Nonlinear Scatterers Research Articles

Non-linear ground deformation detection and monitoring using time series InSAR along the coastal urban areas of Pakistan.

Conventional geodetic methods rely on point measurements, which have drawbacks for detecting and tracking geologic disasters at specific locations. In this study, the time series Interferometric Synthetic Aperture Radar (InSAR) approach was incorporated to estimate non-linear surface deformation caused by tectonic, shoreline reclamation, and other anthropogenic activities in economically important urban regions of Pakistan's southern coast, which possesses around 270km. The shoreline is extended from the low-populated area on the premises of the Hub River in the west to the highly populated Karachi City and Eastern Industrial Zone, where we collected the Sentinel-1A C-band data from 2017 to 2023 to address urban security and threats to human life and property. The main advantage of opting for the non-linear persistent scatterer interferometric SAR (PSInSAR) approach for this study is that it exposes minute movements without any prior consideration of conventional monitoring techniques, making it valid in continuously varying regions. An average vertical displacement range of - 170 to + 82mm per year was found, which was used to investigate the potential correlation with the most effective causative parameters of deformation. The densely populated areas of the study area experience an annual subsidence of 170mm, and the less populated western region experiences an uplift of 82mm annually. Land deformation varies along the coast of the study area, where the eastern region is highly reclaimed and is affected by erosion. Groundwater table-depleting regions experienced high levels of land subsidence, and tectonic activities controlled vertical displacement in the region. Major variation was detected after an earthquake occurred along fault lines. This study was designed because a non-linear approach is required to address ground movement activities acutely, and it will make it possible to plan surface infrastructure and handle issues brought on by subsidence more effectively.

Nonreciprocal scattering and unidirectional cloaking in nonlinear nanoantennas

Abstract Reciprocal scatterers necessarily extinguish the same amount of incoming power when excited from opposite directions. This property implies that it is not possible to realize scatterers that are transparent when excited from one direction but that scatter and absorb light for the opposite excitation, limiting opportunities in the context of asymmetric imaging and nanophotonic circuits. This reciprocity constraint may be overcome with an external bias that breaks time-reversal symmetry, posing however challenges in terms of practical implementations and integration. Here, we explore the use of tailored nonlinearities combined with geometric asymmetries in suitably tailored resonant nanoantennas. We demonstrate that, under suitable design conditions, a nonlinear scatterer can be cloaked for one excitation direction, yet strongly scatters when excited at the same frequency and intensity from the opposite direction. This nonreciprocal scattering phenomenon opens opportunities for nonlinear nanophotonics, asymmetric imaging and visibility, all-optical signal processing and directional sensing.

Chirp-coded ultrasound for localization of linear and nonlinear scatterers in isotropic media

Chirp-coded ultrasound has been under active research for reciprocal Time Reversal with Nonlinear Elastic Wave Spectroscopy for ultrasonic wave focusing and additionally detection and analysis of nonlinear defects. Localization and imaging of defects under these principles, without scanning or use of other complicated methods, is an open problem. Frequency Modulated Constant Wave technology is widely known in radar applications where the distance to multiple reflecting targets, their velocities and angles of return are found from the chirp signal. These principles are not yet widely used in ultrasound technology. Chirp-coded ultrasound is common between the two methods and enable to maximize total power on target due to longer transmitted signals (as opposed to pulsed operation). This work proposes to unite the Frequency-Modulated Constant-Wave scatterer localization with reciprocal Time Reversal – Nonlinear Elastic Wave Spectroscopy principles to enable the localization of scatterers distant from the transducers and the analysis of their nonclassical nonlinearity which often can be caused by microdamage or cracking. In this paper only the first part (localization of scatterers using frequency-modulated constant wave ultrasound) of the problem is investigated. The main goal is to verify the feasibility of the method for ultrasound in solids and identify the main problems to be solved. Physical experiments and simulations are used to ascertain the detectability of linear and nonlinear scatterers in an isotropic solid medium (acrylic) using ultrasound. Potential problems with this approach are identified, to be solved in future work. In the future, this approach could enable to spatially filter the return signals, enabling to use reciprocal time reversal for focusing the wave energy in space directly onto selected scatterers, using the simplest of test setups: one transmitting and two receiving transducers.

Multiple scattering of local nonlinear resonators on a thin plate

Developing nonlinear resonant metamaterial plates requires an effective wave simulation method to analyze the wave interactions between multiple nonlinear scatterers. The multiple scattering method has the advantages of high computational efficiency and closed-form displacement solutions in modeling the finitely periodic scatterer array. However, the multiple scattering method of nonlinear scatterers is absent in the available studies of plate structures. In this paper, a nonlinear multiple scattering approach is formulated and analyzed for thin plates with nonlinear resonant scatterers. The resonant scatterer consists of an inner plate with a local resonator modeled by the nonlinear mass-spring system. The motion equation of resonant scatterers is solved using the perturbation technology and wave expansion method. The T-matrix of the resonant scatterer of each order is then derived at the arbitrary harmonic frequency from continuous interfacial conditions of resonant scatterers. Finally, the multiple scattering is formulated for a finitely periodic array of resonant scatterers on a thin plate. Numerical simulations capture the scattering characteristics and stop-band formations of fundamental and second-harmonic waves. Furthermore, the finitely periodic array of nonlinear and linear resonant scatterers achieves the nonreciprocal transmission of flexural waves. These numerical results demonstrate the potential applications of the proposed method in designing metamaterial-based plates with complex transmission properties.

Nonreciprocal total cross section of quantum metasurfaces

Abstract Nonreciprocity originating from classical interactions among nonlinear scatterers has been attracting increasing attention in the quantum community, offering a promising tool to control excitation transfer for quantum information processing and quantum computing. In this work, we explore the possibility of realizing largely nonreciprocal total cross sections for a pair of quantum metasurfaces formed by two parallel periodic arrays of two-level atoms. We show that large nonreciprocal responses can be obtained in such nonlinear systems by controlling the position of the atoms and their transition frequencies, without requiring that the environment in which the atoms are placed is nonreciprocal. We demonstrate the connection of this effect with the asymmetric population of a slowly decaying dark state, which is critical to obtain large nonreciprocal responses.

MUSIC Based Microwave Imaging of Nonlinear Point-Like Scatterers

Narrowband localization of point-like nonlinear scatterers in a homogeneous background medium is investigated. A theoretical framework is provided based on Multiple Signal Classification (MUSIC) imaging, formerly developed for time-reversal imaging of point-like targets in cluttered environment. Numerical simulations are provided to assist in understanding the relations between various aspects of the imaging method. Numerical evidence shows that for the same signal to noise ratio, higher order harmonics (second and third harmonics) resulting from nonlinear scattering, have better imaging resolutions compared to the fundamental harmonic corresponding to linear scattering.

Nonlinear multiple scattering of flexural waves in elastic beams: Frequency conversion and non-reciprocal effects

Multiple scattering from a cluster of nonlinear point attachments on a beam is formulated and analyzed. The nonlinear equation of motion is solved using a perturbation strategy. The analytical solution is implemented for two common mass–spring–damper systems and for either nonlinear stiffness or nonlinear damping of power-law dependence. The nonlinearity generates harmonic waves at frequencies that are multiples of the incident-wave frequency, and also shifts the linear response of the fundamental frequency. In addition to asymmetric reflection, which is also achievable using linear scatterers with damping, the cluster of nonlinear scatterers can produce asymmetric transmission, thus breaking reciprocity of the system. Analytical results for a single scatterer are presented and validated using Finite Element Method simulations with perfect agreement. A two-scatterer nonlinear cluster acts as a filter that is tunable by the incident amplitude and a three-scatterer cluster that acts as a non-reciprocal frequency converter are considered, demonstrating the potential of the proposed framework for the design of nonlinear scatterer clusters with more complicated scattering properties.

Implementation of Non-Linear Non-Parametric Persistent Scatterer Interferometry and Its Robustness for Displacement Monitoring.

To derive surface displacement, interferometric stacking with synthetic aperture radar (SAR) data is commonly used, and this technique is now in the implementation phase in the real world. Persistent scatterer interferometry (PSI) is one of the most universal approaches among in- terferometric stacking techniques, and non-linear non-parametric PSI (NN-PSI) was proposed to overcome the drawbacks of PSI approaches. The estimation of the non-linear displacements was successfully conducted using NN-PSI. However, the estimation of NN-PSI is not always stable with certain displacements because wider range of the velocity spectrum is used in NN-PSI than the conventional approaches; therefore, a calculation procedure and parameter optimization are needed to consider. In this paper, optimized parameters and procedures of NN-PSI are proposed, and real data processing with Sentinel-1 in the Kanto region in Japan was conducted. We confirmed that the displacement estimation was comparable to the measurement of the permanent global positioning system (GPS) stations, and the root mean square error between the GPS measurement and NN-PSI estimation was less than 3 mm in two years. The displacement over 2 ambiguity, which the conventional PSI approach wrongly reconstructed, was also quantitatively validated and successfully estimated by NN-PSI. As a result of the real data processing, periodical displacements were also reconstructed through NN-PSI. We concluded that the NN-PSI approach with the proposed parameters and method enabled the estimation of several types of surface displacements that conventional PSI approaches could not reconstruct.

Comprehensively Efficient Analysis of Nonlinear Wire Scatterers Considering Lossy Ground and Multi-tone Excitations

In this paper based on intelligent water drops algorithm (IWD), comprehensively nonlinear analysis of nonlinearly loaded wire scatterers are carried out. The analyses involve two stages. First, the problem is modeled as a nonlinear multi-port equivalent circuit and it is then reformulated into an optimization problem which is solved by the IWD. The simulation results are compared with harmonic balance (HB), arithmetic operator method (AOM), approximate methods and experiment. Analysis of the problem under strongly nonlinear loads, presence of lossy ground, multi-port structures, and multi-ton excitations are included to cover all the complex aspects. In one hand, the proposed modeling approach is in excellent agreement with other conventional techniques. On the other hand, the run time is considerably reduced.

SAR Tomography via Nonlinear Blind Scatterer Separation

Layover separation has been fundamental to many synthetic aperture radar applications, such as building reconstruction and biomass estimation. Retrieving the scattering profile along the mixed dimension (elevation) is typically solved by inversion of the SAR imaging model, a process known as SAR tomography. This paper proposes a nonlinear blind scatterer separation method to retrieve the phase centers of the layovered scatterers, avoiding the computationally expensive tomographic inversion. We demonstrate that conventional linear separation methods, e.g., principle component analysis (PCA), can only partially separate the scatterers under good conditions. These methods produce systematic phase bias in the retrieved scatterers due to the nonorthogonality of the scatterers' steering vectors, especially when the intensities of the sources are similar or the number of images is low. The proposed method artificially increases the dimensionality of the data using kernel PCA, hence mitigating the aforementioned limitations. In the processing, the proposed method sequentially deflates the covariance matrix using the estimate of the brightest scatterer from kernel PCA. Simulations demonstrate the superior performance of the proposed method over conventional PCA-based methods in various respects. Experiments using TerraSAR-X data show an improvement in height reconstruction accuracy by a factor of one to three, depending on the used number of looks.

Optimal pump excitation frequency for improvement of damage detection by nonlinear vibro acoustic modulation method in a multiple scattering sample

We present a method to systematically optimize nonlinear damage detection in multiple scattering media by the nonlinear Vibro-Acoustic Modulation (VAM) technique. The latter consists here of exciting a medium simultaneously with a high frequency ultrasonic sinusoidal burst and with a low frequency continuous sinusoidal wave. Modulation of the high frequency (probe) by the low frequency (pump) is made possible by the presence of nonlinear scatterers, i.e. cracks, defects. A signal processing technique consisting of a closed loop system drives the automatic adaptation of the pumping frequency, yielding to the optimization of the nonlinear modulation (NM) of the output probing coda signal without a priori information on the medium and the scatterers. The correlation coefficient between a reference output probe signal without the pumping wave and an output modulated probe signal with a pumping wave was considered as our cost function. A multiple scattering solid beam where nonlinear scatterers can be controllably added or removed is designed and tested. The first step of this study is an empirical search of the correlation coefficient dependency on the pumping frequency to verify the performances of the proposed method. Then the implemented optimization algorithm based on genetic algorithm (GA) is used to find automatically the optimal pumping frequency. The obtained optimization results show a good agreement with the empirical study. Moreover, the genetic algorithm allowed to find the optimal pump frequency adapted to each configuration of nonlinear scatterers. This relatively fast search of the optimal nonlinear response could be extended to nonlinear scatterer imaging applications using the information on the resonant modes spatial shapes together with the associated optimal response.

Fundamental wave amplitude difference imaging for detection and characterization of embedded cracks

An ultrasonic technique for imaging nonlinear scatterers, such as partially-closed cracks, buried in a medium has been recently proposed. The method called fundamental wave amplitude difference (FAD) consists of a sequence of acquisitions with different subsets of elements for each line of the image. An image revealing nonlinear scatterers in the medium is reconstructed line by line by subtracting the responses measured with the subsets of elements from the response obtained with all elements transmitting. In order to get a better insight of the capabilities of FAD, two metallic samples having a fatigue or thermal crack are inspected by translating the probe with ultrasonic beam perpendicular (i.e. parallel) to the crack direction which is the most (i.e. less) favorable case. Each time, the responses of the linear scatterers (i.e. conventional image) and nonlinear scatterers (i.e. FAD image) are compared in term of intensity and spatial repartition. FAD exhibits higher detection specificity of the crack with a better contrast than conventional ultrasound imaging. Moreover, we observe that both methods give complementary results as nonlinear and linear scatterers are mostly not co-localized. In addition, we show experimentally that FAD resolution in elevation and lateral follows the same rule as the theoretical resolution of conventional ultrasonic technique. Finally, we report that FAD gives the possibility to perform parametric studies which let the opportunity to address the physical mechanisms causing the distortion of the signal. FAD is a promising and reliable tool which can be directly implemented on a conventional open scanner ultrasound device for real-time imaging. This might contribute to its fast and wide spread in the industry.

Coding of Probe Signals in the Tomography of Acoustic Nonlinear Parameters

Different ways of coding radiated signals that probe a tomographized object such as a liquid medium are compared in order to reconstruct the spatial distribution of acoustic nonlinear parameters using a small number of transducers. The results from reconstructing model nonlinear scatterers are discussed. The region of spatial frequencies available for reconstruction is analyzed.

Orienting fatigue cracks using contact acoustic nonlinearity in scattered plate waves

Targeting quantitative delineation of nonlinear scatterers in elastic media and undersized fatigue cracks in particular, the present study is dedicated to investigation, from analytical, numerical, and experimental perspectives, of the underlying mechanism of interaction between guided ultrasonic waves (GUWs) and ‘breathing’ fatigue cracks—a representative nonlinear scatterer type. Under the modulation of probing GUWs, a ‘breathing’ crack scatters GUWs, in which the crack-triggered contact acoustic nonlinearity (CAN) is embodied. Analytical modeling demonstrates that the extracted CAN manifests unique scattering patterns associated with the crack slant, on which basis the crack can be oriented, without requiring reference to baseline signals. Experimental validation corroborates analytical prediction, in which an embryonic fatigue crack in an aluminum plate waveguide is oriented accurately and visualized in a pixelated image.

Asymptotic analysis of resonances of small volume high contrast linear and nonlinear scatterers

We consider the asymptotic analysis of the resonances of high contrast small volume scatterers for linear and nonlinear scalar waves. The resonance problem is formulated as a nonlinear eigenvalue problem. We derive asymptotic formulae for linear scatterers and nonlinear scatterers of the Kerr type. Our results are illustrated with numerical examples.

A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterers

Consider the scattering of a time-harmonic plane wave by heterogeneous media consisting of linear or nonlinear point scatterers and extended obstacles. A generalized Foldy–Lax formulation is developed to take fully into account of the multiple scattering by the complex media. A new imaging function is proposed and an FFT-based direct imaging method is developed for the inverse obstacle scattering problem, which is to reconstruct the shape of the extended obstacles. The novel idea is to utilize the nonlinear point scatterers to excite high harmonic generation so that enhanced imaging resolution can be achieved. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.

Time reversal invariance for a nonlinear scatterer exhibiting contact acoustic nonlinearity

The time reversal invariance of an ultrasonic plane wave interacting with a contact interface characterized by a unilateral contact law is investigated analytically and numerically. It is shown analytically that despite the contact nonlinearity, the re-emission of a time reversed version of the reflected and transmitted waves can perfectly recover the original pulse shape, thereby demonstrating time reversal invariance for this type of contact acoustic nonlinearity. With the aid of finite element modelling, the time-reversal analysis is extended to finite-size nonlinear scatterers such as closed cracks. The results show that time reversal invariance holds provided that all the additional frequencies generated during the forward propagation, such as higher harmonics, sub-harmonics and zero-frequency component, are fully included in the retro-propagation. If the scattered waves are frequency filtered during receiving or transmitting, such as through the use of narrowband transducers, the recombination of the time-reversed waves will not exactly recover the original incident wave. This discrepancy due to incomplete time invariance can be exploited as a new method for characterizing damage by defining damage indices that quantify the departure from time reversal invariance. The sensitivity of these damage indices for various crack lengths and contact stress levels is investigated computationally, indicating some advantages of this narrowband approach relative to the more conventional measurement of higher harmonic amplitude, which requires broadband transducers.

Baseline-free damage detection in composite plates based on the reciprocity principle

Lamb wave based damage detection techniques have been widely used in composite structures. In particular, these techniques usually rely on reference signals, which are significantly influenced by the operational and environmental conditions. To solve this issue, this paper presents a baseline-free damage inspection method based on the reciprocity principle. If a localized nonlinear scatterer exists along the wave path, the reciprocity breaks down. Through estimating the loss of reciprocity, the delamination could be detected. A reciprocity index (RI), which compares the discrepancy between the signal received in transducer B when emitting from transducer A and the signal received in A when the same source is located in B, is established to quantitatively analyze the reciprocity. Experimental results show that the RI value of a damaged path is much higher than that of a healthy path. In addition, the effects of the parameters of excitation signal (i.e., central frequency and bandwidth) and the position of delamination on the RI value are discussed. Furthermore, a RI based probabilistic imaging algorithm is proposed for detecting delamination damage of composite plates without reference signals. Finally, the effectiveness of this baseline-free damage detection method is validated by an experimental example.

Pulse inversion therapy for improved monitoring of blood-brain barrier opening

Microbubble-based ultrasound therapy has enabled non-invasive and reversible opening of the blood-brain barrier (BBB). However, the skull limits our ability to monitor microbubble activity due to high attenuation and beam aberrations. In ultrasound imaging, pulse inversion is used to cancel echoes from linear scatterers by summing the signal obtained from consecutive positive (phase: 0o degrees) and negative (phase: 180o degrees) pulses, thus facilitating imaging of non-linear scatterers such as microbubbles. Here, we adapt the pulse inversion technique to improve monitoring of BBB opening, by transmitting consecutive therapeutic pulses of inverse polarity. Pulse inversion therapy (PIT) was achieved by synchronizing the emission of inverted short pulses (pulse length: 2–3 cycles, PRF: 2 kHz, and pressure: 400 kPa) through a focused 0.5 MHz therapeutic transducer driven by two function generators. A concentric P12-5 linear array was used to passively capture the microbubble emissions. Absolute time-of-flight information was introduced in the beamforming since emission and reception were synchronous. PIT suppressed the signals from linear scatterers within the focal region by up to 6 dB in a gelatine phantom containing microbubbles and in mice in vivo, compared to positive-only pulses. Ongoing in vivo work aims at correlating the BBB opening with the microbubble signal identified by PIT.

Nonlinear Lamb wave based DORT method for detection of fatigue cracks

This research reports a selective detecting and focusing approach for fatigue cracks through use of decomposition of the time reversal operator (DORT) in combination with nonlinear Lamb waves. In the proposed approach, the time reversal operator (TRO) is only decomposed at the second-harmonic frequency, which has been widely utilized in recent years to evaluate micro-damage, rather than the fundamental frequency in the traditional DORT method. Further, an imaging algorithm based on the total focus method is introduced to locate nonlinear scatterers. The proposed approach is experimentally investigated to locate two fatigue cracks with different fatigue cycles in an aluminum plate with a set of surface bounded piezoelectric (PZT) transducers. The results show that the significant eigenvalues are related to the fatigue cycles of fatigue cracks when the TRO is decomposed at the second-harmonic frequency, and the number of significant eigenvalues is exactly equal to the number of fatigue cracks. The two fatigue cracks are selectively located accurately and are also distinguished from linear scatterer by use of the proposed method.