable to other classical wave systems due to the ubiquity of wave phenomena.

Multifunctional applications of topological valley-locked elastic waves

Topological valley metamaterial in classical wave systems has shown great potential for manipulating electromagnetic, acoustic, and elastic waves due to the defect-immune and lossless energy properties. The application prospects of topological valley material on signal processing, structural damage detection, and energy harvesting are worth exploring further. In this study, we combine the valley Hall effect and the tunneling effect of local resonant metamaterials to reveal some novel coupling transport phenomena in elastic systems. Some potential applications are explored experimentally and numerically. First, we implement a low-frequency (<1 kHz) valley-locked waveguide in heterostructures based on the topological valley edge state of the local resonant metamaterial. The robustness of the topological valley-locked waveguide under wide valley-locked layers, impurities, disorder, and bends is verified. Next, we introduce tunneling phenomena into the topological valley-locked waveguide, enabling the realization of an on-off controllable heterojunction by sandwiching crystals with different Dirac cones. The difference between the transmission characteristics of valley-locked waveguides under different tunneling layers (potential barrier and well) is revealed. Finally, we explore potential applications such as signal splitters, energy concentrators, and logical gates, both numerically and experimentally. Beyond the presented applications, this research has promising application prospects for vibration signal processing and high-performance energy harvesting.

Observation of robust edge mode and in-gap corner mode in Kagome surface-wave photonic crystals.

Recent theory has demonstrated that Kagome photonic crystals (PCs) support first-order and second-order topological phenomena. Here, we extend the topological physics of the Kagome lattice to surface electromagnetic waves and experimentally show a Kagome surface-wave PC. Under the protection of first-order and second-order topologies, both robust edge modes and in-gap corner modes are observed. The robust transport of edge modes is demonstrated by high transmission through the waveguide with a sharp bend. The localized corner mode is found at the corner with one isolated rod when a triangle-shaped sample is constructed. Our work not only shows a platform to mimic the topological physics in classical wave systems, but also offers a potential application in designing high-performance photonic devices.

Classical Majorana-like zero modes in an acoustic Kitaev chain

The one-dimensional Kitaev chain, being one of the most significant superconductor models that support Majorana fermions, has been considered as a highly probable method to host nonlocal qubits for topological quantum computation. Here we theoretically introduce the concept into the classical-wave systems and report the first experimental prototype of the acoustic Kitaev chain. We rigorously demonstrate the acoustic correspondence of the Kitaev chain and experimentally observe the classical unpaired Majorana-like zero mode in a well-designed acoustic spinless $p$-wave superconductor. In particular, clear physical evidence also demonstrates such exotic acoustic modes can be manipulated to a certain extend like a quasiparticle, which is directly identified by employing a Kitaev ``keyboard.'' These results are expected to open new avenues for novel applications of topological acoustics.

Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks

Flat-band topologies and localizations in noninteracting systems are extensively studied in different quantum and classical-wave systems. Recently, the exploration on the novel physics of flat-band localizations and topologies in interacting systems has aroused great interest. In particular, it is theoretically shown that the strong interaction could drive the formation of nontrivial topological flat bands; even dispersive trivial bands dominate the single-particle counterparts. However, the experimental observation of those interesting phenomena is still lacking. Here, we experimentally simulate the interaction-induced flat-band localizations and topological edge states in electrical circuit networks. We directly map the eigenstates of two correlated bosons in one-dimensional Aharonov-Bohm cages to modes of two-dimensional circuit lattices. In this case, by tuning the effective interaction strength through circuits' groundings, the two-boson flat bands and topological edge states are detected by measuring frequency-dependent impedance responses and voltage dynamics in the time domain. Our finding suggests a flexible platform to simulate the interaction-induced flat-band topology, and may possess potential applications in designing novel electronic devices.

Manipulation of electromagnetic waves induced by pseudomagnetic fields in two dimensional photonic crystals

Many interesting phenomena, such as quantization of Landau levels and quantum Hall effect, can occur in an electronic system under a strong magnetic field. However, photons do not carry charge, and they do not have many properties induced by external magnetic fields, either. Recently, the pseudomagnetic field, an artificial synthetic gauge field, has attracted intense research interest in classical wave systems, in which the propagation of the wave can be manipulated like in a real magnetic field. The photonic crystal is an optical structure composed of periodic material distributions and provides a good platform for studying the control of electromagnetic waves. In this work, we construct a uniform pseudomagnetic field by introducing uniaxial linear gradient deformation of metallic rods in a two-dimensional photonic crystal. The strong pseudomagnetic field leads to the quantization of photonic Landau levels in photonic crystal. The sublattice polarization of &lt;i&gt;n&lt;/i&gt; = 0 Landau level is also demonstrated in our simulations. Unlike the real magnetic field, the pseudomagnetic fields of photonic crystal is opposite in two inequivalent energy valleys, and the time-reversal symmetry of the system is not broken. Our designed gradient photonic crystals support the transport of edge state in the gap between &lt;i&gt;n&lt;/i&gt; = 0 and &lt;i&gt;n&lt;/i&gt; = ±1 Landau levels. The edge state can propagate unidirectionally when it is excited by a chiral source. When a gaussian beam impinges on the photonic crystal, the propagating paths of two splitting beams can be controlled, which gives rise to the bend of two beams. Two photonic crystals with opposite pseudomagnetic fields are assembled together, and the interesting phenomenon of “snake-state” can be obtained. Our proposal opens the way for designing information processing devices by manipulating electromagnetic waves.