Bragg Scattering Research Articles

Compressed sensing two-dimensional Bragg scatter imaging.

Here we introduce a new reconstruction technique for two-dimensional Bragg scattering tomography (BST), based on the Radon transform models of Webber and Miller [Inverse Probl. Imaging15, 683 (2021).10.3934/ipi.2021010]. Our method uses a combination of ideas from multibang control and microlocal analysis to construct an objective function which can regularize the BST artifacts; specifically the boundary artifacts due to sharp cutoff in sinogram space (as observed in [arXiv preprint, arXiv:2007.00208 (2020)]), and artifacts arising from approximations made in constructing the model used for inversion. We then test our algorithm in a variety of Monte Carlo (MC) simulated examples of practical interest in airport baggage screening and threat detection. The data used in our studies is generated with a novel Monte-Carlo code presented here. The model, which is available from the authors upon request, captures both the Bragg scatter effects described by BST as well as beam attenuation and Compton scatter.

Numerical Modelling and Optimization of Two-Dimensional Phononic Band Gaps in Elastic Metamaterials with Square Inclusions

A numerical simulation study on elastic wave propagation of a phononic composite structure consisting of epoxy and tungsten carbide is presented for low-frequency elastic wave attenuation applications. The calculated dispersion curves of the epoxy/tungsten carbide composite show that the propagation of elastic waves is prohibited inside the periodic structure over a frequency range. To achieve a wide bandgap, the elastic composite structure can be optimized by changing its dimensions and arrangement, including size, number, and rotation angle of square inclusions. The simulation results show that increasing the number of inclusions and the filling fraction of the unit cell significantly broaden the phononic bandgap compared to other geometric tunings. Additionally, a nonmonotonic relationship between the bandwidth and filling fraction of the composite was found, and this relationship results from spacing among inclusions and inclusion sizes causing different effects on Bragg scatterings and localized resonances of elastic waves. Moreover, the calculated transmission spectra of the epoxy/tungsten carbide composite structure verify its low-frequency bandgap behavior.

Broadband frequency control of light using synthetic frequency lattices formed by four-wave-mixing Bragg scatterings

Recent exploration in synthetic frequency lattices has re-formed the methods of manipulating the light spectrum by analogizing the diffraction management in real space, which can be created by employing electro-optic modulation (EOM) in dielectric waveguides or ring resonators. In the presence of effective gauge potential, that is, the accumulated phase of mode transfer between adjacent lattice sites, the frequency spectrum of incident light can be flexibly tailored. However, the finite bandwidth and modulation depth of EOM vastly restrain the frequency shift and efficiency of mode transfer. Here we experimentally demonstrate that the synthetic frequency lattice can be created with the nonlinear process of four-wave-mixing Bragg scattering. The bandwidth of frequency manipulation is expanded up to terahertz and the frequency shift can be larger than 200 GHz. Furthermore, we can realize effects such as negative refraction and perfect imaging in frequency dimension by changing the effective gauge potentials. The study provides a powerful and promising approach to precisely control light frequency in broadband and may benefit all-optical modulation in optical telecommunication systems.

Closed-form bandgap design formulas for beam-type metastructures

Metastructures have received increasing attention because of their unique bandgap behavior that can be utilized to control vibration and noise of mechanical structures. This work is aimed to develop efficient formulas for bandgap estimation and design of flexural beam-type metastructures containing a periodic array of single-frequency force resonators. First, closed-form formulas are developed for a fast yet accurate estimation of the lowest two bandgaps, which may be formed by local resonance (LR) mechanism or Bragg scattering (BS) mechanism. Such formulas are shown to be more general than existing well-known closed-form formulas, which are only applicable to the case of deep-subwavelength LR-type bandgap. Second, closed-form formulas are proposed for a straightforward design of two particular cases of improved bandgaps compared with typical deep-subwavelength LR-type bandgap. One particular case is an ultra-wide near-coupled pseudo bandgap formed by strong interaction of the LR and BS mechanisms. Another particular case is an LR-type bandgap possessing significant attenuation performance at its bandgap center, and also having a broader effective width than the typical deep-subwavelength LR-type bandgap. Moreover, the broad applicability of the developed closed-form formulas is numerically verified by addressing bandgap design problems associated with simple and advanced multi-scale beam-type metastructures.

Bragg scattering tomography

Here we introduce a new forward model and imaging modality for Bragg Scattering Tomography (BST). The model we propose is based on an X-ray portal scanner with linear detector collimation, currently being developed for use in airport baggage screening. The geometry under consideration leads us to a novel two-dimensional inverse problem, where we aim to reconstruct the Bragg scattering differential cross section function from its integrals over a set of symmetric \begin{document}$ C^2 $\end{document} curves in the plane. The integral transform which describes the forward problem in BST is a new type of Radon transform, which we introduce and denote as the Bragg transform. We provide new injectivity results for the Bragg transform here, and describe how the conditions of our theorems can be applied to assist in the machine design of the portal scanner. Further we provide an extension of our results to \begin{document}$ n $\end{document} -dimensions, where a generalization of the Bragg transform is introduced. Here we aim to reconstruct a real valued function on \begin{document}$ \mathbb{R}^{n+1} $\end{document} from its integrals over \begin{document}$ n $\end{document} -dimensional surfaces of revolution of \begin{document}$ C^2 $\end{document} curves embedded in \begin{document}$ \mathbb{R}^{n+1} $\end{document} . Injectivity proofs are provided also for the generalized Bragg transform.

Microlocal Analysis of Generalized Radon Transforms from Scattering Tomography

Here we present a novel microlocal analysis of generalized Radon transforms which describe the integrals of $L^2$ functions of compact support over surfaces of revolution of $C^{\infty}$ curves $q$. We show that the Radon transforms are elliptic Fourier integral operators (FIO) and provide an analysis of the left projections $\Pi_L$. Our main theorem shows that $\Pi_L$ satisfies the semiglobal Bolker assumption if and only if $g=q'/q$ is an immersion. An analysis of the visible singularities is presented, after which we derive novel Sobolev smoothness estimates for the generalized Radon FIO. Our theory has specific applications of interest in Emission Compton Scattering Tomography (ECST) and Bragg Scattering Tomography (BST). We show that the ECST and BST integration curves satisfy the semiglobal Bolker assumption and provide simulated reconstructions from ECST and BST data. Additionally, we give example “sinusoidal" integration curves which do not satisfy Bolker and provide simulations of the image artifacts. The observed artifacts in reconstruction are shown to align exactly with our predictions.

Coherent confinement and unidirectional dynamics of a wave packet induced by a non-Hermitian Su-Schrieffer-Heeger segment

The competition between staggered imaginary potentials and lattice dimerization results in a unidirectional propagating coalescing state of a non-Hermitian Su-Schrieffer-Heeger (SSH) ring at an exceptional point. A segment of the SSH ring inherits the unidirectional feature and exhibits some intriguing dynamic behaviors when it is embedded in a Hermitian chain as a $\mathcal{PT}$-symmetric scattering center. Based on the Bethe ansatz scattering solution for the interface between Hermitian and non-Hermitian regions, we show that the SSH scattering center supports the following wave-packet dynamics. (i) A left incident wave packet is allowed perfect transmission, while a right incident wave packet stimulates an amplified reflecting wave train with the length proportional to the size of the SSH segment. Accordingly, a unidirectional invisibility of Bragg scatterers is observed when a multi-SSH segment is considered. (ii) A left incident wave packet can be well confined in a SSH segment if the right lead is removed. (iii) In addition, a wave packet is perfectly absorbed when its size closes to the length of the SSH segment. The underlying mechanism stems from a subtle property of the SSH segment, which supports two quasicoalescing wave packets but with opposite group velocities. Our findings are applicable to the schemes of realizing quantum state storage, quantum diode, and lasing device.

Higher-Order Topological States in Surface-Wave Photonic Crystals.

Photonic topological states have revolutionized the understanding of the propagation and scattering of light. The recent discovery of higher‐order photonic topological insulators opens an emergent horizon for 0D topological corner states. However, the previous realizations of higher‐order topological insulators in electromagnetic‐wave systems suffer from either a limited operational frequency range due to the lumped components involved or a bulky structure with a large footprint, which are unfavorable for achieving compact photonic devices. To overcome these limitations, a planar surface‐wave photonic crystal realization of 2D higher‐order topological insulators is hereby demonstrated experimentally. The surface‐wave photonic crystals exhibit a very large bulk bandgap (a bandwidth of 28%) due to multiple Bragg scatterings and host 1D gapped edge states described by massive Dirac equations. The topology of those higher‐dimensional photonic bands leads to the emergence of in‐gap 0D corner states, which provide a route toward robust cavity modes for scalable compact photonic devices.

The Optimized Small Incidence Angle Setting of a Composite Bragg Scattering Model and its Application to Sea Surface Wind Speed Retrieval

The normalized radar cross section (NRCS) of microwave backscattering from a rough sea surface can be described by a composite Bragg scattering (CBS) model, which is a combination of a two-scale backscatter model and a geometric optics model. For small local radar incidence angles that are smaller than a given angle setting, the two-scale backscattering mechanism of the sea surface is replaced by a geometric optics solution for specular reflection. In this study, an optimized setting of 18 degrees for the small incidence angle is determined by comparing the NRCSs between 52 RADARSAT-2 (R2) synthetic aperture radar (SAR) images and the CBS model with simultaneous sea surface wind derived by meteorological mooring buoys located in the northern South China Sea. By using the CBS model with the optimized incidence angle setting of 18° and the nearly simultaneous wind directions of the Advanced Scatterometer (ASCAT) as the input, sea surface wind speeds are retrieved from 46 R2 SAR images at C-band and from 2 COSMO-SkyMed (CSK) SAR images at X-band for the application study. The average root mean square error of the C-band R2 SAR retrieval results validated against nearly simultaneous measurements of ASCAT is 1.5 m/s, while the same value is 1.6 m/s for the X-band CSK SAR image. The results also indicate that the optimized small incidence angle setting of the CBS model found in this study is relatively reliable under sea surface wind speed conditions less than 14.0 m/s.

Tuning bandgaps in metastructured beams: numerical and experimental study

Tunable metastructures (including phononic crystals and metamaterials) have the unique advantage that one can change the operating frequency and acoustic wave characteristics as needed. In this paper, the bandgap characteristics and their controllability of a metastructured beam with mass-spring oscillators and under an axial force are investigated in depth both by the finite element method and by experiment. The experimental and numerical results indicate that there is one local resonance (LR) bandgap and multiple Bragg scattering (BS) bandgaps. The width and position of each bandgap can be tuned effectively by adjusting the axial force, lattice constant, and spring stiffness, and a super wide pseudo-gap can be obtained under suitable conditions. By integrating different mass-spring oscillators into one metastructured beam, the bandgap width can be broadened and pseudogap- like characteristics can be achieved. By changing the number of different oscillators, the propagating distance of elastic waves in the beam can also be controlled. It is further revealed that point defects have a large influence on the BS bandgaps but little effect on the LR bandgap. The present work provides an important reference for the optimal design of adjustable high-performance metastructures.

The Doppler Spectrum of the Microwave Radar Signal Backscattered From the Sea Surface in Terms of the Modified Bragg Scattering Model

Significant progress has been made in the study of electromagnetic wave scattering from the sea surface. Essential results were obtained in solving applied problems, but there are still unsolved problems in the scattering theory. The radar backscatter cross section is usually used to solve remote sensing tasks, although the Doppler spectrum (DS) of the scattered microwave signal contains more information about sea waves. The concept of a two-scale model of the scattering surface is used in this article. Correct allowance for large-scale waves, in comparison with radar wavelength, in deriving theoretical formulas enabled us to develop a modified Bragg scattering model. It is based on the previously developed scattering model that is refined here to take into account the contribution of the horizontal component of the orbital velocity to the DS. It is shown that allowance for large-scale waves limits the growth of the radar cross section of the Bragg component with a decrease in the incidence angle, which allows using the resonant scattering model at small incidence angles. An additional result is that the modified model of the DS can also be used in the range of middle incidence angles because it takes into account the contribution of the horizontal component of the orbital velocity. It is shown that if the correlation between large-scale and small-scale components of sea waves is neglected, the new formulas pass into the known formulas for the DS within the framework of the Bragg scattering model.

Natural sound (scale) reflecting speaker

In the natural sound music hall, due to rejection of the electronic facilities, engineers need to design an architectural construct to improve the acoustic effect. Rather, it is widely spread to use horn-like construct to improve acoustic energy distributed on the audience. On the other hand, there has not been a suitable nonelectronic device to act as a reflecting speaker. Thus, we propose the concept of Natural sound (Scale) Reflecting Speaker, aiming to control the energy distribution on the stage, so singers could hear their own voice and perform more excellent. In addition, the reflecting speaker consists of multiple coupled Helmholtz resonators. Theoretically, by combining Helmholtz resonances and Bragg scatterings, acoustic negative reflection is achieved at the Bragg blazing points and non-Bragg blazing points. Meanwhile, owing to couplings among these blazing points, broadband, and wide-angle acoustic negative reflection would also be achieved. Finally, we could illustrate the fundamental feasibility of the device via theoretical derivation, computer simulation, and basic experiments. Therefore, it is significant for natural sound music hall to apply to the reflecting speaker in the future.

Lightweight architected hollow sphere foams for simultaneous noise and vibration control

Phononic metamaterials, composed of periodically topological structures and materials dispersions, can manipulate acoustic or elastic wave propagation, but not concurrently in most cases. Here we report a new type of three-dimensional (3D) architected hollow sphere foams that can attenuate acoustic and elastic waves synchronically. Our numerical simulation results reveal that the acoustic wave attenuation is attributed to local resonances in the drilled hollow spheres, which act as Helmholtz resonators. The elastic wave mitigation stems from Bragg scatterings in the 3D architected periodic hollow sphere foams. The numerically predicted acoustic and elastic wave band gaps are further validated against the corresponding transmission spectra, which are obtained by performing frequency domain analysis. Notably, elastic wave band gap properties can be decoupled from acoustic wave and independently tuned by tailoring the connectivity among the hollow spheres. The findings reported here offer new opportunities to design lightweight architected metamaterials to simultaneously control undesired noise and vibration over a wide frequency range.

Optical Single-Sideband Generation by Dual-Stage Four-Wave Mixing Bragg Scattering

In this letter, we propose a novel approach for optical single-sideband (SSB) generation by utilizing four-wave mixing Bragg scattering (FWM-BS). The scheme comprises three stages: the initial FWM-BS stage, the spectral phase control stage, and the final FWM-BS stage. Constructive or destructive interference can occur between the sidebands generated in the two FWM-BS stages, depending on the spectral phase mask applied between the stages. By applying an appropriate phase mask, one sideband can be eliminated by destructive interference, while the other sideband is magnified by constructive interference, thus realizing SSB generation. Both upconverted and downconverted SSB generations can be achieved. To verify the scheme, we experimentally demonstrate 50-GHz optical frequency upconversion and downconversion separately for multi-channel 16-Gbaud QPSK signals.

Discrete Electronic Subbands due to Bragg Scattering at Molecular Edges.

The discretization of the electronic structure of nanometer-size solid systems due to quantum confinement and the concomitant modification of their physical properties is one of the cornerstones for the development of nanoscience and nanotechnology. In this Letter we demonstrate that the Bragg scattering of Cu(111) surface-state electrons by the periodic arrangement of tetracyanoquinodimethane molecules at the edges of self-assembled molecular islands, along with the dominant contribution of backscattering processes to the electronic density of states, discretizes the possible values of the electron momentum parallel to the island edge. The electronic structure consists thus of a discrete number of subbands which occur in a nonclosed space, and therefore without quantum confinement.

Three-dimensional periodic materials as seismic base isolator for nuclear infrastructure

Recent advance of periodic materials from the field of solid-state physics into that of earthquake engineering has resulted in a novel seismic isolation technique. In this study, we developed a new configuration of structural foundation using a three-dimensional (3D) periodic material for seismic isolation of critical infrastructure, particularly nuclear infrastructure. To this aim, we first performed analytical and finite element studies to compare two different types of 3D unit cells, i.e., Bragg Scattering and Locally resonant unit cells, to investigate their characteristics and applicability as a seismic isolator. We then designed a large scale test specimen based on the Bragg-scattering type unit cell using common construction materials: reinforced concrete blocks and polyurethane sheets. The designed test specimen was constructed and tested using a shake table subjected to different types of excitations in the horizontal and vertical directions as well as the torsional mode. The dynamic response of a small modular reactor (SMR) building model protected by the 3D periodic foundation demonstrates that 90% response reduction was achieved within the frequency band gaps. The response attenuation was achieved in all three tested directions. Moreover, the periodic foundation-isolated SMR building exhibited a stable response with negligible rocking on the structural system.

Second-order topology and multidimensional topological transitions in sonic crystals

Topological insulators with unique gapless edge states have revolutionized the understanding of electronic properties in solid materials. These gapless edge states are dictated by the topological invariants associated with the quantization of generalized Berry phases of the bulk energy bands through the bulk-edge correspondence, a paradigm that can also be extended to acoustic and photonic systems. Recently, high-order topological insulators (HOTIs) are proposed and observed, where the bulk topological invariants result in gapped edge states and in-gap corner or hinge states, going beyond the conventional bulk-edge correspondence. However, the existing studies on HOTIs are restricted to tight-binding models which cannot describe the energy bands of conventional sonic/photonic crystals that are due to multiple Bragg scatterings. Here, we report theoretical prediction and experimental observation of acoustic second-order topological insulators (SOTI) in two-dimensional (2D) sonic crystals (SCs) beyond the tight-binding picture. We observe gapped edge states and degenerate in-gap corner states which manifest bulk-edge correspondence in a hierarchy of dimensions. Moreover, topological transitions in both the bulk and edge states can be realized by tuning the angle of the meta-atoms in each unit-cell, leading to various conversion among bulk, edge and corner states. The emergent properties of the acoustic SOTIs open up a new route for topological designs of robust localized acoustic modes as well as topological transfer of acoustic energy between 2D, 1D and 0D modes.

A Mild-Slope System for Bragg Scattering of Water Waves by Sinusoidal Bathymetry in the Presence of Vertically Sheared Currents

Extended mild-slope models (MMSs) are examined for predicting the characteristics of normally incident waves propagating over sinusoidal bottom topography in the presence of opposing shearing currents. It is shown that MMSs are able to provide quite good predictions in the case of Bragg scattering of waves over rippled bathymetry without a current, but fail to provide good predictions concerning the resonant frequency in the additional presence of a current. In order to resolve the above mismatch, a two-equation mild-slope system (CMS2) is derived from a variational principle based on the representation of the wave potential expressed as a superposition of the forward and backward components. The latter system is compared against experimentally measured data collected in a wave flume and is shown to provide more accurate predictions concerning both the resonant frequency and the amplitude of the reflection coefficient. Future work will be devoted to the examination of the derived model for a more general wave system over realistic seabed topography.

Study on Bragg and Non-Bragg Scattering Mechanism and Frequency Shifts From Time-Varying Periodic Water Wave

In this paper, Bragg and non-Bragg scattering mechanisms and frequency shifts from time-varying periodic water wave are studied from three aspects: wave tank measurements with an ultrahigh frequency radar, numerical simulation using the method of moments, and theoretical derivation applying the small perturbation method. The scattering field, radar cross section (RCS), and frequency shifts are discussed in both horizontal and vertical polarizations. The wave tank observations show that backscattering enhancement occurs when water wavelength is an integer multiple of Bragg wavelength, and there are several Doppler harmonics with frequency shifts of water-wave frequency and its integer multiples. Numerical simulations indicate that these Doppler harmonics except the one associated with the water-wave phase velocity are caused by the water surface edge effect. Moreover, theoretical analyses, numerical simulations, and wave tank experiments all show a clear exponential relationship between backscattering RCS and wave height. In addition, we further analyze the bistatic scattering and find that the scattering field is composed of plane waves propagating in the directions determined by water wavelength and radio wavelength, the bistatic frequency shift is the harmonic frequency of water wave, and the bistatic RCS also has an exponential relation with water-wave height.

Wave propagation in viscoelastic phononic crystal rods with internal resonators

In the present work, the wave propagation in a viscoelastic phononic crystal rod with internal periodic dissipative resonators is investigated. The Kelvin-Voigt model is utilized to describe the viscoelastic behavior of host materials. The Bloch theorem is adopted to analyze the band structure of the rod. The effect of the free oscillation frequency of the resonators on the band structure is firstly studied. It is found that by tailoring the dynamic characteristics of the resonators, the coupling of the Bragg scattering (BS) and local resonance (LR) mechanisms can be harnessed to effectively widen the band gaps and enhance the wave attenuation. Then, the effects of the viscosity of the host materials and the damping of the resonators on the band structure, especially the two nearly coalescent band gaps (the first Bragg and LR ones), are investigated respectively. Furthermore, the combined effect of the two dissipative sources is also discussed. The present work is expected to be helpful to the design and applications of phononic crystals and metamaterials.