Non-collinear Wave Research Articles

Enhancing the efficiency of high-order harmonics with two-color non-collinear wave mixing in silica

The emission of high-order harmonics from solids under intense laser-pulse irradiation is revolutionizing our understanding of strong-field solid-light interactions, while simultaneously opening avenues towards novel, all-solid, coherent, short-wavelength table-top sources with tailored emission profiles and nanoscale light-field control. To date, broadband spectra in solids have been generated well into the extreme-ultraviolet (XUV), but the comparatively low conversion efficiency in the XUV range achieved under optimal conditions still lags behind gas-based high-harmonic generation (HHG) sources. Here, we demonstrate that two-color high-order harmonic wave mixing in a fused silica solid is more efficient than solid HHG driven by a single color. This finding has significant implications for compact XUV sources where gas-based HHG is not feasible, as solid XUV wave mixing surpasses solid-HHG in performance. Moreover, our results enable utilizing solid high-order harmonic wave mixing as a probe of structure or material dynamics of the generating solid, which will enable reducing measurement times compared to the less efficient regular solid HHG. The emission intensity scaling that follows perturbative optical wave mixing, combined with the angular separation of the emitted frequencies, makes our approach a decisive step for all-solid coherent XUV sources and for studying light-engineered materials.

Experimental study on the nonlinear mixing of ultrasonic waves in concrete using an array technique

This research develops a procedure that combines ultrasonic array technology with non-collinear ultrasonic wave mixing to detect and scan internal microscale damage in concrete. Exploiting the underlying mechanics of nonlinear wave mixing, two incident shear wave beams generated by two ultrasonic transducer arrays (and with frequencies low enough to propagate without being overly scattered by the aggregate) are used to create a longitudinal mixed wave, the amplitude of which is a direct measure for the amount of localized, internal damage. The arrays enable beam steering, making it possible to scan for damage along an arc. The effectiveness of the proposed technique is demonstrated by characterizing different types of microscale damage embedded at known locations in a concrete prism specimen. These results establish the feasibility of using a nonlinear wave mixing array technique for the efficient inspection of internal microscale damage in a large concrete structure.

Numerical study on passive structural control of semi-submersible floating wind turbine considering non-collinear wind and waves

Floating offshore wind turbines have great potential in the deep-sea regions and they often suffer from the combined action of wind and waves, which affects the safety of wind turbines and the stability of power generation. At present, the tuned mass dampers installed in the wind turbine nacelles are widely used to control the vibration of wind turbine structures, but their mass are relatively small and have limited effectiveness on the large motion of floating offshore wind turbines. Moreover, the motion control of floating offshore wind turbines is mostly considered under the condition that the wind and waves are collinear while the non-collinear condition has been rarely investigated. Therefore, the tuned mass damper system installed in the nacelle and the platform of semi-submersible floating offshore wind turbine is studied through numerical methods in this research, and the non-collinear wind and waves conditions are considered. The results show that the high-frequency tuned mass damper installed in the nacelle is effective to reduce the response of tower but has little effect on the platform. The low-frequency tuned mass damper works well to control the response of tower and platform no matter it is installed in the nacelle or in the platform. For the irregular wave, the effect of tuned mass damper is not obvious and the large-mass one even increases the response. For the non-collinear wind and wave, the tuned mass dampers installed in the nacelle and platform at the same time have the best effect to reduce the response of wind turbine for various wind-wave angles.

Optimization of mooring line design parameters using Mooring Optimization Tool for FPSO (MooOpT4FPSO) with the consideration of integrated design methodology

Optimization of mooring line design parameters including line azimuth angles, line diameter, line length and mooring radius is presented for a turret-moored FPSO. The optimization procedure is implemented using a Mooring Optimization Tool for FPSO (MooOpT4FPSO), which is an in-house optimization tool purposely developed for this purpose. The tool is a synchronisation of the Regrouping Particle Swarm Optimization (RegPSO) algorithm with commercial software, OrcaFlex. Case studies using a validated numerical FPSO model moored with multicomponent mooring lines acted upon by non-collinear wave, wind and current were analysed using the developed tool. To take into consideration the interaction of the riser system in the optimization procedure, the integrated design methodology was adopted where the riser safe operation (SAFOP) zone diagram combined with the offset diagram is used for the verification/assessment of the design criteria of the risers and mooring lines. The optimized FPSO model offsets in eight directions are found to be within the riser safe operation zone. Based on the results, the tool was able to simultaneously optimise the mooring line diameter, line length, mooring radius, and azimuth angles of the turret FPSO to achieve a specific offset. Application of the tool can help the industry save material (by reduction of line diameter and length) and consequently the overall project cost, in addition to the reduction of structural payload exerted on the platform. Furthermore, the tool has an automatic search capability, which is an improvement to the conventional mooring design approach that is based on a trial-and-error approach.

Nonreciprocal Transmission of Non-collinear Mixing Wave in Nonlinear Elastic Wave Metamaterial

Nonreciprocal Transmission of Non-collinear Mixing Wave in Nonlinear Elastic Wave Metamaterial

Use of a non-collinear wave mixing technique to image internal microscale damage in concrete

This research demonstrates the feasibility of using a non-collinear wave mixing technique to image internal microscale damage throughout the interior volume of a relatively large (28 cm thick) concrete component. By exploiting the underlying mechanics of nonlinear wave mixing, it is possible to mix two incident waves with frequencies low enough to propagate without being scattered by the inherently heterogenous, concrete microstructure, while still being sensitive to damage features with length scales well below these incident wavelengths. For this study, scanning and imaging is accomplished by manually adjusting the locations of the two incident waves, while a knowledge of the wave speeds in concrete plus synchronization identifies the location of the mixing zone—the specific volume of concrete being imaged. The viability of the proposed technique is demonstrated by examining a concrete prism specimen with known, embedded internal microscale damage.

Triangular Pair Density Wave in Confined Superfluid ^{3}He.

Recent advances in experiment and theory suggest that superfluid ^{3}He under planar confinement may form a pair density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a unidirectional stripe phase predicted by Vorontsov and Sauls in 2007, recent nuclear magnetic resonance measurements of the superfluid order parameter rather suggest a two-dimensional PDW with noncollinear wave vectors, of possibly square or hexagonal symmetry. In this Letter, we present a general mechanism by which a PDW with the symmetry of a triangular lattice can be stabilized, based on a superfluid generalization of Landau's theory of the liquid-solid transition. A soft-mode instability at a finite wave vector within the translationally invariant planar-distorted B phase triggers a transition from uniform superfluid to PDW that is first order due to a cubic term generally present in the PDW free-energy functional. This cubic term also lifts the degeneracy of possible PDW states in favor of those for which wave vectors add to zero in triangles, which in two dimensions uniquely selects the triangular lattice.

Self-heterodyned detection of dressed state coherences in helium by noncollinear extreme ultraviolet wave mixing with attosecond pulses

Noncollinear wave-mixing spectroscopies with attosecond extreme ultraviolet (XUV) pulses provide unprecedented insight into electronic dynamics. In infrared and visible regimes, heterodyne detection techniques utilize a reference field to amplify wave-mixing signals while simultaneously allowing for phase-sensitive measurements. Here, we implement a self-heterodyned detection scheme in noncollinear wave-mixing measurements with a short attosecond XUV pulse train and two few-cycle near infrared (NIR) pulses. The initial spatiotemporally overlapped XUV and NIR pulses generate a coherence of both odd (1snp) and even (1sns and 1snd) parity states within gaseous helium. A variably delayed noncollinear NIR pulse generates angularly-dependent four-wave mixing signals that report on the evolution of this coherence. The diffuse angular structure of the XUV harmonics underlying these emission signals is used as a reference field for heterodyne detection, leading to cycle oscillations in the transient wave-mixing spectra. With this detection scheme, wave-mixing signals emitting from at least eight distinct light-induced, or dressed, states can be observed, in contrast to only one light induced state identified in a similar homodyne wave-mixing measurement. In conjunction with the self-heterodyned detection scheme, the noncollinear geometry permits the conclusive identification and angular separation of distinct wave-mixing pathways, reducing the complexity of transient spectra. These results demonstrate that the application of heterodyne detection schemes can provide signal amplification and phase-sensitivity, while maintaining the versatility and selectivity of noncollinear attosecond XUV wave-mixing spectroscopies. These techniques will be important tools in the study of ultrafast dynamics within complex chemical systems in the XUV regime.

Fatigue crack inspection and characterisation using non-collinear shear wave mixing

In recent years, nonlinear ultrasonic techniques have been developed rapidly for defect detection and characterization at its early development stage. In this paper, non-collinear shear wave mixing is used for fatigue crack detection and characterization, exploring how orientation and size may be determined. This is achieved through measuring the amplitude of the generated longitudinal wave from a crack of interest. This amplitude is a function of the interaction angle and frequency ratio of two incident shear waves and the resulting amplitude parameter space is termed the nonlinear fingerprint of the crack. Numerical analysis of the nonlinear interaction between two incident shear waves and cracks was performed using two-dimensional finite element models to explore a broader parameter space than possible experimentally. It is shown that the interaction angle which leads to the maximum generated longitudinal wave amplitude is related to the orientation angle of the crack. To confirm these conclusions the model was validated using experimental measurements of vertical fatigue cracks grown using 3-point bending tests from initiation notches. The polarity flipping method was used to improve signal to noise ratio in such measurements. It is shown that there is a good agreement between the experimentally measured fingerprints and those simulated using finite element methods. Finally, an approximate method for sizing fatigue cracks was introduced that uses multiple non-collinear measurements along the crack length to determine its extent. As expected, the measured sizes from the proposed method indicate greater crack lengths than seen with linear ultrasonic phased array images due to the closed fatigue cracks being undetectable with linear arrays.

High harmonics diffraction caused by an ellipticity grating

We study the generation of high-harmonic beams by the non-collinear wave mixing of two circularly or elliptically polarized fundamental beams. Changing the ellipticity of the two fundamental beams changes the electric field structure in the focal plane, generating multiple high harmonics beamlets. We show that the ellipticity dependence of the harmonic dipole modulates the near-field harmonic intensity, resulting in the diffraction of the generated harmonics in the far-field.

Analytical and numerical modelling of non-collinear wave mixing at a contact interface

An analytical model is presented for wave mixing of two incident non-collinear plane waves at a plane contact interface characterised by a nonlinear traction law that is representative of rough-surface contact, where the normal response is described by a quadratic nonlinearity whereas the tangential response is linear. The approach relies on a decomposition of the scattered field into contributions exhibiting distinctive symmetries with respect to the interface, combined with a perturbation analysis that treats the nonlinear response as a small correction relative to a linear response. The decomposition is shown to lead to uncoupled governing equations, thereby enabling explicit analytical formulae to be derived for the scattered field amplitudes for a linear interface, which in turn provides the source terms for determining the amplitudes and directions of the nonlinear mixed waves. The characteristics of ultrasound wave mixing at an interface are thus shown to differ in several respects from bulk wave mixing due to material nonlinearity. In particular, interface mixing generates mixed waves at the sum and difference frequencies that propagate in both forward and backward directions (transmitted and reflected), whereas bulk mixing only produces a forward propagating mixed wave at the sum frequency. The directions of propagation for interface mixing are determined from the sum or difference of the components of the incident wave vectors parallel to the interface, coupled with the sum or difference of the frequencies, which constitutes a generalisation of Snell's law. These directions generally differ from the sum of the wave vectors that provides the propagation direction for bulk mixing. A computational model is also presented that confirms these predictions of the analytical model. The implications of both models for the design and interpretation of experimental investigations are briefly discussed.

Autoionization dynamics of (2P1/2)ns/d states in krypton probed by noncollinear wave mixing with attosecond extreme ultraviolet and few-cycle near infrared pulses.

The autoionization dynamics of the (2P1/2)ns/d Rydberg states in krypton are investigated using spatially isolated wave-mixing signals generated with a short train of subfemtosecond extreme ultraviolet (XUV) pulses and noncollinear, few-cycle near infrared pulses. Despite ubiquitous quantum beat oscillations from XUV-induced coherences within the excited-state manifold, these wave-mixing spectra allow for the simultaneous evaluation of autoionization lifetimes from a series of Rydberg states above the first ionization potential. Experimentally measured lifetimes of 22 ± 8 fs, 33 ± 6 fs, and 49 ± 6 fs for the wave-mixing signals emitting from the (2P1/2)6d/8s, (2P1/2)7d/9s, and (2P1/2)8d/10s resonances compare favorably with lifetimes for the (2P1/2)6d, 7d, and 8d Rydberg states determined from spectral linewidths. Analysis of the quantum beats reveals that the enhancement of wave-mixing pathways that couple the (2P1/2)nd states to themselves leads to individual reporter state-dependent decays in the wave-mixing signals. The results demonstrate the promise of wave-mixing spectroscopies with subfemtosecond XUV pulses to provide valuable insights into processes governed by electronic dynamics.

Location and Length Measurement of Invisible Fatigue Crack in Metal Components Using Wave Mixing Methods

Abstract For the invisible fatigue crack embedded in metal components, wave mixing methods are applied for the fatigue crack location and length measurement. When two incident waves meet within a component, a nonlinear interaction occurs and a third wave is generated, which is related to the damage degree of the meeting position of the two incident waves. When the delay time of incident waves changed in collinear wave mixing experiments, different meeting positions along the length direction of components were detected. The relationship between the sideband amplitude at difference or sum frequencies and delay time is obtained, and the delay time corresponding to the maximum amplitude is applied to locate the fatigue crack along the length direction. Then, adjusting the placing locations of transducers in the noncollinear wave mixing experiment, the meeting position of incident waves is controlled at the fatigue crack decided by the collinear wave mixing experiment. Next, changing the separation distance of two transmitters, the detection positions would be along the vertical direction of the components. The mixing nonlinear parameters of different detection positions are calculated, and the length of the fatigue crack can be measured in a vertical direction based on the distribution of the mixing nonlinear parameter.

Steering the propagation direction of a non-linear acoustic wave in a solid material

In this research non-collinear wave mixing is used as a non-destructive testing method where the amplitude of the scattering wave contains information on the condition of a material. The practical implementation of non-collinear wave mixing as a non-destructive testing technique is limited by many factors such as the geometry and shape of the structure, the accessibility to the specimen’s surfaces and the ultrasonic sensors available to perform measurements. A novel approach to steer the propagation direction of a generated wave from the mixing of two incident acoustic waves is proposed. The angle of the scattering wave is controlled by the frequencies of the two interaction waves, rather than by the angle between these waves. The scattering amplitude was analytically solved for the longitudinal plus shear interaction process. The analytical solution was validated with experiments. The model qualitatively agrees with the experiments. Furthermore, the possibility to use a wider range of excitation frequencies of the incident waves was found. This is a great advantage in applications where the space and access to the specimen under test is limited.

Fatigue crack detection and fatigue damage imaging using the non-collinear transverse wave mixing technique

ABSTRACTFor the fatigue crack embedded in metallic components, the non-collinear transverse wave mixing technique is applied to detect them and image the fatigue damage around crack. When two non-collinear transverse waves with same frequency meet in components, a resonance longitudinal wave can be generated if the resonance condition is satisfied; the mixing nonlinear parameter is applied to evaluate the nonlinearity of detection positions. The non-collinear wave mixing experiments are conducted on components with different length of fatigue crack. By changing the relative position of transducers, different detection positions can be controlled. According to the distribution of mixing nonlinear parameter at vertical direction, the length of fatigue crack at vertical direction can be measured. Furthermore, the mixing nonlinear parameters of different detection positions around fatigue crack are measured, the image of mixing nonlinear parameter can visualise the damage around fatigue crack which is very easy to assess the fatigue damage of components.

Evaluation of Fatigue Crack Orientation Using Non-collinear Shear Wave Mixing Method

In this paper, a non-collinear shear wave mixing technique is proposed for evaluation of fatigue crack orientation. Numerical analysis of the nonlinear interaction of two shear waves with crack is performed using two-dimensional finite-element simulations. The simulation results show that the nonlinear interaction of the two shears waves with cracks leads to the generation of transmitted and reflected sum-frequency longitudinal waves (SFLW), moreover the propagation direction of reflected SFLW is correlated with the orientation of crack, which can be used for crack orientation evaluation. Non-collinear wave-mixing experiments were conducted on specimens with fatigue crack. The experimental results show that the directivity of the generated SFLW agrees well with the simulation results, and non-collinear shear wave mixing has potential use in fatigue crack orientation evaluation.

Excited-state vibronic wave-packet dynamics in H2 probed by XUV transient four-wave mixing

Author(s): Cao, W; Warrick, ER; Fidler, A; Leone, SR; Neumark, DM | Abstract: The complex behavior of a molecular wave packet initiated by an extreme ultraviolet (XUV) pulse is investigated with noncollinear wave mixing spectroscopy. A broadband XUV pulse spanning 12-16 eV launches a wave packet in H2 comprising a coherent superposition of multiple electronic and vibrational levels. The molecular wave packet evolves freely until a delayed few-cycle optical laser pulse arrives to induce nonlinear signals in the XUV via four-wave mixing (FWM). The angularly resolved FWM signals encode rich energy exchange processes between the optical laser field and the XUV-excited molecule. The noncollinear geometry enables spatial separation of ladder and V- or Λ-type transitions induced by the optical field. Ladder transitions, in which the energy exchange with the optical field is around 3 eV, appear off axis from the incident XUV beam. Each vibrationally revolved FWM line probes a different part of the wave packet in energy, serving as a promising tool for energetic tomography of molecular wave packets. V- or Λ-type transitions, in which the energy exchange is well under 1 eV, result in on-axis nonlinear signals. The first-order versus third-order interference of the on-axis signal serves as a mapping tool of the energy flow pathways. Intra- and interelectronic potential energy curve transitions are decisively identified. The current study opens possibilities for accessing complete dynamic information in XUV-excited complex systems.

Scanning non-collinear wave mixing for nonlinear ultrasonic detection and localization of plasticity

Non-collinear wave mixing recently has been proposed to detect and localize micro-damage in materials. It is proved sensitive to the interaction angle α of the incident waves. In this work, the relationship between the acoustic nonlinearity parameter χ and the α is studied by numerical simulations and experimental measurements based on the nonlinear interaction of two shear waves. A single-peak change in the normalized acoustic nonlinearity parameter χ′ of the mixing wave versus the incident angle is observed from numerical simulations and then is verified by experiments. The results show a -6 dB decrease of χ′ corresponds to a deviation of about 4° in the incident angle. Meanwhile, the detection and localization of plastic deformation is also conducted on an aluminum alloy based on the scanning of non-collinear wave mixing, in which the distribution of the acoustic nonlinearity is similar to that of the plastic strain.

Evaluation and Life Extension of Asphalt Pavements Using Rejuvenators and Noncollinear Ultrasonic Wave Mixing: A Review

Except for the relatively small zones within pavements that are subjected to loadings, the primary challenge in asphalt concrete (AC) pavement design and maintenance is to prevent and/or control environmentally induced distresses. Distresses, including block and thermal cracking, and possibly raveling of construction joints, tend to accelerate with time; as a result, it is critical to evaluate the state of crack resistance in asphalt pavement surfaces before and after maintenance treatments. A review of the use of noncollinear wave mixing to evaluate oxidative aging of AC pavements, and the used of rejuvenators in oxidized pavements toward extension of pavement life, is presented. The approach requires no core extraction. Results show that the noncollinear wave mixing can evaluate the state of oxidative aging of AC pavements. Results also indicate that the use of rejuvenators is a successful strategy of pavement maintenance and sustainability.

Distribution of the amplitude of the magnetic potential of diffractive beams generated in a ferrite slab by a surface spin wave incident on a slit in an opaque screen

The total magnetic potential generated in the far field of a ferrite slab as a result of a plane noncollinear surface spin wave incident on a slit in an opaque screen is investigated. The dependence of the potential amplitude from the polar angle in the plane of a ferrite slab is calculated for different orientations of the screen with relative to an external magnetic field magnetizing the slab. It is found that two diffractive beams are generated in the slab as a result of spin diffraction on the slit. The angular width of each beam depends largely on the slit’s orientation and can be greater or smaller than value λ n /D (where D is the slit’s width and λ n is the length of the spin wave corresponding to each beam).