Wave Dispersion Research Articles

Efficient Simultaneous Second Harmonic Generation and Dispersive Wave Generation in Lithium Niobate Thin Film

AbstractLithium niobate thin film (LNTF) is a promising platform for ultra‐low loss nonlinear integrated photonics. Here, the simultaneous generation of second harmonic wave (SHW) and dispersive wave (DW) are demonstrated in a single LNTF under the pump of a femtosecond pulse laser, with a conversion efficiency exceeding 25%. The second harmonic generation (SHG) uses the modal phase matching mechanism based on the second‐order nonlinear effect, while the DW generation is based on the perturbations of soliton dynamics caused by self‐phase modulation and higher‐order dispersion. Notably, significant and symmetrical SHW and DW patterns are observed, which exhibit strong spatial dispersion properties. A comprehensive analysis of the phase‐matching conditions are conducted for SHG and DW generation and provide a clear elucidation of the spectral properties of different regions of the emitted light patterns. Additionally, the evolution of the pump light in LNTF is thoroughly investigated, and the solutions of the generalized Schrödinger equation are in good agreement with these experimental results. This work sheds new light on the rich physics of nonlinear optical interactions on LNTF, and by utilizing the synergistic effect of second‐order and third‐order nonlinear effects, this study anticipates achieving efficient and high energy on‐chip broadband frequency conversion and supercontinuum generation across octaves.

The Energy Dispersion of Magnetic Rossby Waves in the Quasi-geostrophic Shallow Water Magnetohydrodynamic Theory

Abstract This research firstly comprehensively investigates the energy dispersion of magnetic Rossby waves in zonally non-uniform basic state by applying the quasi-geostrophic (QG) shallow water magnetohydrodynamic (SWMHD) equations. The eddy momentum and heat flux transported by Magnetic Rossby waves, which can be described by the group velocity vector, have significant impacts on the large-scale dynamics of various celestial bodies. The findings suggest that the energy dispersion paths, also called rays, are curves and restricted in limited regions in the non-uniform basic states, in contrast with straight lines in the uniform basic states. Furthermore, the limited propagative regions are influenced by three important meridional locations, which are defined as the symmetric turning location, the asymmetric turning location, and the critical location. The first two reflect rays and the third one acts as an asymptote. The propagative region that is enclosed by a turning location and a critical location is more general. Besides, the occurrence of the asymmetric turning location, which is mainly depended on the distribution of the zonal basic flow, is a quite new feature of the energy dispersion for magnetic Rossby waves since there is no asymmetric turning location for Rossby waves on the Earth’s atmosphere and ocean. The results have important applications in illustrating interactions between magnetic Rossby waves and zonally basic states and in explaining the maintenance of the zonal flow and meridional circulation of various celestial bodies.

Mode-locking dynamics of triple attractors in a wavelength-multiplexing fiber laser

We demonstrate the coexistence of triple attractors in a mode-locked ring fiber laser with equal dual-gain-channel. Even under identical cavity conditions, quantum noise can evolve into three distinct stable states: tightly bound soliton, asynchronous dual-wavelength pulses, and loosely bound soliton. The mode-locking dynamics reveal that the final state depends on whether the dispersive wave or the residual noise pulse dominates the gain competition, which is significantly influenced by the modulation depth of the saturable absorber. By reducing the modulation depth from 70% to 5%, the probability of forming asynchronous dual-wavelength pulses increases from 33% to 90%. Our findings offer what we believe to be new insights into the dynamics of dual-gain-channel fiber laser and underscore the critical role of the saturable absorber in wavelength-multiplexing.

Ultrasound evaluation of kidney and liver involvement in Bardet-Biedl syndrome.

Bardet-Biedl syndrome (BBS) is a rare autosomal-recessive ciliopathy with pathogenic variants in 26 BBS genes. It affects multiple organs, including the kidney and liver, with varying degrees regarding extent and time of first manifestation. Structural renal anomalies are an early feature and end-stage kidney disease (ESKD) cumulates to 25% in adulthood. Early-onset hyperphagia-associated obesity is another major symptom and contributes to liver pathology, presenting as steatosis/fibrosis. Aim of this study is the evaluation of high-end ultrasound (US) technologies in BBS patients regarding their potential to discriminate liver and kidney tissue pathology at an early stage. Patients with genetically proven BBS were recruited from the University Children's Hospital of Essen and from BBS patient days hosted in Germany. Acute illness was an exclusion criterion. Clinical and laboratory data were extracted from patients' digital records or medical letters. High-resolution ultrasound (US) imaging was utilized, including attenuation imaging (ATI), shear wave elastography (SWE) and dispersion (SWD) of liver tissue. 49 BBS patients (24/49 male; 1.1-51.0years, mean 17.8years) were included in the study. Mean body weight (SDS 2.13 ± 1.33) and BMI (SDS 2.64 ± 1.18) were increased. Structural kidney abnormalities (dysplasia, cysts) were present in 75% (36/48), and persistent fetal lobulation in 44% (21/48). Renal function was impaired in 27% (13/49) of whom 3 had ESKD (kidney transplantation (n = 2), hemodialysis (n = 1)). Elevation of liver enzymes was detected in 38% (16/42). In 51% (25/49) ATI of liver tissue was increased, indicating hepatic steatosis, and correlated with BMI SDS, liver size, and enzymes. SWE was elevated in 61% (30/49), suggesting hepatic fibrosis, and it correlated with BMI and GGT. Patients with pathogenic variants in BBS10 showed a tendency towards higher ATI, reduced GFR, and higher BMI SDS. We detected kidney and liver abnormalities in a higher percentage of BBS patients than previously reported, indicating a high sensitivity and diagnostic yield of the evaluated high-end US applications. ATI detected liver pathology early (partially prior to liver enzymes) and revealed differences related to the affected genes. Evidence of tissue pathology at an early stage may improve diagnostics and the evaluation of therapeutic approaches.

Response of a relativistically streaming pulsar plasma

The response tensor is derived for a relativistically streaming, strongly magnetized, one-dimensional Jüttner distribution of electrons and positrons, referred to as a pulsar plasma. This is used to produce a general treatment of wave dispersion in a pulsar plasma. Specifically, relativistic streaming, the spread in Lorentz factors in a pulsar rest frame and cyclotron resonances are taken into account. Approximations to the response tensor are derived by making approximations to relativistic plasma dispersion functions appearing in the general form of the response tensor. The cold-plasma limit, the highly relativistic limit and limits related to cyclotron resonances are considered. The theory developed in this paper has applications to generalized Faraday rotation in pulsars and magnetars.

Effects of dispersive waves on mode families in microresonators with avoided mode-crossing

Effects of dispersive waves on mode families in microresonators with avoided mode-crossing

Nonlinear joint inversion of Rayleigh and Love wave dispersion curves based on Pearson correlation coefficient and thickness mean sharing

AbstractThe joint inversion of Rayleigh and Love waves plays a crucial role in mitigating the non‐uniqueness of surface wave inversion results and enhancing the stability of these inversions. Existing approaches to the joint inversion of Rayleigh and Love wave dispersion curves, which rely on conventional objective functions, often struggle with complex stratigraphic configurations and yield results of limited accuracy. This study introduces two novel nonlinear joint inversion techniques for Rayleigh and Love waves: Pearson correlation coefficient and thickness mean sharing. The Pearson correlation coefficient approach employs the Pearson correlation coefficient and alternating iterative objective functions to synchronize the shear wave velocity structures derived from Rayleigh and Love waves, thereby enhancing the accuracy of the joint inversion. Conversely, the thickness mean sharing method computes an average of the thickness values obtained in each iteration of the inversion, utilizing the traditional joint inversion objective function. Tests on three distinct stratigraphic structures—characterized by increasing velocity, high‐speed hard interlayers and low‐speed soft interlayers—as well as on measured data, demonstrate that the proposed methods significantly improve the stability and accuracy of nonlinear joint inversion.

On the dispersive shock waves of the defocusing Kundu–Eckhaus equation in an optical fiber

On the dispersive shock waves of the defocusing Kundu–Eckhaus equation in an optical fiber

Total resonant terahertz absorption enabled by a large-scale adjustable admittance inverse matching in a metal groove with graphene

Abstract We propose a tunable terahertz (THz) perfect absorber based on a metal groove with graphene-loaded dielectric resonator and theoretically study its basic properties. The proposed absorber allows switching between the regimes of perfect absorption at the Fabry-Perot resonance excited near the cut-off frequency of the metal groove and almost total reflection away from the resonance by changing the Fermi energy in graphene. For this purpose, we propose a “bottom up” approach which is based on tuning the admittance of input line (the metal groove in our case) instead of the structure admittance in order to reach the perfect admittance matching condition. We demonstrate that this effect can be realized at arbitrary selected frequency in the entire THz range due to the dispersion of incoming wave in metal groove, which ensures a large-scale tunability of its characteristic admittance. As a result, the total absorption can be realized in the Fabry-Perot resonance even in a simple graphene-loaded dielectric cavity for any admittance of graphene layer, which is advantageous as compared to majority of existing THz absorbers with more complicated design.

Waves Generated by the Horizontal Motions of a Bottom Disturbance

Waves generated by a horizontally moving disturbance on the seabed have been studied by developing two numerical models, namely, the Navier–Stokes and the Green–Naghdi equations. Various geometries of the bottom disturbances are considered, and waves generated due to a single motion and multiple oscillatory motions of the bottom disturbances are investigated by the two models. Discussion is provided on how the motion of the disturbance on the seafloor results in the generation of surface waves. The wave-field parameters investigated include the surface elevation, velocity, pressure fields and wave celerity. A parametric study is conducted to assess the effect of the geometry of the disturbance and the kinematic characteristics on the wave generation. It is shown that both linear and nonlinear waves can be generated by a horizontally moving disturbance on the seabed. Long waves, followed by a series of dispersive waves, are produced by the single motion of the bottom disturbance. It is also found that, under appropriate conditions, there would be a balance between nonlinearity and dispersion, such that the generated waves propagate over a flat seafloor with little to no change in their form and shape.

Exact solitary wave solutions for a coupled gKdV–Schrödinger system by a new ODE reduction method

AbstractA new method is developed for finding exact solitary wave solutions of a generalized Korteweg–de Vries equation with ‐power nonlinearity coupled to a linear Schrödinger equation arising in many different physical applications. This method yields 22 solution families, with . No solutions for were known previously in the literature. For , four of the solution families contain bright/dark Davydov solitons of the 1st and 2nd kind, obtained in recent literature by basic ansatz applied to the ordinary differential equation (ODE) system for traveling waves. All of the new solution families have interesting features, including bright/dark peaks with (up to) symmetric pairs of side peaks in the amplitude and a kink profile for the nonlinear part in the phase. The present method is fully systematic and involves several novel steps that reduce the traveling wave ODE system to a single nonlinear base ODE for which all polynomial solutions are found by symbolic computation. It is applicable more generally to other coupled nonlinear dispersive wave equations as well as to nonlinear ODE systems of generalized Hénon–Heiles form.

ULTRASONIC INTERROGATION TECHNIQUE FOR DETECTING HATCH ANGLE VARIATIONS IN ADDITIVE MANUFACTURING BY PHONONIC LATTICE STRUCTURES

Abstract Additive Manufacturing/3D Printing (AM/3DP) has revolutionized part production by enabling the creation of intricate internal structures and complex geometries from diverse materials directly from digital design files. Among powder-based metal AM/3DP methods, Selective Laser Melting (SLM) is widely used in advanced applications such as biomedical devices and aerospace parts. Despite considerable progress in AM/3DP and SLM, at present, challenges in print quality persist, and vast resources for post-production quality assessment are allocated. The quality of SLM prints is influenced by various process and design parameters, such as the accuracy of hatch angle deposition, laser intensity/power, scanning speed of the laser beam, print line spacing, layer depth, printing chamber conditions, and the material's physical and chemical properties. Direct ultrasonic Non-Destructive Evaluation (NDE) offers comprehensive internal inspection and real-time data acquisition ability; however, in AM/3DP it faces severe limitations due to a build's intricate internal and external geometric features. In the current study, we present a Phononic Crystal Artifact (PCA)-based real-time ultrasonic NDE quality monitoring framework and show offline its utility in detecting and evaluating hatch angle variations, a critical process parameter. A PCA is substantially simpler and smaller than the actual build but represents its critical geometric and structural intricacies and mechanical properties. The current offline study demonstrates that hatch angle variations can be monitored from ultrasonic responses' spectral modal frequency peaks and wave dispersion relations.

Identification of moment equations via data-driven approaches in nonlinear Schrödinger models

IntroductionThe moment quantities associated with the nonlinear Schrödinger equation offer important insights into the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities are amenable to both analytical and numerical treatments.MethodsIn this paper, we present a data-driven approach associated with the “Sparse Identification of Nonlinear Dynamics” (SINDy) to capture the evolution behaviors of such moment quantities numerically.Results and DiscussionOur method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available.

Shear wave speed, dispersion slope and anisotropy evaluation using cardiac shear wave elastography in patients with Fabry disease

Abstract Background Cardiac shear wave imaging has been proposed to investigate left ventricular myocardial alterations non-invasively. Dispersion slope and anisotropy are fundamental properties that have not been studied in Fabry disease (FD) patients yet. Purpose The aim of this study was to determine and compare shear wave propagation speed, dispersion slope and fractional anisotropy in FD patients and healthy controls. Methods We prospectively included 20 FD patients and 20 healthy controls (HC). Shear wave speed, dispersion slope and fractional anisotropy were measured non-invasively in anteroseptal basal segment using an ultrasound for cardiac shear wave imaging. Echocardiography, electrocardiogram and laboratory evaluations were performed. Results Shear wave propagation speed was higher in FD patients than in HC group (1.46 ± 0.12 m/s and 1.36 ± 0.17 m/s, p = 0.03). No difference was found in dispersion slope (11.4 m/s/kHz in FD group and 11.3 m/s/kHz in HC group, p = 0.6). Fractional anisotropy was 0.05 ± 0.04 in FD group and 0.05 ± 0.04 in HC group, p = 0.4. Conclusion Shear wave speed was higher in FD patients compared to control group. Dispersion slope and fractional anisotropy in FD group did not reveal significant difference to the control group.

Observation of Two-Dimensional Dam Break Flow and a Gaseous Phase of Solitons in a Photon Fluid.

We report the observation of a two-dimensional (2D) dam break flow of a photon fluid in a nonlinear optical crystal. By precisely shaping the amplitude and phase of the input wave, we investigate the transition from one-dimensional (1D) to 2D nonlinear dynamics. We observe wave breaking in both transverse spatial dimensions with characteristic timescales determined by the aspect ratio of the input box-shaped field. The interaction of dispersive shock waves propagating in orthogonal directions gives rise to a 2D ensemble of solitons. Depending on the box size, we report the evidence of a dynamic phase characterized by a constant number of solitons, resembling a 1D soliton gas in integrable systems. We measure the statistical features of this gaslike phase. Our findings pave the way to the investigation of collective solitonic phenomena in two dimensions, demonstrating that the loss of integrability does not disrupt the dominant phenomenology.

Dynamic of bifurcation, chaotic structure and multi soliton of fractional nonlinear Schrödinger equation arise in plasma physics

In this study, we examine the third-order fractional nonlinear Schrödinger equation (FNLSE) in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document}-dimensional, by employing the analytical methodology of the new extended direct algebraic method (NEDAM) alongside optical soliton solutions. In order to better understand high-order nonlinear wave behaviors in such systems, the researched model captures the physical and mathematical properties of nonlinear dispersive waves, with applications in plasma physics and optics. With the aid of above mentioned approach, we rigorously assess the novel optical soliton solutions in the form of dark, bright–dark, dark–bright, periodic, singular, rational, mixed trigonometric and hyperbolic forms. Additionally, stability assessments using conserved quantities, such as Hamiltonian property, and consistency checks were used to validate the solutions. The dynamic structure of the governing model is further examined using chaos, bifurcation, and sensitivity analysis. With the appropriate parameter values, 2D, 3D, and contour plots can all be utilized to graphically show the data. This work advances our knowledge of nonlinear wave propagation in Bose–Einstein condensates, ultrafast fibre optics, and plasma physics, among other areas with higher-order chromatic effects.

Low-frequency propagating and evanescent waves in strongly inhomogeneous sandwich plates

The paper aims at studying dispersion of elastic waves in a sandwich plate with the parameters, characteristic of aerogel core and hard skin layers, typical for aerospace applications including optimal design of fuselage structural components. The proposed approach relies on multiparametric analysis, taking into account the effect of strong transverse inhomogeneity. It is demonstrated that both an additional low-frequency propagating wave and a slowly decaying evanescent one appear due to a high contrast in geometric and mechanical parameters of the layers. The key findings include the derivation of two-mode asymptotic expansions of the full dispersion relation at the low-frequency limit, as well as elucidation of the non-trivial link between long-wave evanescent and propagating modes. A sophisticated composite nature of the obtained expansions involving various shortened forms is investigated. The range of validity for each of these forms over frequency and wave-number domains is evaluated. Comparison of asymptotic results with the numerical solution of the full dispersion relation is presented.

Three methods of visco‐acoustic migration based on the De Wolf approximation and comparison of their migration images

AbstractThe viscosity of a medium affects the amplitude attenuation and velocity dispersion of seismic waves. Therefore, it is necessary to consider these factors during migration. First, to eliminate the viscous effect of a medium, we combine the Futterman model with the integral equation of the De Wolf approximation to construct a compensation operator of the De Wolf approximation for a visco‐acoustic medium. Next, we use the visco‐acoustic screen approximation method to realize the continuation operator then establish a prestack depth migration algorithm. Finally, an error analysis, impulse response test and model test are performed. The results show that three different generalized visco‐acoustic screen methods (phase screen method, generalized screen method and extended local Born Fourier method) can satisfactorily compensate for the attenuation of deep interface amplitude. Among these methods, the visco‐acoustic extended local Born Fourier method has the highest accuracy and the best compensation effect.

Wave dispersion in a damped beam supported by cubic nonlinear springs: A multiscale freewave approach

Wave dispersion in a damped beam supported by cubic nonlinear springs: A multiscale freewave approach

Hydrodynamics of a discrete conservation law

AbstractThe Riemann problem for the discrete conservation law is classified using Whitham modulation theory, a quasi‐continuum approximation, and numerical simulations. A surprisingly elaborate set of solutions to this simple discrete regularization of the inviscid Burgers' equation is obtained. In addition to discrete analogs of well‐known dispersive hydrodynamic solutions—rarefaction waves (RWs) and dispersive shock waves (DSWs)—additional unsteady solution families and finite‐time blowup are observed. Two solution types exhibit no known conservative continuum correlates: (i) a counterpropagating DSW and RW solution separated by a symmetric, stationary shock and (ii) an unsteady shock emitting two counterpropagating periodic wavetrains with the same frequency connected to a partial DSW or an RW. Another class of solutions called traveling DSWs, (iii), consists of a partial DSW connected to a traveling wave comprised of a periodic wavetrain with a rapid transition to a constant. Portions of solutions (ii) and (iii) are interpreted as shock solutions of the Whitham modulation equations.