Superior robustness of anomalous non-reciprocal topological edge states.

Robustness against disorder and defects is a pivotal advantage of topological systems1, manifested by the absence of electronic backscattering in the quantum-Hall2 and spin-Hall effects3, and by unidirectional waveguiding in their classical analogues4,5. Two-dimensional (2D) topological insulators4-13, in particular, provide unprecedented opportunities in a variety of fields owing to their compact planar geometries, which are compatible with the fabrication technologies used in modern electronics and photonics. Among all 2D topological phases, Chern insulators14-25 are currently the most reliable designs owing to the genuine backscattering immunity of their non-reciprocal edge modes, brought via time-reversal symmetry breaking. Yet such resistance to fabrication tolerances is limited to fluctuations of the same order of magnitude as their bandgap, limiting their resilience to small perturbations only. Here we investigate the robustness problem in a system where edge transmission can survive disorder levels with strengths arbitrarily larger than the bandgap-an anomalous non-reciprocal topological network. We explore the general conditions needed to obtain such an unusual effect in systems made of unitary three-port non-reciprocal scatterers connected by phase links, and establish the superior robustness of anomalous edge transmission modes over Chern ones to phase-link disorder of arbitrarily large values. We confirm experimentally the exceptional resilience of the anomalous phase, and demonstrate its operation in various arbitrarily shaped disordered multi-port prototypes. Our results pave the way to efficient, arbitrary planar energy transport on 2D substrates for wave devices with full protection against large fabrication flaws or imperfections.

Extreme Spatial Dispersion in Nonlocally Resonant Elastic Metamaterials.

To date, the vast majority of architected materials have leveraged two physical principles to control wave behavior, namely, Bragg interference and local resonances. Here, we describe a third path: structures that accommodate a finite number of delocalized zero-energy modes, leading to anomalous dispersion cones that nucleate from extreme spatial dispersion at 0 Hz. We explain how to design such zero-energy modes in the context of elasticity and show that many of the landmark wave properties of metamaterials can also be induced at an extremely subwavelength scale by the associated anomalous cones, without suffering from the same bandwidth limitations. We then validate our theory through a combination of simulations and experiments. Finally, we present an inverse design method to produce anomalous cones at desired locations in k space.

Parallel temporal signal processing enabled by polarization-multiplexed programmable THz metasurfaces.

Under the trends of multifunctionality, tunability, and compactness in modern wave-based signal processors, in this paper, we propose a polarization-multiplexed graphene-based metasurface to realize distinct mathematical operators on the parallel time-domain channels enabled by vertical and horizontal polarizations. The designed metasurface is composed of two perpendicularly-oriented graphene strips for each of which the chemical potential can be dynamically tuned through a DC biasing circuit. The programmable metasurface exhibits two orthogonal channels through which the time-domain input signals are elaborately processed by separate mathematical functions. Several illustrative examples are presented demonstrating that the proposed device can operate on different time-domain analog computing modes such as fractional-order differentiator and phaser at the same time. The strategy introduced in this paper will enable real-time parallel temporal analog computing and has potentially essential applications in terahertz spectroscopy architectures, communication systems, and computing technologies.

Topological optomechanically induced transparency.

The interaction of optical and mechanical degrees of freedom can lead to several interesting effects. A prominent example is the phenomenon of optomechanically induced transparency (OMIT), in which mechanical movements induce a narrow transparency window in the spectrum of an optical mode. In this Letter, we demonstrate the relevance of optomechanical topological insulators for achieving OMIT. More specifically, we show that the strong interaction between optical and mechanical edge modes of a one-dimensional topological optomechanical crystal can render the system transparent within a very narrow frequency range. Since the topology of a system cannot be changed by slight to moderate levels of disorder, the achieved transparency is robust against geometrical perturbations. This is in sharp contrast to trivial OMIT which has a strong dependency on the geometry of the optomechanical system. Our findings hold promise for a wide range of applications such as filtering, signal processing, and slow-light devices.

Zero-Index Weyl Metamaterials.

Depending on the geometry of their Fermi surfaces, Weyl semimetals and their analogs in classical systems have been classified into two types. In type-I Weyl semimetals (WSMs), the conelike spectrum at the Weyl point is not tilted, leading to a pointlike closed Fermi surface. In type-II WSMs, on the contrary, the energy spectrum around the Weyl point is strongly tilted such that the Fermi surface transforms from a point into an open surface. Here, we demonstrate, both theoretically and experimentally, a new type of (classical) Weyl semimetal whose Fermi surface is neither a point nor a surface, but a flat line. The distinctive Fermi surfaces of such semimetals, dubbed as type-III or zero-index WSMs, gives rise to unique physical properties: one of the edge modes of the semimetal exhibits a zero index of refraction along a specific direction, in stark contrast to type-I and type-II WSMs for which the index of refraction is always nonzero. We show that the zero-index response of such topological phases enables exciting applications such as extraordinary wave transmission.

Slow light engineering in resonant photonic crystal line-defect waveguides.

Slow light plays an outstanding role in a wide variety of optical applications, from quantum information to optical processing. While slow optical guiding in photonic crystal waveguides is typically based on Bragg band gaps occurring in non-resonant photonic crystals, here we explore the possibility to leverage the hybridization photonic band gaps of resonant photonic crystals to induce a different form of slow light guiding. We study a line-defect waveguide in a periodic structure composed of high-permittivity resonant dielectric objects and exploit the different guiding mechanisms associated with the hybridization band gap to induce slow light in the resonant phase of the crystal. We demonstrate quantitatively that this method can, in principle, produce high group indices over large bandwidths with potential values of group-index bandwidth products up to 0.67.

Nonlinear Second-Order Topological Insulators.

We demonstrate, both theoretically and experimentally, the concept of nonlinear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of nonlinearity. We show that one-dimensional edge states and zero-dimensional corner states can be induced in a trivial crystal insulator made of evanescently coupled resonators with linear and nonlinear coupling coefficients, simply by tuning the intensity. This allows global external control over topological phase transitions and switching to a phase with nonzero bulk polarization, without requiring any structural or geometrical changes. We further show how these nonlinear effects enable dynamic tuning of the spectral properties and localization of the topological edge and corner states. Such self-induced second-order topological insulators, which can be found and implemented in a wide variety of physical platforms ranging from electronics to microwaves, acoustics, and optics, hold exciting promises for reconfigurable topological energy confinement, power harvesting, data storage, and spatial management of high-intensity fields.

Topological Fano Resonances.

The Fano resonance is a widespread wave scattering phenomenon associated with a peculiar asymmetric and ultrasharp line shape, which has found applications in a large variety of prominent optical devices. While its substantial sensitivity to geometrical and environmental changes makes it the cornerstone of efficient sensors, it also renders the practical realization of Fano-based systems extremely challenging. Here, we introduce the concept of topological Fano resonance, whose ultrasharp asymmetric line shape is guaranteed by design and protected against geometrical imperfections, yet remaining sensitive to external parameters. We report the experimental observation of such resonances in an acoustic system, and demonstrate their inherent robustness to geometrical disorder. Such topologically protected Fano resonances, which can also be found in microwave, optical, and plasmonic systems, open up exciting frontiers for the generation of various reliable wave-based devices including low-threshold lasers, perfect absorbers, ultrafast switches or modulators, and highly accurate interferometers, by circumventing the performance degradations caused by inadvertent fabrication flaws.

Acoustic rat-race coupler and its applications in non-reciprocal systems.

Waveguide hybrid junctions, such as Magic-T and rat-race couplers, have been of great interest in microwave technology not only for their applications in power monitoring, but also for design and synthesis of various non-reciprocal devices including electromagnetic circulators and isolators. Here, an acoustic rat-race coupler is designed and demonstrated for the first time, working on the basis of constructive and destructive interferences between the clockwise and counterclockwise of a ring resonator. It is then shown how the sound isolation provided by such a coupler enables the realization of an acoustic four-port circulator, a device which has not been reported as yet. Many other promising acoustic devices comprising power combiners, power dividers, mixers, and modulators can be envisioned to be implemented based on the proposed rat-race coupler.

Nonreciprocal Gain in Non-Hermitian Time-Floquet Systems.

We explore the unconventional wave scattering properties of non-Hermitian systems in which amplification or damping are induced by time-periodic modulation. These non-Hermitian time-Floquet systems are capable of nonreciprocal operations in the frequency domain, which can be exploited to induce novel physical phenomena such as unidirectional wave amplification and perfect nonreciprocal response with zero or even negative insertion losses. This unique behavior is obtained by imparting a specific low-frequency time-periodic modulation to the complex coupling between lossless resonators, promoting only upward frequency conversion, and leading to nonreciprocal parametric gain. We provide a full-wave demonstration of our findings in a one-way microwave amplifier, and establish the potential of non-Hermitian time-Floquet devices for insertion-loss free microwave isolation and unidirectional parametric amplification.

Drexhage's Experiment for Sound.

Drexhage's seminal observation that spontaneous emission rates of fluorophores vary with distance from a mirror uncovered the fundamental notion that a source's environment determines radiative linewidths and shifts. Further, this observation established a powerful tool to determine fluorescence quantum yields. We present the direct analogue for sound. We demonstrate that a Chinese gong at a hard wall experiences radiative corrections to linewidth and line shift, and extract its intrinsic radiation efficiency. Beyond acoustics, our experiment opens new ideas to extend the Drexhage experiment to metamaterials, nanoantennas, and multipolar transitions.

Negative refraction and planar focusing based on parity-time symmetric metasurfaces.

We introduce a new mechanism to realize negative refraction and planar focusing using a pair of parity-time symmetric metasurfaces. In contrast to existing solutions that achieve these effects with negative-index metamaterials or phase conjugating surfaces, the proposed parity-time symmetric lens enables loss-free, all-angle negative refraction and planar focusing in free space, without relying on bulk metamaterials or nonlinear effects. This concept may represent a pivotal step towards loss-free negative refraction and highly efficient planar focusing by exploiting the largely uncharted scattering properties of parity-time symmetric systems.

Metamaterial buffer for broadband non-resonant impedance matching of obliquely incident acoustic waves.

Broadband impedance matching and zero reflection of acoustic waves at a planar interface between two natural materials is a rare phenomenon, unlike its optical counterpart, frequently observed for polarized light incident at the Brewster angle. In this article, it is shown that, by inserting a metamaterial layer between two acoustic materials with different impedance, it is possible to artificially realize an extremely broadband Brewster-like acoustic intromission angle window, in which energy is totally transmitted from one natural medium to the other. The metamaterial buffer, composed of acoustically hard materials with subwavelength tapered apertures, provides an interesting way to match the impedances of two media in a broadband fashion, different from traditional methods like quarter-wave matching or Fabry-Pérot resonances, inherently narrowband due to their resonant nature. This phenomenon may be interesting for a variety of applications including energy harvesting, acoustic imaging, ultrasonic transducer technology, and noise control.

Experimental observation of topological transition in linear and nonlinear parametric oscillators.

Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is perturbed by a continuously parametrized defect. Initially in one of its stable states, the oscillator will be perturbed by the defect and finally reach another stable state, which can be its initial one or the other one. For some critical value of the defect parameter, the final state changes abruptly. We theoretically and experimentally investigate such transition both in the linear and nonlinear cases, and the effect of nonlinearities is discussed. A topological interpretation in terms of winding number is proposed, and we show that winding changes correspond to singularities in the temporal dynamics. An experimental observation of such transition is performed using parametric Faraday instability at the surface of a vibrated fluid.

Loss-compensated non-reciprocal scattering based on synchronization.

Breaking the reciprocity of wave propagation is a problem of fundamental interest, and a much-sought functionality in practical applications, both in photonics and phononics. Although it has been achieved using resonant linear scattering from cavities with broken time-reversal symmetry, such realizations have remained inescapably plagued by inherent passivity constraints, which make absorption losses unavoidable, leading to stringent limitations in transmitted power. In this work, we solve this problem by converting the cavity resonance into a limit cycle, exploiting the uncharted interplay between non-linearity, gain, and non-reciprocity. Remarkably, strong enough incident waves can synchronize with these self-sustained oscillations and use their energy for amplification. We theoretically and experimentally demonstrate that this mechanism can simultaneously enhance non-reciprocity and compensate absorption. Real-world acoustic scattering experiments allow us to observe non-reciprocal transmission of audible sound in a synchronization-based three-port circulator with full immunity against losses.

Wave-momentum shaping for moving objects in heterogeneous and dynamic media.

Light and sound waves can move objects through the transfer of linear or angular momentum, which has led to the development of optical and acoustic tweezers, with applications ranging from biomedical engineering to quantum optics. Although impressive manipulation results have been achieved, the stringent requirement for a highly controlled, low-reverberant and static environment still hinders the applicability of these techniques in many scenarios. Here we overcome this challenge and demonstrate the manipulation of objects in disordered and dynamic media by optimally tailoring the momentum of sound waves iteratively in the far field. The method does not require information about the object's physical properties or the spatial structure of the surrounding medium but relies only on a real-time scattering matrix measurement and a positional guide-star. Our experiment demonstrates the possibility of optimally moving and rotating objects to extend the reach of wave-based object manipulation to complex and dynamic scattering media. We envision new opportunities for biomedical applications, sensing and manufacturing.

Anomalous-Chern Steering of Topological Nonreciprocal Guided Waves.

Nonreciprocal topological edge states based on external magnetic bias have been regarded as the last resort for genuine unidirectional wave transport, showing superior robustness over topological states with preserved time-reversal symmetry. However, fast and efficient reconfigurability of their trajectory has remained a formidable challenge due to the difficulty in controlling the spatial distribution of magnetic fields over large areas and short times. Here, this persistent issue is solved by leveraging the rich topology of unitary scattering networks, and achieve fast steering of nonreciprocal topological transport at an interface between a Chern and an anomalous topological insulator, without having to control a magnetic field. Such interface can be drawn by doping the network with scatterers located at the center of each link, whose level of reflection is electrically tuned. With experiments in the GHz range, the possibility to actively steer the way of unidirectional edge states is demonstrated, switching the transmission path thousands of times per second in a fully-robust topological heterostructure. The approach represents a significant step towards the realization of practical reconfigurable topological meta-devices with broken time-reversal symmetry, and their application to future robust communication technologies.

Anomalous and Chern topological waves in hyperbolic networks.

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental work has been limited to time-reversal invariant systems made of coupled discrete resonances, leaving the more interesting case of robust, unidirectional edge wave transport completely unobserved. Here, we report a non-reciprocal hyperbolic network that exhibits both Chern and anomalous chiral edge modes, and implement it on a planar microwave platform. We experimentally evidence the unidirectional character of the topological edge modes by direct field mapping. We demonstrate the topological origin of these hyperbolic chiral edge modes by an explicit topological invariant measurement, performed from external probes. Our work extends the reach of topological wave physics by allowing for backscattering-immune transport in materials with synthetic non-Euclidean behavior.

Extraordinary sound transmission through density-near-zero ultranarrow channels.

We introduce the acoustic equivalent of "supercoupling" by studying the anomalous sound transmission and uniform energy squeezing through ultranarrow acoustic channels filled with zero-density metamaterials. As a realistic example, we propose their realization by inserting transverse membranes with a subwavelength period along the channel, and we prove a novel form of acoustic tunneling based on impedance matching and infinite phase velocity at the zero-density operation. We envision applications in sensing, noise control, cloaking, and energy harvesting.