Break Reciprocity Research Articles

Metamaterials with Reprogrammable Reciprocity

Metamaterials composed of asymmetric elements have been shown to break reciprocity; permitting the propagation of waves in one direction. The configuration of these metamaterials typically limits the propagation of the wave to a single direction, speed, or occurrence with little or no tunability. Here we present---theoretically, numerically, and experimentally---a simple design approach for reprogrammable metamaterials, which allows for all of these parameters to be tuned, enabled, disabled, or reset. We present a map of different geometries that allow for reciprocal and nonreciprocal wave propagation and attenuation. We show how a single design can be programmed on demand to support wave propagation and attenuation in both directions (reciprocal) or wave propagation in only one direction (nonreciprocal). In addition, we demonstrate real-time control of the wave velocity, both in amplitude and direction, as it propagates through the metamaterial. We show speeding up, slowing down, or complete reversal of the propagating wave direction. Furthermore, we show that the waves maintain a constant velocity regardless of the impulse magnitude, and even along a curved path. Our metamaterial could open exciting possibilities for designing nonlinear materials with exotic topological properties.

Information conduction and convection in noiseless Vicsek flocks.

Physical interactions generally respect certain symmetries, such as reciprocity and energy conservation, which survive in coarse-grained isothermal descriptions. Active many-body systems usually break such symmetries intrinsically, on the particle level, so that their collective behavior is often more naturally interpreted as a result of information exchange. Here we study numerically how information spreads from a "leader" particle through an initially aligned flock, described by the Vicsek model without noise. In the low-speed limit of a static spin lattice, we find purely conductive spreading, reminiscent of heat transfer. Swarm motility and heterogeneity can break reciprocity and spin conservation. But what seems more consequential for the swarm response is that the dispersion relation acquires a significant convective contribution along the leader's direction of motion.

One-Way Acoustic Guiding Under Transverse Fluid Flow

In a moving acoustic medium, sound waves travel differently with and against the fluid flow. This well-established acoustic effect is backed by the intuition that the fluid velocity bias imparts momentum on the propagating acoustic waves, thus violating reciprocity. Based on this conception, fluid flow that is transverse to the wave direction of propagation will not break reciprocity. In this paper we contrast this common wisdom and theoretically show that the interplay between transverse mean flow and transverse structural gliding asymmetry can yield strong nonreciprocity and even, surprisingly, one-way acoustic waveguiding. To demonstrate that, we analyze a waveguide that comprises a few adjacent acoustic subdiffraction chains, i.e., linear chains of acoustic scatterers with monopolar or dipolar response. The structure is embedded within a medium with mean flow velocity that is transverse to the waveguide axis. We find the symmetry breaking conditions under which nonreciprocity is obtained, and we show how, under transverse mean flow, with Mach numbers as low as 0.02, one-way propagation of the acoustic wave is obtained on a sub-wavelength-thick acoustic waveguide. To demonstrate the phenomenon, we introduce two models. One in which the scatterers are assumed to be pointlike and the flow is homogeneous, and a second, in which we accommodate the issue of possible wakes created by the presence of scatterers inside the flow. The latter setup exhibits no direct interaction of the scatterers with the flow, by placing the waveguide in a quiescent medium adjacent to a flowing medium. Our results push forward the understanding of acoustic nonreciprocity, and may open another venue for the design of nonreciprocal acoustic wave devices for various applications.

Nonreciprocal infrared absorption via resonant magneto-optical coupling to InAs.

Nonreciprocal elements are a vital building block of electrical and optical systems. In the infrared regime, there is a particular interest in structures that break reciprocity because their thermal absorptive (and emissive) properties should not obey the Kirchhoff thermal radiation law. In this work, we break time-reversal symmetry and reciprocity in n-type–doped magneto-optic InAs with a static magnetic field where light coupling is mediated by a guided-mode resonator structure, whose resonant frequency coincides with the epsilon-near-zero resonance of the doped indium arsenide. Using this structure, we observe the nonreciprocal absorptive behavior as a function of magnetic field and scattering angle in the infrared. Accounting for resonant and nonresonant optical scattering, we reliably model experimental results that break reciprocal absorption relations in the infrared. The ability to design these nonreciprocal absorbers opens an avenue to explore devices with unequal absorptivity and emissivity in specific channels.

Realisation of nonreciprocal transmission and absorption using wave-based active noise control

Nonreciprocal acoustic devices typically break reciprocity by introducing nonlinearities or directional biasing. However, these devices are generally not fully adaptable and often use resonant cavities, which only exhibit nonreciprocal behaviour over a narrow bandwidth. Therefore, to overcome these challenges, this paper investigates how wave-based active control can be used to achieve broadband nonreciprocal behaviour in a one-dimensional environment. Wave-based controller architectures are described for both transmission and absorption control and, through simulation and experimental implementations, it is shown that they can achieve broadband nonreciprocal behaviour. Importantly, the direction of nonreciprocal behaviour can be straightforwardly reversed.

Atomic spin-controlled non-reciprocal Raman amplification of fibre-guided light

In a non-reciprocal optical amplifier, gain depends on whether the light propagates forwards or backwards through the device. Typically, one requires either the magneto-optical effect, temporal modulation or optical nonlinearity to break reciprocity. By contrast, here we demonstrate non-reciprocal amplification of fibre-guided light using Raman gain provided by spin-polarized atoms that are coupled to the nanofibre waist of a tapered fibre section. The non-reciprocal response originates from the propagation-direction-dependent local polarization of the nanofibre-guided mode in conjunction with polarization-dependent atom–light coupling. We show that this novel mechanism can also be implemented without an external magnetic field and that it allows us to fully control the direction of amplification via the atomic spin state. Our results may simplify the construction of complex optical networks. Moreover, by using other suitable quantum emitters, our scheme could be implemented in photonic integrated circuits and circuit quantum electrodynamics. Researchers demonstrate non-reciprocal amplification of nanofibre-guided light using Raman gain provided by nearby spin-polarized atoms. The direction of amplification can be controlled via the atomic spin state.

Nonreciprocity and Mode Conversion in a Spatiotemporally Modulated Elastic Wave Circulator

Acoustic and elastic metamaterials with time- and space-dependent material properties have received great attention recently as a means to break reciprocity for propagating mechanical waves, achieving greater directional control. One nonreciprocal device that has been demonstrated in the fields of acoustics and electromagnetism is the circulator, which achieves unirotational transmission through a network of ports. This work investigates an elastic wave circulator composed of a thin elastic ring with three semi-infinite elastic waveguides attached, creating a three-port network. Nonreciprocity is achieved for both longitudinal and transverse waves by modulating the elastic modulus of the ring in a rotating fashion. Two numerical models are derived and implemented to compute the elastic wave field in the circulator. The first is an approximate model based on coupled-mode theory, which makes use of the known mode shapes of the unmodulated system. The second model is a finite-element approach that includes a Fourier expansion in the harmonics of the modulation frequency and radiation boundary conditions at the ports. The coupled-mode model shows excellent agreement with the finite-element model and the conditions on the modulation parameters that enable a high degree of nonreciprocity are presented. This work demonstrates that it is possible to create an elastic wave circulator that enables nonreciprocal mode-splitting of an incident longitudinal wave into outgoing longitudinal and transverse waves.

Drifting Electrons: Nonreciprocal Plasmonics and Thermal Photonics

Light propagates symmetrically in opposite directions in most materials and structures. This fact -- a consequence of the Lorentz reciprocity principle -- has tremendous implications for science and technology across the electromagnetic spectrum. Here, we investigate an emerging approach to break reciprocity that does not rely on magneto-optical effects or spacetime modulations, but is instead based on biasing a plasmonic material with a direct electric current. Using a 3D Green function formalism and microscopic considerations, we elucidate the propagation properties of surface plasmon-polaritons (SPPs) supported by a generic nonreciprocal platform of this type, revealing some previously overlooked, anomalous, wave-propagation effects. We show that SPPs can propagate in the form of steerable, slow-light, unidirectional beams associated with inflexion points in the modal dispersion. We also clarify the impact of dissipation (due to collisions and Landau damping) on nonreciprocal effects and shed light on the connections between inflexion points, exceptional points at band edges, and modal transitions in leaky-wave structures. We then apply these concepts to the important area of thermal photonics, and provide the first theoretical demonstration of drift-induced nonreciprocal radiative heat transfer between two planar bodies. Our findings may open new opportunities toward the development of nonreciprocal magnet-free devices that combine the benefits of plasmonics and nonreciprocal photonics for wave-guiding and energy applications.

Reciprocity of thermal diffusion in time-modulated systems

The reciprocity principle governs the symmetry in transmission of electromagnetic and acoustic waves, as well as the diffusion of heat between two points in space, with important consequences for thermal management and energy harvesting. There has been significant recent interest in materials with time-modulated properties, which have been shown to efficiently break reciprocity for light, sound, and even charge diffusion. However, time modulation may not be a plausible approach to break thermal reciprocity, in contrast to the usual perception. We establish a theoretical framework to accurately describe the behavior of diffusive processes under time modulation, and prove that thermal reciprocity in dynamic materials is generally preserved by the continuity equation, unless some external bias or special material is considered. We then experimentally demonstrate reciprocal heat transfer in a time-modulated device. Our findings correct previous misconceptions regarding reciprocity breaking for thermal diffusion, revealing the generality of symmetry constraints in heat transfer, and clarifying its differences from other transport processes in what concerns the principles of reciprocity and microscopic reversibility.

Non-Reciprocal Amplification of Light Using Cold Atoms Coupled to an Optical Nanofiber

Optical nanofibers realized as the waist of tapered silica fibers can be used to trap and optically interface laser-cooled atoms. Building on this system, we experimentally show a novel scheme for the nonreciprocal Raman amplification of light. While typically either the magneto-optical effect, a temporal modulation or an optical nonlinearity is employed to break reciprocity, in our approach, this results from the spin of the atoms forming the gain medium. By taking advantage of the inherent spin-momentum locking present in optical nanofibers, we perform an experiment in which we set the amplification direction by a suitable preparation of the atomic spin state. Our approach is general and, suitable quantum emitters provided, could also be implemented beyond the optical domain of the electromagnetic spectrum.

Breaking reciprocity through nonlocal coupling in elastodynamic systems

A commonly studied structure in active metamaterial research is an elastodynamic beam outfitted with piezoelectric patches with electronic circuitry used to modify the beam’s local material properties. These active beams have been used to validate a variety of conceptual strategies, including those to reduce vibrations, enhance flexural wave sensing, and break reciprocity. Here, we show how the coupling of adjacent piezoelectric patches can be used to create a nonlocal metamaterial featuring the highly nonreciprocal transmission of flexural waves. We discuss how a modified Bernoulli–Euler beam theory was used to design a controller to drive a piezoelectric patch using the signal from a spatially separate patch. We discuss conditions for stability and present experimental data validating model predictions.

Decoherence effects break reciprocity in matter transport

The decoherence of quantum states defines the transition between the quantum world and classical physics. Decoherence or, analogously, quantum mechanical collapse events pose fundamental questions regarding the interpretation of quantum mechanics and are technologically relevant because they limit the coherent information processing performed by quantum computers. We have discovered that the transition regime enables a novel type of matter transport. Applying this discovery, we present nanoscale devices in which decoherence, modeled by random quantum jumps, produces fundamentally novel phenomena by interrupting the unitary dynamics of electron wave packets. Noncentrosymmetric conductors with mesoscopic length scales act as two-terminal rectifiers with unique properties. In these devices, the inelastic interaction of itinerant electrons with impurities acting as electron trapping centers leads to a novel steady state characterized by partial charge separation between the two leads, or, in closed circuits to the generation of persistent currents. The interface between the quantum and the classical worlds therefore provides a novel transport regime of value for the realization of a new category of mesoscopic electronic devices.

Acoustic spoof surface plasmon polaritons for filtering, isolation and sensing

We study a waveguide structure supporting acoustic spoof plasmon polaritons (aSSPPs) perturbed by a defect, whose specifically tailored geometry enables controllable transmission characterized by a uniform phase distribution and very steep narrowband response. The structure is analyzed using transmission-line theory and numerical simulations, providing evidence for its use in advanced filters, isolators and sensor technology. In order to demonstrate the applicability of the aSSPP waveguide with defect, two selective narrowband filter designs are discussed and explored. Furthermore, we propose an acoustic isolator that exploits steady fluid flow to break reciprocity and provide large isolation in a narrowband region. We also propose a sensor for liquid analytes, in which the grooves of the aSSPP waveguide serve as microfluidic channels, while the sensing principle is based on the spectral shift of the transmission peak for different mixtures of water and glycerol. The sensor shows a good sensitivity and fast response, with a potential for further development for applications in water quality monitoring.

Nonlinearity-Induced Nonreciprocity—Part I

Nonreciprocal electromagnetic devices allow signals to propagate asymmetrically along opposite directions, enabling essential functionalities for several microwave and optical technologies. Branching out from the conventional approach involving a dc magnetic bias, different avenues have been investigated over the past two decades to break reciprocity without the need for magneto-optical materials. In particular, nonlinearity-based approaches have recently attracted considerable attention, due to their simple implementation and bias-free operation, which make their fabrication and system integration particularly appealing. Nonetheless, these advantages are accompanied by limitations that need to be carefully assessed when using these devices for practical applications. In the first part of this work, we discuss the fundamental principles of nonlinearity-based nonreciprocal devices. We introduce a general model for two-port nonlinear resonators and show how to design a nonlinear system yielding highly nonreciprocal port-to-port transmission under continuous-wave excitation. We then analyze quantitatively the main limitations of these devices: the limited power and spectral bandwidth, the response under pulsed excitation, and the breakdown of nonreciprocity under simultaneous two-port excitation. In the second part, we will deepen our analysis by considering more complex scenarios involving coherent and incoherent two-port excitations and multiresonator systems offering more flexibility in the response.

Transistor-Loaded Nonmagnetic Nonreciprocal Metasurfaces

Reciprocal metasurfaces represent prominent compact structures for bidirectional and frequency-invariant transformation of electromagnetic waves. However, their application to modern wireless communication are limited due to their reciprocal response and lack of a controllable, versatile and programmable mechanism. On the other hand, nonreciprocal metasurfaces are capable of steering electromagnetic waves unidirectionally, leading to functionalities that are far beyond the capabilities of conventional static metasurfaces. In addition, they are controllable and programmable through their active constituents. This paper provides an overview on recent progress and opportunities offered by transistor-loaded metasurfaces to break reciprocity, and discusses their potential for low-energy, compact, and integrated nonreciprocal devices and systems.

Bidirectional Elastic Diode with Frequency-Preserved Nonreciprocity

The study of nonreciprocal wave propagation is of great interest for both fundamental research and engineering applications. Here we demonstrate theoretically and experimentally a bidirectional, nonreciprocal, and high-quality diode that can rectify elastic waves in both forward and backward directions in an elastic metamaterial designed to exhibit enhanced nonlinearity of resonances. This diode can preserve or vary frequency, rectify low-frequency long wave with small system size, offer high-quality insulation, can be modulated by amplitude, and break reciprocity of both the total energy and fundamental wave. We report three mechanisms to break reciprocity: the amplitude-dependent band gap combining interface reflection, chaotic response combining linear band gap, amplitude-dependent attenuation rate in damping diode. The bidirectional diode paves ways for mutually controlling information and energy transport between two sources, which can be used as wave insulators.

Free-Space Nonreciprocal Transmission Based on Nonlinear Coupled Fano Metasurfaces

Optical nonlinearities can enable unusual light–matter interactions, with functionalities that would be otherwise inaccessible relying only on linear phenomena. Recently, several studies have harnessed the role of optical nonlinearities to implement nonreciprocal optical devices that do not require an external bias breaking time-reversal symmetry. In this work, we explore the design of a metasurface embedding Kerr nonlinearities to break reciprocity for free-space propagation, requiring limited power levels. After deriving the general design principles, we demonstrate an all-dielectric flat metasurface made of coupled nonlinear Fano silicon resonant layers realizing large asymmetry in optical transmission at telecommunication frequencies. We show that the metrics of our design can go beyond the fundamental limitations on nonreciprocity for nonlinear optical devices based on a single resonance, as dictated by time-reversal symmetry considerations. Our work may shed light on the design of flat subwavelength free-space nonreciprocal metasurface switches for pulsed operation which are easy to fabricate, fully passive, and require low operation power. Our simulated devices demonstrate a transmission ratio >50 dB for oppositely propagating waves, an operational bandwidth exceeding 600 GHz, and an insertion loss of <0.04 dB.

Up‐And‐Coming Advances in Optical and Microwave Nonreciprocity: From Classical to Quantum Realm

Reciprocity is a fundamental physical principle that roots in the time‐reversal symmetry of physical laws. It allows making predictions on any arbitrary complex system's response and operation and hence simplifies the analysis. However, there are many practical situations in which it is advantageous to break reciprocity, e.g., isolators preventing wave scattering back to lasers and generators, full‐duplex systems for multiplexing transmission and receiving in the same channel, nonreciprocal cavity excitation, and protection of fragile states of superconductor quantum computers from thermal noise. The most widespread approach to time‐reversal symmetry breaking and nonreciprocity based on magnetic field biasing suffers from bulkiness, cost ineffectiveness, and loss, motivating researchers and engineers to search for more practical approaches. Herein, the up‐and‐coming advances in optical nonreciprocity, including new materials (Weyl semimetals, topological insulators, metasurfaces), active structures, time‐modulation, parity‐time (PT)‐symmetry breaking, nonlinearity combined with a structural asymmetry, quantum nonlinearity, unidirectional gain and loss, chiral quantum states and valley polarization are overviewed. A general description of nonreciprocal systems is provided and the pros and cons of the mentioned approaches to nonreciprocity are discussed.

Non-Hermitian Skin Effect in a Non-Hermitian Electrical Circuit.

The conventional bulk-boundary correspondence directly connects the number of topological edge states in a finite system with the topological invariant in the bulk band structure with periodic boundary condition (PBC). However, recent studies show that this principle fails in certain non-Hermitian systems with broken reciprocity, which stems from the non-Hermitian skin effect (NHSE) in the finite system where most of the eigenstates decay exponentially from the system boundary. In this work, we experimentally demonstrate a 1D non-Hermitian topological circuit with broken reciprocity by utilizing the unidirectional coupling feature of the voltage follower module. The topological edge state is observed at the boundary of an open circuit through an impedance spectra measurement between adjacent circuit nodes. We confirm the inapplicability of the conventional bulk-boundary correspondence by comparing the circuit Laplacian between the periodic boundary condition (PBC) and open boundary condition (OBC). Instead, a recently proposed non-Bloch bulk-boundary condition based on a non-Bloch winding number faithfully predicts the number of topological edge states.

Microwave Nonreciprocity

In this article, we provide a comprehensive review of past and present efforts in the field of microwave nonreciprocity with an emphasis on the most commonly used nonreciprocal devices, namely gyrators, isolators, and circulators. After discussing the origin and history of such efforts, we elaborate on the pros and cons of four distinct approaches to break reciprocity which include magnetic biasing of ferrite materials, intrinsic nonreciprocity of solid-state devices, nonlinearities with geometric asymmetries, and finally, periodic spatiotemporal variation. We subsequently pay due attention to the spatiotemporal approach and show that the recently emerging proposals to achieve magnet-free nonreciprocity with linear, periodically time-varying circuits can compete with traditional ferrite devices and even outperform them in several metrics, thus opening the door to exciting venues for miniaturized low-cost and high-performance nonreciprocal devices with numerous applications ranging from full-duplex communications and quantum computing to biomedical imaging and radar systems.