Parity-Time Synthetic Phononic Media

Total acoustic transmission in a honeycomb network empowered by compact acoustic isolator

In recent years, acoustic metamaterials have exhibited extraordinary potential for manipulating the propagation of sound waves. However, it has been a challenge to control the propagation of sound waves through arbitrary pathways in a network. In this work, we designed a compact three-port isolator that can produce giant acoustic nonreciprocity by introducing actively controlled CNT films to the device without altering the geometric symmetry of it. This concept is subsequently applied to construct a 4 × 7 honeycomb network, in which, total transmission of sound wave in arbitrary pathway can be slickly achieved. Unlike the acoustic topological insulator, which only supports total transmission of arbitrary pathway in the band gap, our method provides more degrees of freedom and can be realized at any frequency. This ability opens up a new method for routing sound waves and exhibits promising applications ranging from acoustic communication to energy transmission.

Scattering Properties of an Acoustic Anti-Parity-Time-Symmetric System and Related Fabry–Perot Resonance Mode

The pursuit of artificial structures exhibiting unusual acoustic properties is a major scientific endeavor, in which anti-parity-time (PT) symmetry has been coming into view recent years. At the same time, with the emergence of new acoustic metamaterials, the classical Fabry–Perot resonance mode also exhibits fascinating scattering features similar to those of the anti-PT-symmetric system. We derive the generalized relation for the scattering parameters of an acoustic anti-PT-symmetric system with a transfer matrix, including conjugate bidirectional reflection coefficients and pure real feature of transmission coefficient. In the absence of the real or the imaginary (representing gain/loss) part of the refractive index, the anti-PT-symmetric system degrades into a pair of complementary media, resulting in the bidirectional total transmission. Moreover, a Fabry–Perot resonance mode exhibiting conjugate bidirectional reflection coefficients and a pure imaginary transmission coefficient has been demonstrated. Our results are meaningful for guiding the experimental test of an acoustic anti-PT-symmetric system and the design of associated bidirectional response prototype devices.

Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system

Non-Hermitian systems with parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. As the counterpart of conventional PT symmetry, anti-parity-time (APT) symmetry may lead to new insights and applications. Complementary to PT-symmetric systems, non-reciprocal and chiral mode switching for symmetry-broken modes have been reported in optics with an exceptional point dynamically encircled in the parameter space of an APT-symmetric system. However, it has remained an open question whether and how the APT-symmetry-induced chiral mode transfer could be realized in mechanical systems. This paper investigates the implementation of APT symmetry in a three-element mass–spring system. The dynamic encircling of an APT-symmetric exceptional point has been implemented using dynamic-modulation mechanisms with time-driven stiffness. It is found that the dynamic encircling of an exceptional point in an APT-symmetric system with the starting point near the symmetry-broken phase leads to chiral mode switching. These findings may provide new opportunities for unprecedented wave manipulation in mechanical systems.

Physics of surface vibrational resonances: pillared phononic crystals, metamaterials, and metasurfaces

The introduction of engineered resonance phenomena on surfaces has opened a new frontier in surface science and technology. Pillared phononic crystals, metamaterials, and metasurfaces are an emerging class of artificial structured media, featuring surfaces that consist of pillars-or branching substructures-standing on a plate or a substrate. A pillared phononic crystal exhibits Bragg band gaps, while a pillared metamaterial may feature both Bragg band gaps and local resonance hybridization band gaps. These two band-gap phenomena, along with other unique wave dispersion characteristics, have been exploited for a variety of applications spanning a range of length scales and covering multiple disciplines in applied physics and engineering, particularly in elastodynamics and acoustics. The intrinsic placement of pillars on a semi-infinite surface-yielding a metasurface-has similarly provided new avenues for the control and manipulation of wave propagation. Classical waves are admitted in pillared media, including Lamb waves in plates and Rayleigh and Love waves along the surfaces of substrates, ranging in frequency from hertz to several gigahertz. With the presence of the pillars, these waves couple with surface resonances richly creating new phenomena and properties in the subwavelength regime and in some applications at higher frequencies as well. At the nanoscale, it was shown that atomic-scale resonances-stemming from nanopillars-alter the fundamental nature of conductive thermal transport by reducing the group velocities and generating mode localizations across the entire spectrum of the constituent material well into the terahertz regime. In this article, we first overview the history and development of pillared materials, then provide a detailed synopsis of a selection of key research topics that involve the utilization of pillars or similar branching substructures in different contexts. Finally, we conclude by providing a short summary and some perspectives on the state of the field and its promise for further future development.

Optical Energy-Difference Conservation in a Synthetic Anti-PT-Symmetric System

Anti-parity-time (APT) symmetry is associated with various effects beyond the fundamental limitations implied in the standard Hermitian-Hamiltonian dynamics. Here, we create an optical APT-symmetric system in a synthetic frequency domain using a conventional fiber without intrinsic gain or loss and experimentally reveal photonic APT-symmetric effects, including energy-difference conservation and synchronized power oscillation, which have not yet been confirmed experimentally in the optical domain. The optical fiber-based APT-symmetric system has a long interaction length because of its negligible loss, and the APT-symmetric Hamiltonian is precisely tunable with optical pumping density and phase mismatch. On this basis, we observe the phase transition at exceptional points, energy-difference conservation, and synchronized power oscillation. Our results provide a robust theoretical and experimental framework connecting the emerging non-Hermitian physics with technologically important nonlinear fiber-optic interactions.

Topological mode switching in modulated structures with dynamic encircling of an exceptional point

Exceptional points are special degeneracies occurring in non-Hermitian systems at which both eigenfrequencies and eigenmodes coalesce simultaneously. Fascinating phenomena, including topological, non-reciprocal and chiral energy transfer between normal modes, have been envisioned in optical and photonic systems with the exceptional point dynamically encircled in the parameter space. However, it has remained an open question of whether and how topological mode switching relying on exceptional points could be achieved in mechanical systems. The present paper studies a two-mode mechanical system with an exceptional point and implements the dynamic encircling of such a point using dynamic modulation mechanisms with time-driven elasticity and viscosity. Topological mode switching with robustness against the input state and loop trajectories has been demonstrated numerically. It is found that the dynamical encircling of an exceptional point with the starting point near the symmetric phase leads to chiral mode transfer controlled mainly by the encircling direction, while non-chiral dynamics is observed for the starting point near the broken phase. Analyses also show that minor energy input is required in the process of encircling the exceptional point, demonstrating the intrinsically motivated behaviour of topological mode switching.

Anomalous Topological Edge States in Non-Hermitian Piezophononic Media

The bulk-boundary or bulk-edge correspondence is a principle relating surface confined states to the topological classification of the bulk. By marrying non-Hermitian ingredients in terms of gain or loss with media that violate reciprocity, an unconventional non-Bloch bulk-boundary correspondence leads to unusual localization of bulk states at boundaries-a phenomenon coined non-Hermitian skin effect. Here, we numerically employ the acoustoelectric effect in electrically biased and layered piezophononic media as a solid framework for non-Hermitian and nonreciprocal topological mechanics in the MHz regime. Thanks to a non-Hermitian skin effect for mechanical vibrations, we find that the bulk bands of finite systems are highly sensitive to the type of crystal termination, which indicates a failure of using traditional Bloch bands to predict the wave characteristics. More surprisingly, when reversing the electrical bias, we unveil how topological edge and bulk vibrations can be harnessed either at the same or opposite interfaces. Yet, while bulk states are found to display this unconventional skin effect, we further discuss how in-gap edge states in the same instant, counterintuitively are able to delocalize along the entire layered medium. We foresee that our predictions will stimulate new avenues in echo-less ultrasonics based on exotic wave physics.

Pseudochirality: A Manifestation of Noether's Theorem in Non-Hermitian Systems

Noether's theorem relates constants of motion to the symmetries of the system. Here we investigate a manifestation of Noether's theorem in non-Hermitian systems, where the inner product is defined differently from quantum mechanics. In this framework, a generalized symmetry that we term pseudochirality emerges naturally as the counterpart of symmetries defined by a commutation relation in quantum mechanics. Using this observation, we reveal previously unidentified constants of motion in non-Hermitian systems with parity-time and chiral symmetries. We further elaborate the disparate implications of pseudochirality induced constant of motion: It signals the pair excitation of a generalized "particle" and the corresponding "hole" but vanishes universally when the pseudochiral operator is antisymmetric. This disparity, when manifested in a non-Hermitian topological lattice with the Landau gauge, depends on whether the lattice size is even or odd. We further discuss previously unidentified symmetries of this non-Hermitian topological system, and we reveal how its constant of motion due to pseudochirality can be used as an indicator of whether a pure chiral edge state is excited.

Parity-Time Symmetry in Non-Hermitian Complex Optical Media

The exploration of quantum-inspired symmetries in optical and photonic systems has witnessed immense research interest both fundamentally and technologically in a wide range of subject areas in physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory and recently ramified into a diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant application prospects and engineering of novel materials. In addition, there has been increasing research interest in many emerging directions beyond optics and photonics. Here, the state-of-the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings are brought together, and key concepts, a background, and a detailed perspective on new emerging directions are described. It can be anticipated that this trendy field of interest will be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, optoelectronics, and beyond, and will offer distinctive application prospects in novel functional materials.

Tunable photo-responsive elastic metamaterials

The metamaterial paradigm has allowed an unprecedented space-time control of various physical fields, including elastic and acoustic waves. Despite the wide variety of metamaterial configurations proposed so far, most of the existing solutions display a frequency response that cannot be tuned, once the structures are fabricated. Few exceptions include systems controlled by electric or magnetic fields, temperature, radio waves and mechanical stimuli, which may often be unpractical for real-world implementations. To overcome this limitation, we introduce here a polymeric 3D-printed elastic metamaterial whose transmission spectrum can be deterministically tuned by a light field. We demonstrate the reversible doubling of the width of an existing frequency band gap upon selective laser illumination. This feature is exploited to provide an elastic-switch functionality with a one-minute lag time, over one hundred cycles. In perspective, light-responsive components can bring substantial improvements to active devices for elastic wave control, such as beam-splitters, switches and filters.

Ultrathin Acoustic Parity-Time Symmetric Metasurface Cloak

Invisibility or unhearability cloaks have been made possible by using metamaterials enabling light or sound to flow around obstacle without the trace of reflections or shadows. Metamaterials are known for being flexible building units that can mimic a host of unusual and extreme material responses, which are essential when engineering artificial material properties to realize a coordinate transforming cloak. Bending and stretching the coordinate grid in space require stringent material parameters; therefore, small inaccuracies and inevitable material losses become sources for unwanted scattering that are decremental to the desired effect. These obstacles further limit the possibility of achieving a robust concealment of sizeable objects from either radar or sonar detection. By using an elaborate arrangement of gain and lossy acoustic media respecting parity-time symmetry, we built a one-way unhearability cloak able to hide objects seven times larger than the acoustic wavelength. Generally speaking, our approach has no limits in terms of working frequency, shape, or size, specifically though we demonstrate how, in principle, an object of the size of a human can be hidden from audible sound.

Asymmetric scattering of flexural waves in a parity-time symmetric metamaterial beam

Non-Hermitian parity-time (PT) symmetric systems that possess real eigenvalues have been intensively investigated in quantum mechanics and rapidly extended to optics and acoustics demonstrating a lot of unconventional wave phenomena. Here, a PT symmetric metamaterial beam is designed based on shunted piezoelectric patches and asymmetric wave scattering in the form of flexural waves is demonstrated through analytical and numerical approaches. The gain and loss components in the PT symmetric beam are realized by the introduction of negative and positive resistances into the external shunting circuits, respectively. Effective medium theory and transfer matrix method are employed to determine the effective material parameters and scattering properties of the PT symmetric metamaterial beam. Unidirectional reflectionlessness has been demonstrated analytically and numerically, together with illustrations of the PT phase transition and exceptional points. The tunability of exceptional points is studied by changing the spacing between piezoelectric patches and shunting circuit parameters. The design explores complex material parameters of the beam structure, and could open unique ways to asymmetric wave control, enhanced sensing, amplification, and localization of flexural waves.

Non-Hermitian Sonic Second-Order Topological Insulator

Topological phases of matter that have been recently extended to topological phases of sound can confine acoustic energy at the corners of higher-order topological insulators. We broaden this concept by incorporating parity-time symmetry and show new topologically protected confinement rules that are dictated by the geometrical arrangement of gain and loss units. Particularly, our findings reveal how sound trapping occurs at all corners when parity-time symmetry is intact, beyond the exceptional point within the broken phase; however, opposite corners sustain either sink- or sourcelike states that could lead to novel non-Hermitian guides for sound.

Valley Physics in Non-Hermitian Artificial Acoustic Boron Nitride

The valley can serve as a new degree of freedom in the manipulation of particles or waves in condensed matter physics, whereas systems containing combinations of gain and loss elements constitute rich building units that can mimic non-Hermitian properties. By introducing gain and loss in artificial acoustic boron nitride, we show that the acoustic valley states and the valley-projected edge states display exotic behaviors in that they sustain either attenuated or amplified wave propagation. Our findings show how non-Hermiticity introduces a mechanism in tuning topological protected valley transports, which may have significance in advanced wave control for sensing and communication applications.

Fine manipulation of sound via lossy metamaterials with independent and arbitrary reflection amplitude and phase

The fine manipulation of sound fields is critical in acoustics yet is restricted by the coupled amplitude and phase modulations in existing wave-steering metamaterials. Commonly, unavoidable losses make it difficult to control coupling, thereby limiting device performance. Here we show the possibility of tailoring the loss in metamaterials to realize fine control of sound in three-dimensional (3D) space. Quantitative studies on the parameter dependence of reflection amplitude and phase identify quasi-decoupled points in the structural parameter space, allowing arbitrary amplitude-phase combinations for reflected sound. We further demonstrate the significance of our approach for sound manipulation by producing self-bending beams, multifocal focusing, and a single-plane two-dimensional hologram, as well as a multi-plane 3D hologram with quality better than the previous phase-controlled approach. Our work provides a route for harnessing sound via engineering the loss, enabling promising device applications in acoustics and related fields.

Unidirectional Wave Vector Manipulation in Two-Dimensional Space with an All Passive Acoustic Parity-Time-Symmetric Metamaterials Crystal

Exploring the concept of non-Hermitian Hamiltonians respecting parity-time symmetry with classical wave systems is of great interest as it enables the experimental investigation of parity-time-symmetric systems through the quantum-classical analogue. Here, we demonstrate unidirectional wave vector manipulation in two-dimensional space, with an all passive acoustic parity-time-symmetric metamaterials crystal. The metamaterials crystal is constructed through interleaving groove- and holey-structured acoustic metamaterials to provide an intrinsic parity-time-symmetric potential that is two-dimensionally extended and curved, which allows the flexible manipulation of unpaired wave vectors. At the transition point from the unbroken to broken parity-time symmetry phase, the unidirectional sound focusing effect (along with reflectionless acoustic transparency in the opposite direction) is experimentally realized over the spectrum. This demonstration confirms the capability of passive acoustic systems to carry the experimental studies on general parity-time symmetry physics and further reveals the unique functionalities enabled by the judiciously tailored unidirectional wave vectors in space.

Breaking the barriers: advances in acoustic functional materials

Acoustics is a classical field of study that has witnessed tremendous developments over the past 25 years. Driven by the novel acoustic effects underpinned by phononic crystals with periodic modulation of elastic building blocks in wavelength scale and acoustic metamaterials with localized resonant units in subwavelength scale, researchers in diverse disciplines of physics, mathematics, and engineering have pushed the boundary of possibilities beyond those long held as unbreakable limits. More recently, structure designs guided by the physics of graphene and topological electronic states of matter have further broadened the whole field of acoustic metamaterials by phenomena that reproduce the quantum effects classically. Use of active energy-gain components, directed by the parity–time reversal symmetry principle, has led to some previously unexpected wave characteristics. It is the intention of this review to trace historically these exciting developments, substantiated by brief accounts of the salient milestones. The latter can include, but are not limited to, zero/negative refraction, subwavelength imaging, sound cloaking, total sound absorption, metasurface and phase engineering, Dirac physics and topology-inspired acoustic engineering, non-Hermitian parity–time synthetic active metamaterials, and one-way propagation of sound waves. These developments may underpin the next generation of acoustic materials and devices, and offer new methods for sound manipulation, leading to exciting applications in noise reduction, imaging, sensing and navigation, as well as communications.

Tunable Asymmetric Transmission via Lossy Acoustic Metasurfaces

In this study, we show that robust and tunable acoustic asymmetric transmission can be achieved through gradient-index metasurfaces by harnessing judiciously tailored losses. We theoretically prove that the asymmetric wave behavior stems from loss-induced suppression of high order diffraction. We further experimentally demonstrate this novel phenomenon. Our findings could provide new routes to broaden applications for lossy acoustic metamaterials and metasurfaces.

Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling

We propose a scheme to achieve a controllable unidirectional reflectionless propagation at exceptional point (EP) in a non-ideal parity-time metasurface consisting of two silver ring resonators. The unidirectional reflectionless propagation can be manipulated by simply adjusting the angle of incident wave and the distance s between two silver rings based on the far field coupling. In addition, the angle of incident wave in a wide range of ∼25° is available to achieve the unidirectional reflectionless propagation. Moreover, the unidirectional reflectionless propagation at EP is insensitive to the polarization of incident wave due to the two-ring structure.

PT-Symmetric Scattering in Flow Duct Acoustics

We show theoretically and experimentally that the propagation of an acoustic wave in an airflow duct going through a pair of diaphragms, with equivalent amounts of mean-flow-induced effective gain and loss, displays all the features of a parity-time (PT) symmetric system. Using a scattering matrix formalism, we observe, experimentally, the properties which reflect the PT symmetry of the scattering acoustical system: the existence of spontaneous symmetry breaking with symmetry-broken pairs of scattering eigenstates showing amplification and reduction, and the existence of points with unidirectional invisibility.

Multiple Quantum Wells for PT-Symmetric Phononic Crystals

We demonstrate that the parity-time symmetry for sound is realized in laser-pumped multiple-quantum-well structures. Breaking of the parity-time symmetry for the phonons with wave vectors corresponding to the Bragg condition makes the structure a highly selective acoustic wave amplifier. Single-mode distributed feedback phonon lasing is predicted for structures with realistic parameters.

Coherent perfect absorption in one-sided reflectionless media

In optical experiments one-sided reflectionless (ORL) and coherent perfect absorption (CPA) are unusual scattering properties yet fascinating for their fundamental aspects and for their practical interest. Although these two concepts have so far remained separated from each other, we prove that the two phenomena are indeed strictly connected. We show that a CPA–ORL connection exists between pairs of points lying along lines close to each other in the 3D space-parameters of a realistic lossy atomic photonic crystal. The connection is expected to be a generic feature of wave scattering in non-Hermitian optical media encompassing, as a particular case, wave scattering in parity-time (PT) symmetric media.