Plane Wave Research Articles

Theoretical study of optoelectronic, elastic and mechanical properties of gallium modified barium titanate (Ba1-xGaxTiO3) perovskite ceramics by DFT

In this report, we study the gallium modified Barium titanate (Ga-BTO) Ba1-xGaxTiO3 with (x = 50 %) perovskite ceramics, which have not been synthesized experimentally to date. The density functional theory-based full potential linear augmented plane wave has been employed to determine the optoelectronic, elastic, and mechanical properties of pure and modified BaTiO3. Completely relaxed 2 × 2× 2 of primitive five atoms’ cells has been used for calculations. A large cut-off energy of 120 Ry has been used to eliminate the basics of plane wave-indicating wave functions. The influence of substitution of Ga on electronic structure and optical parameters such as reflectivity, refractivity, dielectric function, optical conductivity, extinction, and absorption coefficients are analyzed and elucidated with TDOS and PDOS. The Ga modified BTO manifests a forbidden energy gap of 1.84 eV. The static dielectric constant Ɛ1(o) has values of 8.8 and 100 for pure and modified compounds respectively. Ga dopant improved the polarizing power of BTO and for the doped BTO imaginary part, Ɛ2(ω)showed a prominent peak located at 3.9 eV. The optical properties show that perovskite compound substituted with Ga is a good absorber in the ultraviolet region and the modified material has a small value of reflectivity and static refractive index 12.2. The general profiles of optical spectra of modified BaTiO3 display highly desirable features like the prominent peaks of optical conductivity obtained at 4.2 and 5.8 eV for modified BTO that make it a promising candidate for optoelectronic and spintronics. Ga-modified BTO has higher ductility, modulus (169.96 GPa), and anisotropy (2.949) than pure BTO found by analyzing their elastic and mechanical properties.

Single-unit metalens integrated micro light-emitting diodes

Metalenses, characterized by their discontinuous local phase shifts, are optically analogous to macroscopic curved lenses but are flat and scaled down to micrometer dimensions. Their compactness and compatibility with semiconductor manufacturing processes facilitate monolithic integration into existing optical devices. Here, we report on the integration of metalenses with micro light-emitting diodes (μ-LEDs), resulting in enhanced extraction efficiency and directionality. The metalenses were composed of identical nanohole units, each 150 nm in diameter, strategically arranged to induce desired local phase shifts at specific coordinates by varying the density of these units. Both simulated and experimental results demonstrated that these easy-configuration metalenses effectively focused a plane wave at a predetermined spot and collimated a diverging light source at the focal spot, exemplifying optical reciprocity. When integrated with ultraviolet (λ = 390 nm) 60 μm-sized μ-LEDs, the metalenses significantly improved device performance, exhibiting a 338% enhancement in peak intensity and a ±8° reduction in beam divergence compared to an unpatterned μ-LED. We believe that metalens-integrated μ-LEDs with high brightness, directionality, and resolution are optimally suited for near-eye applications, including virtual reality and augmented reality displays.

Modulational instability, modulated wave, and optical solitons for a generalized highly dispersive cubic-quintic-septic-nonic medium with self-frequency shift and self-steepening nonlinear terms

In this research, we delve into a generalized highly dispersive (HD) nonlinear Schrödinger equation, enriched with cubic-quintic-septic-nonic (CQSN) nonlinearities. The core of our investigation revolves around the perturbation of plane waves, aiming to understand their stability characteristics in such a complex medium. We investigate the influence of various factors such as the amplitude of the plane wave, perturbed wave number, nonic nonlinear term, and fourth-order dispersion term. Our findings indicate that increasing the amplitude of the plane wave widens the modulation instability (MI) bands and amplifies the MI growth rate. In contrast, increasing the nonic nonlinear term has opposing effects, narrowing the MI bands and diminishing the amplitude of the MI growth rate. Increasing the fourth-order dispersion term does not affect the amplitude of the MI growth rate but narrows the MI bands. The observed pattern of increasing and then decreasing MI intensity with rising K can be attributed to the complex interplay among phase matching conditions, dispersion effects, and nonlinear saturation. Initially, higher K enhances phase matching and boosts MI growth. However, as K increases further, the combined influence of dispersion and nonlinear effects can diminish the effectiveness of phase matching, resulting in a reduction in MI intensity. A significant portion of our work is dedicated to identifying and analyzing modulated rational, polynomial Jacobi elliptic function solutions, and the emergence of optical solitons within this framework. These findings provide new insights into the nonlinear dynamics underpinning the generalized HDNLSE, enriched with CQSN nonlinearities, offering valuable contributions to the theoretical understanding of such phenomena.

Persistent gravitational wave observables: nonlinearities in (non-)geodesic deviation

Abstract The usual gravitational wave memory effect can be understood as a change in the separation of two initially comoving observers due to a burst of gravitational waves. Over the past few decades, a wide variety of other, ‘persistent’ observables which measure permanent effects on idealized detectors have been introduced, each probing distinct physical effects. These observables can be defined in (regions of) any spacetime where there exists a notion of radiation, such as perturbation theory off of a fixed background, nonlinear plane wave spacetimes, or asymptotically flat spacetimes. Many of the persistent observables defined in the literature have only been considered in asymptotically flat spacetimes, and the perturbative nature of such calculations has occasionally obscured deeper relationships between these observables that hold more generally. The goal of this paper is to show how these more general results arise, and to do so we focus on two observables related to the separation between two, potentially accelerated observers. The first is the curve deviation, which is a natural generalization of the displacement memory, and also contains what this paper proposes to call drift memory (previously called ‘subleading displacement memory’) and ballistic memory. The second is a relative proper time shift that arises between the two observers, either at second order in their initial separation and relative velocity, or in the presence of relative acceleration. The results of this paper are, where appropriate, entirely non-perturbative in the curvature of spacetime, and so could be used beyond leading order in asymptotically flat spacetimes.

Investigating the multifaceted characteristics of Ba2FeWO6 double perovskite: Insights from density functional theory

This study undertook a comprehensive examination of the double perovskite complex Ba2FeWO6, investigating its structural, electrical, magnetic, thermal and elastic characteristics. The study used density functional theory (DFT), specifically the full potential linearized augmented plane wave (FP-LAPW) method. It also used different approximations, including the generalized gradient approximation (GGA) and the modified Trans-Blaha (TB-mBJ) approach, to improve the accuracy of the band gap estimation more accurate. Additionlly, the GGA + U approach, incorporating the Hubbard correction term (U), was utilized. Our findings indicate that Ba2FeWO6 exhibits indirect half-metallic band gaps in the (L-X) direction, with value of 0.91 eV and a net magnetic moment of 4 μB, predominatly influenced by the iron atom. The compound demonstrated exceptional characteristics suitable for thermoelectric applications, particularly at lower temperatures. Furthermore, the elasticity analysis revealed low brittleness, facilitates its manipulation in manufacturing procedures.

Exploring the dynamic interplay of intermodal and higher order dispersion in nonlinear negative index metamaterials

Our study delves into the intricate interplay of various factors within metamaterials, with a focus on modulation instability. Through our research, we elucidate the intricate dynamics involving intermodal dispersion, self-steepening effect, higher order dispersion, and plane wave amplitude, showcasing their competition and influence on modulation instability phenomena. We aim to explore the impact of intermodal dispersion and higher-order effects by numerically solving the generalized nonlinear Schrödinger equation (NLSE), which models the propagation of a few-cycle pulse in a nonlinear metamaterial. Our modulation instability (MI) analysis captures the complex dynamics these factors introduce. We demonstrate the spatiotemporal evolution of MI under different parameter values, revealing how these variations influence the instability’s development and characteristics. This approach provides a detailed understanding of the system’s behavior across various conditions, highlighting the roles of intermodal dispersion and higher-order effects. We demonstrate that the behavior of modulation instability bands and their reliance on parameters such as self-steepening and wave amplitude is contingent upon the specific characteristics of the optical setup and medium dispersion properties

Resonant solutions of the non-linear Schrödinger equation with periodic potential *

The goal is construction of stationary solutions close to non-trivial combinations of two plane waves at high energies for a periodic non-linear Schrödinger Equation in dimension two. The corresponding isoenergetic surface is described for any sufficiently large energy k 2. It is shown that the isoenergetic surface corresponding to k 2 is essentially different from that for the zero potential even for small potentials. We use a combination of the perturbative results obtained earlier for the linear case and a method of successive approximation.

Production of high-purity non-diffracting optical vortex arrays with high topological charge

In this paper, we have realized the high purity non-diffracting optical vortex arrays with a high topological charge using quasi-symmetrical plane waves for the first time. The triangular vortex arrays with l = ±2 can be generated by six quasi-symmetrical plane waves, and the square vortex arrays with l = ±3 can be generated by eight quasi-symmetrical plane waves. The adjacent vortex units have opposite topological charges. We have also obtained the relations between the periods of the field formed by the six/eight quasi-symmetrical plane waves and the periods of the field formed by the three/four symmetrical plane waves. The simulation and experimental results demonstrate the feasibility of this method.

An efficient ultrasonic wavenumber-domain plane wave imaging method towards the inspection of curved structures

Ultrasonic phased array testing is commonly employed for inspecting curved structures. Conventional plane wave imaging techniques, based on delay-and-sum in the time-domain, offer high image quality and inspection accuracy but suffer from low frame rates due to their high computational complexity. In this work, an efficient wavenumber-domain imaging method that combines non-stationary wavefield extrapolation and f-k migration is proposed for curved structure inspection. Special emission focal laws are designed to generate a sequence of steered plane waves through the curved interface. The raw data is then extrapolated to the top boundary of the region of interest, followed by f-k migration to reconstruct images with high time efficiency. Simulation and experimental evaluations demonstrate a time reduction by a factor of up to 32.24 compared to conventional time-domain plane wave image reconstruction with equivalent image quality, highlighting its potential for monitoring flaws in real-time.

The [formula omitted]-Adic Schrödinger equation and the two-slit experiment in quantum mechanics

p-Adic quantum mechanics is constructed from the Dirac–von Neumann axioms identifying quantum states with square-integrable functions on the N-dimensional p-adic space, QpN. This choice is equivalent to the hypothesis of the discreteness of the space. The time is assumed to be a real variable. The p-adic quantum mechanics is motivated by the question: what happens with the standard quantum mechanics if the space has a discrete nature? The time evolution of a quantum state is controlled by a nonlocal Schrödinger equation obtained from a p-adic heat equation by a temporal Wick rotation. This p-adic heat equation describes a particle performing a random motion in QpN. The Hamiltonian is a nonlocal operator; thus, the Schrödinger equation describes the evolution of a quantum state under nonlocal interactions. In this framework, the Schrödinger equation admits complex-valued plane wave solutions, which we interpret as p-adic de Broglie waves. These mathematical waves have all wavelength p−1. In the p-adic framework, the double-slit experiment cannot be explained using the interference of the de Broglie waves. The wavefunctions can be represented as convergent series in the de Broglie waves, but the p-adic de Broglie waves are just mathematical objects. Only the square of the modulus of a wave function has a physical meaning as a time-dependent probability density. These probability densities exhibit interference patterns similar to the ones produced by ‘quantum waves’. In the p-adic framework, in the double-slit experiment, each particle goes through one slit only. The p-adic quantum mechanics is an analog (or model) of the standard one under the hypothesis of the existence of a Planck length. The precise connection between these two theories is an open problem. Finally, we propose the conjecture that the classical de Broglie wave-particle duality is a manifestation of the discreteness of space–time.

Analysis of reflection of wave propagation in magneto-thermoelastic nonlocal micropolar orthotropic medium at impedance boundary

PurposeThis study aims to examine the plane wave reflection problem in micropolar orthotropic magneto-thermoelastic half space, considering the influence of impedance as a boundary in a nonlocal elasticity.Design/methodology/approachThis study presents the novel formulation of governing partial differential equations for micropolar orthotropic medium with impact of nonlocal thermo-elasticity under magnetic field.FindingsThis study provides the numerical results validation for a particular numerical data and expression for the amplitude ratios of reflected waves and identifies the existence of four different waves, namely, quasi longitudinal displacement qCLD-wave, quasi thermal wave qCT-wave, quasi transverse displacement qCTD-wave and quasi-transverse micro-rotational qCTM-wave. The study derives the velocity equation giving the speed and phase velocity of these waves. The study also shows that the small-scale size effect gives significant impact on phase velocity.Research limitations/implicationsThe graphical analysis examines the variation of speeds and coefficients of attenuation of these waves due to frequency, magnetic field and nonlocal parameters. Also, significant conclusions on the variation of reflection coefficient against nonlocal parameter, frequency, impedance parameter and angle of incidence are provided graphically.Practical implicationsThe creation of more effective micropolar orthotropic anisotropic materials which are very useful in the daily life and their applications in earth science are greatly impacted by the findings of this study.Originality/valueThe authors of the submitted document initiated and produced it collectively, with equal contributions from all members.

A Visual Representation for Accurate Local Basis Set Construction and Optimization: A Case Study of SrTiO3 with Hybrid DFT Functionals

The linear combination of atomic orbitals (LCAO) method is advantageous for calculating important bulk and surface properties of crystals and defects in/on them. Compared to plane wave calculations and contrary to common assumptions, hybrid density functional theory (DFT) functionals are actually less costly and easier to implement in LCAO codes. However, choosing the proper basis set (BS) for the LCAO calculations representing Guassian-type functions is crucial, as the results depend heavily on its quality. In this study, we introduce a new basis set (BS) visual representation, which helps us (1) analyze the collective behavior of individual atoms’ shell exponents (s, p, and d), (2) better compare different BSs, (3) identify atom-type invariant relationships, and (4) suggest a robust method for building a local all-electron BS (denoted as BS1) from scratch for each atom type. To compare our BS1 with the others existing in the literature, we calculate the basic bulk properties of SrTiO3 (STO) in cubic and tetragonal phases using several hybrid DFT functionals (B3LYP, PBE0, and HSE06). After adjusting the exact Hartree–Fock (HF) exchange of PBEx, HSEx, and the state-of-the-art meta-GGA hybrid r2SCANx functionals, we find the r2SCAN15 and HSE27 for BS1, with the amount of exact HF exchange of 0.15 and 0.27, respectively, perform equally well for reproducing several most relevant STO properties. The proposed robust BS construction scheme has the advantage that all parameters of the obtained BS can be reoptimized for each new material, thus increasing the quality of DFT calculation predictions.

Nonlinear stability of planar viscous shock wave to three-dimensional compressible Navier–Stokes equations

We prove the nonlinear stability of the planar viscous shock up to a time-dependent shift for the three-dimensional (3D) compressible Navier–Stokes equations under the generic perturbations, in particular, without zero mass conditions. Moreover, the time-dependent shift function keeps the shock profile shape time-asymptotically. Our stability result is unconditional for the weak planar Navier–Stokes shock. Our proof is motivated by the a -contraction method (a kind of weighted L^{2} -relative entropy method) with time-dependent shift for the stability of viscous shock in the one-dimensional (1D) case. Instead of the classical anti-derivative techniques, we perform the stability analysis of the planar Navier–Stokes shock in the original H^{2} -perturbation framework and therefore zero mass conditions are not necessarily needed, which, in turn, brings out the essential difficulties due to the compressibility of viscous shock. Furthermore, compared with 1D case, there are additional difficulties coming from the wave propagations along the multi-dimensional transverse directions and their interactions with the viscous shock. To overcome these difficulties, a multi-dimensional version of the sharp weighted Poincaré inequality, a -contraction techniques with time-dependent shift, and some essential physical structures of the multi-dimen­sional Navier–Stokes system are fully used.

A transcranial multiple waves suppression method for plane wave imaging based on Radon transform

Transcranial ultrasound imaging presents a significant challenge due to the intricate interplay between ultrasound waves and the heterogeneous human skull. The skull’s presence induces distortion, refraction, multiple scattering, and reflection of ultrasound signals, thereby complicating the acquisition of high-quality images. Extracting reflections from the entire waveform is crucial yet exceedingly challenging, as intracranial reflections are often obscured by strong amplitude direct waves and multiple scattering. In this paper, a multiple wave suppression method for ultrasound plane wave imaging is proposed to mitigate the impact of skull interference. Drawing upon prior research, we developed an enhanced high-resolution linear Radon transform using the maximum entropy principle and Bayesian method, facilitating wavefield separation. We detailed the process of wave field separation in the Radon domain through simulation of a model with a high velocity layer. When plane waves emitted at any steering angles, both multiple waves and first arrival waves manifested as distinct energy points. In the brain simulation, we contrasted the characteristic differences between skull reflection and brain-internal signal in Radon domain, and demonstrated that multiples suppression method reduces side and grating lobe levels by approximately 30 dB. Finally, we executed in vitro experiments using a monkey skull to separate weak intracranial reflection signals from strong skull reflections, enhancing the contrast-to-noise ratio by 85 % compared to conventional method using full waveform. This study deeply explores the effect of multiples on effective signal separation, addresses the complexity of wavefield separation, and verifies its efficacy through imaging, thereby significantly advancing ultrasound transcranial imaging techniques.

An application of a beamforming technique, linear acoustic array and robot for pipe condition localization

Pipe inspection robots with sensors significantly enhance the maintenance of water systems by enabling early defect detection and reducing the risks of leaks and environmental damage. This paper introduces a sparse representation acoustic beamformer designed to locate artefacts within pipes using a short linear microphone array on a robot. The primary contributions include: (i) a new acoustic beamforming approach based on sparse representation that accurately predicts pipe conditions with a localization error within 3 % of the sensing distance; (ii) an enhanced beamforming algorithm combining plane wave and first non-axisymmetric mode, extending the frequency range from < 1300 Hz to < 2200 Hz in a 150 mm diameter pipe (an increase by 1.69 times), effectively managing unwanted acoustic reverberations and distinguishing blockages from lateral connections; and (iii) a novel robust algorithm predicting pipe length with an error margin within 2 %. This research advances acoustic sensing technologies for autonomous mobile robots inspecting buried pipes.

Reflection and transmission of plane waves at interface between two transversely isotropic microstretch half-spaces

Reflection and transmission of plane waves at interface between two transversely isotropic microstretch half-spaces

[formula omitted] First-principles calculations of optoelectronic characteristics of [formula omitted]&[formula omitted] doped [formula omitted] for energy renewable devices applications [formula omitted]

This research study investigates the structural and optoelectronic characteristics of Eu3+&Tb3+ doped BaSiO3 for energy renewable device applications, using FPLAW (full potential linear augmented plane wave) technique as applied in WIEN-2k code. The generalized gradient approximation has been utilized as the exchange-correlation functional for electrical and optical characteristic computations with Hubbard correction. Electronic characteristics demonstrate semiconducting nature, with a direct bandgap having a value of 1.1 eV for Eu3+ doped BaSiO3 and shows metallic nature, with bandgap 1.4 eV for Tb3+ doped BaSiO3. BaSiO3 Doped with Eu3+ and Tb3+ absorb ultraviolet photons substantially also reflect photons in infrared and visible wavelengths slightly. Such optical properties could be beneficial in optoelectronic device applications. When we doped the parent material, we observed overlap between the CB (conduction band) and VB (valence band), with many of them crossing near to the Fermi level. In electronic properties, for each doped material. The dielectric constant ε(ω), extinction coefficient K(ω), optical loss L(ω), refractive index n(ω), reflectivity R(ω) and absorption coefficient α(ω) being a function of incident photon energies were calculated to examine optical characteristics. BaSiO3 Doped with Eu3+ and Tb3+ absorb ultraviolet photons substantially also reflect photons in infrared and visible wavelengths slightly. Such optical properties could be beneficial in optoelectronic device applications.

Deep coherence learning: An unsupervised deep beamformer for high quality single plane wave imaging in medical ultrasound

Plane wave imaging (PWI) in medical ultrasound is becoming an important reconstruction method with high frame rates and new clinical applications. Recently, single PWI based on deep learning (DL) has been studied to overcome lowered frame rates of traditional PWI with multiple PW transmissions. However, due to the lack of appropriate ground truth images, DL-based PWI still remains challenging for performance improvements. To address this issue, in this paper, we propose a new unsupervised learning approach, i.e., deep coherence learning (DCL)-based DL beamformer (DL-DCL), for high-quality single PWI. In DL-DCL, the DL network is trained to predict highly correlated signals with a unique loss function from a set of PW data, and the trained DL model encourages high-quality PWI from low-quality single PW data. In addition, the DL-DCL framework based on complex baseband signals enables a universal beamformer. To assess the performance of DL-DCL, simulation, phantom and in vivo studies were conducted with public datasets, and it was compared with traditional beamformers (i.e., DAS with 75-PWs and DMAS with 1-PW) and other DL-based methods (i.e., supervised learning approach with 1-PW and generative adversarial network (GAN) with 1-PW). From the experiments, the proposed DL-DCL showed comparable results with DMAS with 1-PW and DAS with 75-PWs in spatial resolution, and it outperformed all comparison methods in contrast resolution. These results demonstrated that the proposed unsupervised learning approach can address the inherent limitations of traditional PWIs based on DL, and it also showed great potential in clinical settings with minimal artifacts.

A DFT study to explore structural, elastic, mechanical, phonon, electronic and optical properties of halide perovskites AgXF3(X=Be,Ca)$$ {\mathrm{AgXF}}_3\left(\mathrm{X}=\mathrm{Be},\mathrm{Ca}\right) $$ with PBEsol, TB‐mBJ and SCAN functionals

AbstractFirst principles calculations have been performed using full potential linearized augmented plane wave, FP‐LAPW, within Wien2k to elucidate structural, elastic, mechanical, phonon, electronic and optical properties of lead free halide perovskites . The energy volume curve fitting is used to examine structural stability. For structural optimization and mechanical properties, we employed Perdew–Burke–Ernzerhof generalized gradient approximation and PBEsol, revised for solids, exchange and correlation functional. The optimized lattice constant of and is 3.631 and 4.349Å. The elastic constant , and are computed to extract different mechanical parameters like Poisson's ratio, Pugh's ratio, bulk modulus, shear modulus, Young's modulus, anisotropic ratio, Cauchy pressure and shear constant. The mechanical parameters exhibit greater structural, mechanical and dynamical stability of than . The electronic and optical properties are calculated by using TB‐mBJ and SCAN potentials in addition to PBEsol. The electronic band gap of and is 4.71 and 6.01 eV with TB‐mBJ and both perovskites are indirect band gap materials. The optical response of these perovskites against wide range of incident electromagnetic radiation is assessed by calculating absorption, reflection, optical conductivity, dielectric constant, energy loss function and refraction. Strong absorption, high optical conductivity and low reflectivity indicates that and are promising materials for photovoltaic applications.

Topology optimization of blazed gratings under conical incidence

A topology optimization method is presented and applied to a blazed diffraction grating in reflection under conical incidence. This type of grating is meant to disperse the incident light on one particular diffraction order, and this property is fundamental in spectroscopy. Conventionally, a blazed metallic grating is made of a sawtooth profile designed to work with the ±1st diffraction order in reflection. In this paper, we question this intuitive triangular pattern and look for optimal opto-geometric characteristics using topology optimization based on finite element modelling of Maxwell’s equations. In practical contexts, the grating geometry is mono-periodic, but it is enlightened by a 3D plane wave with a wave vector outside of the plane of invariance. Consequently, this study deals with the resolution of direct and inverse problems using the finite element method in this intermediate state between 2D and 3D: the so-called conical incidence. A multi-wavelength objective is used in order to obtain a broadband blazed effect. Finally, several numerical experiments are detailed. Our numerical results show that it is possible to reach a 98% diffraction efficiency on the −1st diffraction order if the optimization is performed on a single wavelength, and that the reflection integrated over the [400,1500] nm wavelength range can be 29% higher in absolute terms, 56% in relative terms, than that of the sawtooth blazed grating when using a multi-wavelength optimization criterion (from 52% to 81%).