Nonreciprocal Wave Research Articles

Broadband composite nonreciprocal polarization wave plates and optical isolators

We theoretically study a technique for a broadband nonreciprocal wave retarder whose quarter-wave plate phase retardation is the same in forward and backward directions. The system is built using a number of sequential nonreciprocal wave plates. The proposed device can also be utilized to create a broadband optical diode, which consists of two achromatic quarter-wave plates, one reciprocal and the other non-reciprocal, that are sandwiched between two polarizers aligned in parallel.

Giant Surface Acoustic Wave Nonreciprocity with Low Magnetoacoustic Insertion Loss in CoFeB/Ru/CoFeB Synthetic Antiferromagnets

Giant Surface Acoustic Wave Nonreciprocity with Low Magnetoacoustic Insertion Loss in CoFeB/Ru/CoFeB Synthetic Antiferromagnets

Programming nonreciprocity and harmonic beam steering via a digitally space-time-coded metamaterial antenna

Recent advancement in digital coding metasurfaces incorporating spatial and temporal modulation has enabled simultaneous control of electromagnetic (EM) waves in both space and frequency domains by manipulating incident EM waves in a transmissive or reflective fashion, resulting in time-reversal asymmetry. Here we show in theory and experiment that a digitally space-time-coded metamaterial (MTM) antenna with spatiotemporal modulation at its unit cell level can be regarded as a radiating counterpart of such digital metasurface, which will enable nonreciprocal EM wave transmission and reception via surface-to-leaky-wave transformation and harmonic frequency generation. Operating in the fast wave (radiation) region, the space-time-coded MTM antenna is tailored in a way such that the propagation constant of each programmable unit cell embedded with varactor diodes can toggle between positive and negative phases, which is done through providing digital sequences by using a field-programmable gate array (FPGA). Owing to the time-varying coding sequence, harmonic frequencies are generated with different main beam directions. Furthermore, the space time modulation of the digitally coded MTM antenna allows for nonreciprocal transmission and reception of EM waves by breaking the time-reversal symmetry, which may enable many applications, such as simultaneous transmitting and receiving, unidirectional transmission, radar sensing, and multiple-input and multiple-output (MIMO) beamformer.

The non-reciprocal wave propagation in random piezoelectric composites with aligned semi-spheroid inclusions

The non-reciprocal wave propagation characteristics of 3D random piezoelectric composites with aligned semi-spheroid inclusions are theoretically predicted. The self-consistent equations about the frequency-dependent effective properties are established, in which the volume average of dynamic Green's operators in semi-spheroid domain is involved. Due to the non-centrosymmetric inclusions, the composites macroscopically exhibit non-reciprocity, i.e. the effective properties, wave speed, acoustic impedance, attenuation and resonance frequency under the two waves of identical form but incident in opposite directions are different. The numerical results show that when the aspect ratio of the inclusion is large, the differences of the effective wave speed and impedance in two opposite directions are significant, which provides a possible means for modulation of wave propagation in the 3D random composites.

Magnetic Damping and Dzyaloshinskii-Moriya Interactions in Pt/Co2FeAl/MgO Systems Grown on Si and MgO Substrates.

Spin-pumping-induced damping and interfacial Dzyaloshinskii-Moriya interaction (iDMI) have been studied in Pt/Co2FeAl/MgO systems grown on Si or MgO substrates as a function of Pt and Co2FeAl (CFA) thicknesses. For this, we combined vibrating sample magnetometry (VSM), microstrip ferromagnetic resonance (MS-FMR), and Brillouin light scattering (BLS). VSM measurements of the magnetic moment at saturation per unit area revealed the absence of a magnetic dead layer in both systems, with a higher magnetization at saturation obtained for CFA grown on MgO. The key parameters governing the spin-dependent transport through the Pt/CFA interface, including the spin mixing conductance and the spin diffusion length, have been determined from the CFA and the Pt thickness dependence of the damping. BLS has been used to measure the spin wave non-reciprocity via the frequency mismatch between the Stokes and anti-Stokes lines. iDMI has been separated from the contribution of the interface perpendicular anisotropy difference between Pt/CFA and CFA/MgO. Our investigation revealed that both iDMI strength and spin pumping efficiency are higher for CFA-based systems grown on MgO due to its epitaxial growth confirmed by MS-FMR measurements of the in-plane magnetic anisotropy. This suggests that CFA grown on MgO could be a promising material candidate as a spin injection source via spin pumping and for other spintronic applications.

High wave vector non-reciprocal spin wave beams

We report unidirectional transmission of micron-wide spin waves beams in a 55 nm thin YIG. We downscaled a chiral coupling technique implementing Ni80Fe20 nanowires arrays with different widths and lattice spacing to study the non-reciprocal transmission of exchange spin waves down to λ ≈ 80 nm. A full spin wave spectroscopy analysis of these high wavevector coupled-modes shows some difficulties to characterize their propagation properties, due to both the non-monotonous field dependence of the coupling efficiency, and also the inhomogeneous stray field from the nanowires.

Rotating spacetime modulation: Topological phases and spacetime Haldane model

Topological photonics has recently emerged as a very general framework for the design of unidirectional edge waveguides immune to back-scattering and deformations, as well as other platforms that feature extreme nonreciprocal wave phenomena. While the topological classification of time invariant crystals has been widely discussed in the literature, the study of spacetime crystals formed by time-variant materials remains largely unexplored. Here, we extend the methods of topological band theory to photonic crystals formed by inclusions that are subject to a spacetime rotating-wave modulation that imitates a physical rotating motion. By resorting to an approximate nonhomogeneous effective description of the electromagnetic response of the inclusions, it is shown that they possess a bianisotropic response that breaks the time-reversal symmetry and may give rise to non-trivial topologies. In particular, we propose an implementation of the Haldane model in a spacetime modulated photonic crystal.

Energy trapping in a phononic crystal cavity enhanced by nonreciprocal acoustic wave transmission

Defect mode induced energy trapping at the bandgap frequency of a phononic crystal has been widely explored. Unlike this extensively used mechanism, this work reports the use of nonreciprocity in the transmission band to trap energy inside a phononic crystal cavity. Passive nonreciprocity is due to natural viscosity of the background liquid (water) and asymmetry of aluminum scatterers. The level of non-resonant energy trapping was compared for three cavities with different symmetry. Enhancement of energy trapping at a frequency of 624 kHz was observed experimentally for the cavity where nonreciprocity suppresses acoustic radiation into environment. Experimental results were further investigated and confirmed using finite element numerical analysis.

Nonreciprocal collective magnetostatic wave modes in geometrically asymmetric bilayer structure with nonmagnetic spacer.

Nonreciprocity, i.e. inequivalence in amplitudes and frequencies of spin waves propagating in opposite directions, is a key property underlying functionality in prospective magnonic devices. Here we demonstrate experimentally and theoretically a simple approach to induce frequency nonreciprocity in a magnetostatically coupled ferromagnetic bilayer structure with a nonmagnetic spacer by its geometrical asymmetry. Using Brillouin light scattering, we show the formation of two collective spin wave modes in Fe81Ga19/Cu/Fe81Ga19 structure with different thicknesses of ferromagnetic layers. Experimental reconstruction and theoretical modeling of the dispersions of acoustic and optical collective spin wave modes reveal that both possess nonreciprocity reaching several percent at the wavenumber of 22 × 104 rad cm-1. The analysis demonstrates that the shift of the amplitudes of counter-propagating coupled modes towards either of the layers is responsible for the nonreciprocity because of the pronounced dependence of spin wave frequency on the layers' thickness. The proposed approach enables the design of multilayered ferromagnetic structures with a given spin wave dispersion for magnonic logic gates.

Experimental demonstration of broadband reconfigurable mechanical nonreciprocity

Breaking reciprocity has recently gained significant attention due to its broad range of applications in engineering systems. Here, we introduce the first experimental demonstration of a broadband mechanical beam waveguide, which can be reconfigured to represent wave nonreciprocity. This is achieved by using spatiotemporal stiffness modulation with piezoelectric patches in a closed-loop controller. Using a combination of analytical methods, numerical simulations, and experimental measurements, we show that contrary to the conventional shunted piezoelectrics or nonlinearity based methods, our setup is stable, less complicated, reconfigurable, and precise over a broad range of frequencies. Our reconfigurable nonreciprocal system has potential applications in phononic logic, wave diodes, energy trapping, and localization.

Non-reciprocal wave propagation in time-modulated elastic lattices with inerters

Non-reciprocal wave propagation in acoustic and elastic media has received much attention of researchers in recent years. This phenomenon can be achieved by breaking the reciprocity through space- and/or time-dependent constitutive material properties, which is an important step in overcoming the limitations of conventional acoustic- and phononic-like mechanical lattices. A special class of mechanical metamaterials with non-reciprocal wave transmission are latices with time-modulated mass and stiffness properties. Here, we investigate the non-reciprocity in elastic locally resonant and phononic-like one-dimensional lattices with inerter elements where mass and stiffness properties are simultaneously modulated through inerters and springs as harmonic functions of time. By considering the Bloch theorem and Fourier expansions, the frequency-band structures are determined for each configuration while asymmetric band gaps are found by using the weighting and threshold method. The reduction in frequency due to introduced inerters was observed in both phononic and locally resonant metamaterials. Dynamic analysis of finite-length lattices by the finite difference method revealed a uni-directional wave propagation. Special attention is given to phononic-like lattice based on a discrete-continuous system of multiple coupled beams. Moreover, the existence of edge modes in the discrete phononic lattice is confirmed through the bulk-edge correspondence and their time evolution quantified by the topologically invariant Chern number. The proposed methodology used to investigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices.

Nonreciprocal spin waves in ferrimagnetic domain-wall channels

We theoretically investigate the propagation of spin waves confined in a N\'eel-type ferrimagnetic domain-wall channel in the presence of the interfacial Dzyaloshinskii-Moriya interaction (DMI). We observe a nonreciprocal spin-wave propagation induced by the antisymmetric chiral DMI, which can be manipulated by changing the net angular momentum or the polarity of domain walls. Considering that the band gap of spin waves excited in domain walls is significantly reduced, the three-magnon processes are applied to nonlinearly detect this bounded mode in the narrow channel, which enables us to quantify the frequency and the wave vector by analyzing the spectrum of the transmitted spin wave outside the domain wall and to determine the DMI strength. These findings are useful for fabricating energy-efficient magnetic devices and measuring the interfacial DMI in ultra narrow ferrimagnetic stripes.

Engineering nonreciprocal wave dispersion in a nonlocal micropolar metabeam

Active metamaterials with electronic control schemes can exhibit nonreciprocal and/or complex elastic coefficients that result in non-Hermitian wave phenomena. Here, we investigate theoretically and experimentally a non-Hermitian micropolar metabeam with piezoelectric elements and electronic nonlocal feed-forward control. Since the nonlocal feed-forward control breaks spatial reciprocity, the proposed metabeam supports nonreciprocal flexural wave propagation, featuring unidirectional amplification/attenuation and non-Hermitian skin effect. Theoretical homogenization modeling is developed to consider the nonlocal effect into an effective complex bending stiffness. The unidirectional wave amplification/attenuation is attributed to the energy conversion between electrical power and mechanical work. The non-Hermitian skin effect, characterized by a winding number, is the manifestation of the flexural nonreciprocity and admits an extensive number of localized bulk eigenmodes on open boundaries. The nonlocal metabeam is also employed to engineer the anomalous wave dispersion such as tunable roton-like dispersion and band tilting. The nonlocal micropolar metabeam could pave the ways for designing non-Hermitian topological mechanical metamaterials featuring programmable nonreciprocal wave transmission and engineering roton-like wave dispersion relations under ambient environments.

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.

Nonreciprocal spin waves driven by left-hand microwaves

It is a conventional wisdom that a left-hand microwave cannot efficiently excite the spin wave (SW) in ferromagnets, due to the constraint of angular momentum conservation. In this work, we show that the left-hand microwave can drive nonreciprocal SWs in the presence of a strong ellipticity-mismatch between the microwave and precessing magnetization. A critical frequency is predicted, at which the left-hand microwave cannot excite SWs. Away from it the SW amplitude sensitively depends on the ellipticity of left-hand microwaves, in sharp contrast to the case driven by right-hand ones. By tuning the microwave frequency, we observe a switchable SW non-reciprocity in a ferromagnetic single layer. A mode-dependent mutual demagnetizing factor is proposed to explain this finding. Our work advances the understanding of the photon-magnon conversion, and paves the way to designing diode-like functionalities in nano-scaled magnonics.

NonReciprocal Wave Propagation in Space-Time Modulated Media

We show the possibility of achieving nonreciprocal wave propagation in space-time modulated media and give an asymptotic analysis of the nonreciprocity property in terms of the amplitude of the time modulation. Such modulation causes a folding of the band structure of the material, which may induce degenerate points. By breaking time-reversal symmetry, we show that these degeneracies may open into nonsymmetric, unidirectional band gaps. Finally, we illustrate our results by several numerical simulations.

Omnidirectional flat bands in chiral magnonic crystals

The magnonic band structure of two-dimensional chiral magnonic crystals is theoretically investigated. The proposed metamaterial involves a three-dimensional architecture, where a thin ferromagnetic layer is in contact with a two-dimensional periodic array of heavy-metal square islands. When these two materials are in contact, an anti-symmetric exchange coupling known as the Dzyaloshinskii–Moriya interaction (DMI) arises, which generates nonreciprocal spin waves and chiral magnetic order. The Landau–Lifshitz equation and the plane-wave method are employed to study the dynamic magnetic behavior. A systematic variation of geometric parameters, the DMI constant, and the filling fraction allows the examination of spin-wave propagation features, such as the spatial profiles of the dynamic magnetization, the isofrequency contours, and group velocities. In this study, it is found that omnidirectional flat magnonic bands are induced by a sufficiently strong Dzyaloshinskii–Moriya interaction underneath the heavy-metal islands, where the spin excitations are active. The theoretical results were substantiated by micromagnetic simulations. These findings are relevant for envisioning applications associated with spin-wave-based logic devices, where the nonreciprocity and channeling of the spin waves are of fundamental and practical scientific interest.

Non-Hermitian elastodynamics in gyro-odd continuum media

Linear elasticity has long been considered a well-established research area using conservative field theory. However, the discovery of odd-elasticity challenges the essential energy conservation assumption, which together with gyroscopic ingredients compromise the fundamental theory of elasticity, but to the same effect, enable new directions in active elastodynamics. Here, we consider two-dimensional continuum mechanics in a more general framework containing active constituents from both gyroscopic and odd-elastic effects, which gives rise to non-reciprocal and non-Hermitian elastic waves in a highly unconventional guise. We discuss how these unusual media can extract energy from odd-elastic engine cycles comprising remarkable features of stability transitions, in which the energy exchange process reverses. Beyond bulk waves, akin to the unidirectional characteristics of a 2D quantum-Hall insulator, we demonstrate the existence of non-Hermitian Rayleigh surface waves which, in contrast to the classical ones in passive solids, display one-way and interference-free transport characteristics, which even remain resilient in finite sharp or curved geometries. The findings reported here may provide new possibilities to manipulate elastic waves in unusual ways.

Acoustic topological beam nonreciprocity via the rotational Doppler effect.

Reciprocity is a fundamental principle of wave physics related to time-reversal symmetry. Nonreciprocal wave behaviors have been pursued for decades because of their great scientific significance and tremendous potential applications. However, nonreciprocity devices have been based on manipulation of non-topological charge (TC) in most studies to date. Here, we introduce the rotational Doppler effect (RDE) into the acoustic system to achieve nonreciprocal control of the TC beam. We use the metasurface to generate a vortex beam with a defined TC. By rotating the metasurface with specific angular velocity, the wave vector of the transmitted wave obtains positive and negative transition flexibly due to the RDE. As a result, isolated and propagating states of the vortex beam can be realized by controlling the rotation direction, representing nonreciprocal propagation. Our work also provides an alternative method for the application of TC beams and the realization of nonreciprocity.

Digitally tunable non-reciprocal wave propagation using piezoelectric metamaterials with synthetic impedance circuits

One common approach to enable non-reciprocal wave propagation in elastic media relies on introducing a directional bias by parameter modulation (e.g., stiffness modulation) in space and time. Researchers have successfully demonstrated non-reciprocal wave propagation by coupling elastic waveguides with magnetic electrical coil elements, piezoelectric elements shunted to capacitive analog circuits, or rotating mechanical resonators. The existing efforts are often limited by narrow operation frequency ranges and cumbersome implementations that lack smooth modulation (e.g., with analog circuit elements and switches). In this work, we demonstrate precise and smooth non-reciprocal wave propagation in a piezoelectric metamaterial by connecting each unit cell to a digitally controlled synthetic impedance circuit. The effective impedance of each unit cell can be externally controlled according to a desired space-time modulation scheme over a wide frequency range. We present numerical and experimental investigations on the dynamics of a piezoelectric metamaterial beam with 30 bimorph unit cells whose impedances can be varied smoothly. Specifically, we employ the spatiotemporal modulation on synthetic inductance circuits rather than capacitive. Experimental results are presented for various space-time modulation profiles, investigating the effects of the inductance value (target frequency), as well as the modulation frequency and amplitude on digitally tunable non-reciprocal wave propagation.