Tilted Wave Research Articles

Investigating exact solutions, sensitivity, and chaotic behavior of multi-fractional order stochastic Davey–Sewartson equations for hydrodynamics research applications

Our research aims to explore the fractional derivative of the Stochastic Davey–Stewartson equation (FDSDSEs) and make contributions in seven aspects: Firstly, we discovered previously unknown exact solutions for FDSDSEs, including Weierstrass elliptic function solutions. These findings provide new insights for our understanding and analysis of these equations. Secondly, we analyzed the effect of noise on stochastic solutions. We found that higher noise intensity can disrupt patterns and result in flatter surfaces. However, we observed that multiplicative noise can stabilize the solution to some extent. This reveal the role of noise in stochastic dynamics and has important implications for wave behavior in the ocean environment. Thirdly, we emphasized the impact of fractional derivatives on noise dynamics. Our research indicates the importance of considering the order of derivatives α in analysis and modeling. Different order derivatives have different effects on noise, which is significant for ocean researchers in selecting appropriate derivatives to study stochastic systems. Fourthly, we compared the effects of different fractional derivatives on noise in stochastic solutions. We found that choosing appropriate derivative orders can more accurately describe wave behavior in the ocean environment. This discovery has important implications for improving wave models and predicting ocean waves. Fifthly, we studied the influence of tilted wave variations in FDSDSE solutions. We observed spiral-like patterns, providing new insights into wave propagation in the ocean. This is significant for understanding wave behavior in the ocean and relevant ocean engineering applications. Sixthly, we explored the phase diagrams and chaotic behavior of FDSDSE through sensitivity analysis and perturbation factors. This enhances our understanding of practical applications and control strategies in ocean hydrodynamics research and is also important for delving into the dynamic behavior and phase diagrams of these equations. Finally, we compared our research results with well-known wave phenomena in the ocean through visualization, highlighting the practical relevance of our study. These comparisons involve random propagation of ocean solitary waves, twisting propagation of ocean waves, and rotating propagation of solitary waves, providing some inspiration for advancing the fields of ocean science and engineering.

Efficient and accurate intensity diffraction tomography of multiple-scattering samples.

Optical Diffraction Tomography (ODT) is a label-free method to quantitatively estimate the 3D refractive index (RI) distributions of microscopic samples. Recently, significant efforts were directed towards methods to model multiple-scattering objects. The fidelity of reconstructions rely on accurately modelling light-matter interactions, but the efficient simulation of light propagation through high-RI structures over a large range of illumination angles is still challenging. Here we present a solution dealing with these problems, proposing a method that allows one to efficiently model the tomographic image formation for strongly scattering objects illuminated over a wide range of angles. Instead of propagating tilted plane waves we apply rotations on the illuminated object and optical field and formulate a new and robust multi-slice model suitable for high-RI contrast structures. We test reconstructions made by our approach against simulations and experiments, using rigorous solutions to Maxwell's equations as ground truth. We find the proposed method to produce reconstructions of higher fidelity compared to conventional multi-slice methods, especially for the challenging case of strongly scattering samples where conventional reconstruction methods fail.

Efficient Dense Orbital Angular Momentum Demultiplexing Enabled by Quasi‐Wavelet Conformal Mapping

AbstractOrbital angular momentum (OAM) has recently attracted increasing interest in optical communications for capacity scaling by OAM mode‐division multiplexing (MDM). OAM (de)multiplexer is crucial to the success of OAM‐MDM communications. Scalable and efficient dense OAM demultiplexing is highly desired, but full of challenges. Here, a quasi‐wavelet conformal mapping method is proposed and demonstrated to implement scalable and efficient dense OAM demultiplexing. The OAM mode is divided at the input plane into multiple concentric rings, which are mapped to multiple tilted plane waves and arranged side by side in a line. The engineered transformed light beams with periodic extension and increased length enable narrow focused spot width, reduced beam overlap, and suppressed demultiplexing crosstalk. The quasi‐wavelet conformal mapping method is compared with conventional log‐polar transformation scheme and hybrid log‐polar and fan‐out technique, and the crosstalk matrix for OAM demultiplexing is measured. Efficient OAM demultiplexing is demonstrated for 15 OAM modes (OAM−7 to OAM+7) with a maximum crosstalk of −12.1 dB in the experiment. Moreover, the method is also applied to system‐level data‐carrying OAM‐MDM communications with favorable performance. The demonstrated quasi‐wavelet conformal mapping method may pave the way for future ultrahigh capacity dense OAM‐MDM communications with a large number of OAM modes.

Dynamics of the Transient Negative Eddy Response to Zonal-Mean Zonal Wind Variations

Abstract Many studies have focused on the long-term positive feedback between annular mode zonal wind (U) perturbations and the eddy momentum fluxes (M). Lagged correlation analysis between U and M anomalies, however, shows that a transient period of negative eddy forcing follows the peak in zonal wind anomalies. This negative forcing is more ubiquitous than the positive feedback because it occurs for all U EOFs not just EOF1. It has been hypothesized that this response is either 1) an intrinsic feature of the eddies independent of the U or 2) caused by U-induced changes in Rossby wave reflection. Here it is shown that the response can be reproduced in a GCM by imposing a rapid change in U; therefore, mechanism 1 does not appear to be relevant. Furthermore, the transient response can be generated in a model when there are no turning latitudes; therefore, mechanism 2 does not appear to be relevant. Instead it is shown that the transient response is due to the adjustment of a preexisting eddy field to a change in the background wind. This transient effect is negative when the meridional scale of the U change is small enough compared to the waves, and vice versa. The sign of the initial response depends on the relative size of advection by U versus retrogression by the background vorticity gradient on the meridional tilt of the Rossby waves. Finally, it is shown that this transient response has a large damping effect on U variability.

Complex illumination system for fast interferometric measurements

Freeform metrology is an enabling technology for today’s research and advanced manufacturing. The Tilted Wave Interferometer is a full field measurement system for fast and flexible measurements. It is based on an off-axis illumination scheme based on a microlens array. In this contribution, we present a novel illumination system for the tilted wave interferometer, that allows to reduce the measurement time by a factor of four using parallelization based on wavelength multiplexing. Here we present a design solution that utilizes the flexibility of 3D-printing. The microlenses are realized as multi-order diffractive optical elements, providing a high efficiency compared to colorfilter based realizations. To boost the light efficiency of the novel illumination system further, a field lens functionality is added to the system by adding individual micro-prisms to each microlens. The system is manufactured by the use of grayscale two-photon polymerisation.

Tilted Wave Fizeau Interferometer for flexible and robust asphere and freeform testing

Tilted Wave Interferometry (TWI) is a measurement technique for fast and flexible interferometric testing of aspheres and freeform surfaces. The first version of the tilted wave principle was implemented in a Twyman-Green type setup with separate reference arm, which is intrinsically susceptible to environmentally induced phase disturbances. In this contribution we present the TWI in a new robust common-path (Fizeau) configuration. The implementation of the Tilted Wave Fizeau Interferometer requires a new approach in illumination, calibration and evaluation. Measurements of two aspheres and a freeform surface show the flexibility and also the increased stability in both phase raw data and surface measurements, which leads to a reduced repeatability up to a factor of three. The novel configuration significantly relaxes the tolerances of the imaging optics used in the interferometer. We demonstrate this using simulations on calibration measurements, where we see an improvement of one order of magnitude compared to the classical Twyman-Green TWI approach and the capability to compensate higher order error contributions on the used optics.

Gravitational waves from spectator Gauge-flation

We investigate the viability of inflation with a spectator sector comprised of non-Abelian gauge fields coupled through a higher order operator. We dub this model “spectator Gauge-flation”.We study the predictions for the amplitude and tensor tilt of chiral gravitational waves and conclude that a slightly red-tilted tensor power spectrum is preferred with . As with related models, the enhancement of chiral gravitational waves with respect to the single-field vacuum gravitational wave background is controlled by the parameter γ=g2 Q2/H2, where g is the gauge coupling, H is the Hubble scale and Q is the VEV of the SU(2) sector.The requirement that the SU(2) is a spectator sector leads to a maximum allowed value for γ, thereby constraining the possible amplification.In order to provide concrete predictions, we use an α-attractor T-model potential for the inflaton sector. Potential observation of chiral gravitational waves with significantly tilted tensor spectra would then indicate the presence of additional couplings of the gauge fields to axions, like in the spectator axion-SU(2) model, or additional gauge field operators.

Preliminary Significant Wave Height Retrieval from Interferometric Imaging Radar Altimeter Aboard the Chinese Tiangong-2 Space Laboratory

The interferometric imaging radar altimeter (InIRA) aboard the Chinese Tiangong-2 space laboratory is the first spaceborne imaging radar working at low incidence angles. This study focuses on the retrieval of significant wave heights (SWHs) from InIRA data. The retrieved SWHs can be used for correcting the sea state bias of InIRA-derived sea surface heights and can supplement SWH products from other spaceborne sensors. First, we analyzed tilt, range bunching and velocity bunching wave modulations at low incidence angles, and we found clear dependencies between the SWH and two defined factors, range and azimuth integration, for ocean waves in the range and azimuth directions, respectively. These dependencies were further confirmed using InIRA measurements and collocated WaveWatch III (WW3) data. Then, an empirical orthogonal SWH model using the range and azimuth integration factors as model inputs was proposed. The model was segmented by the incidence angle, and the model coefficients were estimated by fitting the collocation at each incidence angle bin. Finally, the SWHs were retrieved from InIRA data using the proposed model. The retrievals were validated using both WW3 and altimeter (JASON2, JASON3, SARAL, and HY2A) SWHs. The validation with WW3 data shows a root mean square error (RMSE) of 0.43 m, while the average RMSE with all traditional altimeter data is 0.48 m. This indicates that the InIRA can be used to measure SWHs.

Point diffraction interferometer with tilted waves for measuring complex surfaces

Recently, much attention has been paid to optical components with complex surfaces because they can significantly optimize the aberrations of optical systems. However, a complex surface introduces several difficulties for precise measurement. To address this challenge, we propose tilted-wave point diffraction interferometer (TPDI) for measurements of complex surfaces. TPDI combines the advantages of tilted-wave interferometry and point diffraction interferometry, thus enabling high-precision measurements of complex surfaces; moreover, this method has demonstrated good efficiency and versatility. We adopt a fiber array (FA) to generate diffractive tilted waves to compensate for the local gradient of the test specimen. Unlike the classical PDI, which focuses more on the beam quality of the on-axis diffractive wave, the proposed system requires better quality for both the on-axis and off-axis diffractive waves. Therefore, the main parameters of the FA that may introduce measurement errors are analyzed, including the end face roughness of the array, the quality of diffractive wavefronts, and the initial optical path differences. Finally, the measurement result of the high-order hyperboloid verifies that our TPDI is effective and its precision of testing a complex surface is better than λ / 37 (rms, λ = 632.8 nm).

Lamellar instabilities during scanning laser melting of Al–Cu eutectic and hypoeutectic thin films

Scanning laser melting was employed to investigate directional solidification in Al–Cu thin films, 200 and 500 nm thick. The Al–Cu alloy films, with both eutectic and hypoeutectic compositions, were co-deposited on fused silica substrates by magnetron sputtering. Melting of the films was carried out in air using a CW laser, as a function of the scan velocity, v, up to 5 cm/s. For eutectic films, regular lamellar microstructure was observed over the entire range of velocities studied. Interlamellar spacings, λ, below 50 nm were readily produced. Results were found to be consistent with studies on bulk Al–Cu alloys, obeying the classic steady state lamellar growth relationship, λ2v = K. However, the value of the constant, K is significantly larger in thin films when compared to bulk. This is attributed to constraints on mechanisms for spacing adjustment in two-dimensional eutectic systems. In the hypoeutectic thin films, a complex lamellar structure was observed as the scan velocity was reduced. Regions of straight lamellae, oscillatory lamellae, solitary tilt waves, and recurring extreme lamellar branching events coexisted across the melt track. Fourier analysis was used to quantify the chaotic area fraction of the films. The transition to chaos occurred as the G/v ratio increased, attributed to approaching a re-entrant eutectic-to-dendritic transition from above. Approaches to further refine laser melting in thin eutectic films in order to better control solidification processes are discussed.

Detection of living cervical cancer cells by transient terahertz spectroscopy.

The photonic energy of terahertz wave is in the same order of magnitude as the rotational and vibrational energy levels of organic and biological macromolecules, so it has unique advantages in detecting cells and biological macromolecules. However, in the life environment, the dynamic time scale of cell-environment interaction and structural conformation change of biological macromolecules are within picosecond to millisecond, and water has strong absorption to terahertz wave, which has become the bottleneck problem for the detection of cells and biological macromolecules by terahertz technology. In this article, we developed a set of terahertz single measurement system based on the tilt wave front of grating pulse technique. The system was employed for the terahertz detection of trace living cervical cancer cells. We achieved transient detection of the terahertz pulse time-domain waveform of the living HeLa cells. The characteristic absorption peaks were identified by Lambert-Beer law, respectively, at 0.49, 0.71, 1.04, 1.07, 1.26 and 1.37 THz. The absorbance is proportional to the cell concentration.

3041Wall shear stress measurement by ultrafast vector flow imaging for atherosclerotic carotid stenosis

Abstract Background Carotid plaque vulnerability assessment is an important factor in guiding the decision to treat significant carotid stenosis. Ultrafast Ultrasound Imaging (UF) offers the possibility of evaluating local flow velocities over an entire 2D image, allowing access to velocity measurements in contact with the arterial wall and to measure the wall shear stress (WSS). Purpose To evaluate the feasibility of WSS measurement in a prospective series of patients with carotid stenosis. Methods A 7.5 MHz linear probe of an Aixplorer scanner was used. UF acquisitions had 3 tilted plane waves transmits (−10; 0; 10°) and an effective frame rate of 5000Hz. We evaluated the flow velocity in 5 areas of the carotid wall: common carotid artery (1), plaque ascent (2), plaque peak (3), plaque descent (4), internal carotid artery (5) (Figure). WSS was computed with the vector field speed using the following formula, WSS=μ·δn·v with v the blood velocity, n the normal vector to the vessel wall and μ, the blood viscosity, calculated from the hematocrit value for each patient. WSS measurement method was first validated using a laminar flow phantom and known viscosity. And then, 33 patients were then prospectively evaluated, with a median carotid stenosis degree of 80% [75–85]. Results Significant correlation was found between in vitro measurement and the theoretical WSS values (R2=0.95; p<0.001).In patients,the maximum WSS value over the cardiac cycle follows the shape of the plaque with an increase during the ascend, reaching its maximum value of 3.57 Pa [2.47–4.45] at the peak of the plaque, and a fall after passing the peak (0.99 Pa [0.8–1.32]) lower than the WSS values in the non-stenotic areas (1.55 Pa [1.13–1.90] for the common carotid artery) (Table). Table 1 Wall's area Wall shear stress (Pa) Min Max Delta 1. Common carotid artery 0.14 [0.05–0.27] 1.55 [1.13–1.90] 0.73 [0.55–0.96] 2. Plaque's ascent 0.39 [0.24–0.59] 2.63 [1.89–3.28] 1.20 [0.89–1.79] 3. Plaque's peak 0.60 [0.32–0.89] 3.57 [2.47–4.45] 1.78 [1.44–2.46] 4. Plaque's descent 0.16 [0.13–0.22] 0.99 [0.80–1.32] 0.52 [0.34–0.73] 5. Internal carotid artery 0.17 [0.13–0.35] 1.37 [1.04–1.75] 0.72 [0.50–0.87] Results are median [25th–75th percentile]. Figure 1 Conclusion UF provide reliable WSS values. High WSS was present at the peak of the plaque, whereas lowest WSS values were found at the post-stenotic zone. WSS evaluation may help to better characterize the carotid plaque vulnerability.

Simultaneous removal of nonrotationally symmetric errors in tilted wave interferometry

The tilted wave interferometer has been developed as a fast and accurate instrument for the measurement of aspheric and freeform surfaces. We present a method for increasing its robustness and flexibility. Tilted wave interferometry crucially depends on accurate calibration and any changes to a calibrated setup require, in general, a recalibration. Therefore, we propose a method for simultaneous topography reconstruction and elimination of errors arising from such changes. An approach to identify trends in systematic errors for the complex non-null setup with a large number of blackbox model parameters is worked out. The procedure allows deriving an error removal scheme for nonrotationally symmetric components based on measurements in different rotational positions. The feasibility and benefit of the error elimination method are shown both by simulation methods and dedicated experiments. A significant reduction of systematic errors even in a miscalibrated state is achieved. Hence, recalibrations are avoided and measurement time and flexibility are improved.

Dependence of Texture Tilt and Excitation Efficiency of Shear Waves for ZnO Films on Working Gas Pressure in a DC Magnetron System

Dependence of the texture tilt and excitation efficiency of shear waves on the working gas pressure in an interval of 0.14–0.74 mTorr that corresponds to the transition from collisionless to almost diffusion deposition is studied for the ZnO films with a thickness of about 0.45–1.2 μm that are synthesized in a planar dc magnetron system. It is shown that an increase in the pressure from about 0.14–0.24 to 0.74 mTorr causes a decrease in the tilt angle of the column texture from ~25°–27° to ~7° and a decrease in the efficiency of acoustic excitation. Films that are synthesized at pressures of ~0.14–0.24 mTorr close to the transition from the Townsend to glow discharge exhibit the highest excitation efficiency of shear waves. For such films, the insertion loss reaches a minimum level at thicknesses of 0.45–0.75 μm and the number of echo pulses amounts to 20–40, so that the reflected sound can be observed with a delay of up to 80 μs at a length of an acoustic guiding crystal of 10 mm.

Inflationary perturbations with Lifshitz scaling

Instead of Lorentz invariance, gravitational degrees of freedom may obey Lifshitz scaling at high energies, as it happens in Hořava's proposal for quantum gravity. We study consequences of this proposal for the spectra of primordial perturbations generated at inflation. Breaking of 4D diffeomorphism (Diff) invariance down to the foliation-preserving Diff in Hořava-Lifshitz (HL) gravity leads to appearance of a scalar degree of freedom in the gravity sector, khronon, which describes dynamics of the time foliation. One can naively expect that mixing between inflaton and khronon will jeopardize conservation of adiabatic perturbations at super Hubble scales. This indeed happens in the projectable version of the theory. By contrast, we find that in the non-projectable version of HL gravity, khronon acquires an effective mass which is much larger than the Hubble scale well before the Hubble crossing time and decouples from the adiabatic curvature perturbation ζ sourced by the inflaton fluctuations. As a result, at super Hubble scales the adiabatic perturbation ζ behaves as in an effectively single field system and its spectrum is conserved in time. Lifshitz scaling is imprinted in the power spectrum of ζ through the modified dispersion relation of the inflaton. We point out violation of the consistency relation between the tensor-to-scalar ratio and the spectral tilt of primordial gravitational waves and suggest that it can provide a signal of Lorentz violation in inflationary era.

Understanding the variation of stratosphere–troposphere coupling during stratospheric northern annular mode events from a mass circulation perspective

We revisit the various stratosphere–troposphere coupling relation from the perspective of the meridional mass circulation. We constructed 10-hPa northern annular mode (NAM) phase composites to show the typical spatiotemporal evolution of circulation anomalies during the NAM’s life cycle. Our results indicate that there is large case-to-case difference in the temporal evolution and vertical profile of polar temperature anomalies during NAM events, which shows no strong dependence on the intensity and duration of NAM events, but agrees well with the variations of the three branches of mass circulation at 60°N: the stratospheric poleward warm air branch (ST), the poleward warm air branch in the upper troposphere (WB), and the equatorward cold air branch in the lower troposphere (CB). Such correspondence is due to the dynamic heating and cooling anomalies associated with the redistribution of air masses by the anomalous meridional mass circulation in different isentropic layers. The various relationship among the three mass circulation branches is attributed to anomalous wave activities. The amplitude and westward tilt of waves are always stronger (weaker) throughout the stratosphere before (after) the peak time of negative NAM events, leading to a stronger (weaker) ST before (after) the peak time. Variations in WB and CB are mostly dependent on wave variabilities in the mid- to lower troposphere, leading to variations in the timing of in- or out-of-phase coupling of the ST with the WB and CB, and thus various thermostructure during NAM events. At a later stage of the negative NAM events when the polar temperature becomes colder and the polar jet recovers, the weakened baroclinic instability in the lower stratosphere provides favorable conditions for the strengthening of the WB and CB if wave activities strengthen in the troposphere during that period.

Зависимость наклона текстуры и эффективности возбуждения сдвиговых волн пленками ZnO от давления рабочего газа в магнетронной системе на постоянном токе

AbstractDependence of the texture tilt and excitation efficiency of shear waves on the working gas pressure in an interval of 0.14–0.74 mTorr that corresponds to the transition from collisionless to almost diffusion deposition is studied for the ZnO films with a thickness of about 0.45–1.2 μm that are synthesized in a planar dc magnetron system. It is shown that an increase in the pressure from about 0.14–0.24 to 0.74 mTorr causes a decrease in the tilt angle of the column texture from ~25°–27° to ~7° and a decrease in the efficiency of acoustic excitation. Films that are synthesized at pressures of ~0.14–0.24 mTorr close to the transition from the Townsend to glow discharge exhibit the highest excitation efficiency of shear waves. For such films, the insertion loss reaches a minimum level at thicknesses of 0.45–0.75 μm and the number of echo pulses amounts to 20–40, so that the reflected sound can be observed with a delay of up to 80 μs at a length of an acoustic guiding crystal of 10 mm.

Big steps in advances of doppler ultrasound

Doppler Ultrasound is clinically important for evaluation of various hepatic vascular disease as well as hepatic vessel evaluation after liver transplantation. However, there are some limitations in conventional Doppler methods as follows: 1) time consuming and labor intensive and 2) limited slow flow sensitivity. There are two recently advanced Doppler signal-processing methods (i.e., UltraFast and superb microvascular imaging), which overcome those limitations. UltraFast Doppler ultrasound, which emerged with the advent of massive parallel computing (or processing) capabilities, transmits several tilted plane waves into the medium and coherently sums the backscattered echoes to reconstruct US images, leading to a marked increase in the frame rate, while conventional ultrasound imaging involves sequential medium insonification via focused beams and successive image reconstruction. A stored UltraFast Doppler clip contains information on both spectral analysis and color-coded flow imaging and could be retrospectively evaluated quantitative analysis, because UltraFast ultrasound has high spatio-temporal resolution. Superb microvascular imaging (SMI, Cannon Medical Systems Corporation, Tochigi, Japan) uses a different kind of adaptive wall filter, which could minimize the flash artifact and increased sensitivity to slow flow and improve the signal detection of flow from small vessels. Therefore, in clinical practice, UltraFast Doppler can be performed by anyone. If the exam protocol such as acquisition of clip by less experienced sonographer and evaluation by retrospective wave reconstruction by specialist can be established, efficient work force management can be possible. Superb Microvascular imaging can distinguish very slow portal flow by portal hyper tension and so forth from thrombus. Thrombus can be evaluated with almost the same resolution as CT. The weak flow of a small hepatic artery hiding by vigorous flow of portal vein after liver transplantation can be also distinguished. In conclusion, smart application of recent advanced Doppler technique will help comprehensive assessment of hepatic vascular abnormalities.

Modeling optical memory effects with phase screens.

During the last decade, optical memory effects have been explored extensively for various applications. In this letter we propose phase screen models to facilitate the analysis and the simulation of wave propagation through optical media that exhibits memory effects. We show that the classical optical memory effect, which implies tilt wave correlations of the input and the scattered fields, can be readily modeled by a single random phase screen. For the recently discovered generalized optical memory effect, which implies the existence of shift wave correlations in addition to the tilt correlation, we propose an appropriate generalized random phase screen model.

Measuring aspheres quickly: tilted wave interferometry

Functional surfaces with a rising degree of complexity are becoming increasingly important for modern industrial products. It is common knowledge that one cannot produce surfaces better than it is possible to measure them. Consequently, the demand for their effective and precise measurement has increased to the same extent as their production capabilities have grown. Important classes of optical functional surfaces are aspheres and freeforms. Both types of surfaces have become essential parts of modern optical systems such as laser focusing heads, sensors, telescopes, glasses, head-mounted displays, cameras, lithography steppers, and pickup heads. For all of them, the systematic quality control in the process of their fabrication is essential. We review the challenges of asphere and freeform testing and how available metrology systems cope with it. A special focus is on tilted wave interferometry and how it compares to other methods.