Wavefront Curvature Research Articles

A numerical study of Lamb wave localization in thin plates using a passive co-linear phased array

Lamb waves have become increasingly popular in the field of aerospace vehicle non-destructive testing and evaluation as well as structural health monitoring. These guided waves possess the ability to travel long distances and exhibit a notable inclination to interact with existing damage. This work has numerically explored for the first time the use of a passive co-linear phased array to localize emission sources over a wide range of variables. Three localization methods are explored, namely, reverse beamforming, wavefront curvature ranging, and hyperbolic lateration in a direction comparison without modeling transducers. It was shown that both reverse beamforming and wavefront curvature ranging could localize an emission with <1% error in both range and bearing, while hyperbolic lateration was significantly worse. A relationship between bearing error and bearing was demonstrated, presenting the ability to develop new methods with correction factors that can localize emissions with even greater accuracy.

Pattern transformation and control of generalized multi-peak breathing solitons induced by transverse cross modulation

Based on the nonlocal nonlinear Schrödinger equation, the pattern transformation and control of transverse cross-modulated sine-Gaussian (TCMSG) breathing solitons during transmission are studied. Several expressions have been derived, including the transmission, soliton width, phase wavefront curvature, and so on. The study demonstrates that the coefficient of transverse cross modulation term controls the pattern transformation of the TCMSG breathing solitons. TCMSG breathing solitons can form generalized spatial solitons and breathers during transmission. The variation of the soliton width extrema and their change rates with the transverse cross modulation term coefficient is investigated. The influence of the initial incident power and the transverse cross modulation term coefficient on the soliton width change rate and phase wavefront curvature extrema is studied.

Talbot phenomenon in binary optical gratings under Gaussian illumination

Binary optical gratings are used in applications such as optical metrology. Due to the fact, that self-imaging phenomenon depends on the grating fill factor, in present work the effect of fill factor on Talbot image formation has been analyzed when the grating is illuminated with a Gaussian beam. A model based on Fresnel regime is used to determine the intensity distribution in the near field. Self-images are obtained under different initial beam conditions and it is found several regimes of the effect of Gaussian beam intensity distribution on the self-images are found: (I) decreasing intensity of grating slit at the beam border when Gaussian waist radius is 10 times greater than grating period, (II) transforming binary-like self-image to the cosine-like one in case when Gaussian waist radius ranges from 2 to 5 grating periods, and (III) disappearing regular grating structure when Gaussian waist radius is less than grating period. Additionally it is analyzed transform from Fresnel to Fraunhofer regime in case of Gaussian beam and effect of wavefront curvature radius value on the distance where different regimes appear.

Interfacing high numerical aperture metalenses with thermally expanded core fibers via 3D nanoprinting for advanced meta-fiber operation.

This study introduces a novel meta-fiber design that combines single-mode fibers with thermally expanded cores and nano-printed high numerical aperture metalenses. These advanced meta-fibers feature enlarged mode field diameters, offering improved mechanical stability, reduced environmental sensitivity and simplified metalens design by minimizing wavefront curvature. The concept's validity is confirmed through high numerical aperture metalenses, nanoprinted onto thermally expanded core fibers, demonstrating diffraction-limited focusing up to a numerical aperture of 0.9 in air and water. This innovative approach has potential applications in optical trapping, life science imaging, environmental sensing, and fiber-chip coupling in integrated photonics.

Wavefront curvature analysis derived from preprocedural imaging can identify the critical isthmus in patients with postinfarcted ventricular tachycardia

BackgroundWhere activation wavefront curvature is convexly shaped, functional conduction block can occur. ObjectiveThe purpose of this study was to determine whether left ventricular (LV) wall thickness determined from contrast-enhanced computed tomography (CT) is useful in localizing such areas in clinical postinfarction reentrant ventricular tachycardia (VT). MethodsWe evaluated data from 6 patients who underwent catheter ablation for postinfarction VT. CT imaging with inHEART processing was conducted 1–3 days before electrophysiological (EP) study to determine LV wall thickness (T). Activation wavefront curvature was approximated as ΔT/T, where ΔT represents wall thickness change. During EP study, bipolar LV VT electrograms were acquired using a high-density mapping catheter, and activation times were determined. Maps of T, ΔT/T, and VT activation were subsequently compared using statistical analyses. ResultsTwo of 6 cases exhibited dual circuit morphologies, resulting in a total of 8 VT morphologies analyzed. The LV wall near the VT isthmus location tended to be thin, on the order of a few hundred micrometers. Regions of largest ΔT/T partially coincided with the lateral isthmus boundaries where electrical conduction block occurred during VT. ΔT/T at the boundaries, measured from imaging, was significantly larger compared to values at the isthmus midline and to the global LV mean value (P <.001). ConclusionWavefront curvature measured by ΔT/T and caused by source–sink mismatch is dependent on ventricular wall thickness. Areas of high wavefront curvature partly coincide with and may be helpful in locating the VT isthmus in infarct border zones using preprocedural imaging analysis.

Generalized cosine-Gaussian breathing solitons with transverse cross modulation in nonlocal nonlinear media

Based on the nonlocal nonlinear Schrödinger equation, the propagation characteristics of transverse cross-modulated cosine-Gaussian (TCMCG) breathing solitons in strongly nonlocal media are studied. A series of mathematical expressions are provided to describe the propagation dynamics characteristics of the TCMCG breathing solitons, including the soliton width, soliton width change rate, soliton width extreme values, change rates of soliton width extreme values, phase wavefront curvature and phase wavefront curvature extreme values, etc. The research results indicate that by modulating TCMCG breathing solitons, generalized high-order spatial solitons can be formed with periodic changes in light intensity modes but unchanged in beam width. The cosine function parameter has a significant impact on the propagation dynamics characteristics, which appears in the initial expression and plays a cross modulation role in the transverse spatial light intensity. The effect of the initial incident power on soliton width extreme values and phase wavefront curvature extreme values is also discussed.

DG-based joint transmission-reflection traveltime tomography and its application of borehole seismic

Abstract The limitations of the coverage range and density of transmission wave often result in less-than-ideal results in traveltime tomography. In contrast, joint transmission-reflection traveltime tomography can not only recover deep structures that transmission tomography cannot detect but also optimize its inversion results. In this article, we perform joint tomography on borehole seismic (VSP, RVSP and crosswell seismic) data to obtain near-wellbore structures. In the forward part, we solve the factored equation by the discontinuous Galerkin (DG) method to calculate the transmission/reflection traveltime. Due to the large wavefront curvature near the source point, the traveltime errors generated by the numerical simulation will propagate from the source to all the calculation domains. According to the factorization principle, the equation solution is decomposed into two parts to solve the point-source singularity. To further improve the accuracy of solving traveltime, we use the DG method to solve the factored eikonal equation with additive factors (the factored DG method), obtaining second-order accuracy solution. The adjoint-state method is employed in the inversion section to calculate the gradient of the misfit function. And we use the traveltime difference observed inside the model to define the misfit function, which is more suitable for borehole seismic and avoids the influence of surface normal vectors on gradients. Numerical tests applied on models indicate that the joint tomography method has the potential to accurately inverse the seismic structure information near the well and recover the deep underground structure.

Generative adversarial network-enhanced directional seismic wavefield decomposition and its application in reverse time migration

Reverse time migration (RTM) is an accurate method for imaging complex geologic structures without imposing any dip limitations. However, a large amount of high-amplitude low-frequency noise, which is mainly generated by the crosscorrelation of source and receiver wavefields propagating in the same directions, seriously contaminates the image quality. The causal imaging condition with separated up- and downgoing wavefields is an effective approach to reduce these low-frequency artifacts. Explicit up- and downgoing wavefield decomposition based on the Hilbert transform is computationally expensive due to additional wavefield extrapolation and storage for the imaginary parts. Directionally propagating wavefields have distinctive kinematic patterns such as traveltime and wavefront curvature, which provide us an opportunity to implement the wavefield decomposition using the statistical neural network method. Using extrapolated wavefields as the input and the decomposed up-, down-, left-, and rightgoing wavefields as the labeled data, we train a pair of generative adversarial networks to predict the directional wavefields. The training data sets are generated using seismic full-waveform modeling and explicit wavefield decomposition based on the Hilbert transform. Then, the decomposed directional wavefields are incorporated into a novel imaging condition that depends on the subsurface dip angles to compute the reflectivity perpendicular to the reflectors. Numerical experiments demonstrate that our method can produce accurate directional wavefield decomposition results and high-quality reflectivity images without low-wavenumber artifacts.

Curvature-mediated source and sink effects on the genesis of premature ventricular complexes in long QT syndrome.

Premature ventricular complexes (PVCs) are spontaneous excitations occurring in the ventricles of the heart that are associated with ventricular arrhythmias and sudden cardiac death. Under long QT conditions, PVCs can be mediated by repolarization gradient (RG) and early afterdepolarizations (EADs), yet the effects of heterogeneities or geometry of the RG or EAD regions on PVC genesis remain incompletely understood. In this study, we use computer simulation to systematically investigate the effects of the curvature of the RG border region on PVC genesis under long QT conditions. We show that PVCs can be either promoted or suppressed by negative or positive RG border curvature depending on the source and sink conditions. When the origin of oscillation is in the source region and the source is too strong, a positive RG border curvature can promote PVCs by causing the source area to oscillate. When the origin of oscillation is in the sink region, a negative RG border curvature can promote PVCs by causing the sink area to oscillate. Furthermore, EAD-mediated PVCs are also promoted by negative border curvature. We also investigate the effects of wavefront curvature and show that PVCs are promoted by convex but suppressed by concave wavefronts; however, the effect of wavefront curvature is much smaller than that of RG border curvature. In conclusion, besides the increase of RG and occurrence of EADs caused by QT prolongation, the geometry of the RG border plays important roles in PVC genesis, which can greatly increase the risk of arrhythmias in cardiac diseases.NEW & NOTEWORTHY The effects of the curvature or geometry of the repolarization gradient region and wavefront curvature on the genesis of premature ventricular complexes are systematically investigated using computer modeling and simulation. Premature ventricular complexes can be promoted by either positive or negative curvature of the gradient region depending on the source and sink conditions. The underlying mechanisms of the curvature effects are revealed, which provides mechanistic insights into arrhythmogenesis in cardiac diseases.

Predicting second-harmonic generation in shear wave beams in tissue-mimicking phantoms

Planar nonlinear shear waves in isotropic media are subject to only cubic nonlinear effects and generate only odd harmonics during propagation. However, wavefront curvature in shear wave beams breaks the symmetry and yields quadratic nonlinear effects, and therefore, a second harmonic may be present in shear wave beams depending on the polarization of the wave. Focused radially polarized shear wave beams have been generated in tissue-mimicking phantoms [Cormack et al., IEEE TBME (2024)], and it is postulated that the second harmonic may be used to estimate the quadratic nonlinearity in such a medium as an additional biomarker for diseased tissue. Here, an analytical solution obtained in the paraxial approximation for nonlinear propagation of a shear wave beam in an absorbing medium [Spratt et al., AIP Conf. Proc. 1685, 080007 (2015)] is used to characterize the strength of second-harmonic generation. Feasibility of measuring the second harmonic experimentally in a weakly nonlinear, radially polarized focused shear wave beam propagating in a tissue-like medium is explored. Second-harmonic generation in focused shear wave beams with other polarizations is discussed. [P.G.K. was supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

An Extended Polar Format Algorithm for Joint Envelope and Phase Error Correction in Widefield Staring SAR with Maneuvering Trajectory

Polar format algorithm (PFA) is a widely used high-resolution SAR imaging algorithm that can be implemented in advanced widefield staring synthetic aperture radar (WFS-SAR). However, existing algorithms have limited analysis in wavefront curvature error (WCE) and are challenging to apply to WFS-SAR with high-resolution and large-swath scenes. This paper proposes an extended polar format algorithm for joint envelope and phase error correction in WFS-SAR imaging with maneuvering trajectory. The impact of the WCE and residual acceleration error (RAE) are analyzed in detail by deriving the specific wavenumber domain signal based on the mapping relationship between the geometry space and wavenumber space. Subsequently, this paper improves the traditional WCE compensation function and introduces a new range cell migration (RCM) recalibration function for joint envelope and phase error correction. The 2D precisely focused SAR image is acquired based on the spatially variant inverse filtering in the final. Simulation experiments validate the effectiveness of the proposed method.

Complex far fields and optical singularities due to propagation beyond tight focusing: combined effects of wavefront curvature and aperture diffraction

All optical systems, which involve the collimation of a reflected, transmitted or scattered wave subsequent to tight focusing, are subject to two kinds of deviations. One is the wavefront curvature due to inaccurate focal placement of the interface or scatterer particle under consideration, and the other is the diffraction caused by the finite lens aperture. In the present paper we explore these phenomena in detail by considering a rigorous simulated model and an appropriate experimental setup. We hence demonstrate the complicated intensity profiles and optical singularity characteristics of the observed far field. Then we describe ways to minimize these deviations in a general experiment. But more importantly, our analysis proves that these deviations by themselves are significant optical phenomena of fundamental interest. The observed complex field profiles have similarities to standard diffraction-limited tight focal fields, though our field detection is different from the standard schemes. This indicates the relevance of these complex fields to a larger class of systems involving wavefront curvature and aperture diffraction. The detailed analysis and results of the present paper already serve as core explorations of these optical phenomena; and we also suggest future research directions where these system aspects can be purposefully created and explored further.

Two-stage Correction for Wavefront Curvature Effects of PFA in Focusing Non-ideal Circular SAR Data

Two-stage Correction for Wavefront Curvature Effects of PFA in Focusing Non-ideal Circular SAR Data

Dissipative light bullets in a doped and weakly nonlocal optical fiber

The letter introduces an extended (3+1)-dimensional [(3+1)D] nonlocal cubic complex Ginzburg-Landau equation describing the dynamics of dissipative light bullets in optical fiber amplifiers under the interplay between dopants and a spatially nonlocal nonlinear response. The model equation includes the effects of fiber dispersion, linear gain, nonlinear loss, fiber nonlinearity, atomic detuning, linear and nonlinear diffractive transverse effects, and nonlocal nonlinear response. A system of coupled ordinary differential equations for the amplitude, temporal, and spatial pulse widths and position of the pulse maximum, unequal wavefront curvatures, chirp parameters, and phase shift is derived using the variational technique. A stability criterion is established, where a domain of dissipative parameters for stable steady-state solutions is found. Direct integration of the proposed nonlocal evolution equation is performed, which allows us to investigate the evolution of the Gaussian beam along a doped nonlocal optical fiber, showing stable self-organized dissipative spatiotemporal light bullets.

Annular rogue waves in whispering gallery mode optical resonators

Based on the variable-coefficient Lugiato-Lefever equation, nonlinear dynamics of rogue waves in whispering gallery mode optical resonators are studied. By means of the analytical solution in the absence of pump, dynamical behaviors of the rogue waves in the periodic system are discussed. Firstly, the first-order rogue wave under the condition of no pumping has obvious periodic nature, and the periodicity of width and amplitude of rogue wave can be consistent by controlling the wavefront curvature, and the energy of rogue wave remains stable under the small gain parameter, and the inverse diffraction effect makes the center position of rogue wave produce a small offset. In addition, the amplitudes of second-order rogue waves have more complicated periodicity and longer period lengths both with the good stability. At last, the dynamical behaviors of rogue wave after adding external excitation are investigated. Under the periodical external excitation with the lower intensity, rogue wave can achieve a longer stable transmission time, while the smaller wavefront curvature can effectively prolong the stable transmission time of rogue wave. Moreover, we investigate the influence of different forms of external excitation on rogue wave, and the periodical external excitation makes rogue waves more stable than the constant external excitation. These results extend the application of higher-order rogue waves in (2 + 1)-dimensional nonlinear systems, and have implications for the development of high-energy optical pulses.

High-precision laser beam lateral displacement measurement based on differential wavefront sensing.

Accurately lateral displacement measurement is essential for a vast of non-contact sensing technologies. Here, we introduce a high-precision lateral displacement measurement method based on differential wavefront sensing (DWS). Compared to the conventional differential power sensing (DPS) method, the DWS method based on phase readout has the potential to achieve a higher resolution. The beam lateral displacement can be obtained by the curvature distribution of the wavefront on the surface of the detector. According to the theoretical model of the DWS method, the sensitivity of the lateral displacement can be greatly improved by increasing the wavefront curvature of the measured laser beam by means of lenses. An optical system for measuring the lateral displacement of the laser beam is built and calibrated by a high-precision hexapod. The experimental results show that the DWS-based lateral displacement measurement achieves a resolution of 40 pm/Hz1/2 (at 1-10 Hz) with a linear range of about 40 µm, which is consistent with the theoretical model. This technique can be applied to high-precision multi-degree-of-freedom interferometers.

Numerical implementation of three-dimensional vectorial complex ray model and application to rainbow scattering of spheroidal drops.

The rainbow patterns of oblate spheroidal drops have been observed in experiments nearly forty years ago [Nature312, 529 (1984)10.1038/312529a0]. However, the prediction for those complex patterns has been a challenge for conventional light scattering models. The vectorial complex ray model (VCRM) allows to account for the direction, the polarization, the phase, the amplitude and the wavefront curvature of waves and provides a powerful tool for the study of the light/electromagnetic wave interaction with a homogeneous object of any shape with smooth surface. In [Opt. Lett.46, 4585 (2021)10.1364/OL.434149], the authors have reported an important breakthrough of VCRM for the three-dimensional scattering (VCRM3D) and the simulated rainbow patterns of oblate drops. The present paper is devoted to the detailed description of the numerical implementation allowing the simulation of the 3D scattering field by a nonspherical particle. Its ability to predict both the fine and coarse intensity structures of the rainbows and the near-backward scattering patterns of spheroids is demonstrated. This work opens perspectives for exploring the 3D scattering characteristics of large objects with any smooth shape and developing relevant optical techniques for particle characterization.

Source range and depth estimation of propeller cavitation bubble collapse transients in a multipath environment

An experiment is conducted in which a wide aperture array, which is proximate to the sea floor in water 20 m deep, records transits of two motorboats. Occasionally, acoustic transients, which are attributed to collapsing propeller cavitation bubbles, are observed to be superimposed on the continuous broadband radiated noise component of each of the array’s three widely spaced hydrophones. By measuring the time differences of arrival of the transient signals propagating via the direct path at adjacent pairs of hydrophones, passive ranging by wavefront curvature is used to estimate the range and bearing of the transient source. Next, the source depth is estimated by measuring the multipath delay of the surface reflected transient signal. Also, the spectrogram of a single hydrophone’s output is observed to display a Lloyd’s mirror interference pattern due to the direct propagation path of the broadband radiated noise combining with the indirect propagation path signal reflected from the sea floor. The reciprocal of the frequency difference between adjacent destructive interference fringe minima is equal to the multipath time delay. This multipath delay, which equates to the quefrency of the cepstrum’s first rahmonic, contains source range information. The results of the two passive ranging methods are presented.

Evolution and dynamics of spatial self-phase modulation in pyrromethene 567 for all-optical photonic diode applications

Spatial self-phase modulation has emerged as a novel and ubiquitous nonlinear optical effect, revealing potential application in all-optical devices for signal processing. The work investigates the evolution and dynamics of SSPM patterns in pyrromethene 567 (PM 567). A temperature-dependent refractive index gradient which induces a phase shift in the incident beam is responsible for the formation of spatial self-phase modulation. The non-linear response of PM 567 in different solvents and concentrations is investigated and tabulated. The effect of wavefront curvature, path length, and mechanical chopper on the formation of the SSPM patterns was studied. To our knowledge, an optical-diode-based unidirectional generation of spatial self-phase modulation in dyes has been reported for the first time. Simply cascading PM 567 dissolved in DMSO and Methanol having distinct nonlinear optical responses, an all-optical diode for unidirectional light propagation based on spatial self-phase modulation in PM 567 was achieved. The work reveals the potential application of PM 567 for achieving spatial asymmetry in light propagation based on SSPM in photonic devices for all-optical signal processing.

Spherical-wave elastic inversion in transversely isotropic media with a vertical symmetry axis

SUMMARY Although subsurface media are usually assumed to be isotropic, anisotropy is ubiquitous in crustal rocks and leads to the variation of seismic response with direction. Transversely isotropic media with a vertical symmetry axis (VTI media) are widely found in the real world, such as in textured shale reservoirs. Plane-wave reflection coefficients (PRCs) in VTI media have been widely exploited in amplitude variation with offset (AVO) inversion to estimate the elastic and anisotropy parameters of subsurface media. However, the PRCs in VTI media meet some fundamental problems, especially at near-critical or post-critical incidence angles where the spherical-wave effect is significant. To consider the wave front curvature, a complex spherical-wave reflection coefficient (SRC) in VTI media is derived. To better understand the spherical-wave seismic response in VTI media, we investigate the dependence of the complex SRC on frequency, reflector depth and Thomsen anisotropy parameters ($\varepsilon $ and $\delta $). Based on a complex convolution model, a spherical-wave AVO inversion approach in VTI media is proposed to estimate the vertical (symmetry-axis) compressional and shear wave velocities (P and S waves), density and Thomsen anisotropy parameters from observed seismic data with different incidence angle and frequency components. Synthetic data with Gaussian random noise are used to verify the robustness of the spherical-wave AVO inversion approach in VTI media. Field data examples show that the proposed approach can produce reasonable inversion results that match well with the well-logging data.