Nonreciprocal Wave Research Articles

Spectro-spatial analysis of van der Pol-type phononic crystals

Abstract The application of phononic chains as metamaterials demonstrates their remarkable capability to manipulate the propagation of waves. These periodic structures yield frequency-dependent behavior of material comprising characteristics with many possible engineering applications. In this paper, we investigate the weak and general nonlinear behaviors of the van der Pol-type damped phononic chains. The analysis of wave propagation is initially conducted for a one-dimensional structure, and subsequently, is extended to consider the wave motion through two-dimensional and three-dimensional lattices. Results are obtained using the method of multiple scales and a Spectro-spatial analysis by employing the numerical method of the 4th-order Runge–Kutta. A new phase-diagram relation within the chain’s unit cell is also introduced aiming to enhance the numerical findings. Our results indicate that in the weakly nonlinear regime, the van der Pol-type damping closely follows the linear dispersion curve, regardless of the initial amplitude. This suggests a symmetry between energy pumping and dissipation modes, where hardening and softening behaviors align with linear characteristics of common damping mechanisms, such as viscous damping. Additionally, the formulation demonstrates the existence of limit-cycle stability in the motion of each mass. For the general damped system, it is observed that a special frequency exists where the system converges, for all wave numbers similar to the synchronization effect. Hence, the motion and the frequency of all masses are synced. Additionally, non-reciprocal wave propagation is observed, resulting in a bandgap structure with a symmetry breaking occurring near the limit cycle. These results are promising in the fields of wave emitters, wave filters, and signal encryption.

Non-Bloch band theory for time-modulated discrete mechanical systems

This study establishes a non-Bloch band theory for time-modulated discrete mechanical systems. We consider simple mass–spring chains whose stiffness is periodically modulated in time. Using the temporal Floquet theory, the system is characterized by linear algebraic equations in terms of Fourier coefficients. This allows us to employ a standard linear eigenvalue analysis. Unlike non-modulated linear systems, the time modulation makes the coefficient matrix non-Hermitian, which gives rise to, for example, parametric resonance, non-reciprocal wave transmission, and non-Hermitian skin effects. In particular, we study finite-length chains consisting of spatially periodic mass–spring units and show that the standard Bloch band theory is not valid for estimating their eigenvalue distribution. To remedy this, we propose a non-Bloch band theory based on a generalized Brillouin zone. This novel approach, the combination of the temporal Floquet theory for time-modulated systems and generalized Brillouin zone, enables the prediction of eigenvalue distribution under open boundary conditions and also quantitative characterization of non-Hermitian skin modes. The proposed theory is verified by some numerical experiments.

Nonreciprocal damping of spin waves propagating in magnetic domain walls induced by Dzyaloshinskii-Moriya interaction

The nonreciprocity of spin waves refers to the phenomenon that spin waves propagating in opposite directions display different features. This phenomen becomes a fundamental requirement for implementing magnon logic architectures. The nonreciprocal transportion of spin waves induced by Dzyaloshinskii-Moriya interaction (DMI) has been studied extensively. It is characterized by a shift of spin-wave dispersion. Here we report another feature of the DMI-induced nonreciprocity, i.e., the nonreciprocal spin wave damping. We find that the spin waves propagating with opposite wave vectors in magnetic domain wall have different damping, which is frequency dependent and especially evident in low frequancy range. For spin waves with sufficient low frequencies (around 1 GHz), the damping nonreciprocity is so extreme that spin waves can transport only in one direction, thus realizing the spin-wave diode function. The theoretical predictions are validated by micromagnetic simulations. The findings in this work points out a new feature of DMI-induced spin wave nonreciprocity and may be exploited for designing novel magnonic devices.

Inverse design of nonlinear phononic crystal configurations based on multi-label classification learning neural networks

Abstract Phononic crystals, as artificial composite materials, have sparked significant interest due to their novel characteristics that emerge upon the introduction of nonlinearity. Among these properties, second-harmonic features exhibit potential applications in acoustic frequency conversion, non-reciprocal wave propagation, and non-destructive testing. Precisely manipulating the harmonic band structure presents a major challenge in the design of nonlinear phononic crystals. Traditional design approaches based on parameter adjustments to meet specific application requirements are inefficient and often yield suboptimal performance. Therefore, this paper develops a design methodology using Softmax logistic regression and multi-label classification learning to inversely design the material distribution of nonlinear phononic crystals by exploiting information from harmonic transmission spectra. The results demonstrate that the neural network-based inverse design method can effectively tailor nonlinear phononic crystals with desired functionalities. This work establishes a mapping relationship between the band structure and the material distribution within phononic crystals, providing valuable insights into the inverse design of metamaterials.

Wide-angle non-reciprocal thermal radiator based on a periodic toroidal array structure

Non-reciprocal thermal radiation is crucial for energy transfer and storage applications. However, the range of angles of incidence limits the development of non-reciprocal thermal radiation. To address this problem, we have proposed and developed a non-reciprocal thermal radiation device with wide-angle characteristics, which operates in the mid-infrared spectral range. The radiator consists of a silicon-based periodic toroidal array, a Weyl semimetal (WSM), and a metal reflective layer Ag. A strong nonreciprocity of 0.88 is observed at 9.36 μm wavelength and 41.8° angle, while a nonreciprocity of 0.87 can be sustained within the range of 36°–74°. In addition, the nonreciprocity can be maintained above 0.8 in the spectral range of 9.3 μm ∼9.4 μm. Compared with the previous single working angle, our work has dramatically broadened the angle of energy absorption, and the non-reciprocal intensity can be maintained at a high level. Through a detailed analysis of the magnetic field modulus and impedance characteristics at non-reciprocal wavelengths, we reveal that cavity resonance excitation is the core physical process of mid-infrared wide-angle non-reciprocal radiation. In addition, changing the axial vector of the WSM can lead to a redshift of the non-reciprocal wave peaks. The proposed two-dimensional mid-infrared non-reciprocal emitter can realize wide-angle domain emission at specific wavelengths, which is promising for applications in energy storage and conversion systems such as solar cells and thermophotovoltaic cells.

Non-reciprocal wave propagations in a one-dimensional periodic structure modified with a linkage mechanism

Non-reciprocal wave propagations in a one-dimensional periodic structure modified with a linkage mechanism

Broadband non-reciprocal wave suppression and frequency conversion by active metabeams

Non-reciprocal wave propagation has recently attracted considerable attention as it is potentially beneficial to many applications, ranging from waveguiding, sensing, and communication to vibration control. Here, we propose the design of an active metabeam for broadband non-reciprocal wave suppression, that can strongly suppress the transmitted wave for forward incidence and amplify the transmitted wave for backward incidence. The metabeam consists of piezoelectric sensors and actuators connected by a feedforward control loop. We find that the broadband non-reciprocal wave suppression can be realized by making the second forward transmission dip close to the first one, which can be controlled by the distance between the piezoelectric actuators. The broadband non-reciprocal wave suppression of the metabeam is demonstrated via a set of time domain analyses. We further study the frequency conversion effects of the metabeam based on a time-varying transfer function. In particular, we show that among the frequency converted harmonics, those at high frequencies can be eliminated by destructive interference, resulting in an approximate single-frequency conversion in the transmitted wave. Our study advances the field of non-reciprocal mechanics and offers a reliable platform for designing active broadband elastic wave devices, providing a feasible way for asymmetrical energy control, broadband vibration attenuation, and signal processing.

Nonreciprocal field transformation with active acoustic metasurfaces.

Field transformation, as an extension of the transformation optics, provides a unique means for nonreciprocal wave manipulation, while the experimental realization remains a substantial challenge as it requires stringent material parameters of the metamaterials, e.g., purely nonreciprocal bianisotropic parameters. Here, we develop and demonstrate a nonreciprocal field transformation in a two-dimensional acoustic system, using an active metasurface that can independently control all constitutive parameters and achieve purely nonreciprocal Willis coupling. The field-transforming metasurface enables tailor-made field distribution manipulation, achieving localized field amplification by a predetermined ratio. The metasurface demonstrates the self-adaptive capability to various excitation conditions and can be extended to other geometric shapes. The metasurface also achieves nonreciprocal wave propagation for internal and external excitations, demonstrating a one-way acoustic device. The nonreciprocal field transformation not only extends the framework of the transformation theory for nonreciprocal wave manipulation but also holds great potential in applications such as ultrasensitive sensors and nonreciprocal communication.

Introduction of Local Resonators to a Nonlinear Metamaterial With Topological Features

Abstract Recent work in nonlinear topological metamaterials has revealed many useful properties such as amplitude dependent localized vibration modes and nonreciprocal wave propagation. However, thus far, there have not been any studies to include the use of local resonators in these systems. This work seeks to fill that gap through investigating a nonlinear quasi-periodic metamaterial with periodic local resonator attachments. We model a one-dimensional metamaterial lattice as a spring-mass chain with coupled local resonators. Quasi-periodic modulation in the nonlinear connecting springs is utilized to achieve topological features. For comparison, a similar system without local resonators is also modeled. Both analytical and numerical methods are used to study this system. The dispersion relation of the infinite chain of the proposed system is determined analytically through the perturbation method of multiple scales. This analytical solution is compared to the finite chain response, estimated using the method of harmonic balance and solved numerically. The resulting band structures and mode shapes are used to study the effects of quasi-periodic parameters and excitation amplitude on the system behavior both with and without the presence of local resonators. Specifically, the impact of local resonators on topological features such as edge modes is established, demonstrating the appearance of a trivial bandgap and multiple localized edge states for both main cells and local resonators. These results highlight the interplay between local resonance and nonlinearity in a topological metamaterial demonstrating for the first time the presence of an amplitude invariant bandgap alongside amplitude dependent topological bandgaps.

Stress guides in generic static mechanical metamaterials.

The confinement of waves within a waveguide can enable directional transmission of signals, which has found wide applications in communication, imaging, and signal isolation. Extending this concept to static systems, where material deformation is piled up along a spatial trajectory, remains elusive due to the sensitivity of localized deformation to structural defects and impurities. Here, we propose a general framework to characterize localized static deformation responses in two-dimensional generic static mechanical metamaterials, by exploiting the duality between space in static systems and time in one-dimensional non-reciprocal wave systems. An internal time-reverse symmetry is developed by the space-time duality. Upon breaking this symmetry, quasi-static load-induced deformation can be guided to travel along a designated path, thereby realizing a stress guide. A combination of time-reverse and inversion symmetries discloses the parity-time symmetry inherent in static systems, which can be leveraged to achieve directional deformation shielding. The tailorable stress guides can find applications in various scenarios, ranging from stress shielding and energy harvesting in structural tasks to information processing in mechanical computing devices.

Reciprocal and non-reciprocal electromagnetic wave propagation in sub-100 nm epitaxial YIG thin films deposited under different oxygen growth pressure

Directional dependent transport of information in magnetic thin films offers a great opportunity to realize reciprocal and nonreciprocal microwave devices, such as filters, phase shifter, isolators and circulators. Electromagnetic wave (EM) propagation in sub-100 nm thin magnetic film is critical, yet reciprocal and non-reciprocal wave propagation and its accurate measurements remain a challenge. We investigated reciprocal and non-reciprocal wave propagation in 90 nm thick epitaxial thin films of yttrium iron garnet (Y3Fe5O12:YIG) grown by pulse laser deposition (PLD) technique on gadolinium gallium garnet [GGG(100)] substrates. The effect of oxygen growth pressure during deposition of YIG films exhibit directional dependence properties of electromagnetic wave propagation. The reciprocal EM wave propagation was generated by a S-type transmission line to achieve microwave (RF) magnetic fields (hRF) perpendicular to applied dc magnetic fields (HDC), to ensure the ferromagnetic resonance (FMR) condition. The center frequency is tuned up to 20 GHz with an applied magnetic field of 6 kOe. The tuning of the center frequency was achieved as of 85.3 % with HDC of 6 kOe. To achieve non-reciprocal EM-wave propagation one straight microstrip line was used to ensures a parallel configuration (parallel pumping FMR condition) of hRF to HDC. The nonreciprocity observed is due to the presence of gyrotropic properties in the YIG thin films and it enhances when YIG film was placed in asymmetric geometry. Further, oxygen growth pressure (>0.1 mbar) grown YIG films enhances the nonreciprocity by 21.6 %. The experimental results were successfully validated using high-frequency structure simulator (HFSS). Hence, these results indicate that controlled deposition parameters can be a crucial parameter in the design of reciprocal and nonreciprocal microwave signal processing devices.

Coherent Magnons with Giant Nonreciprocity at Nanoscale Wavelengths.

Nonreciprocal wave propagation arises in systems with broken time-reversal symmetry and is key to the functionality of devices, such as isolators or circulators, in microwave, photonic, and acoustic applications. In magnetic systems, collective wave excitations known as magnon quasiparticles have so far yielded moderate nonreciprocities, mainly observed by means of incoherent thermal magnon spectra, while their occurrence as coherent spin waves (magnon ensembles with identical phase) is yet to be demonstrated. Here, we report the direct observation of strongly nonreciprocal propagating coherent spin waves in a patterned element of a ferromagnetic bilayer stack with antiparallel magnetic orientations. We use time-resolved scanning transmission X-ray microscopy (TR-STXM) to directly image the layer-collective dynamics of spin waves with wavelengths ranging from 5 μm down to 100 nm emergent at frequencies between 500 MHz and 5 GHz. The experimentally observed nonreciprocity factor of these counter-propagating waves is greater than 10 with respect to both group velocities and specific wavelengths. Our experimental findings are supported by the results from an analytic theory, and their peculiarities are further discussed in terms of caustic spin-wave focusing.

A Nonreciprocal CRLH Full-Duplex Metamaterial Leaky Wave Antenna Based on Distributed Mixing Principle

A Nonreciprocal CRLH Full-Duplex Metamaterial Leaky Wave Antenna Based on Distributed Mixing Principle

Inertia Modulated Meta-Structure With Time-Varying Inertia Amplification

Abstract In this work, a new inertia modulated meta-structure is proposed to enable time-dependent inertia parameters, and thereby realize non-reciprocal wave propagation via spatiotemporal modulation. The designed cell structure is composed of an oscillatory disk and a mass that slides in a guide embedded in the disk frictionlessly with prescribed motion. Effective moment of inertia and damping coefficients of the rocking motion of the cell structure are rendered time-dependent due to the inertia and Coriolis forces of the periodically sliding mass, which allows us to implement the expected spatiotemporal modulation upon a super-cell. Non-reciprocal propagation behavior of the proposed meta-structure is verified via the theoretical solution of the dispersion relation as well as the dynamic response of a finite array. Effects of modulation parameters, including the frequency, amplitude, and phase, on the unidirectional propagation characteristic are thoroughly investigated.

All-passive microwave-diode nonreciprocal metasurface

Breaking reciprocity in the microwave frequency range is strongly desirable in the development of modern electronic systems, as it enables nonreciprocal wave absorbing, nonreciprocal beam steering, frequency conversion, and protection of sensitive devices from high energy sources. However, the typical approaches involve bulky biasing magnets or complex spatial-temporal modulations. As such, resorting to lightweight and all-passive platforms would result in optimal configurations and efficient integration. Starting from a circuit model, we theoretically demonstrate the nonreciprocal behavior on a transmission line building block creating a strong field asymmetry with a switchable matching stub to enable two distinct working states. After translating to an electromagnetic model, this concept is first proved by simulation and then experimentally verified on a microstrip-line-based diode-integrated metasurface showing nonreciprocal transmission. This printed circuit board design is expected to find various applications in electromagnetic protecting layers, communication systems, microwave isolators and circulators.

Time-modulated inerters as building blocks for nonreciprocal mechanical devices

In this work, we discuss the realization of mechanical devices with non-reciprocal attributes enabled by inertia-amplifying, time-modulated mechanisms. Our fundamental building-block features a mass, connected to a fixed ground through a spring and to a moving base through a mechanism-based inerter. Through analytical derivations and numerical simulations, we provide details on the nonlinear dynamics of such system. We demonstrate that providing a time modulation to the inerter’s base produces two additions on the dynamics of the main spring–mass oscillator: (i) an effective time-modulated mass term, and (ii) a time varying force term; both quantities are functions of the modulating frequency. With specific choices of parameters, the modulation-induced force term – that represents one of the main drawbacks in most experimental realizations of purely time-modulated systems – vanishes and we are left with an effective time-varying mass. We then illustrate that this building block can be leveraged to realize non-reciprocal wave manipulation devices, and concentrate on a non-reciprocal beam-like waveguide. The simple design and the clean performance of our system makes it an attractive candidate for the realization of fully mechanical non-reciprocal devices.

Nonreciprocal wave propagation in a time-space modulated metasurface using the modified plane wave expansion method

The present work focuses on the impact of including the time-space modulation features on the band structure. This study introduces a modified plane wave expansion method for dealing with the out-of-plane wave propagation in a two-dimensional periodic metasurface. The proposed method, which is applied to structures with modulated properties, tackles the constraints of the conventional plane wave method. The characteristics of uncommon systems with space-time-variant properties are explored by analyzing the produced dispersion curves by modified plane wave method. This approach can also resolve the inconsistencies and drawbacks of other similar approaches. Three scenarios are employed to extract the patterns of bandgap regions and discover the impact of time-traveling material features on the creation of bandgap in periodic metasurfaces. The integrity of the introduced method has been established by comparison with data obtained from COMSOL finite element software as well as the reported results in the literature. The secondary objective of this study is to manipulate the location of the bandgap to achieve complete control over the propagation of waves. The effectiveness of the proposed approach becomes more apparent when applied to metamaterials that incorporate piezoelectric materials with discrete structures. This relates primarily to enhanced precision and speed, particularly in higher modes and sheds light on a potential application of extending this scenario to the more complex structures.

Spin waves in monolayers of transition-metal dichalcogenides with Dzyaloshinskii–Moriya interaction

Dzyaloshinski–Moriya interaction, known also as the antisymmetric exchange coupling, leads to a variety of interesting spin phenomena, like spin canting, skyrmion formation, nonreciprocal spin wave propagation, and others. In this paper we analyze spin waves in monolayers of two-dimensional van–der–Waals materials, such as Vanadium–based dichalcogenides, VX2 (X=S, Se, Te) and other materials of similar symmetry. The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Holstein–Primakoff–Bogoliubov transformation.

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.

Acoustic scattering from spatiotemporally modulated domains

Acoustic and elastic metamaterials with space- and time-dependent material properties have received significant attention recently as a means to realize systems that induce nonreciprocal wave propagation in the bulk or enable frequency and mode conversion of fields scattered from metasurfaces. A previous study derived a nonreciprocal Green’s function for flexural waves in a one- and two-dimensional finite plate with a spatiotemporal modulation of the Young’s modulus [Goldsberry et al., J. Acoust. Soc. Am. 150(4), 2021]. In this work, we generalize the nonreciprocal Green’s function approach to the acoustic case of scattering from an inhomogeneity whose properties are general functions of space and time. Canonical geometries where the analytical solution is known for the unmodulated case will be investigated. Computations of the scattered field directivity pattern will then be carried out as a function of the modulation parameters to determine cases that yield a large degree of control over the scattered field directivity pattern for each generated frequency harmonic. [Work supported by ONR.]