Exceptional Points of PT-Symmetric Reflectionless States in Complex Scattering Systems.

We investigate experimentally and analytically the coalescence of reflectionless (RL) states in symmetric complex wave-scattering systems. We observe RL exceptional points (EPs), first with a conventional Fabry-Perot system for which the scattering strength within the system is tuned symmetrically and then with single- and multichannel symmetric disordered systems. We confirm that an EP of the parity-time (PT)-symmetric RL operator is obtained for two isolated quasinormal modes when the spacing between central frequencies is equal to the decay rate into incoming and outgoing channels. Finally, we leverage the transfer functions associated with RL and RL-EP states to implement first- and second-order analog differentiation.

Deeply Subwavelength Localization with Reverberation-Coded Aperture.

Accessing subwavelength information about a scene from the far-field without invasive near-field manipulations is a fundamental challenge in wave engineering. Yet it is well understood that the dwell time of waves in complex media sets the scale for the waves' sensitivity to perturbations. Modern coded-aperture imagers leverage the degrees of freedom (d.o.f.) offered by complex media as natural multiplexor but do not recognize and reap the fundamental difference between placing the object of interest outside or within the complex medium. Here, we show that the precision of localizing a subwavelength object can be improved by several orders of magnitude simply by enclosing it in its far field with a reverberant passive chaotic cavity. We identify deep learning as a suitable noise-robust tool to extract subwavelength localization information encoded in multiplexed measurements, achieving resolutions well beyond those available in the training data. We demonstrate our finding in the microwave domain: harnessing the configurational d.o.f. of a simple programmable metasurface, we localize a subwavelength object along a curved trajectory inside a chaotic cavity with a resolution of λ/76 using intensity-only single-frequency single-pixel measurements. Our results may have important applications in photoacoustic imaging as well as human-machine interaction based on reverberating elastic waves, sound, or microwaves.

Coherent Wave Control in Complex Media with Arbitrary Wavefronts.

Wavefront shaping (WFS) has emerged as a powerful tool to control the propagation of diverse wave phenomena (light, sound, microwaves, etc.) in disordered matter for applications including imaging, communication, energy transfer, micromanipulation, and scattering anomalies. Nonetheless, in practice the necessary coherent control of multiple input channels remains a vexing problem. Here, we overcome this difficulty by doping the disordered medium with programmable meta-atoms in order to adapt it to an imposed arbitrary incoming wavefront. Besides lifting the need for carefully shaped incident wavefronts, our approach also unlocks new opportunities such as sequentially achieving different functionalities with the same arbitrary wavefront. We demonstrate our concept experimentally for electromagnetic waves using programmable metasurfaces in a chaotic cavity, with applications to focusing with the generalized Wigner-Smith operator as well as coherent perfect absorption. We expect our fundamentally new perspective on coherent wave control to facilitate the transition of intricate WFS protocols into real applications for various wave phenomena.

Precise Localization of Multiple Noncooperative Objects in a Disordered Cavity by Wave Front Shaping.

Complicated multipath trajectories of waves in disordered cavities cause object localization to be very challenging with traditional ray-tracing approaches. Yet it is known that information about the object position is encoded in the Green's function. After a calibration step, traditional time-reversal approaches retrieve a source's location from a broadband impulse response measurement. Here, we show that a nonemitting object's scattering contribution to a reverberant medium suffices to localize the object. We demonstrate our finding in the microwave domain. Then, we further simplify the scheme by replacing the temporal degrees of freedom (d.o.f.) of the broadband measurement with spatial d.o.f. obtained from wave front shaping. A simple electronically reconfigurable reflectarray inside the cavity dynamically modulates parts of the cavity boundaries, thereby providing spatial d.o.f. The demonstrated ability to localize multiple noncooperative objects with a single-frequency scheme may have important applications for sensors in smart homes.

Intensity-only measurement of partially uncontrollable transmission matrix: demonstration with wave-field shaping in a microwave cavity.

Transmission matrices (TMs) have become a powerful and widely used tool to describe and control wave propagation in complex media. In certain scenarios the TM is partially uncontrollable, complicating its identification and use. In standard optical wavefront shaping experiments, uncontrollable reflections or imperfect illumination may be the cause; in reverberating cavities, uncontrollable reflections off the walls have that effect. Here we employ phase retrieval techniques to identify such a partially uncontrollable TM solely based on random intensity-only reference measurements. We demonstrate the feasibility of our method by focusing both on a single target as well as on multiple targets in a microwave cavity, using a phase-binary Spatial-Microwave-Modulator.

Spatiotemporal Wave Front Shaping in a Microwave Cavity.

Controlling waves in complex media has become a major topic of interest, notably through the concepts of time reversal and wave front shaping. Recently, it was shown that spatial light modulators can counterintuitively focus waves both in space and time through multiple scattering media when illuminated with optical pulses. In this Letter, we transpose the concept to a microwave cavity using flat arrays of electronically tunable resonators. We prove that maximizing the Green's function between two antennas at a chosen time yields diffraction limited spatiotemporal focusing. Then, changing the photons' dwell time inside the cavity, we modify the relative distribution of the spatial and temporal degrees of freedom (DOF), and we demonstrate that it has no impact on the field enhancement: wave front shaping makes use of all available DOF, irrespective of their spatial or temporal nature. Our results prove that wave front shaping using simple electronically reconfigurable arrays of reflectors is a viable approach to the spatiotemporal control of microwaves, with potential applications in medical imaging, therapy, telecommunications, radar, or sensing. They also offer new fundamental insights regarding the coupling of spatial and temporal DOF in complex media.

Wave-Field Shaping in Cavities: Waves Trapped in a Box with Controllable Boundaries.

Electromagnetic cavities are used in numerous domains of applied and fundamental physics, from microwave ovens and electromagnetic compatibility to masers, quantum electrodynamics (QED), and quantum chaos. The wave fields established in cavities are statically fixed by their geometry, which are usually modified by using mechanical parts like mode stirrers in reverberation chambers or screws in masers and QED. Nevertheless, thanks to integral theorems, tailoring the cavity boundaries theoretically permits us to design at will the wave fields they support. Here, we show in the microwave domain that it is achievable dynamically simply by using electronically tunable metasurfaces that locally modify the boundaries, switching them in real time from Dirichlet to Neumann conditions. We prove that at a high modal density, counterintuitively, it permits us to create wave patterns presenting hot spots of intense energy. We explain and model the physical mechanism underlying the concept, which allows us to find a criterion ensuring that modifying parts of a cavity's boundaries turn it into a completely different one. We finally prove that this approach even permits us, in the limiting case where the cavity supports only well-separated resonances, to choose the frequencies at which the latter occur.

Covert Scattering Control in Metamaterials with Non-Locally Encoded Hidden Symmetry.

Symmetries and tunability are of fundamental importance in wave scattering control, but symmetries are often obvious upon visual inspection, which constitutes a significant vulnerability of metamaterial wave devices to reverse-engineering risks. Here, it is theoretically and experimentally shown that a symmetry in the reduced basis of the "primary meta-atoms" that are directly connected to the outside world is sufficient; meanwhile, a suitable topology of non-local interactions between them, mediated by the internal "secondary" meta-atoms, can hide the symmetry from sight in the canonical basis. Covert symmetry-based scattering control in a cable-network metamaterial featuring a hidden parity ( P $\mathcal {P}$ ) symmetry in combination with hidden- P $\mathcal {P}$ -symmetry-preserving and hidden- P $\mathcal {P}$ -symmetry-breaking tuning mechanisms is experimentally demonstrated. Physical-layer security in wired communications is achieved using the domain-wise hidden P $\mathcal {P}$ -symmetry as a shared secret between the sender and the legitimate receiver. Within the approximation of negligible absorption, the first tuning of a complex scattering metamaterial without mirror symmetry to feature exceptional points (EPs) of PT $\mathcal {PT}$ -symmetric reflectionless states, as well as quasi-bound states in the continuum, is reported. These results are reproduced in metamaterials involving non-reciprocal interactions between meta-atoms, including the first observation of reflectionless EPs in a non-reciprocal system.

Experimentally realized physical-model-based frugal wave control in metasurface-programmable complex media.

Metasurface-programmable radio environments are considered a key ingredient of next-generation wireless networks. Yet, identifying a metasurface configuration that yields a desired wireless functionality in an unknown complex environment was so far only achieved with closed-loop iterative feedback schemes. Here, we introduce open-loop wave control in metasurface-programmable complex media by estimating the parameters of a compact physics-based forward model. Our experiments demonstrate orders-of-magnitude advantages over deep-learning-based digital-twin benchmarks in terms of accuracy, compactness and required calibration examples. Strikingly, our parameter estimation also works without phase information and without providing measurements for all considered scattering coefficients. These unique generalization capabilities of our pure-physics model unlock unforeseen and previously inaccessible frugal wave control protocols that significantly alleviate the measurement complexity. For instance, we achieve coherent wave control (focusing or perfect absorption) and phase-shift-keying backscatter communications in metasurface-programmable complex media with intensity-only measurements. Our approach is also directly relevant to dynamic metasurface antennas, microwave-based signal processors and emerging in situ reconfigurable nanophotonic, optical and room-acoustical systems.

Semantic regularization of electromagnetic inverse problems.

Solving ill-posed inverse problems typically requires regularization based on prior knowledge. To date, only prior knowledge that is formulated mathematically (e.g., sparsity of the unknown) or implicitly learned from quantitative data can be used for regularization. Thereby, semantically formulated prior knowledge derived from human reasoning and recognition is excluded. Here, we introduce and demonstrate the concept of semantic regularization based on a pre-trained large language model to overcome this vexing limitation. We study the approach, first, numerically in a prototypical 2D inverse scattering problem, and, second, experimentally in 3D and 4D compressive microwave imaging problems based on programmable metasurfaces. We highlight that semantic regularization enables new forms of highly-sought privacy protection for applications like smart homes, touchless human-machine interaction and security screening: selected subjects in the scene can be concealed, or their actions and postures can be altered in the reconstruction by manipulating the semantic prior with suitable language-based control commands.

Microwave Speech Recognizer Empowered by a Programmable Metasurface.

Speech recognition becomes increasingly important in the modern society, especially for human-machine interactions, but its deployment is still severely thwarted by the struggle of machines to recognize voiced commands in challenging real-life settings: oftentimes, ambient noise drowns the acoustic sound signals, and walls, face masks or other obstacles hide the mouth motion from optical sensors. To address these formidable challenges, an experimental prototype of a microwave speech recognizer empowered by programmable metasurface is presented here that can remotely recognize human voice commands and speaker identities even in noisy environments and if the speaker's mouth is hidden behind a wall or face mask. The programmable metasurface is the pivotal hardware ingredient of the system because its large aperture and huge number of degrees of freedom allows the system to perform a complex sequence of sensing tasks, orchestrated by artificial-intelligence tools. Relying solely on microwave data, the system avoids visual privacy infringements. The developed microwave speech recognizer can enable privacy-respecting voice-commanded human-machine interactions is experimentally demonstrated in many important but to-date inaccessible application scenarios. The presented strategy will unlock new possibilities and have expectations for future smart homes, ambient-assisted health monitoring, as well as intelligent surveillance and security.

Reflectionless programmable signal routers.

We demonstrate experimentally that reflectionless scattering modes (RSMs), a generalized version of coherent perfect absorption, can be functionalized to perform reflectionless programmable signal routing. We achieve versatile programmability both in terms of operating frequencies and routing functionality with negligible reflection upon in-coupling, which avoids unwanted signal power echoes in radio frequency or photonic networks. We report in situ observations of routing functionalities like wavelength demultiplexing, including cases where multichannel excitation requires adapted coherent input wavefronts. All experiments are performed in the microwave domain based on the same irregularly shaped cavity with strong modal overlap that is massively parametrized by a 304-element-programmable metasurface. RSMs in our highly overdamped multiresonance transport problem are fundamentally intriguing because the simple critical coupling picture for reflectionless excitation of isolated resonances fails spectacularly. We show in simulation that the distribution of damping rates of scattering singularities broadens under strong absorption so that weakly damped zeros can be tuned toward functionalized RSMs.

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.

Intelligent indoor metasurface robotics.

Intelligent indoor robotics is expected to rapidly gain importance in crucial areas of our modern society such as at-home health care and factories. Yet, existing mobile robots are limited in their ability to perceive and respond to dynamically evolving complex indoor environments because of their inherently limited sensing and computing resources that are, moreover, traded off against their cruise time and payload. To address these formidable challenges, here we propose intelligent indoor metasurface robotics (I2MR), where all sensing and computing are relegated to a centralized robotic brain endowed with microwave perception; and I2MR's limbs (motorized vehicles, airborne drones, etc.) merely execute the wirelessly received instructions from the brain. The key aspect of our concept is the centralized use of a computation-enabled programmable metasurface that can flexibly mold microwave propagation in the indoor wireless environment, including a sensing and localization modality based on configurational diversity and a communication modality to establish a preferential high-capacity wireless link between the I2MR's brain and limbs. The metasurface-enhanced microwave perception is capable of realizing low-latency and high-resolution three-dimensional imaging of humans, even around corners and behind thick concrete walls, which is the basis for action decisions of the I2MR's brain. I2MR is thus endowed with real-time and full-context awareness of its operating indoor environment. We implement, experimentally, a proof-of-principle demonstration at ∼2.4 GHz, in which I2MR provides health-care assistance to a human inhabitant. The presented strategy opens a new avenue for the conception of smart and wirelessly networked indoor robotics.

Metasurface-Programmable Wireless Network-On-Chip.

This paper introduces the concept of smart radio environments, currently intensely studied for wireless communication in metasurface-programmable meter-scaled environments (e.g., inside rooms), on the chip scale. Wireless networks-on-chips (WNoCs) are a candidate technology to improve inter-core communication on chips but current proposals are plagued by a dilemma: either the received signal is weak, or it is significantly reverberated such that the on-off-keying modulation speed must be throttled. Here, this vexing problem is overcome by endowing the wireless on-chip environment with in situ programmability which enables the shaping of the channel impulse response (CIR); thereby, a pulse-like CIR shape can be imposed despite strong multipath propagation and without entailing a reduced received signal strength. First, a programmable metasurface suitable for integration in the on-chip environment ("on-chip reconfigurable intelligent surface") is designed and characterized. Second, its configuration is optimized to equalize selected wireless on-chip channels "over the air." Third, by conducting a rigorous communication analysis, the feasibility of significantly higher modulation speeds with shaped CIRs is evidenced. The results introduce a programmability paradigm to WNoCs which boosts their competitiveness as complementary on-chip interconnect solution.

Meta-programmable analog differentiator.

We present wave-based signal differentiation with unprecedented fidelity and flexibility by purposefully perturbing overmoded random scattering systems such that zeros of their scattering matrices lie exactly at the desired locations on the real frequency axis. Our technique overcomes limitations of hitherto existing approaches based on few-mode systems, both regarding their extreme vulnerability to fabrication inaccuracies or environmental perturbations and their inability to maintain high fidelity under in-situ adaptability. We demonstrate our technique experimentally by placing a programmable metasurface with hundreds of degrees of freedom inside a 3D disordered metallic box. Regarding the integrability of wave processors, such repurposing of existing enclosures is an enticing alternative to fabricating miniaturized devices. Our over-the-air differentiator can process in parallel multiple signals on distinct carriers and maintains high fidelity when reprogrammed to different carriers. We also perform programmable higher-order differentiation. Conceivable applications include segmentation or compression of communication or radar signals and machine vision.

Lowering latency and processing burden in computational imaging through dimensionality reduction of the sensing matrix.

Recent demonstrations have shown that frequency-diverse computational imaging systems can greatly simplify conventional architectures developed for imaging by transferring constraints into the digital layer. Here, in order to limit the latency and processing burden involved in image reconstruction, we propose to truncate insignificant principal components of the sensing matrix that links the measurements to the scene to be imaged. In contrast to recent work using principle component analysis to synthesize scene illuminations, our generic approach is fully unsupervised and is applied directly to the sensing matrix. We impose no restrictions on the type of imageable scene, no training data is required, and no actively reconfigurable radiating apertures are employed. This paper paves the way to the constitution of a new degree of freedom in image reconstructions, allowing one to place the performance emphasis either on image quality or latency and computational burden. The application of such relaxations will be essential for widespread deployment of computational microwave and millimeter wave imagers in scenarios such as security screening. We show in this specific context that it is possible to reduce both the processing time and memory consumption with a minor impact on the quality of the reconstructed images.

Diffuse field cross-correlations: Scattering theory and electromagnetic experiments.

The passive estimation of impulse responses from ambient noise correlations arouses increasing interest in seismology, acoustics, optics, and electromagnetism. Assuming the equipartition of the noise field, the cross-correlation function measured with noninvasive receiving probes converges towards the difference of the causal and anticausal Green's functions. Here, we consider the case when the receiving field probes are antennas which are well coupled to a complex medium-a scenario of practical relevance in electromagnetism. We propose a general approach based on the scattering matrix formalism to explore the convergence of the cross-correlation function. The analytically derived theoretical results for chaotic systems are confirmed in microwave measurements within a mode-stirred reverberation chamber. This study provides fundamental insight into the Green's function retrieval technique and paves the way for a new technique to characterize electromagnetic antennas.

Implementing nonuniversal features with a random matrix theory approach: Application to space-to-configuration multiplexing.

We consider the efficiency of multiplexing spatially encoded information across random configurations of a metasurface-programmable chaotic cavity in the microwave domain. The distribution of the effective rank of the channel matrix is studied to quantify the channel diversity and to assess a specific system's performance. System-specific features such as unstirred field components give rise to nontrivial interchannel correlations and need to be properly accounted for in modeling based on random matrix theory. To address this challenge, we propose a two-step hybrid approach. Based on an ensemble of experimentally measured scattering matrices for different random metasurface configurations, we first learn a system-specific pair of coupling matrix and unstirred contribution to the Hamiltonian, and then add an appropriately weighted stirred contribution. We verify that our method is capable of reproducing the experimentally found distribution of the effective rank with good accuracy. The approach can also be applied to other wave phenomena in complex media.

Learned Integrated Sensing Pipeline: Reconfigurable Metasurface Transceivers as Trainable Physical Layer in an Artificial Neural Network.

The rapid proliferation of intelligent systems (e.g., fully autonomous vehicles) in today's society relies on sensors with low latency and computational effort. Yet current sensing systems ignore most available a priori knowledge, notably in the design of the hardware level, such that they fail to extract as much task-relevant information per measurement as possible. Here, a "learned integrated sensing pipeline" (LISP), including in an end-to-end fashion both physical and processing layers, is shown to enable joint learning of optimal measurement strategies and a matching processing algorithm, making use of a priori knowledge on task, scene, and measurement constraints. Numerical results demonstrate accuracy improvements around 15% for object recognition tasks with limited numbers of measurements, using dynamic metasurface apertures capable of transceiving programmable microwave patterns. Moreover, it is concluded that the optimal learned microwave patterns are nonintuitive, underlining the importance of the LISP paradigm in current sensorization trends.