Velocity Mismatch Research Articles

Nonlinear interaction of Lamb waves with fatigue cracks in metal plates under the condition of phase-velocity mismatching

Abstract Nonlinear Lamb waves have been widely acknowledged as an efficient method for evaluating material damage at an early stage. However, due to the dispersive and multimode natures of Lamb waves, nonlinear Lamb waves with exact/approximate phase-velocity matching have been employed in previous research solely for the evaluation of fatigue cracks. Second harmonic Lamb waves can be generated from the contact acoustic nonlinearity (CAN) induced by the “breathing” effect of fatigue cracks. This paper presents a verification of the second harmonic S0 mode Lamb waves due to fatigue crack CAN, despite the mismatch in phase velocity between this mode and the primary S0 mode Lamb waves. This verification is achieved through both simulation and experiment. Consequently, the generation of double-frequency Lamb waves by fatigue cracks under conditions of phase velocity mismatching is validated. Furthermore, the phase-velocity mismatching method is anticipated to exclude material nonlinearity in the detection of fatigue cracks. This method offers a potential for accurate detection and evaluation of fatigue cracks.

Cherenkov second harmonic generation of femtosecond laser pulses in a homogeneous nonlinear crystal

In experiments on second harmonic (SH) generation (SHG), a conical structure of radiation has been observed. In the present study, a non-stationary theory of SH excitation of ultrashort laser pulses with phase modulation has been developed, which explains the properties of such a structure as Cherenkov radiation. Under phase-mismatched interactions, a maximum of the SH spectrum is observed at the Cherenkov angle, which is determined by the ratio of the SH and laser radiation phase velocities. It is shown that tightly focused laser beams are preferred to observe Cherenkov SHG. The SH spectral width depends on the group velocity mismatch and is more complicated on the excited radiation spectrum. The SH energy can be proportional to the crystal length or group delay length depending on their ratio. We also demonstrate that a complex angular distribution of spectral components (an angular chirp) appears within the SH cross-section.

Jet noise of a low bypass turbofan with internal mixing and external plug

Jet noise generated by turbofan engines which are designed for supersonic aircraft operation is expected to remain a challenge for the aerospace industry. For civil supersonic transport, low bypass ratio engines with internal mixing and external plugs are currently seen as promising exhaust architecture to meet aircraft mission and certification requirements. Measurements of the noise from a representative low-bypass ratio long duct mixed flow with external plug exhaust configuration were made, along with corresponding steady-RANS and LES analyses. The measured data showed excess high frequency noise across a wide range of operating conditions as compared to an equivalent single stream jet, or an equivalent uniform jet with internal plug. The absolute levels of the excess noise were relatively insensitive to forward flight, and the excess noise was most dominant when the primary and secondary streams had large velocity and temperature mismatch just upstream of the internal mixer. Preliminary indications from the LES analysis also indicated that significant pressure fluctuations, at the same frequencies which are insensitive to forward flight, develop inside the nozzle as the internal shear layer from the mixer grows and gets accelerated by the external plug. Parametric study test measurements on the fan and core operating conditions were performed, providing support for the hypothesis that the excess noise is generated as the internal shear layer, starting inside the nozzle, gets accelerated by the plug and passes through the weak shock at the nozzle exit where the flow accelerates more and turns over the external plug.

Long-Term Coherent Integration Algorithm for High-Speed Target Detection.

Long-term coherent integration (CI) can effectively improve the radar detection capability for high-speed targets. However, the range walk (RW) effect caused by high-speed motion significantly degrades the detection performance. To improve detection performance, this study proposes an improved algorithm based on the modified Radon inverse Fourier transform (denoted as IMRIFT). The proposed algorithm uses parameter searching for velocity estimation, designs a compensation function based on the relationship between velocity and distance walk and Doppler ambiguity terms, and performs CI based on the compensated signal. IMRIFT can achieve RW correction, avoid the blind-speed sidelobe (BSSL) effect caused by velocity mismatch, and improve detection performance, while ensuring low computational complexity. In addition, considering the relationship between energy concentration regions and bandwidth in the 2D frequency domain, a fast method based on IMIRFT is proposed, which can balance computational cost and detection capacity. Finally, a series of comparative experiments are conducted to demonstrate the effectiveness of the proposed algorithm and the fast method.

Fully spin-polarized, valley-polarized and spin-valley-polarized electron beam splitters utilizing zero-line modes in a three-terminal device

Topological zero-line modes (ZLMs) with spin and valley degrees of freedom give rise to spin, valley and spin-valley transport, which support a platform for exploring quantum transport physics and potential applications in spintronic/valleytronic devices. In this work, we investigate the beam-splitting behaviors of the charge current due to the ZLMs in a three-terminal system. We show that with certain combinations of ZLMs, the incident charge current along the interface between different topological phases can be divided into different polarized currents with unit transmittance in two outgoing terminals. As a result, fully spin-polarized, valley-polarized and spin-valley-polarized electron beam splitters are generated. The mechanism of these splitters is attributed to the cooperative effects of the distribution of the ZLMs and the intervalley and intravalley scatterings that are modulated by the wave-vector mismatch and group velocity mismatch. Interestingly, half-quantized transmittance of these scatterings is found in a fully spin-valley-polarized electron beam splitter. Furthermore, the results indicate that these splitters can be applicable to graphene, silicene, germanene and stanene due to their robustness against the spin–orbit coupling. Our findings offer a new way to understand the transport mechanism and investigate the promising applications of ZLMs.

Noninvasive Advanced Cardiovascular Magnetic Resonance-Derived Fontan Hemodynamics Are Associated With Reduced Kidney Function But Not Albuminuria.

Kidney disease is the most important predictor of death in patients with a Fontan circulation, yet its clinical and hemodynamic correlates have not been well established. A total of 53 ambulatory patients with a Fontan circulation (median age, 16.2 years, 52.8% male patients) underwent advanced cardiovascular magnetic resonance assessment, including 4-dimensional flow imaging and computational fluid dynamics. Estimated glomerular filtration rate (eGFR) <90 mL/min per 1.73 m2 was observed in 20.8% and albumin-to-creatinine ratio >3 mg/mmol in 39.6%. The average eGFR decline rate was -1.83 mL/min per 1.73 m2 per year (95% CI, -2.67 to -0.99; P<0.001). Lower eGFR was associated with older age, larger body surface area at examination, longer time since Fontan procedure, and lower systemic ventricular ejection fraction. Higher albumin-to-creatinine ratio was associated with absence of fenestration at the Fontan operation, and older age and lower systemic ventricular ejection fraction at the assessment. Lower cross-sectional area of the Fontan conduit indexed to flow (r=0.32, P=0.038), higher inferior vena cava-conduit velocity mismatch factor (r=-0.35, P=0.022), higher kinetic energy indexed to flow in the total cavopulmonary connection (r=-0.59, P=0.005), and higher total cavopulmonary connection resistance (r=-0.42, P=0.005 at rest; r=-0.43, P=0.004 during exercise) were all associated with lower eGFR but not with albuminuria. Kidney dysfunction and albuminuria are common among clinically well adolescents and young adults with a Fontan circulation. Advanced cardiovascular magnetic resonance-derived metrics indicative of declining Fontan hemodynamics are associated with eGFR and might serve as targets to improve kidney health. Albuminuria might be driven by other factors that need further investigation.

Quasistatic component generation of group velocity mismatched guided waves in tubular structures for microdamage localization

Quasistatic component (QSC) of guided wave (GW) has relatively low attenuation due to low frequency and high sensitivity to microdamage. The group velocity matching between primary GW and its QSC or higher harmonics usually facilitates the measurement of nonlinear signals due to cumulative effect of amplitude, but it restricts the determination of microdamage location. While group velocity mismatch is general for most of the wave mode pairs in nonlinear GW testing, this study presents a novel method for identifying the location of early stage microdamage using QSC generation of ultrasonic GW propagation in tubular structures under group velocity mismatching condition. A three-dimensional finite element (FE) model is developed to provide insights into the generation and propagation characteristics of the QSC induced by both global material weak nonlinearity and simulated local microdamage in metallic pipes. The FE analysis verifies the L(0,1) mode of the QSC generated from propagations of different fundamental wave modes. The generation efficiency and cumulation feature of the QSC pulse are obtained and discussed. By exploiting the group velocity mismatching condition, a microdamage localization method is proposed based on the L(0,1)-QSC mode pair, which requires one-way excitation of only one primary wave. Experiments are conducted using early corrosion aluminum specimens to investigate the QSC pulse signals and verify the proposed method. The FE and experimental results demonstrate the fundamental properties of QSC generation by GWs in isotropic metallic hollow cylindrical structures. The feasibility of the proposed microdamage localization method is validated experimentally for promising industrial applications.

High efficiency high beam quality third harmonic generation of hundreds femtosecond laser by employing a delay line and LiB3O5 crystals

In this study, efficient third harmonic generation was investigated by employing a delay line and LiB3O5 (LBO) crystals with 600 fs pulse lasers at 1030 nm. We systematically investigated the differences in the frequency conversion of the LBO crystals for second and third harmonic generation with varying beam spots. Specifically, it has been demonstrated that the inclusion of a delay line is necessary to mitigate the group velocity mismatch at hundreds femtosecond laser. The results indicate that the maximum output powers are approximately 16.5 W and 5.6 W at wavelengths of 515 nm and 343 nm, respectively. The corresponding optimal conversion efficiencies are 59.6 % (from 1030 nm to 515 nm) and 20.4 % (from 1030 nm to 343 nm). And the beam quality has improved noticeably at 515 nm (Mx2 = 1.16, My2 = 1.13) and 343 nm (Mx2 = 1.16, My2 = 1.12), in contrast to that at 1030 nm (Mx2 = 1.56, My2 = 1.49).

Mapping Mean Velocity Field over Bed Forms Using Simplified Empirical-Moment Concept Approach

The log-wake law was successful in mapping velocity fields for uniform flow over flat surfaces, even in cases of wake effects (velocity dips, wall effects, and secondary currents). However, natural riverbeds with undulations and bedforms challenge these models. This study introduces a moment-based empirical method for rough estimation of the velocity fields over stationary 2D bedforms. It proposes three polynomial velocity profile templates (first, fifth, and eighth orders) with coefficients deduced analytically while taking into account an array of flow conditions and assumptions, including slip velocity at the bed, mass and moment of momentum conservations, imposing inviscid potential flow near the water surface, and incorporation of near-bed shear stress utilizing a moment-based Chezy formula. Remarkably, the coefficients of these polynomials are primarily reliant on two crucial velocity scales, the depth-averaged velocity (uo) and the moment-derived integral velocity (u1), along with the dimensionless reattachment coefficient (Kr). Validation of the proposed approach comes from ten lab experiments, spanning Froude numbers from 0.1 to 0.32, offering empirical data to validate the obtained velocity profiles and to establish the relationship of the spatial variation in the normalized u1 velocity along bedforms. This study reveals that the assumption of a slip boundary condition at the bed generally enhances the accuracy of predicted velocity profiles. The eighth-order polynomial profile excels within the eddy zone and close to reattachment points, while the fifth-order profile performs better downstream, approaching the crest. Importantly, the efficacy of this approach extends beyond water flow to encompass airflow scenarios, such as airflow over a negative step. The research findings highlight that linear velocity, as employed in Vertically Averaged and Moment models (VAM), exhibits approximately 70% less velocity mismatch compared to constant Vertically Averaged (VA) models. Moreover, the utilization of the fifth-order and eighth-order velocity profiles results in substantial improvements, reducing velocity mismatch by approximately 86% and 90%, respectively, in comparison to VA models. The insights gained from this study hold significant implications for advancing vertically averaged and moment-based models, enabling the generation of approximate yet more realistic velocity fields in scenarios involving flow over bedforms. These findings directly impact applications related to sediment transport and mixing phenomena.

Generation of high-energy near-infrared femtosecond laser pulses by optical parametric amplification in YCOB crystals

"The energy of near-infrared femtosecond laser pulses generated by optical parametric amplification (OPA) in β-barium borate (BBO) crystals pumped by femtosecond Ti:sapphire lasers is restricted to few-mJ due to the 20 mm limited diam- eter of available crystals. In a type I collinear OPA with an yttrium calcium oxoborate (YCOB) crystal, pumped with femtosecond Ti:sapphire lasers at 800 nm wavelength, the 1300 nm signal wavelength and 2080 nm idler wavelength are located in the normal and anomalous group velocity dispersion range, respectively. Due to the small group velocity mismatch (GVM) between signal and idler pulses, as broad as 27 THz gain bandwidth can be obtained in a 3-mm YCOB crystal at 100 GW/cm2 pump intensity. A high parametric gain is the result of the increased parametric interaction length due to the different signs of GVM between pump-signal and pump-idler pulses. More than 10-mJ energy femtosecond laser pulses at 1300 nm wavelength can be generated by OPA in YCOB crystals with larger than 50 mm clear aperture."

Machine-learning iterative optimization for all polarization-maintaining linear cavity Er:fiber laser.

All polarization-maintaining (PM) linear cavity mode-locked fiber lasers are promising ultrafast laser sources due to their compactness and environmental robustness. Here, we demonstrate a linear cavity fiber laser with all-PM configuration experimentally and investigate the mode-locking formation of the laser using a machine-learning iterative optimization method based on the Gaussian process. The optimization algorithm can converge rapidly after only 30 runs. Using the optimized parameters, we simulate the generation of mode-locked pulses from noise. The output spectrum and pulse energy are highly consistent with the experiment. Furthermore, we describe the intracavity dynamic evolution under group velocity mismatch. We then show that the pulse trapping induced by cross-phase modulation leads to the overcompensated time synchronization between the orthogonally polarized components.

Sum-frequency generation at interfaces: A Fresnel story. III. Origin of pseudo-resonant processes in centrosymmetric bulks.

The properties of bulk contribution to sum-frequency generation reflected and transmitted by a finite layer in a multilayer system are described. The leading term is essentially due to the processes emitting in the transmission geometry, in particular for macroscopic layers. For such transmission processes, phase mismatch leads to the production of interference fringes when the layer thickness or a wavelength is tuned, which may be mistaken for resonant processes inside or at the surface of the material. Experimental evidence of such fringes measured from centrosymmetric bulks is provided for a diamond window in the far infrared and suggested for other materials in previously published data. The existence of a stationary point in the phase mismatch, related to the group velocity mismatch, is shown to be the source of another pseudo-resonant process in centrosymmetric calcium and barium fluorides, for which theoretical predictions reproduce the experimental observations.

High Efficiency Third-Harmonic Generation in a Medium with Quadratic Susceptibility Due to Cubic-like Nonlinearity Caused by Cascaded Second-Harmonic Generation

Third-harmonic generation (THG) is of interest for its various applications. We propose using the cascaded second-harmonic generation (SHG) to implement the frequency conversion process, which is similar to that occurring in a medium with cubic susceptibility. Physically, the process is based on consecutive generation of the second-harmonic and the sum frequency in the same crystal with quadratic susceptibility at large phase mismatching between the fundamental wave and the second-harmonic wave. In this case, at phase matching between the fundamental wave and the third-harmonic wave, THG occurs with high efficiency. To demonstrate such a possibility theoretically, we apply the multi-scale method to a set of Schrödinger equations, describing a three-wave interaction with the frequencies ω,2ω and 3ω in a medium with quadratic susceptibility, to derive modified equations describing the frequency tripling process. These equations are solved without using the fundamental wave energy non-depletion approximation. A THG efficiency equal to 94.5% is predicted theoretically. The analytical solution is confirmed by computer simulation results. We study how various factors, such as the incident pulse intensity, phase mismatching between interacting waves, group velocity mismatching of the pulses, and second-order dispersion of the wave packets influence the THG process.

Hyperbolic resonant radiation of concomitant microcombs induced by cross-phase modulation

A high-quality optical microcavity can enhance optical nonlinear effects by resonant recirculation, which provides a reliable platform for nonlinear optics research. When a soliton microcomb and a probe optical field are coexisting in a micro-resonator, a concomitant microcomb (CMC) induced by cross-phase modulation (XPM) will be formed synchronously. Here, we characterize the CMC comprehensively in a micro-resonator through theory, numerical simulation, and experimental verification. It is found that the CMCs spectra are modulated due to resonant radiation (RR) resulting from the interaction of dispersion and XPM effects. The group velocity dispersion induces symmetric RRs on the CMC, which leads to a symmetric spectral envelope and a dual-peak pulse in frequency and temporal domains, respectively, while the group velocity mismatch breaks the symmetry of RRs and leads to asymmetric spectral and temporal profiles. When the group velocity is linearly varying with frequency, two RR frequencies are hyperbolically distributed about the pump, and the probe light acts as one of the asymptotic lines. Our results enrich the CMC dynamics and guide microcomb design and applications such as spectral extension and dark pulse generation.

Second harmonic generation in the presence of walk-off and group velocity mismatch

We study a second harmonic generation interaction geometry in the case where both group velocity mismatch and walk-off have significant impacts. This results in a frequency-converted beam exhibiting a pulse front tilt. Using the global response function of the crystal, we provide an analytical model that allows to predict the spatiotemporal structure of the second harmonic wave packet and verify its validity using numerical simulations and a simple experiment. Distinctive features of this geometry are the suppression of back-conversion and the ability to conserve the fundamental bandwidth in space and time domains. Subsequent compensation of the pulse front tilt should allow efficient generation of ultrashort pulses in the deep ultraviolet.

Exploiting Unit Circle Roots for Improved Radar Moving Target Detection in Low Rank Clutter With Limited Secondary Data

Measured radar clutter often exhibits a low-rank structure that can be exploited for designing adaptive moving target detectors to reduce the amount of secondary data necessary for desirable detection performance. It has been shown recently that for symmetrically spaced pulse trains significant performance improvements can be achieved by constraining the roots of the Adaptive Matched Filter (AMF) polynomial onto the unit circle (UC) that satisfies a theoretical property of the known-covariance AMF. In this paper, the UC-roots approach is extended to develop a generalized likelihood ratio test (GLRT) for radar moving target detection in low-rank clutter with limited secondary data. The proposed unit circle GLRT (UC-GLRT) uses the properties of orthogonal projection matrices to enforce the UC roots constraint. The asymptotic performance analysis of the proposed UC-GLRT conducted in this paper is verified by simulation. Simulation studies with limited secondary data demonstrate the superior performance of the UC-GLRT approach over several existing detectors. Clutter rank and target velocity mismatch issues are also studied.

206 nm deep ultraviolet laser generated from fifth harmonic of femtosecond fiber laser

Deep ultraviolet (DUV) femtosecond laser, which combines the advantages of high single-photon energy of DUV laser with high peak power of femtosecond laser, is widely used in scientific research, biomedicine, material processing and so on. However, in the process of generating DUV femtosecond laser based on nonlinear frequency conversion is encountered a problem that the group velocity mismatch caused by dispersion makes the temporal walk-off of the nonlinear frequency conversion larger than the pulse duration of the femtosecond laser, thus making the generation of the DUV femtosecond laser very difficult. In this work, based on a Yb-doped fiber femtosecond laser, the delay line is optimized to precisely compensate for the spatial and temporal walk-off, so DUV femtosecond laser possesses the following performances: the center wavelength is 206 nm, the repetition rate is 1 MHz, the maximum output power is 102 mW, the maximum conversion efficiency is 4.25% from near infrared to DUV, the root mean square (RMS) power stability is 0.88% within 3 h, and the peak-to-peak power stability is 3.75%. The evolution of laser spectra and beam quality in the process of second harmonic generation (SHG), fourth harmonic generation (FHG) and sum-frequency generation (SFG) are also systematically studied. The experimental results provide a basis for generating DUV femtosecond laser from femtosecond fiber lasers.

The surprising persistence of time-dependent quantum entanglement

The mismatch between elegant theoretical models and the detailed experimental reality is particularly pronounced in quantum nonlinear interferometry (QNI). In stark contrast to theory, experiments contain pump beams that start in impure states and that are depleted, quantum noise that affects—and drives—any otherwise gradual build up of the signal and idler fields, and nonlinear materials that are far from ideal and have a complicated time-dependent dispersive response. Notably, we would normally expect group velocity mismatches to destroy any possibility of measurable or visible entanglement, even though it remains intact—the mismatches change the relative timings of induced signal–idler entanglements, thus generating ‘which path’ information. Using an approach based on the positive-P representation, which is ideally suited to such problems, we are able to keep detailed track of the time-domain entanglement crucial for QNI. This allows us to show that entanglement can be—and is—recoverable despite the obscuring effects of real-world complications; and that recovery is attributable to an implicit time-averaging present in the detection process.

Novel soliton solutions for the fractional three-wave resonant interaction equations

Abstract In this article, we obtained new infinite sets of exact soliton solutions for the nonlinear evolution system of three-wave resonant interaction equations. The solved system contains the non-zero second-order dispersion coefficients, the non-zero phase velocity mismatch, and the conformable fractional time derivative of order between zero and one. The solution method is a constructed ansatz that consists of linear combinations of the tan and cotan hyperbolic functions with complex coefficients. We stated clear systematic steps toward writing an exact soliton solution for the studied system. To show the efficiency of this method, we introduced some numerical examples on each obtained set of solutions. The computations showed that similar solutions can be obtained if one replaces the tan and cotan hyperbolic functions with the tan and cotan trigonometric functions. The new obtained fractional solutions could be useful in studying the broad applications of triad resonances in plasma physics and in nonlinear optics.

High-performance SH-SAW resonator using optimized 30° YX-LiNbO3/SiO2/Si

With the rapid development of 5G technology, acoustic wave filters with large bandwidths are urgently required to deal with the explosive increase in data traffic. Recently, there is extensive attention paid to shear-horizontal (SH) surface acoustic wave (SAW) resonators based on lithium niobate (LiNbO3) substrates, thanks to its large effective coupling coefficient (k2eff). However, because of the bulk acoustic wave (BAW) energy radiation into the LiNbO3 substrate, it is very challenging to obtain a high quality factor (Q) for SH-SAW resonators. In this study, a 30° YX-LiNbO3/SiO2/Si SAW resonator with the SH mode is proposed to achieve a large coupling and a high Q simultaneously. By bonding a LiNbO3 thin film onto a thermally oxidized Si(100) substrate, the velocity mismatch between the piezoelectric layer and the SiO2/Si substrate could significantly reduce the BAW energy leakage. Finite element method simulation is employed to optimize the cut angle of the LiNbO3 film and the thickness of each layer. The fabricated SH-SAW resonators with a resonant frequency of 924 MHz yield a k2eff of 24.8% and a maximum of Bode-Q (Bode-Qmax) of 1107. In comparison with the previously reported same-type SAW resonators, a higher Bode-Qmax is demonstrated in this work when their k2eff is larger than 20%, providing a potential solution to enable wideband tunable filters in the 5G communication system.