Group Velocity Of Mode Research Articles

Highly sensitive plasmonic nanoridge hyperbolic metamaterial for biosensing

Artificially designed hyperbolic metamaterials (HMMs) with extraordinary optical anisotropy can support highly sensitive plasmonic sensing detections, showcasing significant potential for advancements in medical research and clinical diagnostics. In this study, we develop a gold nanoridge HMM and disclose the plasmonic sensing physical mechanism based on this type of HMM through theoretical and experimental studies. We determine that the high modal group velocity of plasmonic guided modes stemming from a large transverse permittivity of HMMs directly results in high sensitivity. By combining electron-beam lithography, oxygen plasma etching, and electroplating, the fabricated gold nanoridge array possesses an extremely high structural filling ratio that is difficult to obtain through conventional processes. This leads to a large transverse permittivity and enables highly confined and ultra-sensitive bulk plasmon–polariton (BPP) guided modes. By exciting these modes in the visible to near-infrared region, we achieve a record sensitivity of 53,300 nm/RIU and a figure of merit of 533. Furthermore, the developed plasmonic nanoridge HMM sensor exhibits an enhanced sensitivity of two orders of magnitude compared to that of the same type of HMM sensor in label-free biomolecule detection. Our study not only offers a promising avenue for label-free biosensing but also holds great potential to enhance early disease detection and monitoring.

Investigation of Lamb wave modes recognition and acoustic emission source localization for steel plate based on golden jackal optimization VMD parameters and CWT

Accurate identification of Lamb wave modes in acoustic emission(AE) signals propagating on steel plates is crucial for precise source localization. In this paper, we propose a novel method that optimizes variational mode decomposition(VMD) parameters using golden jackal optimization(GJO) and identifies Lamb wave modes on steel plates through continuous wavelet transform(CWT). The Hsu-Nielsen source(HNS) is employed as the AE source. The minimum permutation entropy of the AE signal is used as the optimization objective, with GJO adaptively determining the optimal mode number (K) and penalty factor (α) for VMD. The maximum correlation coefficient method is applied to reconstruct the AE waveform, and both A0 and S0 Lamb wave modes are identified in the wavelet time–frequency domain using CWT. Furthermore, an AE source localization algorithm based on the time difference of arrival and the geometric relationship between two sensors is developed, utilizing the group velocity of the S0 mode. The proposed method effectively identifies acoustic wave modes, achieving an average relative localization error of approximately 0.48% for HNS.

Deep sediment heterogeneity inferred using very low-frequency features from merchant shipsa).

The very low-frequency noise from merchant ships provides a good broadband sound source to study the deep layers of the seabed. The nested striations that characterize ship time-frequency spectrograms contain unique acoustic features corresponding to where the waveguide invariant β becomes infinite. In this dataset, these features occur at frequencies between 20 and 80 Hz, where pairs of modal group velocities become equal. The goal of this study is to identify these β = ∞ frequencies in ship noise spectrograms and use them to perform statistical inference for the deep layer sound speeds and thicknesses in the New England Mudpatch for a larger number of ships and acoustic arrays over a larger geographical region than previously studied. Marginal probability distributions of the data indicate that using singular points for a feature-based inversion yields an estimate of the sound speed and a limiting value for the thickness of the first deep layer. Heterogeneity is examined by correlating spatial variability of the deep layer sound speeds with ship tracks.

Low temperature coefficient of frequency AlN Lamb wave resonator using groove structure between interdigital transducers

The lithographically tunable and small size features of Lamb wave resonators (LWRs) take a bright future for their use in high frequency narrow band filters. Resonant frequency drift due to temperature variation has a large impact on the narrower passband and a temperature coefficient of frequency (TCF) closer to 0 can broaden the stable temperature range of the resonator. This paper proposes a method of etching grooves in the area of the piezoelectric layer not covered by the Interdigital transducer (IDT) electrodes to improve the temperature stability of the Lamb resonator. Through the finite element method and theoretical analysis, the phase velocity, group velocity, and TCF dispersion curve of different modes of the resonator with groove structure were determined. The reason for the change of TCF under different normalized thicknesses of AlN was explained through the conversion of the LWR from a contour mode resonator (CMR) to a Cross-Sectional Lamé Mode Resonator. Simulation and test have shown that etching grooves have the effect of reducing TCF by adjusting the electromechanical coupling coefficient. The test shows that 205 nm-depth grooves can lower the TCF of the S0 mode IDT-Open LWR from −13.3 to −5.1 ppm/°C and S1 mode from −36.8 to −9.0 ppm/°C, respectively. The TCF of S0 and S1 mode LWRs decreased by 61.7% and 75.5%, respectively, after 205 nm groove etching. The groove etching method greatly raises the temperature stability of the LWR, enabling Lamb wave filters to operate stably over a wider temperature range.

Non-destructive evaluation of a composite honeycomb sandwich panel with in-plane waviness damage using ultrasonic guided waves

ABSTRACT Composite honeycomb sandwich structures (CHSS) are often manufactured using an autoclave co-cure process, which can introduce in-plane waviness (IW) damage due to fibre misalignment. Such fibre waviness, whether in-plane or out-of-plane, significantly weakens the strength of these structures. Therefore, developing reliable non-destructive evaluation (NDE) techniques is essential for detecting IW. This study presents an NDE technique utilising ultrasonic guided waves (GW) to identify IW damage in CHSS panels. A numerical model was created using COMSOL Multiphysics, where IW damage is simulated through curvilinear coordinate physics, followed by a time-dependent study of GW propagation. This model simulates local fibre orientation changes due to IW damage, enhancing our understanding of GW interaction with IW. Experimental investigations are performed using contact-type transducers to corroborate the numerical observations. The presence of in-plane waviness causes a reduction in the group velocity of the A0 mode, a characteristic that can be exploited for detecting in-plane fibre waviness in CHSS. Also, parametric studies were performed to examine the effects of IW severity (aspect ratio) and increased IW area on GW characteristics. Finally, a technique for IW damage localisation is demonstrated using a convex hull algorithm based on changes in correlation coefficient values of the A0 mode.

Sound attenuation at low to mid frequencies in low velocity seabottoms.

Attenuation is the most difficult seafloor acoustic property to get, particularly at low to mid frequencies. For low velocity bottoms (LVB), it becomes even more challenging, due to its small attenuation and lower velocity (relative to the velocity of the adjacent water). The latter one causes a fatal "seafloor velocity-attenuation couplings" in geo-acoustic inversions. Thus, attenuation inversions for the LVB require an accurate seafloor velocity profile, especially the velocity in the LVB layer. The propagation of explosive sound in the Yellow Sea with a strong thermocline and a top LVB layer exhibits many prominent characteristics: modal dispersion (the ground wave, water wave, Airy phase), two groups of water waves at high frequencies, and the siphon effect which causes abnormally large sound transmission loss at selected frequencies, etc. These observations are used to precisely measure the critical frequency, the Airy frequency, Airy wave velocity, 1st mode group velocity, and to derive the velocities in the LVB layer and in the basement. Using inverted seafloor parameters, the source level-normalized transmission loss and the first mode decay rate in ranges up to 27.66 km, the sound attenuations in the LVB are derived for a frequency range of 13-5000 Hz.

Early-Stage Ice Detection Utilizing High-Order Ultrasonic Guided Waves.

Ice detection poses significant challenges in sectors such as renewable energy and aviation due to its adverse effects on aircraft performance and wind energy production. Ice buildup alters the surface characteristics of aircraft wings or wind turbine blades, inducing airflow separation and diminishing the aerodynamic properties of these structures. While various approaches have been proposed to address icing effects, including chemical solutions, pneumatic systems, and heating systems, these solutions are often costly and limited in scope. To enhance the cost-effectiveness of ice protection systems, reliable information about current icing conditions, particularly in the early stages, is crucial. Ultrasonic guided waves offer a promising solution for ice detection, enabling integration into critical structures and providing coverage over larger areas. However, existing techniques primarily focus on detecting thick ice layers, leaving a gap in early-stage detection. This paper proposes an approach based on high-order symmetric modes to detect thin ice formation with thicknesses up to a few hundred microns. The method involves measuring the group velocity of the S1 mode at different temperatures and correlating velocity changes with ice layer formation. Experimental verification of the proposed approach was conducted using a novel group velocity dispersion curve reconstruction method, allowing for the tracking of propagating modes in the structure. Copper samples without and with special superhydrophobic multiscale coatings designed to prevent ice formation were employed for the experiments. The results demonstrated successful detection of ice formation and enabled differentiation between the coated and uncoated cases. Therefore, the proposed approach can be effectively used for early-stage monitoring of ice growth and evaluating the performance of anti-icing coatings, offering promising advancements in ice detection and prevention for critical applications.

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.

Deep sediment characterization from very low-frequency features from merchant ships

The very low-frequency noise from merchant ships provides a good wideband source to study the deep layers of the seabed. The nested striations which characterize ship spectrograms contain unique acoustic features where the waveguide invariant (β) becomes infinite. This occurs at frequencies between 20 and 80 Hz where pairs of modal group velocities are equal. The goal of this project was to identify the β = ∞ frequencies in ship noise spectrograms and use these frequencies to perform statistical inference for the deep layer sound speeds and thicknesses. The Seabed Characterization Experiment of 2022 on the New England continental shelf had three vertical line arrays strategically placed between two shipping lanes. The average water depth was 75 meters with less than one meter bathymetry change between the arrays. The results of this study are based primarily on five ships. There was a gradual shift in the β = ∞ frequencies between the three arrays, suggesting a gradual change in the deep sediment layers. [Work supported by Office of Naval Research.]

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.