Positive Group Velocity Research Articles

Enhanced damping and bandwidth in roton-like dispersion of a beyond nearest neighbor periodic chain

This paper investigates the intriguing roton-like phenomenon occurring in systems with non-local interactions, wherein a single dispersion curve exhibits positive and negative group velocities. Previous research has predominantly concentrated on investigating the roton dispersion in undamped metamaterials through steady-state vibration and driven wave methodologies. However, exploring transient wave propagation in damped metamaterials, employing a free wave approach to study damping enhancement (metadamping), has received comparatively little attention. Addressing this research gap, the damping of the system is quantified as the rate of decay of transient vibrations. Results show a significant increase in damping and attenuation bandwidth, coinciding with the presence of the roton-like phenomenon. Unlike previous studies on metadamping, the proposed beyond nearest neighbor (BNN) chain simultaneously enhances both damping and reduction in acoustic bandwidth without sacrificing either property. Spatiotemporal domain simulation evidenced the existence of backward propagating wave packets due to a roton-like phenomenon in the specific frequency range.

Negative refraction of elastic waves in two-dimensional inertial amplification metamaterials

Tailoring wave behaviors governed by dispersion relations is a huge challenge in wave manipulation. Inertial amplification (IA) mechanism has been introduced in metamaterials and phononic crystals to obtain a low-frequency bandgap without adding mass to the system. In this work, we demonstrate unique wave propagation behaviors in two-dimensional inertial amplification metamaterials (2D IAMs). Through analytical derivations and numerical simulations, negative refraction and refractive steering of elastic waves are realized with the IA mechanism. The positive (negative) inertia of the system can be tuned by the IA angle, which determines whether the passband of the lattice is positive (negative) group velocity. By analyzing the dispersion relations of the 2D IAMs, we find that the IA angle 45° is the critical point where the group velocity flips. Negative refraction occurs at the interface between two lattices, which have opposite signs of group velocity. We can also achieve a wide range of angles for wave steering in the system. The normalized displacement fields of 2D IAMs are measured via harmonic excitation. We believe that the research results may inspire the design of ‘elastic lenses’ and multifunctional metamaterial devices.

Long‐time asymptotics and the radiation condition with time‐periodic boundary conditions for linear evolution equations on the half‐line and experiment

AbstractThe asymptotic Dirichlet‐to‐Neumann (D‐N) map is constructed for a class of scalar, constant coefficient, linear, third‐order, dispersive equations with asymptotically time/periodic Dirichlet boundary data and zero initial data on the half‐line, modeling a wavemaker acting upon an initially quiescent medium. The large time asymptotics for the special cases of the linear Korteweg‐de Vries and linear Benjamin–Bona–Mahony (BBM) equations are obtained. The D‐N map is proven to be unique if and only if the radiation condition that selects the unique wave number branch of the dispersion relation for a sinusoidal, time‐dependent boundary condition holds: (i) for frequencies in a finite interval, the wave number is real and corresponds to positive group velocity, and (ii) for frequencies outside the interval, the wave number is complex with positive imaginary part. For fixed spatial location , the corresponding asymptotic solution is (i) a traveling wave or (ii) a spatially decaying, time‐periodic wave. The linearized BBM asymptotics are found to quantitatively agree with viscous core‐annular fluid experiments.

Roton-like dispersion via polarisation change for elastic wave energy control in graded delay-lines

While roton dispersion relations had been restricted to correlated quantum systems at low temperature, recent works show the possibility of obtaining this unusual dispersion in acoustic and elastic metamaterials. Such phenomenon has been demonstrated in periodic structures by means of beyond-nearest-neighbour interactions, following the formulation firstly developed by Brillouin in the ′50s. In this paper, we demonstrate both numerically and experimentally that beyond-nearest-neighbour connections are not a necessary condition to obtain this unusual dispersion relation in elasticity. Leveraging the intrinsic complexity of elastic systems supporting different types of waves, we demonstrate that mode locking can be applied to obtain roton dispersion, without the need of elastic or magnetic interactions between non nearest neighbours. Moreover, the combination of roton dispersion and rainbow physics enables spatial separation of the energy fluxes with positive and negative group velocity.

Channeling of weak intramode beams in the field of a strong spatial soliton in a thin left-handed film on a right-handed substrate with Kerr effect

The trapping of weak guided modes by a strip waveguide induced by a strong spatial soliton in a planar waveguide based on a thin left-handed film with a right-handed linear cover and a substrate with the Kerr effect at a frequency near the zero group velocity of the TE mode is considered. It is shown that a bright (dark) soliton can induce a strip waveguide not only for a positive (negative) nonlinear optical coefficient of the substrate, but also for a negative (positive) one, which is due to the existence in the original planar waveguide of guided modes with both positive and negative group velocities.

Nonlocal elasticity of Klein‐Gordon type with internal length and time scales: Constitutive modelling and dispersion relations

AbstractIn this work, a nonlocal elasticity theory with nonlocality in space and time is presented by considering nonlocal constitutive equations with a dynamical scalar nonlocal kernel. Based on the proposed theory, we consider the isotropic nonlocal elasticity of Klein‐Gordon type including a characteristic internal time scale parameter in addition to the characteristic internal length scale parameter. The dispersion relations for homogeneous isotropic media in the framework of nonlocal elasticity of Klein‐Gordon type are analytically determined. The obtained results reveal the ability of the presented nonlocal elasticity model to predict, for the first time in the framework of nonlocal elasticity, in addition to the acoustic modes (low‐frequency modes), optic modes (high‐frequency modes) as well as frequency band‐gaps. The phase and group velocities for all four modes (acoustic and optic branches of longitudinal and transverse waves) are determined showing that all four modes exhibit normal dispersion with positive group velocity. The presented model allows for physically realistic dispersive wave propagation.

Light gap bullets in defocusing media with optical lattices

Searching for three-dimensional spatiotemporal solitons (also known as light/optical bullets) has recently attracted keen theoretical and experimental interests in nonlinear physics. Currently, optical lattices of diverse kinds have been introduced to the stabilization of light bullets, while the investigation for the light bullets of gap type – nonlinear localized modes within the finite gap of the underlying linear Bloch spectrum – is lacking. Herein, we address the formation and stabilization properties of such light gap bullets in periodic media with defocusing nonlinearity, theoretically and in numerical ways. The periodic media are based on two-dimensional periodic standing waves created in a coherent three-level atomic system which is driven to the regime of electromagnetically induced transparency, which in principle can also be replaced by photonic crystals in optics or optical lattices in ground-state ultracold atoms system. The temporal dispersion term is tuned to normal (positive) group velocity dispersion so that to launch the light gap bullets under self-repulsive nonlinearity; two types of such light gap bullets constructed as three-dimensional gap solitons and vortices with topological charge m=1 within the first finite gap are reported and found to be robustly stable in the existence domains. On account of the light bullets were previously limited to the semi-infinite gap of periodic media and continuous nonlinear physical systems, the light gap bullets reported here thus supplement the missing type of three-dimensional spatiotemporal localized modes in periodic media which exhibit finite band gaps.

Experimental Observation of Flat Bands in One-Dimensional Chiral Magnonic Crystals.

Spin waves represent the collective excitations of the magnetization field within a magnetic material, providing dispersion curves that can be manipulated by material design and external stimuli. Bulk and surface spin waves can be excited in a thin film with positive or negative group velocities and, by incorporating a symmetry-breaking mechanism, magnetochiral features arise. Here we study the band diagram of a chiral magnonic crystal consisting of a ferromagnetic film incorporating a periodic Dzyaloshinskii-Moriya coupling via interfacial contact with an array of heavy-metal nanowires. We provide experimental evidence for a strong asymmetry of the spin wave amplitude induced by the modulated interfacial Dzyaloshinskii-Moriya interaction, which generates a nonreciprocal propagation. Moreover, we observe the formation of flat spin-wave bands at low frequencies in the band diagram. Calculations reveal that depending on the perpendicular anisotropy, the spin-wave localization associated with the flat modes occurs in the zones with or without Dzyaloshinskii-Moriya interaction.

Negative group velocity characteristics of spoof surface plasmon polaritons

Although there have been many discussions on negative group velocity (NGV), disagreements over its counter-intuitive explanations are still on the way. In this paper, it is proposed that the negative group velocity is just a component of the actual wave group, which has to be accompanied by a positive group velocity (PGV) component. A composite wave with the NGV component propagates forward in the form of a tumbling vortex as an attenuated or evanescent wave. Negative group velocity exists only in the anomalous dispersion band with resonance absorption. This wave group model is confirmed by the NGV characteristics of spoof surface plasmon polaritons (SSPPs) of spiral-shaped periodic units. In this case, the PGV and NGV waves are formed by the resonance coupling of periodic cells, and the composite SSPP modes have both resonance absorption attenuation and vortex cancellation attenuation.

Wave resonances in the presence of current and the frequency and time-domain interconnection

The current work investigates the relationship between frequency and time domain problems associated with flexural gravity wave motion with oblique incidence and current. Different types of wave resonances such as buckling resonance, primary and secondary blocking resonance, Bragg resonance and interaction among them are discussed. Three propagating wave modes are observed between the primary and secondary blocking points, two of which are associated with positive group velocities and the third one is related to negative group velocities. Again, the Bragg resonance is analyzed for wave scattering problems. The complex porosity parameter is found to have a significant effect on the buckling and blocking resonance but does not affect Bragg resonance. The discontinuity of Bragg reflection is observed at primary and secondary blocking points and the peak values of Bragg reflection increase in the blocking zone. Again, we establish the interconnection between the frequency and time domain by deriving the time-domain solution from the frequency-domain solution and vice versa. The derivation of time-domain solutions using the dispersion relation and method of stationary phase is an intriguing finding. Wave energy and wave packets move faster in co-propagating waves than in counter-propagating waves and shallow water than in finite water depth. To validate the results, time-domain simulation and spectral methods are used.

A revisit of Rayleigh capillary jet breakup at low Ohnesorge number

The average Rayleigh capillary breakup length of a cylindrical Newtonian viscous liquid jet moving with homogeneous velocity must be determined by the selection of normal modes with time-independent amplitude and wavelength. Invariant modes (IMs) with both positive and negative group and phase velocities exist in ample ranges of the parameter domain (Weber and Ohnesorge), which explains (i) the self-sustained average breakup length (long-term resonance) and (ii) the governing role on breakup of both spatial growth rate and wave number of the dominant positive group velocity IM. Published experimental results at low Ohnesorge numbers confirm our proposal.

Negative Refraction in Mechanical Rotator Lattices

This paper presents numerical and experimental investigations of negative refraction at the interface between two mechanical rotator lattices, adding to the recent body of anomalous wave behavior reported for such simple lattices. Each lattice implements easily reconfigured interrotator coupling which determines whether the lattice's passband is acoustic (with positive group velocity) or optic (with negative group velocity). Since the group velocities have opposite signs over the entirety of both lattices' Brillouin zones, the negative refraction at their interface is inherently broadband. The numerical study constructs a large lattice structure for full-wave simulation and quantitatively analyzes the linear and nonlinear negative refraction. The experimental study documents robust negative refraction in a smaller-scale fabricated system and serves as validation for the numerical findings. We observe frequency-dependent transmission in both simulations and experiments. A linear analysis captures the observed phenomenon at low amplitude. At larger amplitudes, numerical simulations are used to document amplitude-dependent transmission. This phenomenon is explained by a nonlinear dispersion shift and transitional evanescent waves analyzed using a perturbation method. A sensitivity test demonstrates the robustness of negative refraction in the proposed rotator lattice structure.

Soliton Beams of Modes with Positive and Negative Group Velocities in a Thin Left-Handed Film on a Right-Handed Kerr Substrate

Soliton Beams of Modes with Positive and Negative Group Velocities in a Thin Left-Handed Film on a Right-Handed Kerr Substrate

Compact, repetition rate locked all-PM fiber femtosecond laser system based on low noise figure-9 Er:fiber laser

We demonstrate a compact femtosecond fiber laser system based on all polarization-maintaining (PM) fiber and fiber components integrated structure. The figure-9 oscillator which incorporated a nonlinear amplifying loop mirror in the cavity features a 103.4-MHz high repetition rate with up to 93.1 dB signal-to-noise ratio of the radio frequency spectrum, 0.0056% [1 Hz, 1 MHz] integrated root-mean-square amplitude noise at the fundamental repetition rate and 63.7-fs timing jitter [100 Hz, 1 MHz]. Meanwhile, the fundamental repetition frequency was also locked to a stable radio frequency reference by using a self-designed frequency actuator and a relative frequency stability of 2.1 × 10−12 at 1-s gate time was obtained. Moreover, benefitting from the large positive group-velocity dispersion and negative third-order dispersion at 1.5-μm wavelength band, we also achieved 48.2 fs compressed pulse duration as well as an amplified average power of 199 mW via one-stage all-PM fiber amplifier and compressor. At last, as a performance proof, by directly splicing 38-cm long PM highly nonlinear fiber to the pulse compressor, a broadband coherent supercontinuum spanning from 950 nm to 2150 nm was generated. Our all-PM fiber laser system is suitable for the further buildup of a low noise PM fiber optical frequency comb.

Low‐Loss Anisotropic Image Polaritons in van der Waals Crystal α‐MoO3

AbstractOrthorhombic molybdenum trioxide (α‐MoO3), a newly discovered polaritonic van der Waals crystal, is attracting significant attention due to its strongly anisotropic mid‐infrared phonon‐polaritons. At the same time, coupling of polariton with its mirror image in an adjacent metal gives rise to a significantly more confined image mode. Here, monocrystalline gold flakes—an atomically flat low‐loss substrate for mid‐infrared image polaritons—are employed to measure the full complex‐valued propagation constant of the hyperbolic image phonon‐polaritons in α‐MoO3 by near‐field probing. The anisotropic dispersion is mapped and the damping of the polaritons propagating at different angles to the crystallographic directions of α‐MoO3 is analyzed. These experiments demonstrate the strongly confined image phonon‐polaritons in α‐MoO3 exhibiting intrinsic limiting lifetime of 4.2 ps and a propagation length of 4.5 times the polariton wavelength, owing to the negligible substrate‐mediated loss. Furthermore, it is shown that the image modes with positive group velocity have simultaneously larger momentum and lifetime compared to their counterparts on a dielectric substrate, while the image modes with negative group velocity possess a smaller momentum. These results spotlight the hyperbolic image phonon‐polaritons as a superior platform for unconventional light manipulation at the nanoscale.

Scattering of long flexural gravity wave due to structural heterogeneity in the framework of wave blocking

Scattering of flexural gravity waves due to an abrupt change in structural heterogeneity is studied within the framework of blocking dynamics in time-space under shallow water approximations. As a special case, wave scattering due to a crack in the ice sheet is obtained. In the presence of compressive force, primary and secondary wave blocking occur at two different time-periods where group velocities vanish. Moreover, for each time-period within the primary and secondary blocking points, three propagating wave modes exist of which two are related with positive group velocities and the other one corresponds to negative group velocity. Subsequently, the energy relation of the scattering problem is derived in the case of multiple propagating wave modes using the conservation of energy flux. Out of the two propagating wave modes having positive group velocities, the energy transfer rate associated with the highest wavenumber is contributing significantly to the energy relation in the vicinity of the primary blocking point, whilst the other mode behaves in a similar manner near the secondary blocking point. Moreover, between the primary and secondary blocking points the incident wave mode changes to account for law of conservation of energy flux. Further, the study reveals that the energy transfer rate and the transmission coefficient are inversely proportional to each other. In case of wave scattering due to heterogeneity in ice sheet, the reflection and transmission coefficients pattern can have more than two removable discontinuities at the blocking points, whilst in the case of wave scattering due to a crack in the ice sheet, only two removable discontinuities appear at the primary and secondary blocking points. However, a jump discontinuity occurs at the point where incident wave mode conversion takes place in both the cases of wave scattering due to heterogeneity/crack in the ice sheet. Besides, irregular behaviour in plate deflection is observed due to the superposition of multiple propagating wave modes for a certain time-period within the blocking limits.

Multifrequency Bessel beams with adjustable group velocity and longitudinal acceleration in free space

The group velocity of an optical beam in free space is usually considered to be equal to the speed of light in vacuum. However, it has been recently realized that, by structuring the beam’s angular and temporal spectra, one can achieve well pronounced and controlled subluminal and superluminal propagation. In this work, we consider multifrequency Bessel beams that are known to propagate without divergence and show a variety of possibilities to adjust the group velocity of the beam by means of designed angular dispersion. We present several examples of multifrequency Bessel beams with negative and arbitrary positive group velocities, as well as longitudinally accelerating beams and beams with periodically oscillating local group velocities. The results of these studies can be of interest to scientists working in the fields of optical beam engineering, light amplitude and intensity interferometry, ultrafast optics, and optical tweezers.

Bragg scattering of long flexural gravity waves by an array of submerged trenches and the analysis of blocking dynamics

Bragg scattering of long flexural gravity waves due to an array of submerged trenches is studied under the shallow water approximation and small amplitude structural response in the presence of lateral compressive force. The group velocity vanishes at two different points in the frequency space for specific values of the compressive force, which are referred to as primary and secondary blocking points. Between these two blocking points, three propagating modes exist for each frequency, of which two are associated with the positive group velocity and one with the negative group velocity. Of the three propagating wave modes, the contribution to the energy relation by the lowest wavenumber is predominant near the secondary blocking frequency. In contrast, the higher wavenumber is dominant in the proximity of the primary blocking frequency. The study reveals the occurrence of Bragg scattering of flexural gravity waves in the presence of compressive force for more than two submerged trenches, which is analogous to that of surface gravity waves. However, within the blocking limits of the compressive force, the superposition of multiple propagating wave modes and the change in the incident wave mode contribute to certain irregularities and an increase in wave amplitude in the Bragg reflection pattern. The response amplitude of the structure and the pulse rate increase with an increase in the number of trenches.

Modulation instability of two TE modes in a thin left-handed film on a nonlinear right-handed substrate

The intramode wave beams in a thin left-handed film on a Kerr substrate are considered at a frequency near zero mode group velocity. Four coupled (1 + 1)-dimensional nonlinear Schrödinger equations, describing the interaction of forward and backward propagating beams with positive and negative group velocities, are derived. It is shown that self- and cross-phase modulation for four simultaneously propagating modes is possible only at strictly matched perturbations of their propagation constants, which is due to the contribution of spatial parametric mixing. The modulation instability of only two waveguide modes is analysed for different versions of their propagation. The specific features of modulation instability, related to the propagation of modes with negative group velocities, are investigated.

Role of intense laser-excited dressed states via electromagnetically induced transparency on the Fresnel-Fizeau photon drag through an asymmetric double quantum dot molecule (GaAs/AlGaAs) in the Λ-type configuration

Hereby, we first report theoretical demonstration on the role of intense laser-excited dressed states on the superluminal-assisted propagation, optical properties, and lateral and rotary photon drag, via electromagnetically induced transparency (EIT). For this, we employed a scheme of an asymmetric double quantum dot molecule GaAs/AlGaAs in the Λ − type configuration. In particular, using the compact density-matrix formulism, we present a detailed analytical solution for the required eigenvalues of the system in view of the dressed states. The dressed-states played a vital role on the formation of EIT and hence the modification of dispersion and absorption spectra of the system via quantum interference. The calculated theoretical results on the optical properties such as absorption and dispersion spectrum, group index, group velocity , group delay, phase delay and photon drag are further elaborated with the aid of numerical simulation. Switching ON the control field, the OFF-field single ON-resonance absorption peak split into an OFF-resonance absorption doublet accompanied by an ON-resonance absorption-less dip in the form of EIT window. Interestingly, the absorption doublet split further into an absorption peak and a gain singlet well below and just above the resonance, at a small control field detuning. Further increase in the control-field detuning resulted in a near-resonance gain singlet. Alongside, by tuning various spectral parameters, we observed an interesting switching from luminal to subluminal and superluminal propagation. The optimal calculated values of positive and negative group velocity are 6 × 10 11 m/s and − 2.5 × 10 11 m/s, respectively. The predicted lateral and rotary photon drag are of order ± 6 × 10 − 8 rad. • Role of dressed sates in view of EIT coherence on the light propagation, optical properties and photon drag. • The nature of dressed states influence largely the optical properties such as group index, group velocity, group delay, and photon drag. • The optimal values of positive and negative group velocity are 6 × 10 11 m/s and − 2.5 × 10 11 m/s, respectively. • The calculated lateral and rotary photon drag are of order ± 6 × 10 − 8 rad.