Group Velocity Of Mode Research Articles

Study on monitoring broken rails of heavy haul railway based on ultrasonic guided wave.

Real-time monitoring of broken rails in heavy haul railways is crucial for ensuring the safe operation of railway lines. U78CrV steel is a common material used for heavy haul line rails in China. In this study, the semi-analytical finite element (SAFE) method is employed to calculate the dispersion curves and modal shapes of ultrasonic guided waves in U78CrV heavy steel rails. Guided wave modes that are suitable for detecting rail cracks across the entire cross-section are selected based on the total energy of each mode and the vibration energy in the rail head, web, and foot. The excitation method for the chosen mode is determined by analyzing the energy distribution of the mode shape on the rail surface. The ultrasonic guided wave (UGW) signal in the rail is analyzed using ANSYS three-dimensional finite element simulation. The group velocity of the primary mode in the guided wave signal is obtained through continuous wavelet transform to confirm the existence of the selected mode. It is validated that the selected mode can be excited by examining the similarity between the vibration shapes of a specific rail section and all modal vibration shapes obtained through SAFE. Through simulation and field verification, the guided wave mode selected and excited in this study demonstrates good sensitivity to cracks at the rail head, web, and foot, and it can propagate over distances exceeding 1 km in the rail. By detecting the reflected signal of the selected mode or the degree of attenuation of the transmitted wave, long-distance monitoring of broken rails in heavy-haul railway tracks can be achieved.

Ultra-high Q resonances based on zero group-velocity modes accompanied by bound states in the continuum in 2D photonic crystal slabs

Optical resonators made of 2D photonic crystal (PhC) slabs provide efficient ways to manipulate light at the nanoscale through small group-velocity modes with low radiation losses. The resonant modes in periodic photonic lattices are predominantly limited by nonleaky guided modes at the boundary of the Brillouin zone below the light cone. Here, we propose a mechanism for ultra-high Q resonators based on the bound states in the continuum (BICs) above the light cone that have zero-group velocity (ZGV) at an arbitrary Bloch wavevector. By means of the mode expansion method, the construction and evolution of avoided crossings and Friedrich-Wintgen BICs are theoretically investigated at the same time. By tuning geometric parameters of the PhC slab, the coalescence of eigenfrequencies for a pair of BIC and ZGV modes is achieved, indicating that the waveguide modes are confined longitudinally by small group-velocity propagation and transversely by BICs. Using this mechanism, we engineer ultra-high Q nanoscale resonators that can significantly suppress the radiative losses, despite the operating frequencies above the light cone and the momenta at the generic k point. Our work suggests that the designed devices possess potential applications in low-threshold lasers and enhanced nonlinear effects.

Thermal stress estimation of a constrained metallic plate using symmetric and antisymmetric Lamb wave group velocities

This paper presents a technique for estimating thermal-induced stress in constrained metallic plates using the group velocity of Lamb waves, the accuracy of which is crucial for assessing the structural integrity and serviceability of metallic structures. However, without the ability to gauge the current stress levels, obtaining such measurements is technically challenging. To overcome this, we propose a thermal stress estimation technique that uses changes in the group velocities of the fundamental symmetric (S0) and antisymmetric (A0) Lamb wave modes caused by thermal and stress variations. First, this study introduces a theoretical-based zero-crossing algorithm to measure the group velocities of S0 and A0 Lamb wave modes. Next, leveraging the acoustoelastic coefficients corresponding to the S0 and A0 modes, which are determined before the plate’s installation, this study generates the lines depicting the changes in group velocity induced by temperature variations (CT) for both the S0 and A0 modes. These CT lines are derived from the lines illustrating changes in group velocity due to thermal stress variations (CTS), which are obtained after plate installation. Ultimately, the generated CT lines can be used to estimate thermal stress throughout the entirety of the plate’s operational life span by isolating the distinct stress variation effects from the CTS lines. The numerical validation results show favorable accuracy in thermal stress estimation in a constrained plate subjected to temperature variation using both S0 and A0 Lamb wave modes, with average errors of 0.63 % and 0.91 %, respectively.

Determination of Young’s Modulus of PET Sheets from Lamb Wave Velocity Measurement

BackgroundThe elastic modulus of polyethylene terephthalate (PET) sheets is typically measured through destructive tests that require specific sample preparation and time-consuming testing procedures.ObjectiveTo improve the efficiency of measuring the elastic modulus of PET sheets, research on a non-destructive measurement approach using guided Lamb waves was conducted.MethodsIn this approach, the group velocity of the zero-order symmetric Lamb wave mode (S0 mode) at a single frequency is first measured from PET sheets. The semi-analytical finite element method (SAFEM) is used as the forward model to calculate the corresponding numerical group velocity. Particle swarm optimisation (PSO) is used to update the elastic modulus in the SAFEM model until the numerical group velocity from the model matches the experimental results.ResultsThe results show that measuring the group velocity data at a single frequency is sufficient for elastic modulus measurement while the material thickness can be assumed as a constant, which improves the efficiency of the measurement. The identified modulus differs from the tensile modulus of the material due to the frequency dependence of the elastic modulus. However, this discrepancy could be eliminated by using a linear regression model.ConclusionsThe method mentioned above can achieve non-destructive and efficient measurement of the elastic modulus of PET sheets, which can potentially be applied for in-line quality inspection in PET bottle production processes.

Intermodal effective phase matching for second harmonic generation of ultrashort pulses in high index contrast optical fibers

Second harmonic generation (SHG) in glass optical fibers calls for creating a second order susceptibility in the fiber glass and for achieving phase matching between the pump and the second harmonic signal. The latter is very challenging when using ultrashort pulses, given that the group velocities of the pump and the second harmonic should also be matched. We have shown in previous work that it is possible to achieve simultaneous modal phase matching (MPM) and group velocity matching (GVM) when the pump and the second harmonic are propagating in the LP01 and LP02 modes, respectively, in high GeO2-content double-clad optical fibers. However, simultaneous MPM and GVM can only be obtained in optical fibers with dedicated designs and within very tight geometrical tolerances. In this paper, we show that instead of considering the matching of phase and group velocities separately, we can consider a more general or “effective” phase matching approach, in which we consider all the dispersion terms up to the second order in the expressions of the propagation constants of the pump and second harmonic signals. This allows introducing the pulse duration as a controllable parameter that helps to enforce the said effective phase matching in fibers with designs that deviate by as much as 10% from the target, while providing for temporal walk-off lengths in excess of several centimeters. The impact of this finding goes beyond SHG only and can be applied to other ultrashort laser pulse-based nonlinear optical processes in fibers and waveguides.

Evidence of zero group velocity at the lowest dispersion branch through local interactions

Zero group velocity (ZGV) modes can be utilized in many applications in both optics and acoustics. There exist numerous realizations of metamaterials with ZGVs at higher dispersion branches. However, to engineer the lowest dispersion branch to retain ZGVs, non-local metamaterials with couplings beyond the nearest neighbor are usually at play (i.e., roton-like dispersion). To date, there exists no realization of roton-like dispersion for the lowest branch without non-local couplings. Non-locality, while rich in dynamics, can render designs rather complex. Here, we provide the first experimental evidence of a ZGV point for the lowest dispersion branch within the first Brillouin zone with local interactions. We utilize nonlinear magnetic lattices as a platform to sculpt our dispersion. Our findings might enable the realization of exotic metamaterials with simple designs.

Robust enhanced acoustic sensing via gradient phononic crystals

In this letter, a gradient phononic crystal (PC) structure is proposed for robust enhanced acoustic sensing. At first, the topologically protected edge states are introduced by breaking the space-inversion symmetry of the PC structure. Then, the topological edge mode dispersion curve and group velocity are demonstrated to be regulated by varying the structure parameters gradually and the edge states can be slowed down to zero group velocity and trapped at different positions. Consequently, topological acoustic rainbow trapping is formed. Furthermore, the robustness and enhancement properties are verified both numerically and experimentally. All the results indicate that the gradient PC structure is able to realize robust enhanced acoustic sensing. This work opens a new vista to improve the robustness of the PC-based enhanced acoustic sensing.

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.

Effect of lattice distortion in high-entropy RE2Si2O7 and RE2SiO5 (RE=Ho, Er, Y, Yb, and Sc) on their thermal conductivity: Experimental and molecular dynamic simulation study

High-entropy materials are considered to be born with lattice distortion, which is still lack of comprehensive investigation in rare earth silicates to date. In this paper, we confirmed the existence of lattice distortions in high-entropy rare-earth silicates via experiments and molecular dynamic simulations. The effects of the lattice distortion on the thermophysical properties are elucidated. Simulation results indicate the lattice distortion is present in both cation and anion sublattice, leading to the compressing and stretching of atomic bond as well as fluctuation of atomic bond strength. Accordingly, lattice distortion in the Si and O sublattice is also verified by the Raman spectra. Furthermore, the thermal conductivity of high-entropy rare earth silicates remarkably reduces and exhibits glass-like behavior, which is confirmed by experiments in cooperation with molecular dynamic simulations. Simulation also reveals that the lifetimes and group velocities of vibrational modes are significantly reduced by lattice distortion, which result in the reduction of overall thermal conductivity of high-entropy rare-earth silicates.

Time spreading of a target echo from a short pulse in a waveguide

The normal mode approach has proven very useful for calculating reverberation in a shallow water waveguide. Generally the calculation is done as a function of range r, then the time dependence t is obtained via t = 2r/c, where c is some average sound speed. This assumes that all the multipath returns from a particular scattering point arrive at the same time. A better time dependence can be obtained by using mode group velocities [D. Ellis, J. Acoust. Soc. Am. 97, 2804–2814 (1995)]. For reverberation from a uniform bottom this only has a small effect compared to the simple approach. However, for a compact scattering feature or target, the time spreading for a short pulse can be quite significant. Analytical results for an isospeed waveguide have been previously obtained using an energy flux approach. Here, a model using modal group velocities is used to calculate the time dependence of an echo from a target or compact reverberation feature. The mode approach extends to a general sound speed profile. One can convolve the impulse response with the amplitude envelope of the transmitted pulse to obtain the echo time decay. [Work supported by Mount Allison University, and US Office of Naval Research.]

Joint geoacoustic inversion based on Pearson correlation coefficient constraints.

This Letter proposes a joint geoacoustic inversion method for modal group velocity dispersion and amplitudes of waveform by incorporating a Pearson correlation constraint. Numerical simulations show that this joint inversion leads to improved geoacoustic inversion performance with smaller uncertainties compared to separate inversion methods when applied to data from a single receiver. Additionally, the effective use of the Wasserstein metric from optimal transport theory is explored and compared to the more-common L2 norm misfit measure. The Letter also presents a qualitative representation of joint inversion convergence obtained through multiple independent runs of genetic algorithms. The algorithm is applied to simulated data.

Shear wave crustal velocity structure in the Garhwal-Kumaon Himalaya based on noise cross-correlation of Rayleigh wave

The tectonics of the Garwal-Kumaon Himalaya is characterized by thrusts, tectonic windows, and klippen. We investigate crustal shear wave velocity variations using ambient noise cross-correlation tomography. The studied region encompasses the Kali River valley in the east to Satluj valley in the west, with the adjoining Indo-Gangetic Plain in the south covering the northern part of the Delhi-Haridwar ridge. The fundamental mode group velocities of Rayleigh waves are extracted from cross-correlation data of 33 broadband seismological stations from a regional seismic network. A total of 374 dispersion curves with a period range of 4–29 s show a group velocity variation between ∼2.3 and ∼ 3.4 km/s. The shear wave velocity structure of the uppermost lithosphere down to ∼50 km obtained by non-linear inversion of the Rayleigh wave dispersion data provides new insight into the geometry of the crust. A large variation in Vs in the range of ∼2.8 to ∼4.7 km/s corresponds to a variety of changes in the tectonic deformation, structure, and crustal thickness of the Himalayan wedge. Thick low-velocity sedimentary formations are identified beneath the Indo-Gangetic Plain and the frontal Himalaya. Anomalous low Vs zones are also observed in the mid-crust beneath the higher Himalaya and southern Tibet, indicating partial melting or the presence of aqueous fluid zones. The high-velocity anomalies may be correlated with duplex structures beneath the Lesser Himalaya and with lithospheric flexure.

One-dimensional regional shear velocity structure from joint inversion of fundamental mode group velocity dispersion measurements of Love and Rayleigh waves: application to the Uttarakhand Himalaya

One-dimensional regional shear velocity structure from joint inversion of fundamental mode group velocity dispersion measurements of Love and Rayleigh waves: application to the Uttarakhand Himalaya

Density functional theory insights of phonons modes behaviours in AlScN for surface acoustic wave applications

In this work, we investigate the phonons modes behaviors of scandium-doped aluminum nitride (Sc-AlN) using first-principles density functional theory (DFT). We analyze the phononic dispersion, phonon density of states, group velocity, and Raman spectra of ScAlN for various scandium concentrations and compare them with undoped AlN. Our results show that Sc doping is significantly affect the phononic properties of AlN, including the formation of defect states within the phononic band gap and changes in the group velocities of phonon modes. Our analysis reveals that the introduction of Sc dopants causes a notable narrowing of the phononic band gap in AlN. Additionally, we observe a zero group velocity in the band gap, indicating the suppression of phononic transmission through the material. Moreover, Sc doping also affects the Raman spectrum of AlN, by inducing new vibrational modes. The known E2(high) peak in the Raman spectrum of AlN shifts to lower frequencies upon Sc doping, and new peaks appear due to the interactions of scandium and the AlN lattice. Our findings highlight the importance of understanding the effects of dopants on the phononic properties of AlScN and have implications for the design and optimization of AlScN-based devices for acoustic wave applications

Defect identification in variable thickness waveguides using SH0 guided wave

Guided waves, especially Lamb waves, propagating in plate-like structures with constant thicknesses have been investigated intensively in the past decades in the context of structural health monitoring (SHM) and non-destructive testing (NDT). However, structures with variable thicknesses are also very common in practice, such as ship hulls whose thickness varies for satisfying various load conditions, and defect identification for such structures is also of importance. In this paper, we compare the propagation characteristics of both Lamb modes and SH0 mode in variable thickness plates and propose to use the SH0 mode for defect identification in such waveguides because of its non-dispersive property. First, the non-dispersive property of the SH0 mode in waveguides with variable thickness is demonstrated in theory. Then, a wave prediction method is adopted to illustrate the differences between the Lamb modes and the SH0 mode when propagating in waveguides with constant or variable thickness. Finally, experiments are conducted on a variable thickness plate to verify the non-dispersive property of the SH0 mode and further compare the results with those of the Lamb modes. Recently developed thickness-poled omnidirectional shear horizontal piezoelectric transducers (OSH-PTs) are used to produce pure SH0 waves. It is observed that the velocity of the Lamb modes may change significantly and the group velocity of the S0 mode even decreases by 55.1% during propagation, which hampers Lamb modes from defect identification in variable thickness plates. By contrast, the SH0 mode is non-dispersive thus promising for damage detection, and its effectiveness for defect localization in such structures is validated experimentally.

Approximation of modal wavenumbers and group speeds in an oceanic waveguide using a neural network.

Underwater acoustic propagation is influenced not only by the property of the water column, but also by the seabed property. Modeling this propagation using normal mode simulation can be computationally intensive, especially for wideband signals. To address this challenge, a Deep Neural Network is used to predict modal horizontal wavenumbers and group velocities. Predicted wavenumbers are then used to compute modal depth functions and transmission losses, reducing computational cost without significant loss in accuracy. This is illustrated on a simulated Shallow Water 2006 inversion scenario.

Coherent Spontaneous Emission from Short Electron Bunches: Competition between Different Transverse Waveguide Modes

In this paper, we study spontaneous coherent undulator emission from a short dense electron bunch. A special “negative-mass” undulator ensuring stabilization of the axial size of the bunch is considered. We focus on the situation where the competition between two different transverse waveguide modes takes place, so that the undulator resonance is provided simultaneously for three waves placed on the dispersion diagram symmetrically with respect to electrons (namely, the group velocity of the higher waveguide mode coincides with the electron velocity, whereas two resonance frequencies of the lower transverse mode correspond to wave group velocities, one of which slightly exceeds the translational velocity of electrons, with the other being less than the electron velocity). We show that the higher waveguide mode can win this competition due to its proximity to group synchronization with the electron bunch.

Ideal Phase-Free Wave Propagation in Air Channel

Despite many intriguing approaches to realize zero-index media by metamaterial, a more common and attractive way to observe phase-invariant phenomenon at finite frequency is actually by the photonic waveguide mode at the cutoff frequency, which can reside in air channel surrounded by photonic band gap media. However, the group velocity of the gap-confined waveguide mode goes to zero (∂ω/∂k = 0) for k = 0 at the cutoff frequency, making it extremely difficult to excite and transport information by the phase advance-free propagation. In this work, we propose a dielectric photonic crystal platform for realizing an ideal air-concentrated phase-free waveguide. The waveguide is designed as a sandwiched structure like a photonic crystal (PC) line defect (e.g., PC-air-PC), which supports a pair of bound states in the continuum (BICs) at the PC-air domain, as well as multiple orders of gap-confined waveguide modes (WMs) inside the air channel. It is shown that the two BIC field distributions are allowed to be of symmetric and antisymmetric characteristics and are respectively coupled to the first- and second-order waveguide mode around k = 0. The interaction between these modes results in a linear band crossing (Δω ∼ k) at finite frequency, leading to the ideal phase-free wave propagation. We numerically and experimentally show the ideal phase-free propagation of the first- and second-order waveguide modes in the air channel. Our work provides an alternative way toward ideal phase-free waveguide, and the results may be of potential application for on-chip communication, qubit entanglement, precise signal processing, etc.

All-optical control of topological valley transport in graphene metasurfaces.

We demonstrate that the influence of Kerr effect on valley-Hall topological transport in graphene metasurfaces can be used to implement an all-optical switch. In particular, by taking advantage of the large Kerr coefficient of graphene, the index of refraction of a topologically-protected graphene metasurface can be tuned via a pump beam, which results in an optically controllable frequency shift of the photonic bands of the metasurface. This spectral variation can in turn be readily employed to control and switch the propagation of an optical signal in certain waveguide modes of the graphene metasurface. Importantly, our theoretical and computational analysis reveals that the threshold pump power needed to optically switch ON/OFF the signal is strongly dependent on the group velocity of the pump mode, especially when the device is operated in the slow-light regime. This study could open up new routes towards active photonic nanodevices whose underlying functionality stems from their topological characteristics.

Design of highly sensitive refractive index sensor based on silicon photonic Mach–Zehnder interferometer

A highly sensitive refractive index sensor based on silicon photonic Mach–Zehnder interferometer is proposed. The device consists of a subwavelength-grating slot waveguide in one arm, as a sensing region, to enhance the light-gas interaction. By optimizing the structure parameters, the device operates near the dispersion turning point when the optical mode group velocity difference between the sensing arm and the other reference arm approaches zero. The RI sensitivity is 9.6×105/RIU and gas pressure sensitivity is as high as 232 nm/MPa. The study results show that the proposed design is a potentially robust refractive index sensor and has a good performance in gas pressure sensing.