Elliptical Gaussian Research Articles

Reordering of point-vortex lattices under anisotropic diffraction: far-field analysis

Abstract A study of the far-field complex amplitude obtained from initially ordered arrays of N × M point-vortices with equal unitary topological charge embedded in carrier beams with different geometry is presented. This can be understood as the final stationary configuration after the dynamical evolution of the vortices upon propagation, and our aim is to investigate the impact of a geometric anisotropy on the diffraction process by using an elliptic Gaussian beam as a carrier and a rectangular vortex lattice. For comparison, illumination by a circular Gaussian beam and a plane wave diffracted by a rectangular aperture are also analyzed. We show that vortices tend to cluster in some regions under high eccentricity of the carrier and there can be an entire redistribution of the vortices depending on the size of the initial array with respect to the size of the carrier, which inherits some geometric characteristics of the latter.

Research on Rail Surface Defect Detection Based on Improved CenterNet

Rail surface defect detection is vital for railway safety. Traditional methods falter with varying defect sizes and complex backgrounds, while two-stage deep learning models, though accurate, lack real-time capabilities. To overcome these challenges, we propose an enhanced one-stage detection model based on CenterNet. We replace ResNet with ResNeXt and implement a multi-branch structure for better low-level feature extraction. Additionally, we integrate SKNet attention mechanism with the C2f structure from YOLOv8, improving the model’s focus on critical image regions and enhancing the detection of minor defects. We also introduce an elliptical Gaussian kernel for size regression loss, better representing the aspect ratio of rail defects. This approach enhances detection accuracy and speeds up training. Our model achieves a mean accuracy (mAP) of 0.952 on the rail defects dataset, outperforming other models with a 6.6% improvement over the original and a 35.5% increase in training speed. These results demonstrate the efficiency and reliability of our method for rail defect detection.

Extended GeV γ-ray emission around the massive star forming region of the W3 complex

ABSTRACT We analyse the GeV γ-ray emission from the W3 complex using about 14 years of Pass 8 data recorded by the Fermi Large Area Telescope (Fermi-LAT). We resolve the γ-ray emissions around W3 into two components: an elliptical Gaussian overlapping with the molecular gas and a point-like source near the cluster W3 Main. The pion-bump feature of SED for the elliptical Gaussian together with the better fitting result of pion decay model favour the hadronic origin. We further argue that the cosmic rays (CRs) could originate from the interactions between cluster winds and the shock produced by the SNR HB3. The point-like source positionally coincident with the star cluster W3 Main indicates it may be directly powered by near clusters, while its fainter γ-ray emissions below 10 GeV are possibly due to the shelter from dense gas making the low-energy CRs incapable of penetrating the dense materials. Meanwhile, we cannot rule out that the γ-ray emissions originate from the interaction of accelerated protons in SNR with the ambient gas.

Statistical modeling of 3D fiber geometry in pultruded GFRP composite: A multi-scale approach

The fiber geometry is a crucial determinant of the fiber reinforced polymer composites’ mechanical properties. Specifically, the manufacturing process of stretching and gradual curving in pultruded composites invariably results in complex 3D fiber geometries. Despite its significance, there is still lacking a statistical method to accurately describe these spatially curved fiber shapes. This paper presents a novel multi-scale mathematical approach for modeling the complex 3D fiber geometry in pultruded glass fiber reinforced polymer (GFRP) composites, which includes the analysis of fiber misalignment and waviness at two scales. At the mesoscopic level, a modified elliptical symmetry angular Gaussian (ESAG) model effectively characterizes the fiber misalignment. Simultaneously, at the micro scale, a cosine series representation is employed for capturing local fiber waviness. The approach is verified with XCT scanning results of pultruded GFRP specimens. The current statistical modeling method provides a multi-scale approach for geometry analysis and further simulation of pultruded composite materials.

IAE-KM3D a 3D Object Detection Method Based on an Improved KM3D Network

Deep learning-based 3D target detection methods need to solve the problem of insufficient 3D target detection accuracy. In this paper, the KM3D network is selected as the benchmark network after the experimental comparison of current mainstream algorithms, and the IAE-KM3D network algorithm based on the KM3D network is proposed. First, the Resnet V2 network is introduced, and the residual module is redesigned to improve the training capability of the new residual module with higher generalization. IBN NET is then introduced to carefully integrate instance normalization and batch normalization as building blocks to improve the model’s detection accuracy in hue- and brightness-changing scenarios without increasing time loss. Then, a parameter-free attention mechanism, Simam, is introduced to improve the detection accuracy of the model. After that, the elliptical Gaussian kernel is introduced to improve the algorithm’s ability to detect 3D targets. Finally, a new key point loss function is proposed to improve the algorithm’s ability to train. Experiments using the KITTI dataset conclude that the IAE-KM3D network model significantly improves detection accuracy and outperforms the KM3D algorithm regarding detection performance compared to the original KM3D network. The improvements for AP2D, AP3D, and APBEV are 5%, 12.5%, and 8.3%, respectively, and only a tiny amount of time loss and network parameters are added. Compared with other mainstream target detection algorithms, Monn3D, 3DOP, GS3D, and FQNet, the improved IAE-KM3D network in this paper significantly improves AP3D and APBEV, with fewer network parameters and shorter time consumption.

Propagation of elliptical Gaussian vortex beam based on angular spectrum representation

Vortex beams with hollow elliptical ring structure have attracted broad interest in applications such as micro-particle trapping and manipulation. The paper investigates the dependence of the hollow elliptic ring structure of vortex beams on the beam order and the topological charge, while propagating in the near- and far-field zones. The electric field of the beam is formulated by using the angular spectrum method, which satisfies rigorously Maxwell's equation. The electric field, linear momentum and orbital angular momentum are calculated. Numerical results show that the hollow elliptical ring structure approximately remains unchanged over a finite propagation distance, accompanied by a rotation whose angle depends on the topological charge. In the far-field zone, the ring structure is broken, leading to two bright spots and several dark islands. It is found that the beam profile in the near-field zone is mainly related to the beam order but in the far-field zone is primarily affected by the topological charge. The results presented in the paper may be useful in predicting and explaining the interaction between the elliptic hollow Gaussian vortex beam and the micro-particles, such as the movement of micro-particles along the orbit and the rolling rotation.

Manipulation of geometric parametric sidebands via elliptical Gaussian beam in graded-index multimode fibers

Geometric parametric instability is a class of processes where the revival of optical beam in a nonlinear multimode graded-index fiber induces a spatial index modification and in turn generates frequency sidebands due to space-time coupling. While current studies have been focusing on breathing Gaussian beams in such settings, the evenly spaced eigenvalue in parabolic fiber indicates that any input condition will experience self-imaging effects under linear conditions. Here we investigate the nonlinear propagation and the corresponding geometric parametric instability sidebands generation associated with elliptical Gaussian beams where the long- and short- axis of the beam oscillates with different phases. We show that, depending on the initial conditions, there are four possible propagation regimes: over-trapping, self-trapping, under-trapping and self-focusing. As a result, the spacing and strength of generated sidebands can be judiciously tuned by the elliptical ratio of elliptical Gaussian beams. At certain conditions, missing-order effect occurs where a set of sidebands completely disappear. We experimentally observed the multiple and a few sidebands of the Gaussian beam and elliptical Gaussian beam in a standard graded-index multimode fiber. In addition, experiments show that GPI sidebands have well-defined and stable bell-shaped near-field profiles. These results pave the way for developing tunable light sources and ultra-broadband supercontinuum generation.

A new approach for the assessment of coastal flooding risk. Application in Rhodes island, Greece

A directional, copula-based, Monte Carlo approach is proposed for the quantitative assessment of a new definition of coastal flooding risk, namely a probability-based index due to extreme combinations of wave conditions and sea levels, which could be a key element for coastal zone planning and management. This approach differs from the standard practice, which focuses on the extreme events and studies either their specific return values or their worst-case scenarios. The adopted approach incorporates mean wave direction as a covariate into the probabilistic representation of sea states, and via the use of a variety of probabilistic and statistical tools, represents a total of five stochastic variables, namely the significant wave height, the peak wave period, the mean wave direction, the storm surge, and tide. Two directional, alternative methods have been developed; a trivariate copula- and a bivariate copula-based method, that seemed to produce quite similar results. Four types of copulas have been examined for their goodness-of-fit, i.e., three Archimedean copulas, namely, the Clayton, the Gumbel, and the Frank copulas, as well as the elliptical Gaussian copula. A comparative analysis of the two methods is performed aiming to point out their pros, as well as their accuracy and complexity issues. The application of the proposed method to the natural beaches of the Rhodes Island in Greece, in combination with a recently developed formula for wave run-up, highlighted the most crucial parameters affecting the coastal flooding risk in the study area.

Spatial shifts of reflected rotating elliptical Gaussian beams from surface phonon polaritons in hyperbolic materials

The effect of surface phonon polaritons (SPhPs) on Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts of reflected rotating elliptical Gaussian beams (REGBs) is investigated in the Otto configuration with a naturally hyperbolic material (NHM) substrate. The spatial shifts are enhanced significantly and adjusted by tuning the REGBs and the optical axis orientation of NHM. The magnitude of GH and IF shifts is easily evaluated by timing the elliptical parameter b02 on the basis of the spatial shift at b0=1.0 when η(=a0/b0)≥2.0. The attenuation total reflection (ATR) spectra are simulated for a hexagonal boron nitride (hBN) substrate. To better understand the impact of SPhPs on the GH and IF shifts, the dispersion curves of SPhPs are calculated. The features of GH and IF shifts around SPhPs can be observed through the frequency scanning along the dispersion curves at a fixed incident angle. The comparison between the ATR spectra and the dispersion curves demonstrates that the enhancement of GH and IF shifts with higher reflection always occurs in the reststrahlen bands (RBs) of NHM once SPhPs are excited. In RB-I, the magnitudes of GH and IF shifts attributable to the SPhPs are located between the peak and dip of a shift curve within a very narrow frequency region. However, in RB-II, the positive maximum values of GH and IF shifts just coincide with the SPhPs. As a result, it is predicted that a relatively large spatial shift will be observed along the frequency scanning line. The large shifts accompanied by the higher reflection may show potential applications in optical or optoelectronic technologies.

Vortex ring reconnections in elliptic Gaussian beams.

We study theoretically accessible optical vortex rings and their topological transformations in superpositions of elliptic and astigmatic Gaussian beams with a plane wave. We demonstrate the birth and death of vortex rings at isolated points on and off the optical axis and their pairwise and higher-order three- and four-ring reconnections.

Manipulating melt pool thermofluidic transport in directed energy deposition driven by a laser intensity spatial shaping strategy

ABSTRACT A three-dimensional thermofluidic coupling transport model is proposed to investigate the influences of different spatial laser intensity profiles (SLIPs), including circular super-Gaussian profile (C-SGP), transverse elliptical Gaussian profile (TE-GP) and longitudinal elliptical Gaussian profile (LE-GP), on the thermofluidic transport characteristics within the melt pool. The results demonstrate that the SLIPs dramatically influence the melt pool geometries, temperature gradient (both in magnitude and direction) at the solidification interface, and fluid flow dynamics. Under the TE-GP strategy, the highest average temperature gradients are observed at the solidification interface. The LE-GP strategy yields the smallest magnitudes and narrowest variation range of the temperature gradient direction angles. The heat transport of the melt pool under the C-SGP and TE-GP strategies are jointly dominated by convective and conductive heat transfer, while those under the LE-GP strategy are dominated by convective heat transfer. Marangoni convection is strongest in the LE-GP strategy and weakest in the TE-GP strategy.

Fourier reciprocity between generalized elliptical Gaussian and elegant elliptical Hermite-Gaussian beams carrying orbital angular momenta.

We explore two distinct families of orbital angular momentum carrying light beams, which we refer to as generalized elliptical Gaussian and elegant elliptical Hermite-Gaussian vortex beams, respectively. We show that the fields of the two vortex families are related via a Fourier transform. Hence, one family can be viewed as a source of the far-field intensity distribution of the other and vice versa. We also examine the orbital angular momentum evolution of both beam families on their free space propagation and establish a relationship between the orbital angular momentum, TC, and beam ellipticity factors. Our results may find applications to optical communications and imaging with structured light.

Design of a compact off-axis two-mirror freeform optical antenna for shaping and transmitting an elliptical beam emitted by laser diode.

Elliptical Gaussian beams generated by laser diodes (LDs) often exhibit asymmetrical divergence angle distribution, which limits their practical applications. In this study, we propose what we believe is a novel approach to shape and collimate the elliptical output beam from a LD. The design process involves the construction of two freeform reflective surfaces on a reference circle using a three-dimensional point-by-point iterative method, based on the law of conservation of energy, the vector reflection theory, and Fermat's principle. The output beam's maximum divergence angle is effectively compressed to 3.1579mrad. The design is compact with a folded optical path and antenna size of 368.8c m 3. This paper presents a comprehensive design and optimization process, along with an in-depth analysis of the system's performance, thereby offering novel insights for emerging optical design practitioners.

Coherence phase spectrum analyzer for a randomly fluctuated fractional vortex beam

Fractional vortex beams exhibit a higher degree of modulation dimensions than conventional vortices, thus inheriting superior anti-turbulent transmission properties through the incorporation of additional coherence modulation. However, aliasing the mixed modes induced by coherence degradation makes the quantitative measurement of the topological charge in fractional vortex beams challenging. In this study, a coherence phase spectrum was introduced, and experimental demonstrations to quantitatively determine the fractional topological charge of partially coherent fractional vortex beams were performed. By leveraging the four-dimensional measurement of a partially coherent light field, the source coherence function was inversely reconstructed, and fractional topological charges were determined with high precision by extracting the phase spectrum of the coherence function. Laguerre–Gaussian, elliptical Gaussian, and plane-wave-fraction vortex beams with various degrees of coherence were used to demonstrate measurement precision. The proposed method is applicable to X-rays and electron vortices. It has potential applications in optical encryption, high-capacity optical communication, and quantum entanglement.

Motion estimation and multi-stage association for tracking-by-detection

Multi-object tracking (MOT) aims to locate and identify objects in videos. As deep learning brings excellent performances to object detection, the tracking-by-detection (TBD) has gradually become a mainstream tracking framework. However, some drawbacks still exist in the current TBD framework: (1) inaccurate prediction of the bounding boxes would occur in the detection part, which is caused by overlooking the actual pedestrian ratio in the surveillance scene. (2) The width of the bounding boxes in the next frame might be indirectly predicted by the aspect ratio, which increases the error of width prediction in the motion prediction part. (3) Association is only performed for high-confidence detection boxes, and the low-confidence boxes caused by occlusion are discarded in the data association part, resulting in fragmentation of trajectories. To address the above issues, we propose a multi-target tracking model incorporating motion estimation and multi-stage association (MEMA). First, the aspect ratio of the ground-true bounding box is introduced to improve the fit of the detection and the ground-true bounding box, and we design the elliptical Gaussian kernel to improve the positioning accuracy of the object center point. Then, the prediction state vector of the Kalman filter is modified to predict the width and its corresponding velocity directly. It can reduce the width error of the prediction box and eliminate the velocity error of the motion estimation, which leads to a more pedestrian-friendly prediction bounding box. Finally, we propose a multi-stage association strategy to correlate different confidence boxes. Without using the appearance feature, the strategy can reduce the impact of occlusion and improve the tracking performance. On the MOT17 test set, the method proposed in this paper achieves a MOTA of 74.3% and an IDF1 of 72.4%, outperforming the current SOTA.

Propagation dynamics of (3+1)-dimensional self-accelerating sinh-Gaussian and cosh-Gaussian wave packets in a harmonic potential

In a harmonic potential, the propagation properties of self-accelerating sinh-Gaussian and cosh-Gaussian wave packets are investigated. Analytical results from a (3+1)-dimensional evolution equation are derived. Changing the distribution factor allows these wave packets to present different forms, including dipoles, elliptic vortex, hollow rings, horizontal figure eight, and elliptic Gaussian. These spatiotemporal wave packets rotate periodically, and the period depends on the potential depth. Their shapes are strongly determined by the distribution factor and the cross-phase factor while propagating. Further, the wave packets with negative chirp parameters can reverse their self-accelerating direction. We also investigate these wave packets’ energy flow and angular moment density to explore their dynamic rotating features. The spatiotemporal self-accelerating sinh-Gaussian and cosh-Gaussian wave packets have distinctive characteristics, which may provide a novel platform for the realization of joint control of the optical field in the spatiotemporal domain.

Gradient torque and its effect on rotational dynamics of optically trapped non-spherical particles in the elliptic Gaussian beam.

Rotational motion of the optically trapped particle is a topic of enduring interest, while the changes of angular velocity in one rotation period remain largely unexplored. Here, we proposed the optical gradient torque in the elliptic Gaussian beam, and the instantaneous angular velocities of alignment and fluctuant rotation of the trapped non-spherical particles are investigated for the first time. The fluctuant rotations of optically trapped particles are observed, and the angular velocity fluctuated twice per rotation period, which can be used to determine the shape of trapped particles. Meanwhile, a compact optical wrench is invented based on the alignment, and its torque is adjustable and is larger than the torque of a linearly polarized wrench with the same power. These results provide a foundation for precisely modelling the rotational dynamics of optically trapped particles, and the presented wrench is expected to be a simple and practical micro-manipulating tool.

Scanning mirror based higher order Bessel-gaussian beams integrated in time (HOBBIT) with applications toward the photoacoustic effect.

We demonstrate a new method for the generation of beams with rapidly tunable orbital angular momentum (OAM). This method is based on using a single-axis scanning galvanometer mirror to add a phase tilt on an elliptical Gaussian beam that is then wrapped to a ring using optics that perform a log-polar transformation. This system can switch between modes in the kHz range and use relatively high power with high efficiency. This scanning mirror HOBBIT system was applied to a light/matter interaction application using the photoacoustic effect, with a 10 dB enhancement of the generated acoustics at a glass/water interface.

Goos–Hänchen and Imbert–Fedorov shifts for rotational elliptical Gaussian beams impinging on graphene–substrate surfaces

This paper derives the analytical solution of Goos–Hänchen and Imbert–Fedorov shifts of rotational elliptical Gaussian beams (REGBs). Furthermore, we find that near the Brewster angle incidence at near-p incident paraxial beam polarization, the values of the beam shifts and the widths of the corresponding resonance shift curves become dependent on the beam waist. By introducing the effective beam waist and rotational phase factor, the causes of the beam shift variation phenomenon are analyzed from the viewpoints of analytical solutions and Fourier optics. Meanwhile, by adjusting the Fermi energy level of graphene, it is found that the direction of GH shift of the elliptical rotating Gaussian beam depends on the reflecting material, and the direction of IF shift depends on the rotational phase of the beam.

Evolution and copula modelling of drought duration and severity over Africa using CORDEX‐CORE regional climate models

AbstractThis study assessed the dependence of drought severity and duration across four subregions (Southern, Western, Eastern and Central) in Africa using copula modelling. The analysis was carried out for the reference period 1991–2020 and the future period 2071–2099. Simulated daily precipitation at a horizontal resolution of 0.22° were obtained from three regional climate models (RCMs) participating in the Coordinated Output for Regional Evaluations within the Coordinated Regional Downscaling Experiment (CORDEX‐CORE). The RCMs were downscaled by three global climate models and validated using three high‐resolution gridded daily precipitation products obtained from The Climate Hazards Group InfraRed Precipitation with Stations data (CHIRPS), Climate Prediction Center Africa Rainfall Climatology Version 2.0 (CPC‐ARC2) and Tropical Applications of Meteorology using SATellite data and ground‐based observations (TAMSAT). Comparison of precipitation from the RCMs with the three gridded reference observations shows relatively good performance across the different regions with median value within the range of 3–5 mm·day−1 in Central Africa, 1.5–4.5 mm·day−1 in Western Africa, 1.8–2.8 mm·day−1 in Eastern Africa and 0.5–2.2 mm·day−1 in Southern Africa. On the other hand, the correlation values of drought duration–severity from CORDEX‐CORE models in the different regions of Africa exhibit predominantly strong values greater than 0.8 for both historical and projected climate. The analysis also considered two families of copulas: Archimedean (Frank, Clayton, Gumbel) and Elliptical (Gaussian, Student's t). The performance of the copula functions were estimated using the Akaike information criteria (AIC). Generally, there is a good agreement in the distribution of observed precipitation among the three observational data products across the subregion of Africa, with slight differences attributed to the different processing algorithms of the products. Across West Africa, mean precipitation values from CPC, CHIRPS and TAMSAT was 2.86, 3.16 and 3.07 mm·day−1, respectively. The CCLM‐NCC underestimated the mean values of precipitation reported in the observation data, while CCLM‐MPI and CCLM‐HAD overestimated the mean values of precipitation in the West Africa region.