Breaking Of Reciprocity Research Articles

Chiral spin selectivity and chiroptical activity in helical molecules.

Chiral structures, breaking spatial inversion symmetry, exhibit non-zero chiroptical activity (COA) due to the coupling between their electric and magnetic responses under external electromagnetic fields, an effect absent in achiral systems. Non-magnetic chiral structures also exhibit Chiral-Induced Spin Selectivity (CISS), primarily detected in two terminal measurements in the linear regime, where spin selection emerges without external magnetic influence. Despite the different origins of these physical phenomena, our model captures the relevant physics required to address CISS as an intrinsic molecular effect with the basic ingredients: (i) chirality/inversion asymmetry, (ii) meV atomic spin-orbit coupling, and (iii) decoherence as a source of reciprocity breaking. In this work, we derived how the electronic system couples with polarized electromagnetic radiation to yield a spin-dependent polarization rotation power, quantified through the Rosenfeld tensor, predicting characteristic spin signatures in the COA. The model also predicts that a net spin polarization manifests in the molecular terminations that have been surmised as an explanation for chiral species separation of racemic mixtures and interactions with surface magnetic domains. A recent sensitive spectroscopic measurement of electron transfer in donor-acceptor complexes is consistent with the standalone CISS effect.

Magneto-optical chiral metasurfaces for achieving polarization-independent nonreciprocal transmission.

Nonreciprocal transmission, resulting from the breaking of Lorentz reciprocity, plays a pivotal role in nonreciprocal communication systems by enabling asymmetric forward and backward propagations. Metasurfaces endowed with nonreciprocity represent a compact and facile platform for manipulating electromagnetic waves in an unprecedented manner. However, most passive metasurfaces that achieve nonreciprocal transmissions are polarization dependent. While incorporation of active elements or nonlinear materials can achieve polarization-independent nonreciprocal metasurfaces, the complicated configurations limit their practical applications. To address this issue, we propose and demonstrate a passive and linear metasurface that combines magneto-optical and chiral effects, enabling polarization-independent isolation. The designed metasurface achieves a transmittance of up to 80%, with a high contrast between forward and backward propagations. Our work introduces a novel mechanism for nonreciprocal transmission and lays the foundation for the development of compact, polarization-insensitive nonreciprocal devices.

Electrically tunable space-time metasurfaces at optical frequencies.

Active metasurfaces enable dynamic manipulation of the scattered electromagnetic wavefront by spatially varying the phase and amplitude across arrays of subwavelength scatterers, imparting momentum to outgoing light. Similarly, periodic temporal modulation of active metasurfaces allows for manipulation of the output frequency of light. Here we combine spatial and temporal modulation in electrically modulated reflective metasurfaces operating at 1,530 nm to generate and diffract a spectrum of sidebands at megahertz frequencies. Temporal modulation with tailored waveforms enables the design of a spectrum of sidebands. By impressing a spatial phase gradient on the metasurface, we can diffract selected combinations of sideband frequencies. Combining active temporal and spatial variation can enable unique optical functions, such as frequency mixing, harmonic beam steering or shaping, and breaking of Lorentz reciprocity.

Digital programming of reciprocity breaking in resonant piezoelectric metamaterials

Digital programming of reciprocity breaking in resonant piezoelectric metamaterials

Nonreciprocal phase shifts in spatiotemporally varying materials

Materials with spatiotemporally varying properties exhibit nonreciprocal wave propagation characteristics. Nonreciprocity is predominantly identified by a left-to-right (L-R) transmission amplitude that is different from the right-to-left (R-L) transmission amplitude; a significant difference in the transmitted amplitudes is often desirable in this context. We review nonreciprocal vibration transmission in discrete mechanical systems with spatiotemporally modulated elasticity. We discuss the importance of the transmitted phase in this context, specifically that the difference between the L-R and R-L transmitted phases can be the main contributor to breaking of reciprocity in short systems. We show that the formulation of the problem in terms of response envelopes provides a computationally efficient path for exploring the steady-state nonreciprocal transmission characteristics of spatiotemporally modulated materials. In particular, we use this technique to identify response regimes that are characterized by a nonreciprocal phase shift in transmitted vibrations while maintaining equal transmitted amplitudes or energies.

Inverse design of optical pulse shapes for time-varying photonics.

Recent advancements in materials and metamaterials with strong, time-varying, nonlinear optical responses have spurred a surge of interest in time-varying photonics. This opens the door to novel optical phenomena including reciprocity breaking, frequency translation, and amplification that can be further optimized by improving the light-matter interaction. Although there has been recent interest in applying topology-based inverse design to this problem, we propose a novel approach in this article. We introduce a method for the inverse design of optical pulse shapes to enhance their interaction with time-varying media. We validate our objective-first approach by maximizing the transmittance of optical pulses of equal intensity through time-varying media. Through this approach, we achieve large, broadband enhancements in pulse energy transmission, including gain, without altering the incident pulse energy. As a final test, we maximize pulse transmission through thin films of indium tin oxide, a time-varying medium when strongly pumped in its ENZ band. Our work presents a new degree of freedom for the exploration, application, and design of time-varying systems and we hope it inspires further research in this direction.

Optical isolators based on nonreciprocal four-wave mixing

In this work we propose and theoretically characterize optical isolators consisting of an all-dielectric and non-magnetic resonator featuring an intensity-dependent refractive index and a strong coherent field propagating in a single direction. Such devices can be straightforwardly realized in state-of-the-art integrated photonics platforms. The mechanism underlying optical isolation is based on the breaking of optical reciprocity induced by the asymmetric action of four-wave mixing processes coupling a strong propagating pump field with co-propagating signal/idler modes but not with reverse-propagating ones. Taking advantage of a close analogy with fluids of light, our proposed isolation mechanism is physically understood in terms of the Bogoliubov dispersion of collective excitations on top of the strong pump beam. A few most relevant set-ups realizing our proposal are specifically investigated, such as a coherently illuminated passive ring resonator and unidirectionally lasing ring or Taiji resonators.

Note on “The breaking of additively reciprocal property of fuzzy preference relations and its implication to decision making under uncertainty”

A recent article by Liu et al. [8] devised measurement models to calculate additive consistency indices and weak transitivity indices for fuzzy preference relations (FPRs) with additive reciprocity breaking (ARB), and developed some decision models, such as the equivalency between FPRs with ARB and inconsistent FPRs with additive reciprocity, the optimization based weak transitivity improving model and priority vector derivation models. This paper utilizes six numerical illustrations to show that the measurement models are technically incorrect and sometimes the decision models are invalid or create contradictory results. New frameworks are proposed to define and measure additive consistency and weak transitivity for FPRs with ARB. Computational formulas are brought forward to acquire interval-valued or intuitionistic fuzzy priority vectors from additively consistent FPRs with ARB, and a linear programming model is built to ascertain interval-valued or intuitionistic fuzzy priority vectors from inconsistent FPRs with ARB.

Breaking reciprocity to realize extreme energy isolation in coupled oscillators

This research investigates the isolation achieved by breaking the reciprocity of between two coupled oscillators. The two oscillators have equal mass and the first one is linearly grounded and called the linear oscillator (LO). The second oscillator is nonlinearly coupled to the LO and is termed the nonlinear oscillator (NO). By breaking dynamical reciprocity using asymmetry and nonlinearity, the LO–NO system is shown to exhibit regimes of extreme energy isolation in only one of the oscillators as well as regimes where energy is exchanged between them. These regimes are shown to arise under both impulsive and harmonic excitation. The resulting system is governed by two nonlinear normal modes (NNMs), which can interact with each other under internal resonance of different ratios. Under different loading scenarios, different energy isolations are illustrated. This research starts with analytical study using numerical simulations that assess how energy distributes in the structure under varying loads. The analytical predictions are validated experimentally for both impulsive and harmonic excitations. The results of this research demonstrate that there remains much to learn about energy transfer in general and the breaking of dynamic reciprocity may lead to new types of acoustic and vibrational metamaterials.

Dark‐State Induced Quantum Nonreciprocity

AbstractWith the development of quantum technologies and their broad applications, the phenomenon of reciprocity breaking has been evolving from an effective tool in classical wave optics and electrodynamics to a promising instrument also for the field of quantum computing and quantum information processing. In this work, nonreciprocal wave phenomena that arise in atom‐like quantum systems are studied. Different approaches to isolation and nonreciprocity in quantum systems are reviewed, with a focus on a specific class of passive devices where nonreciprocity is induced by the system nonlinearity, without the need of an external bias. It is then discussed how to model these effects and what their underlying physics is, outlining how the existence of a slowly‐decaying subradiant state is critical to obtain large nonreciprocal responses. The susceptibility of these devices to changes in the environment is analyzed, together with the opportunities that come from including temporal modulations.

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.

Nonreciprocity and Quantum Correlations of Light Transport in Hot Atoms via Reservoir Engineering.

The breaking of reciprocity is a topic of great interest in fundamental physics and optical information processing applications. We demonstrate nonreciprocal light transport in a quantum system of hot atoms by engineering the dissipative atomic reservoir. Our scheme is based on the phase-sensitive light transport in a multichannel photon-atom interaction configuration, where the phase of collective atomic excitations is tunable through external driving fields. Remarkably, we observe interchannel quantum correlations that originate from interactions with the judiciously engineered reservoir. The nonreciprocal transport in a quantum optical atomic system constitutes a new paradigm for atom-based nonreciprocal optics and offers opportunities for quantum simulations with coupled optical channels.

Acoustic nonreciprocity

Breaking acoustic reciprocity is essential to create robust one-way propagation where sound waves or elastic vibrations are permitted to travel in only one direction. This unidirectional response forms the basis for devices such as acoustic isolators and circulators, and it also unlocks new functionalities for complex systems such as acoustic topological insulators. After reviewing the principles of acoustic reciprocity, we look at techniques to achieve large reciprocity breaking, including nonlinearities, moving media, spatiotemporal modulation, and nonlinear bianisotropy. We then discuss the recent surge of progress in nonreciprocal surface acoustic wave devices and topological acoustic systems, areas which we predict will continue to flourish in the coming years. We anticipate that these and other applications of nonreciprocity will continue to enhance acoustic technology and form the basis for new acoustic devices. Reciprocity is a fundamental principle in wave manipulation, and techniques for breaking its symmetry will continue to be discovered, refined, optimized, and applied to several acoustic domains as the understanding of the underlying principles and new technologies mature.

Toroidal nonreciprocity of optical second harmonic generation

We demonstrate mechanisms of reciprocity breaking in nonlinear optics driven by the toroidal dipole moment which characterizes nontrivial spatial distributions of spins in solids. Using high-resolution femtosecond spectroscopy at electronic resonances in the magnetoelectric antiferromagnet $\mathrm{Cu}{\mathrm{B}}_{2}{\mathrm{O}}_{4}$, we show that nonreciprocity reaches 100% for opposite magnetic fields due to the interference of nonlinear coherent sources of second harmonic generation originating from the toroidal dipole moment, applied magnetic field, and noncentrosymmetric crystal structure. The experimental results are corroborated by theoretical analysis based on the crystal and magnetic symmetry of $\mathrm{Cu}{\mathrm{B}}_{2}{\mathrm{O}}_{4}$. Our findings open degrees of freedom in nonlinear optics and pave the way for future nonreciprocal spin-optronic devices operating on the femtosecond timescale.

Breaking reciprocity in a non-Hermitian photonic coupler with saturable absorption

We study the breaking of reciprocity in non-Hermitian coupled photonic waveguides by the simultaneous action of the nonlinear effect of saturable absorption, and the presence of exceptional points. The nonlinear response of such a system is studied in depth, giving physical insight into the operational principles and fundamental limitations, while producing analytical and semi-analytical results for the transmission and nonreciprocal intensity range. We numerically validate the theoretical results and assess important performance metrics for the nonreciprocal operation of such a device. This novel class of passive non-resonant devices can offer on-chip broadband nonreciprocal operation, making them potentially very important for high-speed applications.

Nonreciprocal and Topological Plasmonics

Metals, semiconductors, metamaterials, and various two-dimensional materials with plasmonic dispersion exhibit numerous exotic physical effects in the presence of an external bias, for example an external static magnetic field or electric current. These physical phenomena range from Faraday rotation of light propagating in the bulk to strong confinement and directionality of guided modes on the surface and are a consequence of the breaking of Lorentz reciprocity in these systems. The recent introduction of relevant concepts of topological physics, translated from condensed-matter systems to photonics, has not only given a new perspective on some of these topics by relating certain bulk properties of plasmonic media to the surface phenomena, but has also led to the discovery of new regimes of truly unidirectional, backscattering-immune, surface-wave propagation. In this article, we briefly review the concepts of nonreciprocity and topology and describe their manifestation in plasmonic materials. Furthermore, we use these concepts to classify and discuss the different classes of guided surface modes existing on the interfaces of various plasmonic systems.

Floquet Analysis of Space-Time Modulated Metasurfaces With Lorentz Dispersion

A rigorous semi-analytical Floquet analysis is proposed for a zero-thickness space-time modulated Huygens' metasurface to model and determine the strengths of the new harmonic components of the scattered fields. The proposed method is based on Generalized Sheet Transition Conditions (GSTCs) treating a metasurface as a spatial discontinuity. The metasurface is described in terms of Lorentzian electric and magnetic surface susceptibilities, $\chi_\text{e}$ and $\chi_\text{m}$, respectively, with parameters (e.g. resonant frequency) that are periodically modulated in both space and time. The unknown scattered fields are expressed in terms of Floquet harmonics, for which the amplitudes can be found by numerically solving a set of linear equations, leading to the total scattered fields. Using existing computational techniques, the method is validated using several examples of pure-space and pure-time modulation with different modulation strengths and pumping frequencies. Finally, two cases of spacetime modulation (standing wave perturbation and a traveling wave perturbation) are presented to demonstrate the breaking of Lorentz reciprocity. The proposed method is simple and versatile and able to determine the steady-state response of a space-time modulated Huygen's metasurface that is excited with an oblique plane wave, or a general incident field such as a Gaussian beam.

Transistor-enabled reciprocity breaking in a mechanical lattice yielding giant isolation and unidirectional propagation

This paper presents non-reciprocal information transfer between two mass-spring chains enabled using an electromechanical cell incorporating a metal–oxide–semiconductor field effect transistor (MOSFET). Mechanical information propagating through an input chain is converted into an electrical signal, and vice versa for an output chain, using a permanent magnet and a conducting coil in each chain. The conducting coils are coupled electrically via a MOSFET, leading to giant isolation and unidirectional signal transfer. We present theory, numerical simulations, and an experimental demonstration of the concept. The proposed system can be implemented as a “sonocoupler”, an acoustic analog of an optocoupler, which can isolate one mechanical system from another while transmitting information in a unidirectional manner.

On nonlinear energy flows in nonlinearly coupled oscillators with equal mass

Due to the near monopoly held by nonlinear energy sinks in the study of targeted energy transfer, little research has been done on the flow of mechanical energy between oscillators with comparable mass. The goal of the present paper is to investigate the flow of mechanical energy between two nonlinearly coupled oscillators with comparable mass that arise due to the breaking of dynamic reciprocity. The first oscillator represents the prototypical linear oscillator (LO), whereas the second oscillator represents a nonlinear oscillator (NO) that is nonlinearly coupled to the LO only. By breaking dynamic reciprocity, one-way energy propagation is achieved in the system, such that energy can only be irreversibly transferred from the NO to the LO. As such, the NO is isolated from the LO for physically reasonable energies whenever it is not directly excited. Moreover, when the NO is directly excited, there exist regimes where the LO, despite being linear and of comparable mass to the NO, behaves like a nonlinear energy sink and parasitically and irreversibly absorbs energy from the NO. The theoretical portion of this works employs direct numerical simulation of the structure to explore the strongly nonreciprocal dynamics and resulting energy transfers. The theoretical results are then verified through experimental measurements of a comparable structure. The present study promotes a new paradigm for investigating energy transfer in mechanical structures and opens the way for passively controlling the flow of energy in complex mechanical systems.

Nonreciprocal cavities and the time-bandwidth limit: reply

We reply to the comment on our recent article [Optica6, 104 (2019)OPTIC82334-253610.1364/OPTICA.6.000104], in which we demonstrated that nonreciprocal cavities comply with the resonance time-bandwidth limit. We fully stand by our original claims and further elucidate how breaking of reciprocity is not required to achieve the large field enhancements and time-bandwidth products observed in the comment and our article. We also further clarify that these hotspots do not overcome the conventional time-bandwidth limit.