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.

Backpropagation-free training of deep physical neural networks.

Recent successes in deep learning for vision and natural language processing are attributed to larger models but come with energy consumption and scalability issues. Current training of digital deep-learning models primarily relies on backpropagation that is unsuitable for physical implementation. In this work, we propose a simple deep neural network architecture augmented by a physical local learning (PhyLL) algorithm, which enables supervised and unsupervised training of deep physical neural networks without detailed knowledge of the nonlinear physical layer's properties. We trained diverse wave-based physical neural networks in vowel and image classification experiments, showcasing the universality of our approach. Our method shows advantages over other hardware-aware training schemes by improving training speed, enhancing robustness, and reducing power consumption by eliminating the need for system modeling and thus decreasing digital computation.

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.

Ultrabroadband sound control with deep-subwavelength plasmacoustic metalayers.

Controlling audible sound requires inherently broadband and subwavelength acoustic solutions, which are to date, crucially missing. This includes current noise absorption methods, such as porous materials or acoustic resonators, which are typically inefficient below 1 kHz, or fundamentally narrowband. Here, we solve this vexing issue by introducing the concept of plasmacoustic metalayers. We demonstrate that the dynamics of small layers of air plasma can be controlled to interact with sound in an ultrabroadband way and over deep-subwavelength distances. Exploiting the unique physics of plasmacoustic metalayers, we experimentally demonstrate perfect sound absorption and tunable acoustic reflection over two frequency decades, from several Hz to the kHz range, with transparent plasma layers of thicknesses down to λ/1000. Such bandwidth and compactness are required in a variety of applications, including noise control, audio-engineering, room acoustics, imaging and metamaterial design.

Anomalous topological waves in strongly amorphous scattering networks.

Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects, or local disorder and can even survive some random deformations of their crystalline structures. However, they always break down when the level of disorder or amorphism gets too large, transitioning to a topologically trivial Anderson insulating phase. We demonstrate a two-dimensional amorphous topological regime that survives arbitrarily strong levels of amorphism. We implement it for electromagnetic waves in a nonreciprocal scattering network and experimentally demonstrate the existence of unidirectional edge transport in the strong amorphous limit. This edge transport is shown to be mediated by an anomalous edge state whose topological origin is evidenced by direct topological invariant measurements. Our findings extend the reach of topological physics to a class of systems in which strong amorphism can induce, enhance, and guarantee the topological edge transport instead of impeding it.

Observation of non-reciprocal harmonic conversion in real sounds.

Reciprocity guarantees that in most media, sound transmission is symmetric between two points of space when the location of the source and receiver are interchanged. This fundamental law can be broken in non-linear media, often at the cost of detrimental input power levels, large insertion losses, and ideally prepared single-frequency input signals. Thus, previous observations of non-reciprocal sound transmission have focused on pure tones, and cannot handle real sounds composed of various harmonics of a low-frequency fundamental note, as generated for example by musical instruments. Here, we extend the reach of non-reciprocal acoustics by achieving large, tunable, and timbre-preserved non-reciprocal transmission of sound notes composed of several harmonics, originating from musical instruments. This is achieved in a non-linear, actively reconfigurable, and non-Hermitian isolator that can handle arbitrarily low input power at any audible frequency, while providing isolation levels up to 30dB and a tunable level of non-reciprocal gain. Our findings may find applications in sound isolation, noise control, non-reciprocal and non-Hermitian metamaterials, and analog audio processing.

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.

Parallel wave-based analog computing using metagratings.

Wave-based signal processing has witnessed a significant expansion of interest in a variety of science and engineering disciplines, as it provides new opportunities for achieving high-speed and low-power operations. Although flat optics desires integrable components to perform multiple missions, yet, the current wave-based computational metasurfaces can engineer only the spatial content of the input signal where the processed signal obeys the traditional version of Snell's law. In this paper, we propose a multi-functional metagrating to modulate both spatial and angular properties of the input signal whereby both symmetric and asymmetric optical transfer functions are realized using high-order space harmonics. The performance of the designed compound metallic grating is validated through several investigations where closed-form expressions are suggested to extract the phase and amplitude information of the diffractive modes. Several illustrative examples are demonstrated to show that the proposed metagrating allows for simultaneous parallel analog computing tasks such as first- and second-order spatial differentiation through a single multichannel structured surface. It is anticipated that the designed platform brings a new twist to the field of optical signal processing and opens up large perspectives for simple integrated image processing systems.

Electromagnetic wave-based extreme deep learning with nonlinear time-Floquet entanglement.

Wave-based analog signal processing holds the promise of extremely fast, on-the-fly, power-efficient data processing, occurring as a wave propagates through an artificially engineered medium. Yet, due to the fundamentally weak non-linearities of traditional electromagnetic materials, such analog processors have been so far largely confined to simple linear projections such as image edge detection or matrix multiplications. Complex neuromorphic computing tasks, which inherently require strong non-linearities, have so far remained out-of-reach of wave-based solutions, with a few attempts that implemented non-linearities on the digital front, or used weak and inflexible non-linear sensors, restraining the learning performance. Here, we tackle this issue by demonstrating the relevance of time-Floquet physics to induce a strong non-linear entanglement between signal inputs at different frequencies, enabling a power-efficient and versatile wave platform for analog extreme deep learning involving a single, uniformly modulated dielectric layer and a scattering medium. We prove the efficiency of the method for extreme learning machines and reservoir computing to solve a range of challenging learning tasks, from forecasting chaotic time series to the simultaneous classification of distinct datasets. Our results open the way for optical wave-based machine learning with high energy efficiency, speed and scalability.

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.

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.

Disorder-Induced Signal Filtering with Topological Metamaterials.

Disorder, ubiquitously present in realistic structures, is generally thought to disturb the performance of analog wave devices, as it often causes strong multiple scattering effects that largely arrest wave transportation. Contrary to this general view, here, it is shown that, in some wave systems with nontrivial topological character, strong randomness can be highly beneficial, acting as a powerful stimulator to enable desired analog filtering operations. This is achieved in a topological Anderson sonic crystal that, in the regime of dominating randomness, provides a well-defined filtering response characterized by a Lorentzian spectral line-shape. The theoretical and experimental results, serving as the first realization of topological Anderson insulator phase in acoustics, suggest the striking possibility of achieving specific, nonrandom analog filtering operations by adding randomness to clean structures.

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.

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.

Topological analog signal processing.

Analog signal processors have attracted a tremendous amount of attention recently, as they potentially offer much faster operation and lower power consumption than their digital versions. Yet, they are not preferable for large scale applications due to the considerable observational errors caused by their excessive sensitivity to environmental and structural variations. Here, we demonstrate both theoretically and experimentally the unique relevance of topological insulators for alleviating the unreliability of analog signal processors. In particular, we achieve an important signal processing task, namely resolution of linear differential equations, in an analog system that is protected by topology against large levels of disorder and geometrical perturbations. We believe that our strategy opens up large perspectives for a new generation of robust all-optical analog signal processors, which can now not only perform ultrafast, high-throughput, and power efficient signal processing tasks, but also compete with their digital counterparts in terms of reliability and flexibility.

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.