Non-dispersive Modes Research Articles

Localized Phonon Transport Study of GaN/SiO2 Core/shell Nanowires under Thermal-Stress Coupling.

In order to comprehensively explore the intricate mechanisms of thermo-mechanical interactions, this study employs the molecular dynamics method to investigate the influence of heat flux density, shell thickness and length, as well as stress on the radial interface phonon transport in GaN/SiO2 core/shell nanowire. Additionally, the surface eigenmode decomposition method is employed to analyze the interface phonon dispersion curves. The investigation reveals that with increasing heat flux density, internal thermal stresses intensify, leading to a complex distribution of thermal stresses within the system. Under the influence of thermal stress, the nonlinear acoustic properties interact with phonon scattering, resulting in the pronounced localization of interface phonons. Compressive stress causes an upshift in low-frequency phonons, while tensile stress induces a downward shift in the high-frequency optical branches at the interface. The localized phonon vibrations at the SiO2/GaN interface under nonuniform stress are identified as the primary cause for the abundant presence of nondispersive phonon modes at the radial interface. By elucidating the subtle interplay between lattice vibrations and stress fields, this study offers a novel and profound understanding of thermo-mechanical coupling effects, thereby providing innovative theoretical foundations for the design and performance management of thermoelectric devices.

Non-dispersive Fano resonances in hybrid plasmonic-distributed Bragg reflector structures

Abstract Fano resonance due to coupling of plasmon mode and Bragg modes is revealed without strong angular dependence based on Au nanoparticle on distributed Bragg reflectors (Au NPoDBRs). This Fano interference involves three-modes-coupling: the nanoparticle’s plasmon resonance, dispersive Bragg modes, and non-dispersive Bragg modes. It can be interpreted as a consequence of two processes: plasmonic coupling between dispersive Bragg modes and broad plasmon mode, and the strong coupling between narrowed plasmonic mode and non-dispersive Bragg mode. This Fano interference shows little dependence on the incidence angle but high tunability with the top-layer thickness, which is exploitable for novel nanophotonic devices with dispersion engineering.

Slow-light effect in symmetry-reduced non-defect photonic crystals

In this study, a two-dimensional low-symmetric photonic crystal (PC) configuration with elliptical geometry is presented and its slow-light (SL) effect is investigated. Reducing the symmetry in the PC unit cell provides slow modes at the higher transverse electric bands. The calculated group index and the corresponding normalized bandwidth equal to {ng, BW}={63.56, 0.0065}. That corresponds to a value of figure of merit (FOM)=0.4344 defined by the product of the average group index and the normalized bandwidth, FOM=〈ng〉BW, which is comparable to the values available in literature. Tracing the whole edges of the Brillouin zone, strongly excited SL modes are observed only along Γ-X but not along Γ-X’ or Γ-M. That condition allows for the design of low-symmetric PC waveguides with finite thicknesses at the expense of lowering group index value. The SL effect is still obtained for the proposed low-symmetric PCs having finite thicknesses, which is numerically proved via finite-difference time-domain methods. It is important to note that non-dispersive SL Bloch modes exist through the non-zero k-vector components of Brillouin zone. Hence, such a defect-free (without either point- or line- defect) SL PC design may have a great potential for the use of compact photonic devices such as in optical switching and biochemical sensing applications.

Selection of Higher Order Lamb Wave Mode for Assessment of Pipeline Corrosion

Hidden corrosion defects can lead to dangerous accidents such as leakage of toxic materials causing extreme environmental and economic consequences. Ultrasonic guided waves showed good potential detecting distributed corrosion in pipeline networks at sufficiently large distances. To simplify signal analysis, traditional guided wave methods use low frequencies where only fundamental modes exist; hence, the small, localized defects are usually barely detectable. Novel techniques frequently use higher order guided wave modes that propagate around the circumference of the pipe and are more sensitive to the localized changes in the wall thickness. However current high order mode guided wave technology commonly uses either non-dispersive shear modes or higher order mode cluster (HOMC) waves that are mostly sensitive to surface defects. As the number of application cases of high order modes to corrosion detection is still limited, a huge potential is available to seek for other modes that can offer improved resolution and sensitivity to localized corrosion type defects. The objective of this work was to investigate higher order modes for corrosion detection and to determine the most promising ones in sense of excitability, leakage losses, propagation distance, and potential simplicity in the analysis. The selection of the proper mode is discussed with the support of phase and group velocity dispersion curves, out of plane and in plane distributions over the thickness and on surface of the sample, and leakage losses due to water load. The analysis led to selection of symmetric S3 mode, while the excitation of it was demonstrated through finite element simulations, taking into account the size of phased array aperture and apodization law and considering two-sided mode generation. Finally, theoretical estimations were confirmed with experiments, demonstrating the ability to generate and receive selected mode. It was shown that S3 mode is a good candidate for corrosion screening around the circumference of the pipe, as it has sufficient propagation distance, can be generated with conventional ultrasonic (UT) phased arrays, has sufficiently high group velocity to be distinguished from co-existing modes, and is sensitive to the loss of wall thickness.

Thermal effects on collective modes in disordered s -wave superconductors

We investigate the effect of thermal fluctuations on the two-particle spectral function for a disordered $s$-wave superconductor in two dimensions, focusing on the evolution of the collective amplitude and phase modes. We find three main effects of thermal fluctuations: (1) the phase mode is softened with increasing temperature, reflecting the decrease of superfluid stiffness; (2) remarkably, the nondispersive collective amplitude modes at finite energy near $\mathbf{q}=[0,0]$ and $\mathbf{q}=[\ensuremath{\pi},\ensuremath{\pi}]$ survive even in the presence of thermal fluctuations in the disordered superconductor; and (3) the scattering of the thermally excited fermionic quasiparticles leads to low-energy incoherent spectral weight that forms a strongly momentum-dependent background halo around the phase and amplitude collective modes and broadens them. Due to momentum and energy conservation constraints, this halo has a boundary which disperses linearly at low momenta and shows a strong dip near the $[\ensuremath{\pi},\ensuremath{\pi}]$ point in the Brillouin zone.

Non-Abelian Thouless pumping in a photonic lattice

Non-Abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate nondispersive modes and show that, when the lattice parameters are slowly modulated, the propagation of the photons bears the fingerprints of the underlying non-Abelian gauge structure. The nondispersive character of the bands enables a high degree of control on photon propagation. Our work paves the way to the generation and detection of non-Abelian gauge fields in photonic and optical lattices.

Controlled imprisonment of wave packet and flat bands in a fractal geometry

The explicit construction of non-dispersive flat band modes and the tunability of has been reported for a hierarchical 3-simplex fractal geometry. A single band tight-binding Hamiltonian defined for the deterministic self-similar non-translationally invariant network can give rise to a countably infinity of such self localized eigenstates for which the wave packet gets trapped inside a characteristic cluster of atomic sites. An analytical prescription to detect those dispersionless states has been demonstrated elaborately. The states are localized over clusters of increasing sizes, displaying the existence of a multitude of localization areas. The onset of localization can, in principle, be ‘delayed’ in space by an appropriate choice of the energy of the electron. The tunability of those states leads to the controlled decay of wave function envelope. The impact of perturbation on the bound states has also been discussed. The analogous wave guide model has also been discussed.

Removing instabilities in the hierarchical equations of motion: Exact and approximate projection approaches.

The hierarchical equations of motion (HEOM) provide a numerically exact approach for computing the reduced dynamics of a quantum system linearly coupled to a bath. We have found that HEOM contains temperature-dependent instabilities that grow exponentially in time. In the case of continuous-bath models, these instabilities may be delayed to later times by increasing the hierarchy dimension; however, for systems coupled to discrete, nondispersive modes, increasing the hierarchy dimension does little to alleviate the problem. We show that these instabilities can also be removed completely at a potentially much lower cost via projection onto the space of stable eigenmodes; furthermore, we find that for discrete-bath models at zero temperature, the remaining projected dynamics computed with few hierarchy levels are essentially identical to the exact dynamics that otherwise might require an intractably large number of hierarchy levels for convergence. Recognizing that computation of the eigenmodes might be prohibitive, e.g., for large or strongly coupled models, we present a Prony filtration algorithm that may be useful as an alternative for accomplishing this projection when diagonalization is too costly. We present results demonstrating the efficacy of HEOM projected via diagonalization and Prony filtration. We also discuss issues associated with the non-normality of HEOM.

Flux modulated flat band engineering in square-kagomé ladder network

The origin of non-dispersive flat band modes for a quasi-one dimensional square-kagomé ladder network is explored analytically by virtue of the real space renormalization group (RSRG) technique. A section of the eigenstates is non-diffusive i.e., localized within a cluster of sub-lattice sites partly by the destructive type of quantum interference and partly by the physical boundary created by the site with zero wave function amplitude. By making the amplitude vanish at the selective sites it becomes possible to confine the incoming excitation within the trapping cell leading to the formation of compact localized states. The effective mass of the particle becomes infinitely large corresponding to those self-localized modes and hence the mobility of the wave train becomes vanishingly small. This quenched kinetic energy leads to a momentum independent contribution to a dispersion curve. The present analysis is corroborated by numerical calculation of spectral landscape and the corresponding dispersion profile. The application of uniform magnetic flux may lead to a comprehensive engineering of the position as well as the curvature of the band. Also, one-to-one mapping between electronic case and photonic case within the tight-binding framework helps us to study the photonic localization in an analogous single mode wave guide system. The concept of slow light eventually introduces the possibility of spatial compression of light energy.

Nature of localized phonon modes of tilt grain boundaries in graphene

In this work, it is reported an investigation of the phonon spectrum of polycrystalline models of graphene, using ab-initio calculations of the phonon dispersion and phonon modes of these systems. Four different models of polycrystalline graphene are considered: one where the lattices of adjacent grains have a relative translation between them, with a translational grain boundary connecting the grains, and three models where the lattices of adjacent grains are tilted relative to each other, with tilt grain boundaries connecting adjacent grains. It is found that tilt grain boundaries introduce high-frequency non-dispersive phonon modes in the phonon spectrum of polycrystalline graphene, and that these modes are strongly localized in the core of the grain boundaries, while no such high-frequency localized modes are found in the case of the translational boundary system. By computing phonon group velocities and specific heats of each system in our study, and by analyzing in detail the patterns of atomic displacements of these localized modes, a consistent interpretation is provided for the experimentally observed trends of the lattice thermal conductivity of polycrystalline graphene samples, as a function of the grain-boundary tilt angle.

On the origin of vibrational properties of calcium manganate based thermoelectric compounds

Vibrational properties of CaO(CaMnO3)m (m = 1, 2, 3, and ∞) thermoelectric (TE) oxides for high-temperature energy conversion applications are studied both experimentally and computationally. Density functional theory (DFT) calculations reveal strong scattering events involving dispersive acoustic phonons and non-dispersive optical modes in the frequency range of 3–5 THz. We demonstrate that the low frequency parts of the phonon spectra are strongly dominated by Ca-sublattice oscillations for all compounds of the CaO(CaMnO3)m (m = 1,2,3, ∞) series, which predicts enhanced phonon scattering upon Ca-sublattice site substitution defects. Accordingly, laser flash analysis (LFA) indicates considerable decrease of thermal conductivity (κ) due to La- substitution for Ca, whereas Nb- substitution for Mn-sites does not affect κ noticeably. It is found that thermal conductivity of CaO(CaMnO3)m compounds is governed by phonon scattering on CaO/CaMnO3 boundaries for m = 1, 2, and 3 and by Umklapp processes for m = ∞. Thermal transport in this system is strongly dominated by acoustic phonon modes possessing much larger Grüneisen parameters (γ) compared to optical ones.

Collective spin waves in arrays of permalloy nanowires with single-side periodically modulated width

We have experimentally and numerically investigated the dispersion of collective spin waves propagating through arrays of longitudinally magnetized nanowires (NWs) with a periodically modulated width. Two nanowire arrays with single-side modulation and different periodicities of modulation were studied and compared to the nanowires with a homogeneous width. The spin-wave dispersion, measured up to the third Brillouin zone of the reciprocal space, revealed the presence of two dispersive modes for the width-modulated NWs, whose amplitude of the magnonic band depends on the modulation periodicity, and a set of nondispersive modes at higher frequency. These findings are different from those observed in homogeneous width NWs where only the lowest mode exhibits sizeable dispersion. The measured spin-wave dispersion has been satisfactorily reproduced by means of the dynamical matrix method. The results presented in this work are important in view of the possible realization of tunable frequency magnonic devices.

Formation of sediment patterns in channel flow: minimal unstable systems and their temporal evolution

The phenomenon of sediment pattern formation in a channel flow is numerically investigated by performing simulations which resolve all the relevant length and time scales of the problem. The numerical approach employed and the flow configuration considered is identical to our previous study (Kidanemariam & UhlmannJ. Fluid Mech., vol. 750, 2014, R2), the only difference being the length of the computational domain. The latter was systematically varied in order to investigate its influence on the initiation and evolution aspects. By successively reducing the streamwise length, the minimum box dimension which accommodates an unstable sediment bed is revealed, thus determining the lower threshold of the unstable modes. For the considered parameter point, the cutoff length for pattern formation lies in the range 75–100 times the particle diameter (3–4 times the clear fluid height). We also simulate the flow in a very long streamwise box with a size of 48 times the clear fluid height (featuring well over one million particles), accommodating approximately 11 initial ripple units with a wavelength in the range of 100–110 particle diameters. The evolution of the amplitude of the patterns exhibits two regimes of growth: an initial exponential regime, with a growth rate independent of the chosen domain size, and a subsequent nonlinear regime which is strongly constrained by the domain length. In the small domain cases, after the initial exponential regime, the ripples evolve steadily, maintaining their shape and migration velocity, at a mean wavelength equal to the length of the domain. The asymmetric ripple shape is characterized by a spectrum which exhibits a power-law decay over the first few dominant non-dispersive modes propagating at the mean dune migration velocity. The rate of particle transport and the mean interface shear stress exhibited an increase with increasing ripple dimensions. Nevertheless, the relationship between the two was observed to be approximately described by the empirical power-law formula for sediment transport by Wong & Parker (J. Hydraul. Engng, vol. 132, 2006, pp. 1159–1168).

Engineering slow light and mode crossover in a fractal-kagome waveguide network

We present an analytically exact scheme of unraveling a multitude of flat, dispersionless photonic bands in a kagome waveguide strip where each elementary plaquette hosts a deterministic fractal geometry of arbitrary size. The number of non-dispersive eigenmodes grows as higher and higher order fractal geometry is embedded in the kagome motif. Such eigenmodes are found to be localized with finite support in the kagome strip and exhibit a hierarchy of localization areas. The onset of localization can, in principle, be delayed in space by an appropriate choice of frequency of the incident wave. The length scale at which the onset of localization for each mode occurs, can be tuned at will as prescribed here using a real space renormalization method. Conventional methods of extracting the non-dispersive modes in such geometrically frustrated lattices fail as a non-translationally invariant fractal decorates the unit cells in the transverse direction. The scheme presented here circumvents this difficulty, and thus may inspire the experimentalists to design similar fractal incorporated kagome or Lieb class of lattices to observe a multifractal distribution of flat photonic bands.

Raman spectroscopy of nondispersive intermediate frequency modes and their overtones in carbon nanotubes

We performed resonance Raman spectroscopy on HiPCO-produced single-walled carbon nanotubes in the spectral region of 846 and , using laser excitation energies between and . We observe a characteristic peak around and its overtones around 1692. Especially the latter was controversially discussed in the past and has been assigned to a double-resonant Raman process involving two oTO phonons. We demonstrate that both peaks slightly depend on the excitation laser energy by means of their shape, intensity, and peak position. Following the model proposed by Dobardžić et al., we relate both peaks to oTO -point phonons. As we analyze both, the first-order band and its overtone simultaneously, we are able to provide a unified explanation of these low-intensity Raman bands in carbon nanotubes. Raman spectrum of an HiPCO-produced buckypaper carbon nanotube sample at 2.33 eV laser energy. Both insets show a magnification of the oTO-related first- and second-order Raman bands, which we discuss in this article.

Spatial sensitivity functions for rapid numerical simulation of borehole sonic measurements in vertical wells

Borehole sonic measurements are routinely used to measure dynamic elastic properties of rock formations surrounding a wellbore. However, shoulder-bed effects, mud-filtrate invasion, and near-wellbore damage often influence the measurements and bias the interpretations. Inversion-based methods can reduce the influence of complex geometric conditions in the estimation of formation properties from sonic logs, but they require fast-forward modeling algorithms. We have developed new spatial sensitivity functions for rapid modeling of borehole sonic measurements, which were equivalent to the Green’s functions of borehole modal wave measurements. An adaptive finite-element (FE) method was used to calculate 1D axial (vertical) and 2D (axial-radial) sensitivity functions, which combined the dependence of sonic logs on the wave mode, frequency, formation properties, and logging-instrument geometry. Semianalytical formulations were also used to calculate the sensitivity functions, which involved modeling the wave propagation through an effective layered medium. The 1D axial sensitivity functions were also extended to quantify propagation properties of nondispersive modes in a borehole. Calculated semianalytical sensitivity coefficients were efficient for rapid simulation of modal frequency dispersion in the presence of a logging tool. Simulated sonic logging measurements across synthetic thinly bedded and invaded formations were compared with numerical simulations obtained with the finite-element method. Our results confirmed the efficiency, reliability, and accuracy of the approximate sonic simulation method. The maximum relative error of the rapid simulation method was consistently less than 4%, with only 2% of the central processing unit time and 2% of the memory usage compared with FE simulations.

Investigation of Scholte and Stoneley Waves in Multi-layered Systems

Interface waves are elastic waves that can propagate at the interface between two solids (Stoneley wave) or between a solid and a liquid (Scholte wave). In this study, properties of generalized Stoneley and Scholte waves are investigated analytically in a multi-layer system with both liquid-solid and solid-solid interfaces. The interface waves are modeled using partial waves in layers with finite thicknesses to trace quasi- and non-dispersive modes. Dispersion curves of the propagating modes and corresponding particle displacement profiles are obtained using numerical solution techniques with the global matrix method. Limiting conditions of quasi-modes are evaluated analytically for thickness and material selection. Furthermore, interference of the two interface waves and plate modes are investigated for small frequency-thickness products in the multi-interface system using dispersion curves and particle displacement profiles. Preliminary sensitivity analyses are also performed for development of multi sensing physical quantities such as temperature, viscosity and density simultaneously using interface waves.

Analysis of cross-correlation and wavelet de-noising for the reduction of the effects of dispersion in long-range ultrasonic testing

Long-range ultrasonic testing (LRUT) involves transmitting a guided ultrasonic wave through a structure and receiving echoes caused by changes in acoustic impedance. There are several modes of propagation of the ultrasonic signal (wave modes) that depend on the structure and the test frequency. Some of these wave modes are dispersive: their velocity changes with frequency. Generally, LRUT procedures are designed such that non-dispersive wave modes are transmitted. However, interaction of the ultrasonic wave with the structure leads to mode conversions, some of which will be to dispersive wave modes. The effect of these dispersive wave modes is to reduce the signal-to-noise ratio (SNR) of the received signal. Cross-correlation and wavelet de-noising are considered here for reduction of the effect of dispersive wavemodes. An LRUT signal with dispersive and non-dispersive wave modes has been simulated and used to test these techniques. Experimental data have also been collected and used to evaluate further these techniques. Cross-correlation of the transmitted and received signals did not lead to significant improvement in SNR in either the simulated or experimental signals and led to a decrease in SNR in many of the simulated signals. Wavelet de-noising appeared to work well on some of the simulated LR UT signals, where the amplitude of the non-dispersive mode was greater than that of the dispersive mode. With the experimental data this technique improved the SNR slightly, but led to distortion of the signal. The results show that neither technique appears to be able to effectively discriminate between dispersive and non-dispersive wave modes.

Short wavelength electromagnetic propagation in magnetized quantum plasmas

The quantum electrodynamical (QED) short wavelength correction on plasma wave propagation for a nonrelativistic quantum plasma is investigated. A general dispersion relation for a thermal multicomponent quantum plasma is derived. It is found that the classical dispersion relation for any wave mode can be modified to include quantum and short wavelength QED effects by simple substitutions of the thermal velocity and the plasma frequency. Furthermore, the dispersion relation has been modified to include QED effects of strong magnetic fields. It is found that strong magnetic fields together with the short wavelength QED correction will induce dispersion both in vacuum and in otherwise nondispersive plasma modes. Applications to laboratory and astrophysical systems are discussed.

Discrete modes of a ferromagnetic stripe dipolarly coupled to a ferromagnetic film: aBrillouin light scattering study

Spin wave excitations in a magnetic structure consisting of a series of long permalloystripes of a rectangular cross section magnetized along the stripe length and situated abovea continuous permalloy film are studied both experimentally and theoretically. Stripes andcontinuous film are coupled by dipole–dipole interaction across 10 nm thick Cuspacers. Experimental measurements made using the Brillouin light scatteringtechnique (with the light wavevector oriented along the stripe width) provideevidence for one dispersive spin wave mode associated with the continuous film andseveral discrete non-dispersive modes resonating within the finite width of thestripes.To interpret the experimental spectra, an analytic theory based on the spin wave formalismfor finite-width magnetic stripes has been developed, achieving a good qualitative andpartly quantitative description of the experimentally observed spin wave spectrum of thesystem. In particular, it is explained why the presence of a continuous magnetic film nearthe magnetic stripe leads to a substantial decrease of the frequencies of the discrete dipolarspin wave modes localized within the stripes. A more quantitative description of themeasured frequencies and of the spatial profiles of the spin wave eigenmodes has beenobtained by numerical calculations performed using a finite element method.