Dispersion Relation Research Articles

Dipolar induced nonreciprocal magnon hybridization in FeNi/YIG bilayers

We investigated the magnon hybridization behavior in FeNi films, which were deposited on the yttrium-iron garnet (YIG) films by using Brillouin light scattering. Nonreciprocal magnon hybridizations have been detected not only on the mode densities but also the dispersion relations. The perpendicular standing spin wave mode confined in the thickness direction hybridized with the top surface magnetostatic surface spin wave at smaller wave vectors range while hybridized with the bottom surface mode at larger wave vectors range. The dipolar interaction between the FeNi layer and the YIG layer should be the main reason for the nonreciprocal hybridization of the two modes in the FeNi layer. The nonreciprocal hybridization characteristics of FeNi/YIG double-layer magnetic films enrich the nonreciprocal magnon hybridization system and might have potential application in constructing spin wave-based devices.

Non-Foster approach to broadband optical metamaterials based on Lorentzian gain materials

All passive metamaterials are inherently narrowband due to fundamental dispersion-energy constraints, and their dispersive properties are usually approximated by a Lorentz model. However, there are broadband active metamaterials in the radio frequency (RF) regime based on negative capacitors with non-Foster dispersion properties. Non-Foster dispersion is usually considered as an “electronic-engineering trick” that cannot be applied at optical frequencies. Here, we demonstrate that the dispersion relation of a RF non-Foster capacitor is similar to that of an optical gain material described by a Lorentz model. This insight paves the way to realize non-Foster optical metamaterial structures. As the simplest example, we develop a broadband non-Foster optical epsilon-near-zero slab with a 1:10 bandwidth.

Rayleigh Waves in a Thermoelastic Half-Space Coated by a Maxwell–Cattaneo Thermoelastic Layer

This paper investigates the propagation of in-plane surface waves in a coated thermoelastic half-space. First, it investigates a special case where the surface layer is described by the Maxwell–Cattaneo thermoelastic approach, while the half-space is filled by a thermoelastic material described by the classical Fourier law for the heat flux. The contact between the layer and the half-space is assumed to be welded, i.e., the displacements and the temperature, as well as the stresses and the heat flux are continuous through the interface of the layer and the half-space. The boundary and continuity conditions of the problem are formulated and then the exact dispersion relation of the surface waves is established. An illustrative numerical simulation is presented for the case of an aluminum thermoelastic layer coating a thermoelastic copper half-space, highlighting important aspects regarding the propagation of Rayleigh waves in such structures. The exact effective boundary conditions at the interface are also established replacing the entire effect of the layer on the half-space. The general case of the problem is also investigated when both the surface layer and the half-space are described by the Maxwell–Cattaneo thermoelasticity theory. This study helps to further understand the propagation characteristics of elastic waves in layered structures with thermal effects described by the Maxwell–Cattaneo approach.

Holographic description of an anisotropic Dirac semimetal

Holographic quantum matter exploits the AdS/CFT correspondence to study systems in condensed matter physics. An example of these systems are strongly correlated semimetals, which feature a rich phase diagram structure. In this work, we present a holographic model for a Dirac semimetal in 2 + 1 dimensions that features a topological phase transition. Our construction relies on deforming a relativistic UV fixed point with some relevant operators that explicitly break rotations and some internal symmetries. The phase diagram for different values of the relevant coupling constants is obtained. The different phases are characterized by distinct dispersion relations for probe fermionic modes in the AdS geometry. We find semi-metallic phases characterized by the presence of Dirac cones and an insulating phase featuring a mass gap with a mild anisotropy. Remarkably, we find as well an anisotropic semi-Dirac phase characterized by a massless a fermionic excitation dispersing linearly in one direction while quadratically in the other.

A higher dimensional model of geophysical fluid with the complete Coriolis force and vortex structure

Here, we present a higher dimensional model from the vorticity equation, which describes the dynamic characteristics of large scale Rossby waves by utilizing the Gardner-Morikawa coordinate transformation and the perturbation method. To reveal the influence of physical parameters on the higher dimensional model, we first give the dispersion relation of the model and the N-soliton solutions by Hirota method. Subsequently, the lump solutions are derived by using the long wave limit method. It demonstrates that the horizontal component of the Coriolis force acts as a forcing force on the nonlinear Rossby waves, and affects the amplitude of the meridional structure. Moreover, under the background of secondary zonal basic flow, for different lump solutions, the flow field will appear dipole blocking or double vortex structure. It is also indicated that the horizontal Coriolis force only causes the vortex to move in the latitudinal direction.

Negative damping of terahertz plasmons in counter-streaming double-layer two-dimensional electron gases

Abstract The plasmon excitation in two-dimensional electron gases (2DEGs) is a significant way of achieving micro-nanoscale terahertz (THz) devices. Here, we establish a kinetic simulation model to study the THz plasmons amplification in a semiconductor double-quantum-well system with counter-streaming electron drift velocities. By comparing the simulation results with theoretical dispersion relations, we confirm two competing mechanisms of negative damping suitable for THz amplification: Cherenkov-type two-stream instability and a new non-Cherenkov mechanism called kinetic relaxation instability. The former is caused by the interlayer coupling of two slow plasmon modes and only exists when the drift velocities are much greater than the fermi velocities. The latter is a statistical effect caused by the momentum relaxation of electron-impurity scattering and predominates at lower drift velocities. We show that an approximate kinetic dispersion relation can accurately predict the wave growth rates of the two mechanisms. The results also indicate that the saturated plasmonic waves undergo strong nonlinearities such as wave distortion, frequency downshift, wave-packet formation, and spectrum broadening. The nonlinear evolution can be interpreted as the merging of bubble structures in the electron phase-space distribution. The present results not only reveal the potential mechanisms of the plasmonic instabilities in double-layer 2DEGs, but also provide a new guideline for the design of on-chip THz amplifiers.

Complex electromagnetism and coupled gravitational-electromagnetic waves in the interstellar medium

Gravito-electromagnetism is an approximation of general relativity that has significant analogies to electromagnetism. We show that the remained asymmetry in those two field equations and the equations of motion can be alleviated through appropriate scaling on the complex plane, thereby allowing gravity and electromagnetism to be combined into a single set of equations for analysis. This enables a more concise and intuitive interpretation of mixed-field interactions of the interstellar medium. The interstellar medium, composed of ionized gas, interacts with both gravitational and electromagnetic fields, and within this medium, gravitational and electromagnetic waves exist in a coupled form. We derive the dispersion relation of these coupled waves tied by the interstellar medium and discuss two branches of wave solutions. These two solutions correspond to the well-known pure gravitational and electromagnetic waves in the classical limit. Based on the characteristics of this coupled wave, we discuss the possible generation of gravitational waves in the interstellar medium and the abnormal behaviors in a medium composed of dark matter that may provide a new methodology for dark matter detection.

Exploring the dynamics of the heavy magnetized dusty plasma in laboratory experiments and solar wind interaction with lunar terminator: Theoretical predictions into the role of polarization force

This study is motivated by the lack of research that connects the dynamics of space dusty plasma (DP) with the existing experimental findings and the role of the magnetic field in the case of massive DP. For that purpose, we presented a theoretical interpretation of the dynamics of strongly (experimental) and weakly (space) magnetized DP, including the influence of the polarization force (PF). We used the multifluid model to describe the dynamics of dust particles while the hot plasma of electrons and ions is described by the Boltzmann distribution. We derived the dispersion relation to investigate the behavior of the compressive dust-acoustic waves (DAWs). To get a full picture of the mechanism of dust particles, we used the reductive perturbation technique to obtain the periodic solution for the Zakharov–Kuznetsov equation (ZK), which is coincidental with the observed wave profiles. In the case of the experimental application, we observed that the non-propagating instability starts at a small value of the polarization parameter (R), which is 0.02. Therefore, for values of R less than 0.02, the linear analysis revealed that increasing the value of the polarization parameter is not significant in distinguishing the growth rates. Moreover, we noted that both R and the applied magnetic field enhance the strength of the wave electric field. Interestingly, calculating the value of the electric field required to levitate the dust particles that are subject to a high magnetic field agrees with our theoretical findings. The current model has also been applied to DP observed in the lunar terminator. Our results reveal no role for the PF in the lunar terminator. The analysis conducted using the New Hampshire Dispersion Relation Solver (NHDS) confirms the dominance of electrostatic modes in response to the solar wind interaction with the lunar terminator. Moreover, at certain values of plasma parameters such as the temperature of solar wind electrons and ions and the density of dust particles and solar wind electrons, there is a cutoff in the fluid dispersion curve corresponding to certain values of the normalized wavenumber. Such electrostatic profiles could contribute to the observed glow in the horizontal direction of the lunar terminator.

Re-assessing special aspects of Dirac fermions in presence of Lorentz-symmetry violation

This paper focuses on additional inspections concerning the fermionic sector of the Standard Model Extension (SME). In this context, our main effort in this contribution is to investigate effects of Lorentz-symmetry violation (LSV) on the Klein Paradox, the Zitterbewegung and its phenomenology in connection to Condensed Matter Physics, Atomic Physics, and Astrophysics. Finally, we discuss a particular realization of LSV in the Dirac equation, considering an asymmetry between space and time due to a scale factor present in the linear momentum of the fermion, but which does not touch its time derivative. We go further and extend the implications of this asymmetry in the situation the scale factor becomes space–time dependent to compute its influence on the kinematics of the Compton effect with the extended dispersion relation for the fermion that scatters the photon.

Trigger mechanism for a singing cavitating tip vortex

The discrete tone radiated from tip vortex cavitation (TVC), known as ‘vortex singing’, was recognized in 1989, but its triggering remains unclear for over thirty years. In this study, the desinent cavitation number and viscous correction are applied to describe the dynamics of cavitation bubbles and the dispersion relation of cavity interfacial waves. The wavenumber-frequency spectrum of the cavity radius from the experiment in CSSRC indicates that singing waves predominantly consist of the stationary double helical modes (kθ = 2- and -2+) and the breathing mode (kθ = 0-), rather than standing waves as assumed in previous literatures. Moreover, two trigger mechanisms, expressed by two triggering lines, are proposed: the twisted TVC, initially at rest, is driven into motion through the corrected natural frequency (fn) due to the step change of the far-field pressure. Subsequently, the frequency associated with the zero-group-velocity point (ῶzgv) at kθ = 0- is excited through ῶi, the frequency at the intersection of dispersion curves at kθ = 0- and -2+, or ῶj, the frequency at the intersection of dispersion curves at kθ = 0- and 2-, corresponding to two types of the vortex singing triggering. These solutions, without empirical parameters, are validated using singing conditions provided by CSSRC and G.T.H., respectively. Furthermore, the coherence and the cross-power spectral density spectrum indicates a large-scale breathing wave propagating along the singing cavity surface and travelling from downstream to hydrofoil tip, providing us a comprehensive understanding for the triggering of vortex singing.

Unveiling the Terahertz Nano-Fingerprint Spectrum of Single Artificial Metallic Resonator.

As artificially engineered subwavelength periodic structures, terahertz (THz) metasurface devices exhibit an equivalent dielectric constant and dispersion relation akin to those of natural materials with specific THz absorption peaks, describable using the Lorentz model. Traditional verification methods typically involve testing structural arrays using reflected and transmitted optical paths. However, directly detecting the dielectric constant of individual units has remained a significant challenge. In this study, we employed a THz time-domain spectrometer-based scattering-type scanning near-field optical microscope (THz-TDS s-SNOM) to investigate the near-field nanoscale spectrum and resonant mode distribution of a single-metal double-gap split-ring resonator (DSRR) and rectangular antenna. The findings reveal that they exhibit a dispersion relation similar to that of natural materials in specific polarization directions, indicating that units of THz metasurface can be analogous to those of molecular structures in materials. This microscopic analysis of the dispersion relation of artificial structures offers new insights into the working mechanisms of THz metasurfaces.

Propagation Characteristics of Electrostatic Surface Plasma Waves at the Spin‐Polarized Quantum Plasma–Vacuum Interface

ABSTRACTThis investigation explores the characteristics of electrostatic surface plasma waves within the framework of a spin‐polarized quantum plasma. Utilizing the spin‐polarized quantum hydrodynamic model and incorporating essential elements like Fermi pressure and Bohm potential, we derive the dispersion relation governing surface plasma waves at a plasma–vacuum interface. Through Fourier decomposition of the hydrodynamic model, we establish the dispersion relation that outlines the behavior of surface plasmons under conditions of small amplitude. Quantum effects, encompassing degenerate pressure, and Bohm potential are considered with specific attention given to the spin polarization effect, treating spin up, and spin down electrons as distinct species. The resulting dispersion relation demonstrates that, regardless of the degree of spin matching, Bohm potential significantly alters the phase speed in the limit of a large wave vector. Increasing spin mismatch in the quantum plasma leads to a decrease in the phase speed of the surface mode for a fixed value of the plasmonic coupling parameter . Our findings bear relevance to graphene‐based plasmonic systems, aligning with some of the observations reported in Gao et al. (2013) and Guo et al. (2019).

Entropy and Negative Specific Heat of Doped Graphene: Topological Phase Transitions and Nernst's Theorem Revisited.

This study explores the thermodynamic properties of doped graphene using an adapted electronic spectrum. We employed the one-electron tight-binding model to describe the hexagonal lattice structure. The dispersion relation for graphene is expressed in terms of the hopping energies using a compositional parameter that characterizes the different dopant atoms in the lattice. The focus of the investigation is on the impact of the compositions, specifically the presence of dopant atoms, on the energy spectrum, entropy, temperature, and specific heat of graphene. The numerical and analytical results reveal distinct thermodynamic behaviors influenced by the dopant composition, including topological transitions, inflection points in entropy, and specific heat divergences. In addition, the use of Boltzmann entropy and the revision of Nernst's theorem for doped graphene are introduced as novel aspects.

Interaction-enhanced nesting in spin-fermion and Fermi-Hubbard models

The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, QN, connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from QN is given by χ−1∝|Δq|. Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a χ−1∝|Δq|2 dependence yields a robust finite-T scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the (t−t′) Hubbard model and found that at large U/t>5.5 before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by χ−1∝|Δq|2. Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state. Published by the American Physical Society 2024

Plasmon scattering at a junction in double-layer two-dimensional electron gas plasmonic waveguide

Abstract The scattering of plasmons at a junction within a double-layer two-dimensional electron gas plasmonic waveguide is studied via a full electromagnetic method. The dispersion relation is derived by utilizing the transfer matrix method and can be extended to the situation of an arbitrary number of layers. By numerically solving the dispersion equations, both the acoustic and optical plasmon modes are identified in this double layer system, and the unstable plasmon modes arising from plasmon coupling in different layers are discussed elaborately. Subsequently, the total fields are expanded with eigenmodes and matched at the interface to analyze the scattering characteristics at the junction. The results indicate that the total power of the plasmon mode is amplified when the electron fluid flows from a high concentration region to a low concentration region, and the amplification is more evident at a higher drift velocity. Additionally, we address the scattering of unstable plasmons caused by the two-stream instability and find that the transmitted plasmons are excited intensively at the incidence of the growing plasmon, leading to the plasmon amplification. The detailed examination of plasmon scattering at junction is the prerequisite for studying more complex structures of terahertz plasmonic devices and comprehending the corresponding amplification mechanism.

Broadband surface wave manipulation by periodic barriers in unsaturated soil.

Periodic wave barriers have been widely used to manipulate elastic waves propagating in saturated and single-phase soil due to their attenuation zone properties. However, it is difficult to promote application of periodic barriers in unsaturated soils due to their complex constitutive relationship. In this study, manipulation of surface waves by periodic in-filled trench barriers in unsaturated soil has been studied based on the periodic theory. The dispersion relations of a periodic structure for surface waves in unsaturated soil are determined. The attenuation mechanism of evanescent surface waves is revealed. Next, the effects of several key parameters of unsaturated soil on the attenuation zones of the periodic in-filled trench barriers are comprehensively discussed. It is found that in a particular range for material parameter, the surface waves are attenuated over the entire frequency range due to the viscosity of fluid. Finally, a periodic in-filled trench barrier is designed according to a field test of ground vibration induced by a train, and its performances in mitigating surface waves propagating in unsaturated and saturated soils are conducted and compared by conducting analysis in time domain. This investigation provides a new insight for manipulating surface waves by periodic barriers. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Harnessing surface plasmon polaritons from nanogroove plasmonic lenses to enhance the EM fields around plasmonic nanoantennas

In this paper, we present a device—consisting of a bowtie nanoantenna surrounded by either an asymmetric plasmonic nanogroove or a symmetric plasmonic nanogroove—that allows improved excitation of the bowtie nanoantenna via interaction between the bowtie nanoantenna and the surface plasmon polaritons (SPPs) generated from the nanogrooves. We study the effect of both a linear plasmonic nanogroove as well as a circular plasmonic nanogroove (i.e., a circular nanogroove plasmonic lens) on the EM fields around a bowtie nanoantenna placed at a certain distance from the nanogroove. We show that the electric field enhancement of a bowtie nanoantenna can be significantly improved by the interaction between the bowtie nanoantenna and the SPPs generated from the nanogrooves. We employed FDTD simulations to calculate quantities such as the electric field enhancements and power coupling into SPPs as well as a finite difference eigenmode solution to obtain dispersion relation of the nanogrooves. The geometrical parameters of the symmetric nanogroove and asymmetric nanogroove were optimized to couple maximum light into SPPs. We show that the bowtie nanoantenna surrounded by a single asymmetric nanogroove plasmonic lens produces a SERS electromagnetic enhancement factor (EMEF) of 1010—even when the gap between the arms of the bowtie nanoantenna is as large as 10 nm—which is three orders of magnitude higher than SERS EMEF of a stand-alone bowtie nanoantenna and one order of magnitude higher than the SERS EMEF of a bowtie nanoantenna surrounded by a single symmetric nanogroove plasmonic lens. In addition, the effect of the radius of nanogroove plasmonic lenses is studied. The calculation of collection efficiencies of Raman signal from the proposed nanostructures shows that ∼62% Raman signal can be collected from the bowtie nanoantenna surrounded by a symmetric nanogroove plasmonic lens or an asymmetric nanogroove plasmonic lens (PL) compared to 10% Raman signal collected from only a bowtie nanoantenna on a silica substrate.

Ion temperature gradient modes modulational stability with kappa-distribution

We investigated the modulational stability and instability of the ion temperature gradient (ITG) mode in electron-ion plasma. Ions are dynamic species, whereas electrons follow a Kappa distribution. We used the reduction perturbation approach to determine the linear dispersion relation for the fluid under consideration. The nonlinear Schrodinger equation describes nonlinear features such as nonlinear modulational stability or instability in the ITG mode. The product of dissipation and nonlinear coefficients, known as LM, contains both modulational stability and instability in the ion temperature gradient mode. Theoretical results are expanded numerically, showing the influence of various plasma parameters on modulational stability and instability, particularly the superthermality coefficient κ e . The current observations may be extended to space and laboratory plasma for modification.

Surface wave isolation by variable depth infilled trenches

Excessive environmental vibrations generated by urban traffic pose adverse effects on nearby structures and residents. These vibrations are predominantly carried by surface waves, which are localized within the surface layer of soil. The isolation of surface waves through the embedding of periodic wave barriers in soils between the source and the receiver has gained significant attention in recent years. In this paper, a novel approach is proposed for isolating surface waves induced by urban traffic through the use of variable depth infilled trenches. This innovative design not only achieves efficient surface wave isolation but also minimizes the consumption of structural materials. Based on the measured dominant frequency range of rail transit and the available soil parameters, variable depth infilled trenches are designed with suitable dimensions. The eigenvalue equation is solved using the finite element method to derive the dispersion relations and bandgap of identical regularly spaced trenches. To study the efficacy of the proposed structure, a finite element model of the soil-infilled trench system is developed using COMSOL. The mechanism underlying the isolation of surface wave is elucidated, and the effect of variable angle α on the isolation efficiency within 40–50 Hz η40−50Hz of surface waves is studied. The results of this study reveal that for variable angle α of 15°, the surface wave isolation efficiency within 40–50 Hz η40−50Hz is 90.9 % and 92.5 % for uniformly increasing depth infilled trenches and uniformly decreasing depth infilled trenches, respectively. Although the surface wave isolation efficiencies predicted for the variable depth infilled trench arrangements are only 93.8 % and 95.5 % of those predicted for the regularly spaced identical infilled trenches, the variable depth arrangements result in a remarkable 34 % reduction in material usage. These findings highlight the potential of the proposed variable depth infilled trenches as a cost-effective and efficient solution for surface wave isolation.

Current Loads on a Horizontal Floating Flexible Membrane in a 3D Channel

A 3D analytical model is formulated based on linearised small-amplitude wave theory to analyse the behaviour of a horizontal, flexible membrane subject to wave–current interaction. The membrane is connected to spring moorings for stability. Green’s function approach is used to obtain the dispersion relation and is utilised in the solution by applying the velocity decomposition method. On the other hand, a brief description of the experiment is presented. The accuracy level of the analytical results is checked by comparing the results of reflection and the transmission coefficients against experimental data sets. Several numerical results on the displacements of the membrane and the vertical forces are studied thoroughly to examine the impact of current loads, spring stiffness, membrane tension, modes of oscillations, and water depths. It is observed that as the value of the current speed (CS) rises, the deflection also increases, whereas it declines in deeper water. On the other hand, the spring stiffness has minimal effect on the vibrations of the flexible membrane. When vertical force is considered, higher oscillation modes increase the vertical loads on the membrane, and for a mid-range wavelength, the vertical wave loads on the membrane grow as the CS increases. Further, the influence of the phase and group velocities are presented. The influences of CS and comparisons between them in terms of water depth are presented and analysed. This analysis will inform the design of membrane-based wave energy converters and breakwaters by clarifying how current loads affect the dynamics of floating membranes at various water depths.