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Field transformation, as an extension of the transformation optics, provides a unique means for nonreciprocal wave manipulation, while the experimental realization remains a substantial challenge as it requires stringent material parameters of the metamaterials, e.g., purely nonreciprocal bianisotropic parameters. Here, we develop and demonstrate a nonreciprocal field transformation in a two-dimensional acoustic system, using an active metasurface that can independently control all constitutive parameters and achieve purely nonreciprocal Willis coupling. The field-transforming metasurface enables tailor-made field distribution manipulation, achieving localized field amplification by a predetermined ratio. The metasurface demonstrates the self-adaptive capability to various excitation conditions and can be extended to other geometric shapes. The metasurface also achieves nonreciprocal wave propagation for internal and external excitations, demonstrating a one-way acoustic device. The nonreciprocal field transformation not only extends the framework of the transformation theory for nonreciprocal wave manipulation but also holds great potential in applications such as ultrasensitive sensors and nonreciprocal communication. Copyright © 2024 the Authors, some rights reserved.

Non-Abelian phenomena arise when the sequence of operations on physical systems influences their behaviors. By possessing internal degrees of freedom such as polarization, light and sound can be subjected to various manipulations, including constituent materials, structured environments, and tailored source conditions. These manipulations enable the creation of a great variety of Hamiltonians, through which rich non-Abelian phenomena can be explored and observed. Recent developments have constituted a versatile testbed for exploring non-Abelian physics at the intersection of atomic, molecular, and optical physics; condensed matter physics; and mathematical physics. These fundamental endeavors could enable photonic and acoustic devices with multiplexing functionalities. Our review aims to provide a timely and comprehensive account of this emerging topic. Starting from the foundation of matrix-valued geometric phases, we address non-Abelian topological charges, non-Abelian gauge fields, non-Abelian braiding, non-Hermitian non-Abelian phenomena, and their realizations with photonics and acoustics and conclude with future prospects. © 2024 American Association for the Advancement of Science. All rights reserved.

Recently, synthetic spin-orbit coupling has been introduced into cold-atom systems for more flexible control of the Hamiltonian, which was further made time varying through two-photon detuning to achieve dynamic control of the cold-atom state. While an intraband transition can be adiabatically obtained, a complete interband transition, rather than a superposition of different bands, obtained through fast sweeping is usually guaranteed by having the positions of the initial and final states be far away from any band gap in the quasimomentum space. Here, by introducing an additional non-Hermitian parameter through an atom-loss contrast together with two-photon detuning as two controllable external parameters, both intraband and complete interband transitions can be achieved independent of the positions of the initial and final states. In addition, a “point-source diagram” approach in the two-dimensional external parameter space is developed to visualize and predict the locations of any nonadiabatic transitions. This control protocol can have potential applications in quantum state control and quantum simulations using cold-atom systems.

Accurately measuring magnetic fields is essential for magnetic-field sensitive experiments in areas like atomic, molecular, and optical physics, condensed matter experiments, and other areas. However, since many experiments are often conducted in an isolated environment that is inaccessible to experimentalists, it can be challenging to accurately determine the magnetic field at the target location. Here, we propose an efficient method for detecting magnetic fields with the assistance of an artificial neural network (NN). Instead of measuring the magnetic field directly at the desired location, we detect fields at several surrounding positions, and a trained NN can accurately predict the magnetic field at the target location. After training, we achieve a below 0.3% relative prediction error of magnetic field magnitude at the center of the vacuum chamber, and successfully apply this method to our erbium quantum gas apparatus for accurate calibration of magnetic field and long-term monitoring of environmental stray magnetic field. The demonstrated approach significantly simplifies the process of determining magnetic fields in isolated environments and can be applied to various research fields across a wide range of magnetic field magnitudes.

Metasurfaces have recently opened up applications in the quantum regime, including quantum tomography and the generation of quantum entangled states. With their capability to store a vast amount of information by utilizing the various geometric degrees of freedom of nanostructures, metasurfaces are expected to be useful for processing quantum information. Here, we propose and experimentally demonstrate a programmable metasurface capable of performing quantum algorithms using both classical and quantum light with single photons. Our approach encodes multiple programmable quantum algorithms and operations, such as Grover's search algorithm and the quantum Fourier transform, onto the same metalens array on a metasurface. A spatial light modulator selectively excites different sets of metalenses to carry out the quantum algorithms, while the interference patterns captured by a single-photon camera are used to extract information about the output state at the selected output directions. Our programmable quantum metasurface approach holds promising potential as a cost-effective means of miniaturizing components for quantum computing and information processing.

Manipulating elastic waves using a transformation approach is challenging due to the complex constitutive relationship. However, for flexural waves, approximated as scalar waves, two straightforward approaches emerge based on geometric curvature and plate thickness. Here, we develop transformation theory to establish equivalence between curved plates of different shapes and thickness profiles. Introducing tailor-made thickness profiles on a given curved shape enables illusion effects, where flexural waves propagate as if on a flat plate or on another curved plate with a totally different configuration. Numerical simulations and experimental field mapping confirm the effectiveness of these illusions. Our approach to flexural wave illusion finds applications in structural designs with material and shape constraints and holds the potential for absorption or vibration control, wavefront shaping, chaotic dynamics, and topology control.

Metasurfaces designed with deep learning approaches have emerged as efficient tools for manipulating electromagnetic waves to achieve beam steering and power allocation objectives. However, the effects of complex environmental factors like obstacle blocking and other unavoidable scattering need to be sufficiently considered for practical applications. In this work, we employ an experiment-based deep learning approach for programmable metasurface design to control powers delivered to specific locations generally with obstacle blocking. Without prior physical knowledge of the complex system, large sets of experimental data can be efficiently collected with a programmable metasurface to train a deep neural network (DNN). The experimental data can inherently incorporate complex factors that are difficult to include if only simulation data are used for training. Moreover, the DNN can be updated by collecting new experimental data on-site to adapt to changes in the environment. Our proposed experiment-based DNN demonstrates significant potential for intelligent wireless communication, imaging, sensing, and quiet-zone control for practical applications.

We demonstrate an integrated deep-learning neural network that generates metasurface designs directly from independent polarization holograms, with a maximum of four different co- and cross- polarization conversion channels. This is achieved by extending the existing DeepCGH network with an inverse designcomponent. Our approach enables a systematic design route for polarization holograms directly from an existing metamaterial library without requiring detailed knowledge of the constraints. Furthermore, it can be adapted for other multiplexing holograms that require automated designs. © 2023, META Conference. All rights reserved.

We develop an approach to map the quantum optical scattering of linear dissipative metasurfaces to Liouvillian dynamics, based on the effective Hamiltonian of the metasurfaces in a fictitious time. Our approach enables us to specify the generalized eigenspace of the Liouvillian superoperator, allowing us to analytically obtain the input-output relationship of the density matrix and the photon transition probabilities. This work facilitates the straightforward modeling of non-Hermitian metasurfaces in the quantum regime, directly from the specification of classical scattering matrix. © 2023, META Conference. All rights reserved.

We propose and experimentally demonstrate a programmable matrix computation in the optical domain using a spatial light modulator (SLM) and a metalens array. Our scheme encodes the programmable matrix to the metalens array by superimposing multiple phase gradients. Meanwhile, the SLM produces a phase-controlled spatial illuminated light which acts as our phase-controlled spatial illuminated light which acts as our input vector. Then, the result can be extracted from the far-field interference pattern constructed by different metalenses using a pattern recognition method. © 2023, META Conference. All rights reserved.

We demonstrate the use of a space-time-coding digital metasurface operating in the microwave regime to experimentally generate various modes of time-varying orbital angular momentum (OAM) beams. By developing a time-domain field mapping technique, we are able to observe the generated time-varying OAM. Moreover, we explore an additional higher-order twist in the wavefront structure of time-varying OAM beams based on the flexible programmability of the metasurface. These proposed time-varying OAM beams hold potential for applications in communication and particle manipulation. © 2023, META Conference. All rights reserved.

We propose and experimentally demonstrate a scheme to remotely and continuously control the vortex beam structure using polarization-entangled photon pairs together with a metasurface. With a heralding technique adopted, the spin-orbit coupling provided by the metasurface translates to a tailor-made entanglement of the orbital angular momentum and the polarization of the signal photon. Then, the polarization of the heralding photon is used to remotely control the vortex structure of the signal photon, directly manifested as a continuous orbital rotation. © 2023, META Conference. All rights reserved.

The effective medium theory is a key concept in metamaterials, with a growing interest in the temporal effec-tive medium when the constitutive parameters are modulated with a period much shorter than the signal period. However, the effective medium with both frequency dispersion and time-varying resonating parameters is not clearly understood. In this work, we establish the temporal effective medium theory for acoustic metamaterials with time-varying frequency dispersion for compressibility. The formulas for the effective medium vary with the modulation of different resonance parameters and the transition from frequency-dispersive to-nondispersive regimes. Through experiments and theoretical models, we determine that time-varying resonance strength corresponds to the temporal average of compressibility beta, time-varying resonating frequency corresponds to the temporal average of 1/(beta-beta 0) in the frequency-dispersive regime, and time-varying modulation amplitude in the nondispersive regime corresponds to the temporal average of 1/beta. These results clarify the effective medium for frequency-dispersive time-varying metamaterials and have potential applications in different classical waves such as acoustics, elastodynamics, and electromagnetism for designing temporal functional devices.

We propose a concept called acoustic amplifying diode combining signal isolation and amplification in a single device. The signal is exponentially amplified in one incident direction with no reflection and is perfectly absorbed in another. The reflection is eliminated from the device in both directions with impedance matching, preventing backscattering to the signal source. Here, we demonstrate the amplifying diode using an active metamaterial with nonreciprocal Willis coupling. We also discuss the situation with the presence of both reciprocal and nonreciprocal Willis couplings for more flexibility in implementation. The coexistence of both amplifier and perfect absorber in opposite incident directions extends the regime of sound isolation and further enables applications in sensing and communication, in which nonreciprocity can play an important role.

Metasurfaces utilize engineered nanostructures to achieve control on all possible dimensions of light, encouraging versatile applications, including beam steering, multifunctional lensing, and multiplexed holograms. Towards the quantum optical regime for metasurfaces, although significant efforts have been put into generating and analyzing specific quantum states, control schemes to further manipulate these quantum states or information are still limited. Here, based on a metasurface, we propose and experimentally demonstrate a continuous heralding scheme to remotely control a vortex beam with high robustness to noise using polarization-entangled photon pairs. Our metasurface entangles polarization and orbital angular momentum (OAM) and the polarization selection on heralding photon erases the which-OAM information on signal photon. It induces an interference of two different OAM states remotely, manifesting a continuous orbital rotation. Our results show that metasurfaces have potential applications in quantum communication and information processing in entangling information with increasing complexity in the content.

Circular dichroism (CD) is an intriguing chiroptical phenomenon associated with the interaction of chiral structures with circularly polarized lights. Although the CD effect has been extensively studied in optics, it has not yet been demonstrated in acoustic systems. Here, we demonstrate the acoustic CD effect in a three-dimensional chiral metamaterial supporting circularly polarized transverse sound. We find that the effect is negligible in the lossy metamaterial possessing C4 rotational symmetry but can be strongly enhanced in the C2-symmetric system with inhomogeneous loss. The phenomena can be understood based on the properties of the metamaterial's complex band structure and the quality factors of its eigenmodes. We show that the enhanced CD in the C2-symmetric system is attributed to the polarization band gaps and the non-Hermitian exceptional points appearing near the Brillouin-zone center and boundaries. The results contribute to the understanding of chiral sound-matter interactions and can find applications in acoustic sensing of chiral structures and sound manipulations based on vector properties.

The recently proposed extreme-ultraviolet beams with time-varying orbital angular momentum (OAM) realized by high-harmonic generation provide extraordinary tools for quantum excitation control and particle manipulation. However, such an approach is not easily scalable to other frequency regimes. We design a space-time-coding digital metasurface operating in the microwave regime to experimentally generate time-varying OAM beams. Due to the flexible programmability of the metasurface, a higher-order twist in the envelope wavefront structure of time-varying OAM beams can be further designed as an additional degree of freedom. The time-varying OAM field patterns are dynamically mapped by developing a two-probe measurement technique. Our approach in combining the programmability of space-time-coding digital metasurfaces and the two-probe measurement technique provides a versatile platform for generating and observing time-varying OAM and other spatiotemporal excitations in general. The proposed time-varying OAM beams have application potentials in particle manipulation, time-division multiplexing, and information encryption.

Recently, multiple studies have suggested that exceptional points (EPs) in lossless nonlinear optical systems can minimize quantum noise arising from the material gain and loss in conventional non-Hermitian systems, offering the possibility of quantum EP sensing. Meanwhile, nonlinear SU(1,1) interferometers have been established as useful in sensing due to their reduced quantum noise. In this work, we demonstrate the existence of EPs in a dual-beam SU(1,1) interferometer with two nonlinear parametric amplifiers. Our analysis of the input-output matrix in terms of joint quadrature amplitudes shows that EPs can be linked to both high signal, through a zero matrix element, and low noise, through noise preservation, in sensing by selecting an appropriate operation gauge of the quadrature amplitudes. Additionally, for a multistage SU(1,1) interferometer, EPs of the overall input-output matrix form multiple bands of high signal-to-noise ratio (SNR) which further separate into two phases indicated by the EPs of the transfer matrix of a repeating unit. Our investigations demonstrate the significance of quantum EPs in quantum interferometer sensing and broaden the operating regimes from diabolical points in some of the conventional SU(1,1) interferometers to EPs while still maintaining a high SNR.

Multiplexing holography with metasurfaces using different degrees of freedom of light has enabled recent applications in display and information processing. In terms of polarization-multiplexed holograms, the most general form is an arbitrary Jones matrix profile in storing the maximum amount of information. It requires a relaxation to bianisotropic metasurfaces from a conventional single-layer implementation of nanostructures, but it will also complicate both the inverse design of the nanostructures and the hologram generation algorithm. Here, an integrated neural network approach, being extended from the recent DeepCGH algorithm, is developed to obtain metasurface structural profiles directly from independent holograms from an arbitrary set of polarizations to another, with maximally four different co- and cross-polarization conversion channels. Such an information-driven approach enables designing complex polarization holograms directly from an existing metamaterial library without detailed physical knowledge on the constraints, and can be extended to other multiplexing holograms to further facilitate an efficient usage of the information stored on a metasurface. © 2023 The Authors. Advanced Optical Materials published by Wiley-VCH GmbH.

Two-photon interference is an important effect that is tightly related to the quantum nature of light. Recently, it has been shown that the photon bunching from the Hong-Ou-Mandel (HOM) effect can be used for quantum imaging in which sample properties (reflection/transmission amplitude, phase delay, or polarization) can be characterized at the pixel-by-pixel level. In this work, we perform Jones matrix imaging for an unknown object based on two-photon interference. By using a reference metasurface with panels of known polarization responses in pairwise coincidence measurements, the object's polarization responses at each pixel can be retrieved from the dependence of the coincidence visibility as a function of the reference polarization. The post-selection of coincidence images with specific reference polarization in our approach eliminates the need in switching the incident polarization and thus parallelized optical measurements for Jones matrix characterization. The parallelization in preparing input states, prevalent in any quantum algorithms, is an advantage of adopting two-photon interference in Jones matrix imaging. We believe our work points to the usage of metasurfaces in biological and medical imaging in the quantum optical regime.

Exceptional points (EPs), which are typically defined as the degeneracy points of a non-Hermitian Hamiltonian, have been investigated in various physical systems such as photonic systems. In particular, the intriguing topological structures around EPs have given rise to novel strategies for manipulating photons and the underlying mechanism is especially useful for on-chip photonic applications. Although some on-chip experiments with the adoption of lasers have been reported, EP-based photonic chips working in the quantum regime largely remain elusive. In the current work, a single-photon experiment was proposed to dynamically encircle an EP in on-chip photonic waveguides possessing passive anti-parity-time symmetry. Photon coincidences measurement reveals a chiral feature of transporting single photons, which can act as a building block for on-chip quantum devices that require asymmetric transmissions. The findings in the current work pave the way for on-chip experimental study on the physics of EPs as well as inspiring applications for on-chip non-Hermitian quantum devices. © 2023 The Author(s)

Second-order phononic topological insulators (SPTIs) featured with topological edge and corner states offer promising ways for steering elastic waves. However, existing SPTIs were mainly designed with trial-and-error procedures, limiting the achievable width of topological bandgaps for tightly confining edge and corner states. Here, we develop a topology optimization approach for designing quantum spin Hall effect-based SPTIs. By simultaneously maximizing the powers emitted by the artificially selected body forces via topology optimization, the dipolar and quadrupolar modes are excited at the desirable frequencies. As a result, topologically nontrivial and trivial phononic crystals (PCs) with a record-breaking size of the overlapped bandgap (36.14%) are created. Thereafter, SPTIs arranged by hexagon and rhombus unit cells extracted from the optimized PCs are successfully created, validating the effectiveness of the optimization results. Additionally, the spatial decay of corner states is quantitatively characterized based on the complex band theory. Our work bridges topology optimization with SPTIs and, meanwhile, enriches the mechanism of corner states. © 2021 Elsevier Ltd

Spin–orbit coupling is an essential mechanism underlying quantum phenomena such as the spin Hall effect and topological insulators1. It has been widely studied in well-isolated Hermitian systems, but much less is known about the role dissipation plays in spin–orbit-coupled systems2. Here we implement dissipative spin–orbit-coupled bands filled with ultracold fermions, and observe parity-time symmetry breaking as a result of the competition between the spin–orbit coupling and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables us to tune the energy gap and close it at the critical dissipation value, the so-called exceptional point3. In the vicinity of the critical point, the state evolution exhibits a chiral response, which enables us to tune the spin–orbit coupling and dissipation dynamically, revealing topologically robust chiral spin transfer when the quantum state encircles the exceptional point. This demonstrates that we can explore non-Hermitian topological states with spin–orbit coupling. © 2022, The Author(s), under exclusive licence to Springer Nature Limited.

We investigate the scattering properties of coupled parity-time (PT) symmetric chiral nanospheres with scattering matrix formalism. The exceptional points, i.e., spectral singularities at which the eigenvalues and eigenvectors simultaneously coalesce in the parameter space, of scattering matrix can be tailored by the chirality of the nanospheres. We also calculate the scattering, absorption and extinction cross sections of the PT-symmetric chiral scatter under illumination by monochromatic left- and right-circularly polarized plane waves. We find that the scattering cross section of the nanostructures exhibits an asymmetry when the plane waves are incident from the loss and gain regions, respectively, especially in the broken phase, and the optical cross section exhibits circular dichroism, i.e., differential extinction when the PT-symmetric scatter is endowed with chirality. In particular, under illumination by linearly polarized monochromatic plane waves without intrinsic chirality, the ellipticity of scattered fields in the forward direction, denoting the chirality of light, becomes larger when the scatter is in the PT-symmetry-broken phase. Our findings demonstrate that the gain and loss can control the optical chirality and enhance the chiroptical interactions and pave the way for studying the resonant chiral light-matter interactions in non-Hermitian photonics. © 2022 Xiaolin Chen et al., published by De Gruyter, Berlin/Boston 2022.

Space−time modulated metamaterials support extraordinary rich applications, such as parametric amplification, frequency conversion, and non-reciprocal transmission. The non-Hermitian space−time varying systems combining non-Hermiticity and space−time varying capability, have been proposed to realize wave control like unidirectional amplification, while its experimental realization still remains a challenge. Here, based on metamaterials with software-defined impulse responses, we experimentally demonstrate non-Hermitian space−time varying metamaterials in which the material gain and loss can be dynamically controlled and balanced in the time domain instead of spatial domain, allowing us to suppress scattering at the incident frequency and to increase the efficiency of frequency conversion at the same time. An additional modulation phase delay between different meta-atoms results in unidirectional amplification in frequency conversion. The realization of non-Hermitian space−time varying metamaterials will offer further opportunities in studying non-Hermitian topological physics in dynamic and nonreciprocal systems. © 2022, The Author(s).

Spin–orbit coupling is an essential mechanism underlying quantum phenomena such as the spin Hall effect and topological insulators1. It has been widely studied in well-isolated Hermitian systems, but much less is known about the role dissipation plays in spin–orbit-coupled systems2. Here we implement dissipative spin–orbit-coupled bands filled with ultracold fermions, and observe parity-time symmetry breaking as a result of the competition between the spin–orbit coupling and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables us to tune the energy gap and close it at the critical dissipation value, the so-called exceptional point3. In the vicinity of the critical point, the state evolution exhibits a chiral response, which enables us to tune the spin–orbit coupling and dissipation dynamically, revealing topologically robust chiral spin transfer when the quantum state encircles the exceptional point. This demonstrates that we can explore non-Hermitian topological states with spin–orbit coupling. © 2022, The Author(s), under exclusive licence to Springer Nature Limited.

Over the past decades, wave localization and a wide variety of related phenomena have come to the forefront of research. Here, we theoretically and experimentally investigate the localization and delocalization of the flat-band states in an acoustic cubic lattice. Under evanescent couplings, the band structure of the designed cubic lattice has two dispersive bands and two degenerate flat bands. According to the analyses, we find that the constructions of flat-band states only depend on the excitation pressures and the coupling coefficients, which are frequency independent. With the flat-band state excitation, the acoustic wave can be either localized or delocalized in the lattice, which is determined by the excitation frequency. When the excitation frequency is close to the flat-band frequency of the lattice, the flat-band state can spread into the whole cubic lattice due to the resonance energy transfer among primitive cells. On the other hand, when the excitation frequency deviates from the flat-band frequency, the flat-band state can be localized in any primitive cell of the designed lattice. This work lays the groundwork for exploring the high-dimensional bound states in acoustic systems and has potential impacts on the applications of acoustic sensing and sound energy harvesting. © 2022 American Physical Society.

We investigate the scattering properties of coupled parity-time (PT) symmetric chiral nanospheres with scattering matrix formalism. The exceptional points, i.e., spectral singularities at which the eigenvalues and eigenvectors simultaneously coalesce in the parameter space, of scattering matrix can be tailored by the chirality of the nanospheres. We also calculate the scattering, absorption and extinction cross sections of the PT-symmetric chiral scatter under illumination by monochromatic left- and right-circularly polarized plane waves. We find that the scattering cross section of the nanostructures exhibits an asymmetry when the plane waves are incident from the loss and gain regions, respectively, especially in the broken phase, and the optical cross section exhibits circular dichroism, i.e., differential extinction when the PT-symmetric scatter is endowed with chirality. In particular, under illumination by linearly polarized monochromatic plane waves without intrinsic chirality, the ellipticity of scattered fields in the forward direction, denoting the chirality of light, becomes larger when the scatter is in the PT-symmetry-broken phase. Our findings demonstrate that the gain and loss can control the optical chirality and enhance the chiroptical interactions and pave the way for studying the resonant chiral light-matter interactions in non-Hermitian photonics. © 2022 Xiaolin Chen et al., published by De Gruyter, Berlin/Boston 2022.

The closed form expressions of the effective properties in periodic fluid laminates are derived thanks to the Padé approximation of the transfer matrix. A second-order Taylor expansion of the transfer matrix elements exhibits Willis coupling. This coupling is the sum of a local term and a nonlocal term. The nonlocal term arises from the apparent bulk modulus in quasi one-dimensional problems. The nonlocality directly impacts the governing equations modeling the acoustic wave propagation in these Willis materials, which then involve convolution products in space. As an example, a two-orthotropic porous material laminate is considered. The theoretically derived effective properties and scattering coefficients are found in excellent agreement with those numerically calculated. The Willis coupling widens the frequency range of validity and accuracy of the effective properties and thus of the calculated scattering coefficients when compared to classical homogenization results for which the Willis coupling is absent. This widening mostly relies on the effect of Willis coupling on the impedance of the fluid laminate. The effective properties are finally derived for a general laminate.

Metasurfaces provide a promising route for structuring light and generating holograms with designed amplitude, phase, and polarization profiles, leading to a versatile platform for integrating and constructing optical components beyond the conventional ones. At the same time, incorporating coincidence in imaging allows a high signal-to-noise ratio for imaging in very low light levels. As beneficial from the recent development in both metasurfaces and single-photon avalanche diode (SPAD) cameras, we combine the polarization-sensitive capability of metasurfaces with Hong-Ou-Mandel (HOM)-type interference in generating images with tailor-made two-photon interference and polarization coincidence signatures. By using orthogonal linear-polarized photons as incidence, correlated, anticorrelated, and uncorrelated polarization coincidence features can be observed within the same image from the pairwise second-order coherence statistics across different pixels of the image. Our work adds polarization to the demonstrated amplitude and phase sensitivity in the domain of “HOM microscopy” and can be useful for biological and security applications.

Second-order phononic topological insulators (SPTIs) featured with topological edge and corner states offer promising ways for steering elastic waves. However, existing SPTIs were mainly designed with trial-and-error procedures, limiting the achievable width of topological bandgaps for tightly confining edge and corner states. Here, we develop a topology optimization approach for designing quantum spin Hall effect-based SPTIs. By simultaneously maximizing the powers emitted by the artificially selected body forces via topology optimization, the dipolar and quadrupolar modes are excited at the desirable frequencies. As a result, topologically nontrivial and trivial phononic crystals (PCs) with a record-breaking size of the overlapped bandgap (36.14%) are created. Thereafter, SPTIs arranged by hexagon and rhombus unit cells extracted from the optimized PCs are successfully created, validating the effectiveness of the optimization results. Additionally, the spatial decay of corner states is quantitatively characterized based on the complex band theory. Our work bridges topology optimization with SPTIs and, meanwhile, enriches the mechanism of corner states.

Metasurfaces with ultrathin artificial structures have attracted much attention because of their unprecedented capability in light manipulations. The recent development of metasurfaces with controllable responses opens up new opportunities in various applications. Moreover, metasurfaces composed of twisted chiral structures can generate asymmetric responses for opposite incidence, leading to more degrees of freedom in wave detections and controls. However, most past studies had focused on the amplitude responses, not to mention using bi-directional phase responses, in the characterization and light manipulation of chiral metasurfaces. Here, we report a birefringent interference approach to achieve a controllable asymmetric bi-directional transmission phase from planar chiral metasurface by tuning the orientation of the metasurface with respect to the optical axis of an add-on birefringent substrate. To demonstrate our approach, we fabricate planar Au sawtooth nanoarray metasurface and measure the asymmetric transmission phase of the metasurface placed on a birefringent sapphire crystal slab. The Au sawtooth metasurface-sapphire system exhibits large oscillatory behavior for the asymmetric transmission phase with the tuning parameter. We confirm our experimental results by Jones matrix calculations using data obtained from full-wave simulations for the metasurface. Our approach in the characterization and light manipulation of metasurfaces with controllable responses is simple and nondestructive, enabling new functionalities and potential applications in optical communication, imaging, and remote sensing.

Space−time modulated metamaterials support extraordinary rich applications, such as parametric amplification, frequency conversion, and non-reciprocal transmission. The non-Hermitian space−time varying systems combining non-Hermiticity and space−time varying capability, have been proposed to realize wave control like unidirectional amplification, while its experimental realization still remains a challenge. Here, based on metamaterials with software-defined impulse responses, we experimentally demonstrate non-Hermitian space−time varying metamaterials in which the material gain and loss can be dynamically controlled and balanced in the time domain instead of spatial domain, allowing us to suppress scattering at the incident frequency and to increase the efficiency of frequency conversion at the same time. An additional modulation phase delay between different meta-atoms results in unidirectional amplification in frequency conversion. The realization of non-Hermitian space−time varying metamaterials will offer further opportunities in studying non-Hermitian topological physics in dynamic and nonreciprocal systems. © 2022, The Author(s).

Over the past two decades, acoustic metamaterials have demonstrated extraordinary wave manipulation capabilities, including negative refraction, cloaking, super-resolution imaging, and oneway topological propagation. Conventionally, most metamaterials are passive and require tailor-made designs to achieve these extraordinary capabilities. Once designed and fabricated, the resultant material properties are often locked into place with limited tunability. Furthermore, imposed by the constraints of passivity and reciprocity, losses inherent in resonating structures inevitably reduce the power efficiency. On the other hand, time-varying metamaterials have been recently proposed with exciting new possibilities in breaking time-reversal symmetry, achieving non-reciprocal wave propagation and controllable frequency conversion. However, conventional passive metamaterials may not offer the required real-time tunability, so most of the proposed non-reciprocal phenomena enabled by time-varying material parameters remain as theoretical proposals. To realize time-varying metamaterials for more non-reciprocal phenomena and to solve the power efficiency issue, I develop an active metamaterial platform using virtualized metamaterials in this thesis. These metamaterials adopt digital feedback through external microcontrollers to achieve real-time tunable resonating responses through programmable digital convolution. Such an approach is feasible in air-borne acoustics in the kHz regime by using fast microcontrollers to complete digital convolution within one sampling period. Such an approach is also suitable for constructing active metamaterials by instructing an anti-Lorentzian resonance which exhibits gain around the resonating frequency while the system poles can still be maintained on the lower half of the complex frequency plane to ensure system stability. These constitute a general way to construct the so-called non- Hermitian metamaterials. Using virtualized metamaterials with

We present a black hole effect by strategically leveraging a conformal mapping in elastic continuum with a curved-space framework, which is less stringent compared to a Schwarzschild model transformed to isotropic refractive-index profiles. In the conformal map approach, the two-dimensional point singularity associated to the black hole effect is accomplished by physical plates with near-to-zero thickness. The analog gravity around the singularity results in highly confined energy and lagged timings within a branch cut of the conformal map. These effects are quantified both numerically and experimentally in reference to control trials in which the thickness is not modulated. The findings would deepen our understanding of the elastic analog in mimicking gravitational phenomena, as well as establish the elastic continuum framework for developing a generic design recipe in the presence of the index singularity. Geometric landscapes with elastically curved surfaces would be applicable in a variety of applications such as sensing, imaging, vibration isolation, and energy harvesting. © 2022 American Physical Society.

In recent years, metasurfaces have attracted a lot of interest in miniaturizing existing optical components either through achieving a smaller size or through integrating different functionalities into a single layer of metamaterial atoms. These are mainly due to the current nano-fabrication capability in putting many nanostructures together in storing a huge amount of information about the wavefront to be created from the metasurfaces. One prominent application is hologram displays in very fine resolution. Moreover, different multiplexing techniques have been explored, e.g., through wavelength, to increase the information capacity of metasurface holograms. One of which is to perform polarization multiplexing. Currently, polarization-multiplexed metasurfaces with 3 independent holograms have been demonstrated. To further store more information on the metasurface, it will be desired to have 4 independent holograms to fully exploit all the 4 matrix elements of Jones matrix or even more degrees of freedom. In this thesis, I investigate the possibility to incorporate 4 independent holograms using the full capacity of a Jones matrix. I investigated the symmetries of metamaterial structures in providing such Jones matrices. I proposed a metasurface design that only uses 2 tunable degrees of freedom in geometry to produce 4 independent holograms. By developing a modified GS algorithm that applies the phase constraints coming from the designs of metasurfaces directly, one can obtain the required overall metasurface design in obtaining 4 holograms. By using such algorithm, I simulated 2 sets of hologram images, each set of 4 corresponding to the 4 combinations of input and output polarization channels of the Jones matrix. While I have proved the feasibility of 4 independent holograms with clear features, the transmission efficiency can be further improved. My findings revealed the possibility of utilizing all unique polarization channels of a single metasurface. By combining

The concept of birefringence, commonly treated as a property resulting from more than one polar-ization, is associated with different refractive indices, depending on polarization. Here, we propose a two-dimensional elastic metamaterial engineered to demonstrate birefringence of single polarization for flexural waves. By adopting a network of beams with "overpass" structures to upset the topology of unit cells from a conventional elastic plate, birefringence of single polarization at low frequencies can be real-ized , confirmed through measured band structures and double refraction of the flexural waves; this is further supported by full-wave simulations and models. Our approach can engineer birefringence at low frequencies in which the wavelength is at least a few times larger than the lattice constant, further allowing efficient control of beam splitting, filtering , multiplexing with applications for elastic wave devices.

We investigate the scattering properties of coupled parity-time (PT) symmetric chiral nanospheres with scattering matrix formalism. The exceptional points, i.e., spectral singularities at which the eigenvalues and eigenvectors simultaneously coalesce in the parameter space, of scattering matrix can be tailored by the chirality of the nanospheres. We also calculate the scattering, absorption and extinction cross sections of the PT-symmetric chiral scatter under illumination by monochromatic left- and right-circularly polarized plane waves. We find that the scattering cross section of the nanostructures exhibits an asymmetry when the plane waves are incident from the loss and gain regions, respectively, especially in the broken phase, and the optical cross section exhibits circular dichroism, i.e., differential extinction when the PT-symmetric scatter is endowed with chirality. In particular, under illumination by linearly polarized monochromatic plane waves without intrinsic chirality, the ellipticity of scattered fields in the forward direction, denoting the chirality of light, becomes larger when the scatter is in the PT-symmetry-broken phase. Our findings demonstrate that the gain and loss can control the optical chirality and enhance the chiroptical interactions and pave the way for studying the resonant chiral light-matter interactions in non-Hermitian photonics. © 2022 Xiaolin Chen et al., published by De Gruyter, Berlin/Boston 2022.

Space−time modulated metamaterials support extraordinary rich applications, such as parametric amplification, frequency conversion, and non-reciprocal transmission. The non-Hermitian space−time varying systems combining non-Hermiticity and space−time varying capability, have been proposed to realize wave control like unidirectional amplification, while its experimental realization still remains a challenge. Here, based on metamaterials with software-defined impulse responses, we experimentally demonstrate non-Hermitian space−time varying metamaterials in which the material gain and loss can be dynamically controlled and balanced in the time domain instead of spatial domain, allowing us to suppress scattering at the incident frequency and to increase the efficiency of frequency conversion at the same time. An additional modulation phase delay between different meta-atoms results in unidirectional amplification in frequency conversion. The realization of non-Hermitian space−time varying metamaterials will offer further opportunities in studying non-Hermitian topological physics in dynamic and nonreciprocal systems. © 2022, The Author(s).

The discovery of non-Hermitian skin effect (NHSE) has opened an exciting direction for unveiling unusual physics and phenomena in non-Hermitian system. Despite notable theoretical breakthroughs, actual observation of NHSE’s whole evolvement, however, relies mainly on gain medium to provide amplified mode. It typically impedes the development of simple, robust system. Here, we show that a passive system is fully capable of supporting the observation of the complete evolution picture of NHSE, without the need of any gain medium. With a simple lattice model and acoustic ring resonators, we use complex-frequency excitation to create virtual gain effect, and experimentally demonstrate that exact NHSE can persist in a totally passive system during a quasi-stationary stage. This results in the transient NHSE: passive construction of NHSE in a short time window. Despite the general energy decay, the localization character of skin modes can still be clearly witnessed and successfully exploited. Our findings unveil the importance of excitation in realizing NHSE and paves the way towards studying the peculiar features of non-Hermitian physics with diverse passive platforms. © 2022, The Author(s).

Metasurfaces, benefiting from the flexibility in engineering the resonance, near-field, symmetry, and scattering properties of individual building blocks, are promising not only for a wide range of practical applications in the classical linear optical regime, but also facilitate research into new unconventional areas. Very recently, we have been witnessing the second quantum revolution in which quantum information processing and computation are becoming a reality. In this review, we will focus on some of the emerging developments of metasurfaces that work in the nonlinear, non-Hermitian, nonclassical, or quantum regime. We review some of the common principles shared by the development of these metasurfaces, including local field enhancement and the consideration of structure, lattice, and time-reversal symmetries.

The rapid progress in the engineering of topological edge/interface states has attracted considerable interest in both photonic and phononic systems originating from their electronic equivalent systems. However, most classical wave types, such as electromagnetic/acoustic waves in topological engineering, are described by two-dimensional (2D) partial differential equations (PDEs), which are not suitable for thin plate motions. We present a 1D elastic topological interface state induced by symmetry breaking to bridge a knowledge gap in 4D PDE, particularly for flexural waves on thin-plate frameworks. We also leverage the localized state at the interface for energy harvesting, which can provide a sufficiently high voltage feeder by piezoelectric effects. © 2022 American Physical Society.

Metasurfaces provide a promising route for structuring light and generating holograms with designed amplitude, phase, and polarization profiles, leading to a versatile platform for integrating and constructing optical components beyond the conventional ones. At the same time, incorporating coincidence in imaging allows a high signal-to-noise ratio for imaging in very low light levels. As beneficial from the recent development in both metasurfaces and single-photon avalanche diode (SPAD) cameras, we combine the polarization-sensitive capability of metasurfaces with Hong-Ou-Mandel (HOM)-type interference in generating images with tailor-made two-photon interference and polarization coincidence signatures. By using orthogonal linear-polarized photons as incidence, correlated, anticorrelated, and uncorrelated polarization coincidence features can be observed within the same image from the pairwise second-order coherence statistics across different pixels of the image. Our work adds polarization to the demonstrated amplitude and phase sensitivity in the domain of “HOM microscopy” and can be useful for biological and security applications.

The closed form expressions of the effective properties in periodic fluid laminates are derived thanks to the Padé approximation of the transfer matrix. A second-order Taylor expansion of the transfer matrix elements exhibits Willis coupling. This coupling is the sum of a local term and a nonlocal term. The nonlocal term arises from the apparent bulk modulus in quasi one-dimensional problems. The nonlocality directly impacts the governing equations modeling the acoustic wave propagation in these Willis materials, which then involve convolution products in space. As an example, a two-orthotropic porous material laminate is considered. The theoretically derived effective properties and scattering coefficients are found in excellent agreement with those numerically calculated. The Willis coupling widens the frequency range of validity and accuracy of the effective properties and thus of the calculated scattering coefficients when compared to classical homogenization results for which the Willis coupling is absent. This widening mostly relies on the effect of Willis coupling on the impedance of the fluid laminate. The effective properties are finally derived for a general laminate.

Second-order phononic topological insulators (SPTIs) featured with topological edge and corner states offer promising ways for steering elastic waves. However, existing SPTIs were mainly designed with trial-and-error procedures, limiting the achievable width of topological bandgaps for tightly confining edge and corner states. Here, we develop a topology optimization approach for designing quantum spin Hall effect-based SPTIs. By simultaneously maximizing the powers emitted by the artificially selected body forces via topology optimization, the dipolar and quadrupolar modes are excited at the desirable frequencies. As a result, topologically nontrivial and trivial phononic crystals (PCs) with a record-breaking size of the overlapped bandgap (36.14%) are created. Thereafter, SPTIs arranged by hexagon and rhombus unit cells extracted from the optimized PCs are successfully created, validating the effectiveness of the optimization results. Additionally, the spatial decay of corner states is quantitatively characterized based on the complex band theory. Our work bridges topology optimization with SPTIs and, meanwhile, enriches the mechanism of corner states.

Spin–orbit coupling is an essential mechanism underlying quantum phenomena such as the spin Hall effect and topological insulators1. It has been widely studied in well-isolated Hermitian systems, but much less is known about the role dissipation plays in spin–orbit-coupled systems2. Here we implement dissipative spin–orbit-coupled bands filled with ultracold fermions, and observe parity-time symmetry breaking as a result of the competition between the spin–orbit coupling and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables us to tune the energy gap and close it at the critical dissipation value, the so-called exceptional point3. In the vicinity of the critical point, the state evolution exhibits a chiral response, which enables us to tune the spin–orbit coupling and dissipation dynamically, revealing topologically robust chiral spin transfer when the quantum state encircles the exceptional point. This demonstrates that we can explore non-Hermitian topological states with spin–orbit coupling. © 2022, The Author(s), under exclusive licence to Springer Nature Limited.

Spin-orbit interactions (SOIs) endow light with intriguing properties and applications such as photonic spin-Hall effects and spin-dependent vortex generations. However, it is counterintuitive that SOIs can exist for sound, which is a longitudinal wave that carries no intrinsic spin. Here, we theoretically and experimentally demonstrate that airborne sound can possess artificial transversality in an acoustic micropolar metamaterial and thus carry both spin and orbital angular momentum. This enables the realization of acoustic SOIs with rich phenomena beyond those in conventional acoustic systems. We demonstrate that acoustic activity of the metamaterial can induce coupling between the spin and linear crystal momentum k, which leads to negative refraction of the transverse sound. In addition, we show that the scattering of the transverse sound by a dipole particle can generate spin-dependent acoustic vortices via the geometric phase effect. The acoustic SOIs can provide new perspectives and functionalities for sound manipulations beyond the conventional scalar degree of freedom and may open an avenue to the development of spin-orbit acoustics.

While Willis coupling has been originally proposed as the analog bianisotropy for elastic waves in a bulk solid, its realizations are currently limited to airborne sound and flexural waves on an elastic beam. Here, we experimentally demonstrate Willis coupling for elastic torsional waves on a thin beam. The design is achieved by breaking mirror symmetry for a metamaterial atom with local resonance for the particular type of elastic waves, which also serves as a universal approach in generating Willis coupling. The investigations will be useful for non-destructive testing on pipes and beam structures with torsional waves. (c) 2022 The Author(s). Published by Elsevier B.V.

Over the past decades, wave localization and a wide variety of related phenomena have come to the forefront of research. Here, we theoretically and experimentally investigate the localization and delocalization of the flat-band states in an acoustic cubic lattice. Under evanescent couplings, the band structure of the designed cubic lattice has two dispersive bands and two degenerate flat bands. According to the analyses, we find that the constructions of flat-band states only depend on the excitation pressures and the coupling coefficients, which are frequency independent. With the flat-band state excitation, the acoustic wave can be either localized or delocalized in the lattice, which is determined by the excitation frequency. When the excitation frequency is close to the flat-band frequency of the lattice, the flat-band state can spread into the whole cubic lattice due to the resonance energy transfer among primitive cells. On the other hand, when the excitation frequency deviates from the flat-band frequency, the flat-band state can be localized in any primitive cell of the designed lattice. This work lays the groundwork for exploring the high-dimensional bound states in acoustic systems and has potential impacts on the applications of acoustic sensing and sound energy harvesting. © 2022 American Physical Society.

Metasurfaces with ultrathin artificial structures have attracted much attention because of their unprecedented capability in light manipulations. The recent development of metasurfaces with controllable responses opens up new opportunities in various applications. Moreover, metasurfaces composed of twisted chiral structures can generate asymmetric responses for opposite incidence, leading to more degrees of freedom in wave detections and controls. However, most past studies had focused on the amplitude responses, not to mention using bi-directional phase responses, in the characterization and light manipulation of chiral metasurfaces. Here, we report a birefringent interference approach to achieve a controllable asymmetric bi-directional transmission phase from planar chiral metasurface by tuning the orientation of the metasurface with respect to the optical axis of an add-on birefringent substrate. To demonstrate our approach, we fabricate planar Au sawtooth nanoarray metasurface and measure the asymmetric transmission phase of the metasurface placed on a birefringent sapphire crystal slab. The Au sawtooth metasurface-sapphire system exhibits large oscillatory behavior for the asymmetric transmission phase with the tuning parameter. We confirm our experimental results by Jones matrix calculations using data obtained from full-wave simulations for the metasurface. Our approach in the characterization and light manipulation of metasurfaces with controllable responses is simple and nondestructive, enabling new functionalities and potential applications in optical communication, imaging, and remote sensing.