Plane Wave Research Articles

Inverse problem-solving method applied to the acoustic characterisation of a thin film via the Debye series method (DSM)

ABSTRACT The study of the ultrasonic acoustic response of materials is of increasing interest for the characterisation of high-frequency applications. In this work, some elastic properties (acoustic velocity and acoustic attenuation) and some physical properties (thickness and density), together with the phase shift of the transducer, are estimated via one method. Scanning acoustic microscopy was performed via an innovative and different method using a high-frequency (50 MHz) planar wave transducer. In addition, the Debye series model (DSM) was used to model the acoustic response of the bilayer structure of the glass substrate and the resin‒epoxy sample. The inverse problem of estimating the acoustic parameters that results in a DSM reflected echo that matches the experimental signal is solved by proposing an innovative step-by-step curve fitting algorithm. The algorithm for solving the inverse problem is then optimised via relative mean square error (RMSE) curves, resulting in a robust method for assessing the uniqueness of the multiparameter solution.

Elastic mechanical thermodynamic and thermoelectric properties of pristine and titanium doped Mg2Si: a density functional theory study

Herein, we report a systematic investigation of the effect of Titanium doping on the structural, elastic, mechanical, thermodynamic, and thermoelectric (TE) dynamics of Mg2Si Compounds using first-principle investigation. The present study has been carried out using the full potential linearized augmented plane wave method as implemented inWien2kcode undermBJexchange potentials. The investigations revealed that Mg2-xTixSi compounds have structural stability with cubic phase (Fm-3msymmetry) and possess degenerate semiconducting nature. The analysis of elastic constants revealed mechanical stability of the investigated compounds following Born criteria. Thermodynamic investigations have been carried out in the temperature range of 100-1500 K at zero pressure and the quantities like heat capacity, Debye temperature, Grüneisen constant, and thermal expansion coefficient have been critically analyzed. Lastly, the TE performance of Mg2-xTixSi compounds has been predicted by estimating the thermopower (S2σ) and TE figure of merit (zT) in the temperature range of 300-1500 K. The predicted value ofzTmaxfor Mg2-xTixSi compound is 0.67 at 800 K forx= 0.25 titanium content, suggesting materials promising application for TE energy harvesting and mechanical devices.

Study of Lanthanide Based Ln2MgSe4 (Ln= Er, Pm) Spinels for Spintronic and Optoelectronic Applications

Abstract Herein, the full potential linearized augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT) is used to examine the physical features of Ln2MgSe4(Ln= Er, Pm) spinel selenides. Exchange correlation energies are estimated through modified Becke-Johnson potential (mBJ). Band structures (BS) and density of states (DOS) data proved that Er2MgSe4is ferromagnetic (FM) semiconductor while Pm2MgSe4is half metallic (HFM) ferromagnetic in nature. The Er-f contributed majorly to the vicinity of Fermi level for both compounds. The structural stability is determined through calculating the tolerance factor and geometry optimization, while thermodynamical stability has been realized by computing the formation enthalpy. Furthermore, various optical parameters have been computed which describe the considered materials’ response to incident light. Our study explored the physical properties of two Ln based spinels which are found to have potential for being used in various optoelectronic and spintronic devices.

PIC simulation of a nonoscillatory perturbation on a subcritical fast magnetosonic shock wave

Abstract We use a two-dimensional particle-in-cell (PIC) simulation to study the propagation of subcritical fast magnetosonic shocks in electron-nitrogen plasma and their stability against an initial deformation. A slab of dense plasma launches two planar blast waves into a surrounding ambient plasma, which is permeated by a magnetic field that points out of the simulation box and is spatially uniform at the start of the simulation. One shock propagates into a spatially uniform ambient plasma. This reference shock has a Mach number of 1.75, and the heating of ions only along the shock normal compresses the ions that cross the shock to twice the upstream density. Drift instabilities lead to rapidly growing electron-cyclotron harmonic waves ahead of the location where the shock's density overshoot peaks, and to slowly growing lower-hybrid waves with a longer wavelength behind it. The second shock wave enters a perturbation layer that deforms it into a sine shape. Once the shock leaves the perturbation layer, the deformation is weakly damped and non-oscillatory, and the shock remains stable. Even without an external perturbation, and for the plasma parameters considered here, drift instabilities will cause ripples in the shock wave. These instabilities lead to a spatially and temporally varying compression of the plasma that crosses the shock.

An Inverse recursive algorithm to retrieve the shape of the inaccessible dielectric objects

A regularized electromagnetic iterative inverse algorithm is formulated and implemented to reconstruct the shape of 2D dielectric objects using the far-field pattern of the scattered field data. To achieve this, an integral operator that maps the unknown boundary of the object onto the far-field pattern of the scattered field is defined and solved for the unknown boundary. The addressed inverse problem has an ill-posed nature and inherits nonlinearity. To overcome these, the proposed solution is linearized via Newton and regularized by Tikhonov in the sense of least squares. Besides, the dominance of the shadow region in the inverse-imaging process is exceeded by considering the superposition of multi-incoming plane waves, leading to less computational cost and a very fast inversion process. Comprehensive numerical analyses are carried out to ascertain the algorithm's feasibility, revealing that it is very efficient and promising.

Dual-spherical-wave optical scanning holographic microscopy with resolution enhancement and an extended depth of field

Conventional optical scanning holographic microscopy (OSHM) is realized by using a plane wave and a spherical wave as the illumination. The resolution of the conventional OSHM is limited by the numerical aperture of the spherical wave and cannot exceed the Rayleigh limit. In this paper, the OSHM by using dual spherical waves as the illumination is studied. The model of a Gaussian wave, together with the constraints on the signal strength and the visibility, are considered in the analysis of the dual-spherical-wave (DS) OSHM. For an object located at the symmetry plane of the DS-OSHM, the resolution can slightly exceed the Rayleigh limit, and the depth of field (DoF) is extended significantly. For a transparent object, the noise in the DS-OSHM is less than that of the conventional OSHM, thanks to the highly divergent scanning beam. If the object is off the symmetry plane, the resolution is still enhanced, but the extension of the DoF is limited. In addition, a clear reconstructed image will be observed not only at the original object plane, but also at its mirror plane. To the best of our knowledge, this phenomenon is reported for the first time.

Quasi-visualizable detection of deep sub-wavelength defects in patterned wafers by breaking the optical form birefringence

Abstract In integrated circuit (IC) manufacturing, fast, nondestructive, and precise detection of defects in patterned wafers, realized by bright-field microscopy, is one of the critical factors for ensuring the final performance and yields of chips. With the critical dimensions of IC nanostructures continuing to shrink, directly imaging or classifying deep-subwavelength defects by bright-field microscopy is challenging due to the well-known diffraction barrier, the weak scattering effect, and the faint correlation between the scattering cross-section and the defect morphology. Herein, we propose an optical far-field inspection method based on the form-birefringence scattering imaging of the defective nanostructure, which can identify and classify various defects without requiring optical super-resolution. The technique is built upon the principle of breaking the optical form birefringence of the original periodic nanostructures by the defect perturbation under the anisotropic illumination modes, such as the orthogonally polarized plane waves, then combined with the high-order difference of far-field images. We validated the feasibility and effectiveness of the proposed method in detecting deep subwavelength defects through rigid vector imaging modeling and optical detection experiments of various defective nanostructures based on polarization microscopy. On this basis, an intelligent classification algorithm for typical patterned defects based on a dual-channel AlexNet neural network has been proposed, stabilizing the classification accuracy of λ/16-sized defects with highly similar features at more than 90%. The strong classification capability of the two-channel network on typical patterned defects can be attributed to the high-order difference image and its transverse gradient being used as the network's input, which highlights the polarization modulation difference between different patterned defects more significantly than conventional bright-field microscopy results. This work will provide a new but easy-to-operate method for detecting and classifying deep-subwavelength defects in patterned wafers or photomasks, which thus endows current online inspection equipment with more missions in advanced IC manufacturing.

Implementation of frozen density embedding in CP2K and OpenMolcas: CASSCF wavefunctions embedded in a Gaussian and plane wave DFT environment.

Most chemical processes happen at a local scale where only a subset of molecular orbitals is directly involved and only a subset of covalent bonds may be rearranged. To model such reactions, Density Functional Theory (DFT) is often inadequate, and the use of computationally more expensive correlated wavefunction (WF) methods is required for accurate results. Mixed-resolution approaches backed by quantum embedding theory have been used extensively to approach this imbalance. Based on the frozen density embedding freeze-and-thaw algorithm, we describe an approach to embed complete active space self-consistent field simulations run in the OpenMolcas code in a DFT environment calculated in CP2K without requiring any external tools. This makes it possible to study a local, active part of a chemical system in a larger and relatively static environment with a computational cost balanced between the accuracy of a WF method and the efficiency of DFT, which we test on environment-subsystem pairs. Finally, we apply the implementation to an oxygen molecule leaving an aluminum (111) surface and a ruthenium(IV) oxide (110) surface.

Energies of an Electron in a One-Dimensional Lattice Using the Dirac Equation: The Coulomb Potential

The energies of an electron in a one-dimensional crystal are studied with both the Schrödinger and Dirac equations using the plane wave expansion method. The crystalline potential sensed by the electron in a cell was calculated by accounting for the Coulombic (electrostatic) interaction between the electron and the surrounding cores (immobile positive ions at the center of the crystal cells). The energies and wave functions of the electron were calculated as a function of four parameters: the period ap of the lattice, the dimension ndim of the matrix in the momentum space, the partition number lpa in which the unit cell is divided to calculate the potential and the number of cores nco that affect the electron. It was found that 8000 cores (surrounding the electron) were needed to reach our convergence criterion. An analytical equation that accurately describes the behavior of the energies in function of the cores that affect the electron was also found. As case studies, the energies for pseudo-lithium and pseudo-graphene were obtained as a first approximation for one-dimensional lattices. Subsequently, the energies of an isolated dimer nanoparticle were also calculated using the supercell method.

Reflection of plane waves in a non-local viscothermoelastic half-space under variable thermal conductivity and microelongation effects

The present work is implicated with the investigation of wave propagation in a homogeneous, isotropic, non-local microelongated viscothermoelastic solid half space with variable thermal conductivity under the dual phase lag (DPL) model. It is found analytically that three coupled longitudinal waves and one independent transverse wave exist in the medium which travel with distinct speeds. Reflection coefficients and energy ratios of various reflected waves are obtained analytically and presented graphically for aluminum epoxy-like material. The variations of these reflection coefficients are analyzed for different values of non-local parameter, microelongational parameter, viscosity and variable thermal conductivity. The expressions of energy ratios acquired in explicit form are also represented graphically as functions of the angle of incidence in accordance with the defined rule of conservation of energy.

KCaAs and KCaP: promising half-Heusler compounds for UV protection and thermoelectric applications

This study investigates the structural, electrical, optical, and thermoelectric properties of the half-Heusler compounds KCaAs and KCaP using the Full-Potential Linearized Augmented Plane Wave (FP-LAPW) method within the framework of density functional theory. Our analysis reveals that both compounds exhibit favourable characteristics for high-performance applications. Specifically, KCaAs and KCaP show high static refractive indices and significant reflectivity in the ultraviolet (UV) range, making them ideal for UV protection and optical devices. Thermoelectric analysis indicates that both materials are p-type semiconductors with high Seebeck coefficients at low temperatures, high electrical conductivity, and relatively low thermal conductivity. The temperature-dependent figure of merit ( ZT ) reveals robust thermoelectric performance across a wide temperature range, with maximum ZT values of approximately 0.77 for both compounds. These results suggest that KCaAs and KCaP are promising candidates for thermoelectric applications, offering significant potential for energy conversion and sustainable energy solutions.

A Geometric View of Seismic Wavefields: Implications for Imaging Dense Clusters of Events

Summary Imaging dense clusters of seismicity is crucial to many problems in seismology: to delineate complex systems of faults, provide constraints on the causes of volcanic and cryogenic swarms, and to shed light on possible means to prevent damaging induced seismicity in mining, geothermal and oil and gas extraction activities. Current imaging methods rely upon high-resolution relative location techniques, commonly requiring arrival-time picks for seismic phases. This paper examines an alternative approach, based upon concepts drawn from differential geometry, that images directly from waveform data. It relies upon the common assumption of spatial continuity of seismic wavefield observations, which implies that a differentiable map exists between the source region to be imaged and waveform observations considered as elements of a vector space. The map creates an image of event clusters on a Riemannian manifold embedded in that vector space. The image can be visualized by projecting the observations into a tangent space of the manifold and is a distorted rendering of cluster geometry. However, the distortion can be predicted and removed if a model for wavefield propagation is available. This visualization approach is applicable to clusters of uniform events with highly similar waveforms, such as are commonly acquired with correlation detectors or other pattern matching techniques. To assess its performance, it is applied to the closely-related reciprocal problem of imaging the (known) geometry of an array from observations by the array of several regional events. Differences between the original problem and its reciprocal analog are noted and controlled for in the analysis. Chief among the differences is the necessity for aligning the waveforms in the original problem, which, to maintain consistency with the original problem, is solved in the reciprocal problem by a generalization of the VanDecar-Crosson algorithm. The VanDecar-Crosson algorithm exhibits a bias, shown through an analysis of the situation when the observed wavefields are adequately modeled as plane waves. In that circumstance, the bias can be predicted and removed. In a test using a portion of a large-N array, this imaging approach is shown to successfully reconstruct the array geometry. The method is applicable directly to infinitesimal array apertures, but is extended to a larger aperture by partitioning the image into local, effectively infinitesimal overlapping subsets. These are inverted, then assembled into a global picture of the array geometry using constraints provided by the overlapped regions. Although demonstrated in a reciprocal array context, the method appears viable for imaging clusters of events with highly similar source mechanisms and time histories.

Generation of bessel-like beam by a binary ultrasonic lens

Bessel beams have already been used in acoustic tweezers, ultrasonic medical imaging, and Doppler velocity estimation due to their non-diffractive and self-healing properties. We proposed a binary ultrasonic lens, with ultra-thin planar periodic structures for efficient conversion of the plane wave into a Bessel-like beam. The effectiveness of long-axis focusing has been demonstrated through simulations and experiments with FWHM of 8.5 mm and 9.5 mm around 10 mm. By varying the operating frequency of the incident wave from 1.9 MHz to 2.2 MHz, the position of the long-axis focusing point can be adjusted experimentally from 23.05 mm to 28.95 mm. Additionally, the beam generated by the binary ultrasonic lens can form a focused sound field when passing through multi-layered tissues and the self-healing capability of the Bessel-like beam has been numerically validated, showing strong robustness. This binary ultrasonic lens for a Bessel-like beam would conform better to ergonomic and miniaturization requirements, and expand versatile applications in clinical diagnosis and therapy.

Generating sub-diffraction microwave needle beam for nondestructive testing by multifunctional transmissive metasurfaces

Sub-diffraction needle beams with high intensity, sub-diffraction focal size, and long depth of focus (DOF) have attracted many researchers’ attention. However, the traditional methods for needle beam generation typically require many devices, such as phase elements, amplitude filters, and lens, which leads to a complex and bulky system and unfavorable for their integration. To address these challenges, we use a single multifunctional transmissive metasurface to convert a linearly polarized plane wave into a needle beam in the microwave range. The guided wave inspired unit cells of the proposed metasurface is designed to simultaneously and independently modulate the polarization and phase of transmitted waves. By imposing the desired polarization and phase distributions on the metasurface, the proposed multifunctional transmissive metasurface can efficiently generate a needle beam with subdiffraction size and extended DOF at 10 GHz when it is illuminated by an x-polarized wave. The proposed metasurface is fabricated, and a sub-diffraction needle beam with good performance is obtained in our measurements. In addition, a proof-of-concept of a high-resolution nondestructive testing experiment based on our designed metasurface is accomplished. Our work is expected to have potential applications in nondestructive testing of materials and structures.

Far field operator splitting and completion in inverse medium scattering

Abstract We study scattering of time-harmonic plane waves by compactly supported inhomogeneous objects in a homogeneous background medium. The far field operator associated to a fixed scatterer describes multi-static remote observations of scattered fields corresponding to arbitrary superpositions of plane wave incident fields at a single frequency. In this work we consider far field operators for systems of two well-separated scattering objects, and we discuss the nonlinear inverse problem to recover the far field operators associated to each of these two scatterers individually. This is closely related to the question whether the two components of the scatterer can be distinguished by means of inverse medium scattering in a stable way. We also study the restoration of missing or inaccurate components of an observed far field operator and comment on the benefits of far field operator splitting in this context. Both problems are ill-posed without further assumptions, but we give sufficient conditions on the diameter of the supports of the scatterers, the distance between them, and the size of the missing or corrupted data component to guarantee stable recovery whenever sufficient a priori information on the location of the unknown scatterers is available. We provide algorithms, error estimates, a stability analysis, and we demonstrate our theoretical predictions by numerical examples.

Influence of metal on the far-exploding surface on fragment deformation behavior under contact explosion

Metals exhibit diverse failure behavior under impact loading. In the context of fragment warheads, preformed fragments also undergo fracture and crushing behaviors when subjected to explosive loading, potentially diminishing the terminal effect and damage capability of the warhead. To address this issue, metal disks of varying impedance were applied to the far-exploding surface of the fragments, and their influence on fragment deformation behavior was examined. The experimental results revealed that when metal disks were attached to the far-exploding surface of the fragments, their fracture behavior changed, and the recovered fragments remained intact axially. Additionally, the axial length of the recovered fragments decreased as the impedance of the metal disk on the far-exploding surface increased. To elucidate the underlying mechanism of this experimental phenomenon, the variation in fragment pressure during the propagation process was calculated by employing theories of planar detonation waves and shock wave propagation in the study. The results indicate that when the impedance of the metal disks on the far-exploding surface is higher than that of the fragments, it leads to an increase in internal pressure and the formation of a compression zone within the fragments, thereby preventing fragment fracture. Conversely, lower impedance results in the formation of a tensile effect within the fragments. The theoretical and experimental results were consistent. Finally, based on the dimensional analysis, the dimensionless models were established to predict fragment deformation and internal pressure values influenced by the metal disk on the far-exploding surface.

Wave patterns of the coupled nonlinear Schrödinger equations in photonic crystal fibers with four-wave mixing

Abstract In this paper, we examine the behavior of modulation instability within photonic crystals. The model employed is the coherent coupled nonlinear Schrödinger equation, incorporating weak birefringence and four-wave mixing, which arises at the edge of the optical mode. The linear analysis is used to derive the modulation instability spectrum. Throughout the modulation instability spectrum, we identify both stable and unstable modes, thereby confirming the breakdown of the plane wave. For certain four-wave mixing parameters, the amplitude of the modulation instability spectrum and its bandwidths expand, creating an opening for localized structures to emerge. Another aspect of this study has been demonstrated in normal and anomalous dispersion regimes where an increasing initial amplitude of the plane wave is fulfilled. Specifically, numerical simulations highlight the occurrence of Benjamin-Feir instability, where wave patterns emerge under the influence of four-wave mixing. Additionally, solitonic waves are generated, demonstrating the presence of Akhmediev breathers and other modulated structures, confirming that photonic crystals with four-wave mixing are conducive to these formations. The findings from this study could inform future research in the development of nonlinear photonic waveguides.

Analysis on scattering and inner near-field characteristics of a uniaxial anisotropic sphere by an off-axis high-order Bessel (vortex) beam

Based on the generalized Lorenz–Mie theory (GLMT) and the Fourier transform method, a theoretical approach is introduced to study the scattering of a uniaxial anisotropic sphere illuminated by an off-axis high-order Bessel (vortex) beam (HOBVB). According to the orthogonality of the associated Legendre function and exponential function, a concise expression of the expansion coefficients of the off-axis HOBVB in terms of the spherical vector wave functions (SVWFs) is derived that can effectively reconstruct the HOBVB with all conical angles. The differences of scattering characteristics of a uniaxial anisotropic sphere illuminated by an on-axis and off-axis HOBVB and a plane wave are exhibited. Influences of the topological charge, conical angle, particle size, and off-axis distance on the angle distributions of the radar cross-section (RCS), scattering and extinction efficiencies, and asymmetric factor are analyzed in detail. The unique internal and near-field distributions of a uniaxial anisotropic spherical particle illuminated by an on-axis and off-axis HOBVB are demonstrated. The results provide insights into the scattering and Bessel beam–matter interactions and may find important applications in optical propagation and optical micromanipulation, microwave engineering, target shielding, and near-field measurement.

EFFECTS OF TEMPERATURE AND STRAIN AMPLITUDE ON LOW-CYCLE FATIGUE PROPERTIES OF NICKEL-BASED SINGLE-CRYSTAL SUPERALLOY DD419

High-temperature and low-cycle fatigue tests were conducted on a nickel-based single-crystal superalloy DD419 under total strain-controlled conditions at 760 °C and 980 °C. The fatigue properties of the alloy are discussed by analysing the fatigue test data. Fracture morphology and dislocation structure were observed using scanning electron microscopy and transmission electron microscopy. At the same strain amplitude, the results indicate that the plastic deformation of the alloy is larger at 980 °C compared to 760 °C. This leads to a lower fatigue strength and shorter fatigue life, along with more severe damage. The value of the strain amplitude affects the cyclic stress response behaviour of the alloy. Under low strain amplitudes, the cyclic stress response behaviour differs between 760 °C and 980 °C. The hysteresis loop exhibits similar shapes at 760 °C and 980 °C, with an increase in the area as the strain amplitude rises. The fatigue fracture analysis indicates that micropores on the surface are the primary fatigue sources at 760 °C, while oxides on the surface are the main fatigue source at 980 °C, leading to cracking due to multiple sources. Moreover, transmission electron microscopy reveals that the deformation mechanism involving dislocations at 760 °C primarily occurs through plane slip and wave slip, whereas at 980 °C, dislocations mainly move through cross slip and climb.

Effect of substitutional Sb doping on the structural stability, half-metallicity, elastic properties, electronic properties, and magnetism of the Co₂MnSn full Heusler compound

We conducted Density Functional Theory (DFT) calculations using the full potential linearized augmented plane wave (FP-LAPW) method to modify the Fermi level by introducing Sb doping into Co2MnSn.This was done through the Generalized Gradient Approximation (GGA) and modified Becke-Johnson (mBJ-GGA) formalisms to enhance spin polarization and suggest signs of half-metallicity. For both ferromagnetic and paramagnetic phases, lattice optimization was performed to identify the stable magnetic structure. The results designate that the doped alloys are stable in a ferromagnetic phase with L21 structure. The calculated elastic constants suggest that the doped alloys meet the criteria for mechanical stability. The magnetism in these compounds is primarily due to the localized moments on the Mn and Co atoms. According to mBJ-GGA calculations, the total magnetic moment slightly increases with Sb doping. Analysis of the optical constants revealed the optoelectronic properties, confirming semiconducting behavior. Doping elements to achieve half-metallicity is demonstrated to be an effective method for discovering new materials suitable for spintronics applications.