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We treat whistler mode radiation from a dipole antenna in a cold magnetized plasma based on the Fresnel zone construction theory. Radiated waves from the antenna with different propagation directions interfere in space. Regions of enhanced waves are formed when the interference is predominantly constructive at the observing point. The coherently enhanced wave propagates at the group velocity. If the antenna is perpendicular to the background magnetic field, the regions of strong waves form two back-to-back Fresnel zones that are parabolic-shaped cones along the background magnetic field from the antenna. The power within each cone drops with distance at a rate of 1/r much more slowly than the 1/r2 thinning of a spherical wave as in vacuum. The total radiation can be approximately derived by the total energy flux integrated over the Fresnel zone. The derived radiation resistance is much greater than that in vacuum. It is proportional to frequency as 1/f2 and proportional to the antenna length as d2. To radiate more power a longer antenna is preferred, a result that is opposite to some previous theoretical studies.

This paper comprehensively investigated noise characteristics of superluminal propagation based on low-noise single-frequency Brillouin lasing oscillation with the aid of a population inversion dynamic grating. Thanks to high-degree polarization alignment between the Brillouin pump and the lased Stokes lightwaves in polarization maintaining fibers, efficient Brillouin lasing resonance with over 10-dB relative intensity noise suppression has been demonstrated to activate Brillouin loss-induced anomalous dispersion in the vicinity of pump signals, benefiting a noise-insensitive superluminal propagation along kilometer-long optical fibers with robust resistance to ambient disturbance. Consequently, sinusoidally modulated pump signals experienced the time advancement of 4634.0 ns at the group velocity of 10.63c. Results show that the variance of the fractional advancement with polarization maintaining fibers is 2.54 × 10−4 which is two orders of magnitude lower than that of conventional single mode fibers. Furthermore, the dependence of the group velocity on the modulation frequency was experimentally investigated, showing good agreement with the theoretical analysis.

The anomalous dispersion observed in wideband Fabry–Perot Antennas formed by multiple coupled cavities, is explained in terms of modal coupling between several leaky waves. In this way, the negative group velocity associated to the homogenized mode, can be explained. Moreover, the enhancement in the radiation pattern bandwidth can also be described from the contribution of these coupled leaky waves to the total interference pattern. Theoretical dispersion results are reported for one-dimensional and two-dimensional Fabry–Perot Antennas with N=2 and N=3 coupled cavities, operating in broadside and off-broadside scanned patterns. The theory is also corroborated with experimental results.

Magnon-mediated angular-momentum flow in antiferromagnets may become a design element for energy-efficient, low-dissipation and high-speed spintronic devices1,2. Owing to their low energy dissipation, antiferromagnetic magnons can propagate over micrometre distances3. However, direct observation of their high-speed propagation has been elusive due to the lack of sufficiently fast probes2. Here we measure the antiferromagnetic magnon propagation in the time domain at the nanoscale (≤50 nm) with optical-driven terahertz emission. In non-magnetic-Bi2Te3/antiferromagnetic-insulator-NiO/ferromagnetic-Co trilayers, we observe a magnon velocity of ~650 km s–1 in the NiO layer. This velocity far exceeds previous estimations of the maximum magnon group velocity of ~40 km s–1, which were based on the magnon dispersion measurements of NiO using inelastic neutron scattering4,5. Our theory suggests that for magnon propagation at the nanoscale, a finite damping makes the dispersion anomalous for small magnon wavenumbers and yields a superluminal-like magnon velocity. Given the generality of finite dissipation in materials, our results strengthen the prospects of ultrafast nanodevices using antiferromagnetic magnons. Magnon-mediated angular-momentum flow in antiferromagnets may become a design element for energy-efficient, low-dissipation and high-speed spintronic devices. Here, terahertz emission measurements in magnetic multilayers unveil a superluminal-like magnon velocity of ~650 km s–1 in the antiferromagnetic insulator NiO at nanoscale distances.

This study focuses on static component generation (SCG) and its measurement wherein a group velocity mismatch (GVM) exists between the primary guided wave and the generated static component (SC). The SCGs by primary S0, A0, and SH0 waves are investigated. It is confirmed that the SCs are S0 mode. The GVM causes the temporal waveforms of the SCs to tend to increase in width with propagation distance. A feasible method is proposed accordingly for measurement of SCG with GVM using only lead zirconic titanate based transducers, wherein the SCs generated by two counter-propagating primary waves are modulated and superposed on each other.

In contrast to topographic laser scanning, laser hydrography must take into account the presence of two media. A pulsed laser beam, which enters the water from the air at an oblique angle, is refracted at the air–water boundary in the direction of the plumb line. This change in the direction described by Snellius’ law is caused by a slower speed of the light wave in the water, i.e., the phase velocity. Light scattering caused by turbidity gives rise to further deviations from the straight path. Together, the slower speed and the turbidity-induced path extension cause a longer pulse round trip time in the water than in the air. For an accurate measurement, it is important to correct this propagation time extension. It is a common practice to assume the phase velocity as the velocity for the laser pulses in water. In a dispersive medium, however, the phase velocity is only an approximation of the velocity of a pulse. In media with chromatic dispersion, the pulses propagate with a different velocity, i.e., the group velocity. In water, using the group velocity instead of the phase velocity reduces the range dependent bias of the depth measurement at a laser wavelength of 532 nm by more than 1.5%. We present an easy to perform an experiment, which shows that the group velocity differs so much from the phase velocity that this difference should be taken into account. We further discuss the use of group velocity to explain the depth bias using examples from the literature.

We investigate the reflection of low-harmonic fast magnetosonic (MS) waves at the local two-ion cutoff frequency (fcutHe+). By comparing the wave signals of the two Van Allen Probes satellites, a distinct boundary where wave energies cannot penetrate inward are found in the time–frequency domain. The boundary is identified as the time series of local fcutHe+. For a certain frequency, there exists a spatial interface formed by fcutHe+, where the incident waves should be reflected. The waves with small incident angles are more likely to penetrate the thin layer where the group velocity reduces significantly and then slow down in a period of several to tens of seconds before the reflection process complete. The cutoff reflection scenario can explain the intense outward waves observed by probe A. These results of MS reflection at fcutHe+ may help to predict the global distribution of MS waves and promote the understanding of wave–particle dynamics in the radiation belt.

Analytical formulas are obtained for all components of the high-frequency field, Poynting vector $$\overrightarrow P $$ , and group velocity vector $$\overrightarrow U $$ of electromagnetic waves propagating in an arbitrary direction in an unbounded bi-gyrotropic medium described by the Hermitian permittivity and permeability tensors. It is proven that the corresponding components of vectors $$\overrightarrow P $$ and $$\overrightarrow U $$ are proportional to each other (therefore, these vectors are parallel) and the ratio between these components is the volume density of the wave energy. The change in the absolute value and orientation of vector $$\overrightarrow U $$ and orientation of vector $$\overrightarrow P $$ depending on the orientation of the wave vector for different types of electromagnetic waves propagating in a ferromagnetic medium (a particular case of a bi-gyrotropic medium) is calculated. It is found that vectors $$\overrightarrow U $$ and $$\overrightarrow P $$ are always identically oriented for waves of all types in a ferromagnetic medium.

The propagation of G-type wave in a viscoelastic stratum lying over a non homogeneous fibre reinforced elastic half space is examined with possible applications. The dispersion equation and maximum energy flow around the stratum are computed in a closed form applying the technique of infinite determinant and Laplace transform under appropriate boundary conditions. The dispersion equation agrees with the pre established results as verified by several authors. The consequences of viscosity, reinforcement and non homogeneity parameter on phase and group velocity have been accentuated through graphs.

Novel approximate methods of wave propagation analysis are developed for functionally graded cylinders with mass and elastic parameters described by continuously differentiable functions of radius. Two of these methods relate to embedding of boundary value problems into corresponding initial value problems and the third method demonstrates methodology of discretization of the physical parameters over cylinder’s cross-section. Frequency spectra diagrams of dilatational and shear waves are plotted for travelling and evanescent regimes. Diagrams of phase and group velocities are plotted for dilatational travelling waves.

International audience; In its original formulation by Forest & Sab (Math. Mech. Solids, 2017), stress gradient elastodynamics incorporate two inner-lengths to account for size effects in continuum theory. Here, an extended one-dimensional stress gradient model is developed by means of Lagrangian formalism, incorporating an additional inner-length and a fourth-order space derivative in the wave equation. Dispersive properties are characterised and hyperbolicity and stability are proven. Group velocity remains bounded in both original and extended models, proving causality is satisfied for both contrary to a usually-accepted postulate. By means of two-scale asymptotic homogeniza-tion, the high-order wave equation satisfied by the stress gradient model is shown to stand for an effective description of heterogeneous materials in the low-frequency range. An upscaling method is developed to identify the stress gradient material parameters and bulk forces on the parameters of elastic micro-structures. Application of the micro-macro procedure to periodic multi-laminates demonstrates the accuracy of the stress gradient continuum to account for the dispersive features of wave propagation. Frequency and time-domain simulations illustrate these properties.

Taking into account damping effects, the propagation-distance dependence of the amplitude of nonlinear guided waves arising from an internal resonance was investigated. In the analysis of Lamb-wave propagation, we introduced nonlinear quadratic effects derived from both geometric and material nonlinearities, referred to as classical nonlinearities, and damping effects by expressing the Lame constants as complex numbers. Assuming a small detuning from the phase matching condition with respect to wavenumber and frequency, and using the method of multiple scales and self-adjointness of the governing equations with boundary conditions, the amplitude equations describing the nonlinear coupling of the two wave modes are derived as solvability conditions. This derivation also provides both physical and mathematical insights into both the phase and group velocity matching conditions. Numerical results obtained from these amplitude equations show that because of the nonlinear coupling an internal resonance between the two modes can occur under the above matching conditions. Without detuning, one mode increases monotonically in amplitude while the other decreases monotonically. Nevertheless, their changes gradually decrease with propagation distance, and each amplitude converges to a finite value. However, with wavenumber and frequency detuning, both amplitudes increase and decrease cyclically with propagation distance, resulting in a weakening of this resonance. Furthermore, results with damping effects show an attenuation of both amplitudes with propagation distance, which limits the distance resonance waves can propagate.

The identification of particle velocity with the velocity of a wave group was a crucial assumption that resolved important inconsistencies in the theoretical developments of Louis de Broglie and Erwin Schrodinger. Interestingly, this was one of the few common aspects of their work. In this paper, we present a reconstruction of how group velocity became essential for both de Broglie and Schrodinger, as well as a comparison of important differences in their theories. Pedagogical lessons to be extracted from this episode are also outlined.

We consider an one-dimensional problem of propagation of a short light pulse in a medium with Lorentz contour of the spectral gain line. Simple approximate formulas for the spatial distribution of the field at any time are obtained. It is shown that not only normalization of the time dependence of the field at a fixed spatial point but also normalization of the spatial distribution of the field at a fixed time occur with increasing path length. It is also shown that the velocity of motion of the spatial maximum of the field is higher than the group velocity and, in any case, as distinct from the group velocity, cannot be smaller than the halved phase velocity of light in this material. Simple expressions for the spatial and temporal growth rates of the field increase in a gain medium are obtained.

The propagation of an ultrasonic gigahertz pulse in a low-temperature crystal containing paramagnetic ions with the inversed population of Zeeman sublevels of the resonance spin–phonon transition has been studied. An integrodifferential parabolic equation with a nonlinear autonomous source and irreversible losses has been obtained in the fast phase relaxation approximation for a local relative deformation of a pulse. The exact analytical solution of this equation in the form of a dissipative soliton with an asymmetric temporal profile has been obtained and analyzed in detail. The velocity of the soliton is close to the linear group velocity of ultrasound. It has shown that such a soliton can be formed only if irreversible losses caused by processes that are not related to spin–phonon transitions exist in addition to losses caused by the phase relaxation of spin–phonon transitions.

In this paper we investigate the influence of rotational viscosity on the plane shear-rotational wave propagation in the linear isotropic reduced Cosserat medium. In such a continuum body points possess independent rotational and translational degrees of freedom, but the material does not resist to the gradient of microrotation. Stress tensor is asymmetric, but the couple stress is zero. For the elastic reduced Cosserat medium a band gap is present, where no running waves exist, and the logarithmic decrement is infinitely large. It was shown before that introducing viscoelasticity we may qualitatively change the dispersion behaviour. This work investigates the case of rotational viscosity, related to the difference between micro- and macrorotation. We show that in this case running decaying waves appear in the band gap domain, and their logarithmic decrement becomes finite. The dispersion relation for the real part of the wave number has a decreasing part. This means that the group velocity of these waves is opposed to their phase velocity, the behaviour characterizing double negative acoustic metamaterials.

Head-on collisional phenomena of ion acoustic (IA) waves in electron–positron–ion magnetized plasmas are investigated through linear and nonlinear analyses. The plasma system is considered collisionless and comprising cold ions, kappa distributed cold electrons, and positrons. Dispersion relation is derived with the aid of the linear perturbation method. The two sided nonlinear Korteweg-de Vries (KdV) equations are derived employing extended Poincare-Lighthill-Kuo (ePLK) method. The effects of wave frequency on linear group velocity with species density ratio are studied. Further, the production of ion acoustic solitons in terms of ion gyrofrequency ( $${\omega }_{\mathrm{g}}$$ ), superthermality parameters for electrons ( $${\kappa }_{\mathrm{e}}$$ ), and positrons ( $${\kappa }_{\mathrm{p}}$$ ) is investigated. Additionally, the effects of obliqueness (angle between magnetic field and wave propagation vector) on nonlinearity coefficient and phase shifts with density ratios (positron to electron and ion to electron) are demonstrated.

This paper considers the question of superluminal (or negative) group velocities of signals in dispersive media, as well as negative group delay times of signals passing through linear filters. It is shown that information can be transmitted only with the help of jumps in the time dependence of a function or its derivatives and, therefore, the information propagation velocity in any (including dispersive, absorbing, or amplifying) medium exactly coincides with the speed of light in vacuum. As for the group velocity of a wave packet, it is only the propagation velocity of its infinitely differentiable envelope, by means of which the transmission of information, strictly speaking, is impossible. Therefore, in regions with anomalous dispersion, the group velocity can be superluminal or negative without violating the “light limitation” of the theory of relativity or the principle of causality. Examples of situations in which superluminal or negative group velocity occurs are given.

The phase and group velocities of propagation of the electric and magnetic fields along the axis of metal carbon nanotubes have been calculated. In the model used, the electron distribution in nanotubes is described by a cylindrical layer of an almost free electron gas disturbed by an external electric field and electron–electron interaction. For a transverse magnetic field (of the TM type) and transverse electric field (of the TE type), the dependences of the field frequency and phase and group velocities on the wavenumber kz have been determined. It has been found that the frequencies of all TE modes increase monotonically with increasing kz, the group velocities are positive, and the directions of propagation of the phase and group waves coincide. For TM-type modes at low kz values, the group velocity is negative and the directions of propagation of the phase wave and the group wave are opposite, which can be of practical importance for creating on their basis tools for controlling the transmission of signals and energy between nanoelectronic elements.

In this paper, the nonlinear ion acoustic rogue waves (IARWs) are investigated in an unmagnetized, collisionless plasma which consist of positive ions, superthermal electrons and positrons, respectively. A nonlinear Schrodinger equation (NLSE) of IAW packets has been obtained by using the reductive perturbation technique. Furthermore, the effects of superthermal electrons and positrons on the nonlinear dispersion relation, the group velocity and the modulational instability of nonlinear ion acoustic wave (IAW) packets have been studied in detail. At the same time, the characteristics of first- and second-order IARW also have been discussed. It seems that there is some significant influence of superthermal electrons and positrons on the nonlinear ion acoustic waves. Meanwhile, it is also found that the first- and second-order IARW consisting of Peregrine breathers can be excited by using the modulational instability in this system.

The propagation of dust-acoustic waves in a dusty plasma bounded in finite symmetrical cylindrical geometry has been theoretically investigated. By using the reductive perturbation method, we obtain a quasi-nonlinear Schrodinger equation. It is shown that there is a dark envelope soliton under certain conditions, while its amplitude will decrease with the time. The dependence of both the dispersion relation and group velocity of envelope solitary waves on the radius of cylinder has been given. Moreover, we define the duration time of dark envelope solitons and give the theoretical ones. It is found that the duration time increases as the radius of cylinder increases, while it decreases as the viscosity coefficient of dusty plasmas increases.

An individual harmonic wave (i.e., having a single frequency and wavelength over all time and space) traveling in a loss-free medium has a single constant speed, which is equal to the magnitude of the phase velocity of the wave. However, when a set of different harmonic waves are traveling in the same direction, they interfere to form wave packets. In general, the peak of a wave packet travels at a speed equal to the magnitude of the group velocity that can be vastly different than the phase speeds of the component harmonic waves, even if the entire set of harmonic waves only differ among themselves slightly in frequency and wavelength. It is difficult for students to understand the origin of this difference from verbal descriptions and static graphs of wave functions at successive instants in times, such as are typically presented in textbooks. However, considerable insight is possible using the free online software Desmos.

This paper presents a frequency domain spectral finite element model (SFEM) for studying wave propagation in laminated composite shell panels. The SFEM formulation is derived using two different theories: (i) the first order shear deformation theory (FSDT) that takes shear deformation into consideration, and (ii) the classical shell theory (CST) that neglects shear deformation. The spectral approach here is based on the use of fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT). The spectral element uses exact shape functions and a frequency dependent exact dynamic stiffness matrix is obtained relating the nodal displacements to the nodal forces of an element. The formulation is validated by comparing the present results for wavenumber dispersion and natural frequencies with the published results. The present SFEM is then used to perform wavenumber dispersion, phase and group velocities, and wave propagation analyses of laminated composite shell panels. The numerical studies show that the wavenumbers obtained from the SFEM based on the CST are significantly different from those of the FSDT at high frequencies. The CST results for the group velocity and wave propagation response to tone burst excitation show significant deviation from the FSDT results for out-of-plane A0 flexural mode even at relatively low frequencies. The orthotropy ratio and lamination arrangements in a composite shell panel have significant effect on the group velocity as well as the flexural mode wave propagation response.

To understand the characteristics of ocean internal waves better, we study the dispersion relation of extended-Korteweg-de Vries (EKdV) equation with quadratic and cubic nonlinear terms in a two-layer fluid by using the Poincare-Lighthill-Kuo (PLK) method which is one of the perturbation methods. Starting from the partial differential equation, the PLK method can be used to solve the dispersion relation of the equation. In this paper, we use PLK method to solve the equation and derive the dispersion relation of EKdV equation which is related to wave number and amplitude. Based on the dispersion relation obtained in this paper, the expressions of group velocity and phase velocity of the equation are obtained. Under the actual hydrological data, the influence of hydrological parameters on the dispersion relation for descending internal wave is discussed. It is hope that the obtained results will be helpful to the study of energy transfer and other internal wave parameters in the future.

The Wave-Particle Duality is a basic property of microscopic particles. As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments. Different from electromagnetic wave, the matter wave’s propagation is not only fast but also adjustable. According to the special relativity theory, the group velocity with which the overall envelope shape of the wave, namely the related particle’s propagation and information convey speed is changeable with its energy and related wavelength, among which only the energy exceeds over the minimum value, the propagation can be starting and the velocity is not allowed to surpass the maximum value i.e. the light speed in vacuum. Take electron as an example, if the free electron beam gains energy higher than around 8.187×10ˉᴵ⁴J and the related wavelength is shorter than around 5.316×10ˉ³nm, the matter wave with information can start to propagate.

The variations in the wave energy and the amplitude along the energy dispersion paths of the barotropic Rossby waves in zonally symmetric basic flow are studied by solving the wave energy equation, which expresses that the wave energy variability is determined by the divergence of the group velocity and the energy budget from the basic flow. The results suggest that both the wave energy and the amplitude of a leading wave increase significantly in the propagating region that is located south of the jet axis and enclosed by a southern critical line and a northern turning latitude. The leading wave gains the barotropic energy from the basic flow by eddy activities. The amplitude continuously climbs up a peak at the turning latitude due to increasing wave energy and enlarging horizontal scale (shrinking total wavenumber). Both the wave energy and the amplitude eventually decrease when the trailing wave continuously approaches southward to the critical line. The trailing wave decays and its energy is continuously absorbed by the basic flow. Furthermore, both the wave energy and the amplitude oscillate with a limited range in the propagating region that is located near the jet axis and enclosed by two turning latitudes. Both the leading and trailing waves neither develop nor decay significantly. The jet works as a waveguide to allow the waves to propagate a long distance.

During the process of Bessel beam generation in free space, spatiotemporal optical wave-packets with tunable group velocities and accelerations can be created by deforming pulse-fronts of injected pulsed beams. So far, only one determined motion form (superluminal or luminal or subluminal for the case of group velocity; and accelerating or uniform-motion or decelerating for the case of acceleration) could be achieved in a single propagation path. Here we show that deformed pulse-fronts with well-designed axisymmetric distributions (unlike conical and spherical pulse-fronts used in previous studies) allow us to obtain nearly-programmable group velocities with several different motion forms in a single propagation path. Our simulation shows that this unusual optical wave-packet can propagate at alternating superluminal and subluminal group velocities along a straight-line trajectory with corresponding instantaneous accelerations that vary periodically between positive (acceleration) and negative (deceleration) values, almost encompassing all motion forms of the group velocity in a single propagation path. Such unusual optical wave-packets with nearly-programmable group velocities may offer new opportunities for optical and physical applications. Unprecedented control of optical beams has allowed demonstration of superluminal or subluminal beams by controlling the phase of the wave-packet. Here, nearly-programmable control of a beam’s group velocity results in alternating acceleration and deceleration regimes in a single propagation path.

We present a method to compute differential coefficients of the first and second orders, for propagation constants of nondegenerate and degenerate modes, propagating in an optical fiber to calculate dispersion characteristics of group velocities (GV) and group-velocity dispersions (GVD). This method automatically differentiates explicit forms of eigenvalues extracted from determinants of a generalized eigenvalue problem. This problem is converted from a nonlinear eigenvalue problem derived from the Trefftz method (e.g., transfer matrix and multipole methods) by the Sakurai–Sugiura method. We compute the differential coefficients of the second order of degenerate modes without computing eigenvectors and their first order differential coefficients in the generalized eigenvalue problems. Therefore, in parametric optimization, we can compute the differential coefficients of all propagating modes without remodeling the waveguide cross-section, as analyzing the whole cross-section avoids the symmetric conditions derived from the numerical model. Computed results with the proposed method for step-index and holey fibers validate the method and its effectiveness. In particular, our results show that our method computes the GV and GVD more accurately than computation using numerical differentiation.

International audience; In the current work, we study the role of chirality and non-centrosymmetry on the nonlinear wave propagation characteristics of periodic architectured media. The considered nonlinearities arise from the higher-order inner element kinematics of the periodic media and are therefore directly related to its structural pattern. Regarding centrosymmetric designs, the frequency corrections obtained -in the context of the Lindstedt-Poincare method- suggest that chiral architectures are more sensitive to inner kinematic nonlinearities than well-known, achiral lattice designs. In particular, for hexachiral lattice designs, non-negligible frequency corrections are obtained, not only for the primal eigenmode, but also for higher-order modes, extensively modifying the linear band diagram structure. To the contrary, for achiral, triangular and square lattice designs, inner kinematic nonlinearities mainly influence the primal, lowest eigenmode, with the higher-order modes to remain practically unaffected. Non-centrosymmetric inner designs modify the linear and nonlinear wave propagation material attributes both for chiral and achiral lattice patterns. However, the frequency ranges affected are strongly lattice dependent, with hexachiral and triangular lattices to be primarily influenced in their high frequency range, contrary to square lattices, which are mainly affected in their low frequency region.

We prove theoretically, that the evolution of optical solitons can be dramatically influenced in the course of nonlinear interaction with much smaller group velocity matched pulses. Even weak pump pulses can be used to control the solitons, e.g., to compensate their degradation caused by Raman-scattering.

The phase and group velocity surfaces are essential for wave propagation in anisotropic media. These surfaces have certain features that, especially, for shear waves result in complications for modelling and inversion of recorded wavefields. To analyse wave propagation in an anisotropic model, it is important to identify these features in both the phase and group domains. We propose few characteristics for this analysis: the energy flux angle, decomposed in the polar and azimuth angle correction angles and enhancement factor, which is able to characterize both singularity points and triplication zones. The very simple equation that controls the triplications is derived in the phase domain. The proposed characteristics are illustrated for elastic and acoustic anisotropic models of different symmetry classes.