One-way Wave Propagation Research Articles

Pseudo-spin polarized one-way elastic wave eigenstates in one-dimensional phononic superlattices

We use a one-dimensional discrete binary elastic superlattice bridging continuous models of superlattices that showcase one-way propagation character and the discrete elastic Su-Schrieffer-Heeger model that does not. By considering Bloch wave solutions of the superlattice wave equation, we demonstrate conditions supporting elastic eigenmodes that do not satisfy translational invariance of Bloch waves over the entire Brillouin zone, unless their amplitude vanishes for some wave number. These modes are characterized by a pseudo-spin, and occur only on one side of the Brillouin zone for given spin, leading to spin-selective one-way wave propagation. We demonstrate how these features result from the interplay of translational invariance of Bloch waves, pseudo-spin, and a Fabry-Pérot resonance condition in the superlattice unit cell.

Pseudo-Spin Polarized One-Way Elastic Wave Eigenstates in One-Dimensional Phononic Superlattices

We investigate a one-dimensional discrete binary elastic superlattice bridging continuous models of superlattices that showcase a one-way propagation character, as well as the discrete elastic Su–Schrieffer–Heeger model, which does not exhibit this character. By considering Bloch wave solutions of the superlattice wave equation, we demonstrate conditions supporting elastic eigenmodes that do not satisfy the translational invariance of Bloch waves over the entire Brillouin zone, unless their amplitude vanishes for a certain wave number. These modes are characterized by a pseudo-spin and occur only on one side of the Brillouin zone for a given spin, leading to spin-selective one-way wave propagation. We demonstrate how these features result from the interplay of the translational invariance of Bloch waves, pseudo-spins, and a Fabry–Pérot resonance condition in the superlattice unit cell.

Experimental evidence of nonreciprocal propagation in space-time modulated piezoelectric phononic crystals

A nonreciprocal system composed of a one-dimensional piezoelectric phononic crystal whose periodic electrical conditions are modulated in time is presented. One-way longitudinal wave propagation is studied experimentally and compared to finite element temporal simulations. The modulation is performed by prescribing grounded or floating potential conditions on a periodic set of electrodes through external circuits. This approach makes it possible to consider a wide range of modulation speeds, and the large number of unit cells of the phononic crystal allows us to characterize experimentally the full dispersion curves of the system. This permits to observe the presence of directional bandgaps and to follow the shift in frequencies of these bandgaps as a function of the modulation speed. The experiments show the linear evolution of the central position of the bandgaps with the increase in the modulation speed, as well as their progressive closure, over a wide range of frequencies. Experiments are also used to estimate the evolution of bandgaps in a dispersive system, a problem discussed in several theoretical works but never observed experimentally. This work may constitute the foundation for experimental analysis of Floquet acoustic metamaterials, accelerated-modulation space-time metamaterials, or acoustic analog of the event horizon.

Enhancing one-way wave equation-based migration with deep learning

One advantage of one-way wave equation-based migration is its low computational cost. However, due to the limited wavefield propagation angle, it is difficult to use one-way wave equation-based migration for high-precision imaging of structures with large inclinations due to issues such as inaccurate amplitudes and migration image artifacts. In addition, when the model has large horizontal velocity differences, it is difficult for the one-way wave propagator to calculate an accurate wavefield phase. Reverse time migration (RTM) based on the two-way wave propagator has a high resolution and avoids the issues associated with one-way wave propagators; however, it has a high computational cost in practical applications. We develop a convolutional neural network (CNN) application mode that improves one migration method by learning from another one and design a CNN with a structure similar to U-net that combines the advantages of both migration methods. The CNN label is the RTM result, and the corresponding input is the result of one-way wave migration with a generalized screen propagator (GSP). The trained CNN model improves the amplitude in the one-way wave migration image and removes the errors caused by large lateral velocity perturbations. Moreover, by maintaining the high migration calculation efficiency, our CNN model allows for a high resolution, few artifacts, and accurate images of steep structures in the one-way wave migration result. With our method, the accuracy of the one-way wave migration result is close to that of the RTM result. The use of GSP-based migration in our CNN model rather than conventional RTM to generate prospecting images can considerably reduce the calculation costs.

Direct expansion of Fourier extrapolator for one-way wave equation using Chebyshev polynomials of the second kind

The Fourier method for one-way wave propagation is efficient but potentially inaccurate in complex media. The implicit finite-difference (FD) method can handle arbitrarily complex media, but it can be inefficient in 3D and has limited dip bandwidth. We have adopted a new Fourier method based on the Chebyshev expansion of the second kind. Theoretical analyses and numerical experiments indicate that our method is comprehensively superior to a similar method based on the Chebyshev expansion of the first kind in terms of balanced amplitude and error tolerance. Within the dip bandwidth from 0° to 65°, the fourth-order form of our method has an error tolerance of 2%, which is approximately one-third that of the Chebyshev expansion of the first kind. Our method also is superior to the implicit FD method in several important aspects: effective bandwidth, computational efficiency, numerical dispersion, and two-way splitting error. It can be easily extended from 2D to 3D compared with the FD method and from low orders to high orders compared with the optimized Chebyshev-Fourier method. Our method finds better imaging results of the SEG/EAGE model by providing a well-focused salt dome, flank, and bottom as well as the detailed structures beneath the salt body, compared with the implicit FD method and the Chebyshev expansion of the first kind; meanwhile, our method has fewer imaging artifacts because it can better position the reflectors.

Comments on “Elegant scheme for one-way wave propagation in Kerr media”

Comments on “Elegant scheme for one-way wave propagation in Kerr media”

Two-way wave equation depth migration using one-way propagator extrapolation

Two-way wave depth migration (TWDM) can achieve a wider imaging angle in media with significant lateral velocity changes and better imaging results for complex structures with high dip angles than in conventional one-way wave depth migration. Conventional one-way wave migration uses a boundary condition to approximately solve the second-order wave equation, leading to limited propagating angles and inaccurate imaging results, especially for complicated structures. Theoretically, a full-wave equation is of second order and requires two boundary conditions to solve it. The dual-sensor acquisition system can provide sufficient boundary conditions; however, it is challenging to acquire ideal, cost-effective, and factual seismic data, particularly in 3D seismic exploration. Overcoming these shortcomings, we propose a solution that uses conventional surface data to accurately estimate the wavefield at the second layer as another boundary condition. Based on the eigen-decomposition theory, a one-way propagator to suit arbitrary variant velocity on the surface is introduced.The conventional Fourier finite-difference (FFD) and generalised screen propagator (GSP) are utilised to perform the proposed TWDM schemes. The impulse responses proved that the proposed scheme using FFD and GSP operators had no limitation on the propagation angle. The single-shot migrated results in the flat model confirmed that the proposed schemes could achieve better amplitude-preserving performance than the conventional one-way schemes. The dip model showed that the proposed scheme was consistent with the characteristics of one-way wave propagators in imaging steep dippings. Imaging results of the Marmousi model further confirmed that the proposed scheme could obtain more accurate imaging sections for complex structures, especially for steep flanks and deep-seated anticlines. The application of actual dual-sensor seismic data demonstrated that the proposed scheme could achieve a higher imaging quality than the dual-sensor method.

One-way wave propagation in the ray-centred coordinate system for vertical transversely isotropic media

One-way wave propagation in the ray-centred coordinate system for vertical transversely isotropic media

Data-driven modeling of nonlinear traveling waves.

Presented is a data-driven machine learning framework for modeling traveling wave spatiotemporal dynamics. The presented framework is based on the steadily propagating traveling wave ansatz, u(x,t)=U(ξ=x-ct+a). For known evolution equations, this coordinate transformation reduces governing partial differential equations to a set of coupled ordinary differential equations (ODEs) in the traveling wave coordinate ξ. Although traveling waves are readily observed in many physical systems, the underlying governing equations may be unknown. For these instances, the traveling wave dynamical system can be modeled empirically with neural ODEs. Presented are these ideas applied to several physical systems that admit traveling waves. Examples include traveling wave fronts, pulses, and wavetrains restricted to one-way wave propagation in a single spatial dimension. Last, applicability to real-world physical systems is presented with an exploration of data-driven modeling of rotating detonation waves.

Physical Observation of a Robust Acoustic Pumping in Waveguides with Dynamic Boundary

Research on breaking time-reversal symmetry to realize one-way wave propagation is a growing area in photonic and phononic crystals and metamaterials. In this Letter, we present physical realization of an acoustic waveguide with spatiotemporally modulated boundary conditions to realize nonreciprocal transport and acoustic topological pumping. The modulated waveguide inspired by a water wheel consists of a helical tube rotating around a slotted tube at a controllable speed. The rotation of the helical tube creates moving boundary conditions for the exposed waveguide sections at a constant speed. We experimentally demonstrate acoustic nonreciprocity and topologically robust bulk-edge correspondences for this system, which is in good agreement with analytical and numerical predictions. The nonreciprocal waveguide is a one-dimensional analog to the two-dimensional quantum Hall effect for acoustic circulators and is characterized by a robust integer-valued Chern number. These findings provide insight into practical implications of topological modes in acoustics and the implementation of higher-dimensional topological acoustics where time serves as a synthetic dimension.

Oscillatory Convection Onset in a Porous Rectangle with Non-analytical Corners

The analytical theory on Darcy–Bénard convection is dominated by normal-mode approaches, which essentially reduce the spatial order from four to two. This paper goes beyond the normal-mode paradigm of convection onset in a porous rectangle. A handpicked case where all four corners of the rectangle are non-analytical is therefore investigated. The marginal state is oscillatory with one-way horizontal wave propagation. The time-periodic convection pattern has no spatial periodicity and requires heavy numerical computation by the finite element method. The critical Rayleigh number at convection onset is computed, with its associated frequency of oscillation. Snapshots of the 2D eigenfunctions for the flow field and temperature field are plotted. Detailed local gradient analyses near two corners indicate that they hide logarithmic singularities, where the displayed eigenfunctions may represent outer solutions in matched asymptotic expansions. The results are validated with respect to the asymptotic limit of Nield (Water Resour Res 11:553–560, 1968).

Elegant scheme for one-way wave propagation in Kerr media

In this article, an intelligent computational scheme is presented for the dynamical solution of fractional-order linear and nonlinear (Kerr nonlinearity) Helmholtz equations with boundary conditions, which have a significant impact on electromagnetics, hydrodynamics and acoustic phenomena. The propagation of electromagnetic waves in Kerr media describes the linearly polarized electric field in an isotropic material, for a range of important phenomena in nonlinear optics and other areas. Here, the generalized Helmholtz equation of $$ n $$ dimensions is considered with fractional-order derivative. The fractional Laplace transform is utilized, and parameter $$ s^{\alpha } $$ is linearized by series expansion. Ultimately, the inverse fractional Laplace transform of this expansion reduces the fractional-order derivative to integer-order derivative. The new attained structure of partial differential equation becomes equivalent to the so-called fractional-order Helmholtz equation. The contribution also provides an artificial neural network-based technique, designed with a metaheuristic algorithm, to analyze the governing model numerically and graphically. Taking sigmoidal function as an activation function, the unsupervised error function is formulated, which is then optimized with the aid of the firefly algorithm (FFA). By using FFA, the minimum search path of the error function is tracked with the convergent values of the network weights. Besides, the validity and accuracy of the adapted technique are ascertained by calculating the error norms that ensure the convergence of the approximation. Accordingly, the achieved facts and figures accentuate comprehensively the novel implication of this attempt.

One-way interfacial waves in aflexuralplate with chiral double resonators.

In this paper, we demonstrate a new approach to control flexural elastic waves in a structured chiral plate. The main focus is on creating one-way interfacial wave propagation at a given frequency by employing double resonators in a doubly periodic flexural system. The resonators consist of two beams attached to gyroscopic spinners, which act to couple flexural and rotational deformations, hence inducing chirality in the system. We show that this elastic structure supports one-way flexural waves, localized at an interface separating two sub-domains with gyroscopes spinning in opposite directions, but with otherwise identical properties. We demonstrate that a special feature of double resonators is in the directional control of wave propagation by varying the value of the gyricity, while keeping the frequency of the external time-harmonic excitation fixed. Conversely, for the same value of gyricity, the direction of wave propagation can be reversed by tuning the frequency of the external excitation. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.

Routing Acoustic Waves via a Metamaterial with Extreme Anisotropy

Routing acoustic waves without backscattering losses is presently of great interest. Unlike both conventional approaches using defects in sonic crystals and emerging approaches based on topological edge states, this study proposes a radically different theoretical framework that utilizes extremely anisotropic media to engineer backscattering-immune waveguides. The exact condition for one-way wave propagation along zigzag paths is derived. The proposal is experimentally validated using spoof surface acoustic waves, and the results could have implications for on-chip wave manipulation, as well as noise control.

Proof of concept of a frequency-preserving and time-invariant metamaterial-based nonlinear acoustic diode

Acoustic filters and metamaterials have become essential components for elastic wave control in applications ranging from ultrasonics to noise abatement. Other devices have been designed in this field, emulating their electromagnetic counterparts. One such case is an acoustic diode or rectifier, which enables one-way wave transmission by breaking the wave equation-related reciprocity. Its achievement, however, has proved to be rather problematic, and current realizations display a number of shortcomings in terms of simplicity and versatility. Here, we present the design, fabrication and characterization of a device able to work as an acoustic diode, a switch and a transistor-like apparatus, exploiting symmetry-breaking nonlinear effects like harmonic generation and wave mixing, and the filtering capabilities of metamaterials. This device presents several advantages compared with previous acoustic diode realizations, including versatility, time invariance, frequency preserving characteristics and switchability. We numerically evaluate its efficiency and demonstrate its feasibility in a preliminary experimental realization. This work may provide new opportunities for the practical realization of structural components with one-way wave propagation properties.

Generalized plane wave expansion method for non-reciprocal discretely modulated waveguides

In this manuscript we investigate one-way wave propagation in spatio-temporal phononic wave-guides in which the modulation of material properties is provided piecewise in space and time. Non-reciprocal dispersion diagram is computed using a generalized plane wave expansion method, whose formulation, provided in the paper, is able to describe how a generic discrete or continuous unit cell is able to break the mirror symmetry in the momentum space, as already shown in other works by means of more expensive and less accurate computational tools. The proposed method is then used to verify a physical interpretation we provided for bandgap formation by means of wave superposition in spatio-temporal modulated waveguides.

Comparison of one-way and full-wave linear propagation models in inhomogeneous medium

One-way wave propagation models based on the parabolic approximation or its wide-angle extensions are often used for describing bounded acoustic beams. Such models are highly demanded when solving nonlinear problems that are computationally intensive and thus technically difficult to solve using full-wave approaches. When describing the propagation of a wave beam in a homogeneous medium, the one-way assumption is fulfilled exactly, and therefore, the inaccuracy is caused only by the limitations of the parabolic approximation. Such an error is significantly reduced within the wide-angle approach and completely disappears when using the exact propagator in the framework of the angular spectrum method. The situation is less obvious in the case of a heterogeneous environment, when a part of the wave energy is inevitably reflected becoming a counter-propagating wave and thus is not taken into account in the one-way approximation. The degree this phenomenon affects the accuracy of the one-way approach is still under discussion. In the current paper, a one-way propagator based on the pseudo-differential wide-angle equation is proposed. The propagator is tested for the homogeneous medium and for several configurations of media with regular and random inhomogeneities. The corresponding solutions are compared with those obtained using the k-Wave toolbox. Results of comparison show how the one-way propagator accuracy depends on the contrast and smoothness of the inhomogeneities. [Work supported by RSF No. 18-72-00196.]

Optical non-reciprocity induced by asymmetrical dispersion of Tamm plasmon polaritons in terahertz magnetoplasmonic crystals.

Nonreciprocal light phenomena, including one-way wave propagation along an interface and one-way optical tunneling, are presented at terahertz frequencies in a system of magnetically controlled multi-layered structure. By varying the surface termination and the surrounding medium, it is found that the nonreciprocal bound or radiative Tamm plasmon polartions can be supported, manipulated, and well excited. Two different types of contributions to the non-reciprocity are analyzed, including the direct effect of magnetization-dependent surface terminating layer as well as violation of the periodicity in truncated multi-layered systems. Calculations on the asymmetrical dispersion relation of surface modes, field distribution, and transmission spectra through the structure are employed to confirm the theoretical results, which may potentially impact the design of tunable and compact optical isolators.

Defect mode-induced unidirectional flexural wave transmission using prismatic beams with concentrated gradient masses

We study and realize unidirectional flexural wave transmission in finite phononic crystal beams based on the boundary defect modes. First, we show that by carrying a periodic array of concentrated masses, conventional prismatic beams become phononic crystal beams having multiple transmittance peaks in odd-order bandgaps. We point out that these bandgap transmittance peaks are induced by pass-band splitting and are essentially defect modes due to the existence of the imperfect boundary in finite beam structures. Significant asymmetric flexural wave propagation can be observed in these defect modes by gradually changing each concentrated mass. Using the spectral element method (SEM), the relationship between the concentrated gradient masses and the directivity at the defect modes is discussed. To realize concentrated gradient masses, we periodically attach near-point-contact steel balls with gradient diameters on a prismatic beam. The formation of the bandgaps and unidirectional displacement transmission are experimentally validated with a high-sensitive point-wise fiber Bragg grating displacement sensing system. Asymmetric one-way flexural wave propagation is further demonstrated in the time domain with a Hanning-windowed tone burst signal excited at the two ends of the phononic crystal beam. Agreements between the SEM and experimental results clearly indicate that the asymmetric one-way flexural wave propagation can be achieved in prismatic beams carrying a periodic array of concentrated gradient masses.

Dial-in Topological Metamaterials Based on Bistable Stewart Platform

Recently, there have been significant efforts to guide mechanical energy in structures by relying on a novel topological framework popularized by the discovery of topological insulators. Here, we propose a topological metamaterial system based on the design of the Stewart Platform, which can not only guide mechanical waves robustly in a desired path, but also can be tuned in situ to change this wave path at will. Without resorting to any active materials, the current system harnesses bistablilty in its unit cells, such that tuning can be performed simply by a dial-in action. Consequently, a topological transition mechanism inspired by the quantum valley Hall effect can be achieved. We show the possibility of tuning in a variety of topological and traditional waveguides in the same system, and numerically investigate key qualitative and quantitative differences between them. We observe that even though both types of waveguides can lead to significant wave transmission for a certain frequency range, topological waveguides are distinctive as they support robust, back scattering immune, one-way wave propagation.