Gaussian Shape Research Articles

Broken phase of parity-time symmetry enables efficient superluminal pulse transmission

Parity-time (PT) symmetric Bragg gratings (PTBGs) exhibit unique band characteristics compared to their traditional counterparts. Notably, when the PT symmetry is broken, the initial bandgap closes, and the upper and lower branches coalesce. We demonstrate that this believed to be novel band dispersion supports fast light, also known as the optical superluminality. A light pulse can propagate through a fiber PTBG with broken PT symmetry, achieving high transmission efficiency (comparable to, and even exceeding, unity) while maintaining its Gaussian shape. This effect offers a significant advantage over superluminal tunneling, where the transmission coefficient is typically very small. We also analyze the transmission of optical precursors and show that they cannot be superluminal, consistent with the principle of causality. This work presents a mechanism for realizing superluminality with some possible applications and underscores the vast potential of non-Hermitian optics.

Wavepacket interference of two photons through a beam splitter: from temporal entanglement to wavepacket shaping

Quantum interferences based on beam splitting are widely used for entanglement. However, the quantitative measurement of the entanglement in terms of temporal modes and wavepacket shaping facilitated by this entanglement remain unexplored. Here we analytically study the interference of two photons with different temporal shapes through a beam splitter (BS) and then propose its application in temporal entanglement and shaping of photons. The temporal entanglement described by Von Neumann entropy is determined by the splitting ratio of BS and temporal indistinguishability of input photons. We found that maximum mode entanglement can be achieved with a 50/50 BS configuration, enabling the generation of a Bell state encoded in temporal modes, independent of the exact form of the input photons. Then, detecting one of the entangled photons at a specific time enables the probabilistic shaping of the other photon. This process can shape the exponentially decaying (ED) wavepacket into the ED sine shapes, which can be further shaped into Gaussian shapes with a fidelity exceeding 99%. The temporal entanglement and shaping of photons based on interference may solve the shape mismatch issues in large-scale optical quantum networks.

Analyzing Stellar Spectra for PRV by Accurate Modeling and Retrieval of Telluric Absorption Features

Ground-based Precision Radial Velocity (PRV) measurements are inevitably impeded by contamination from telluric absorption features, particularly in the infrared region. Thus, it is crucial to improve modeling of the telluric absorption features down to the spectral noise level. As part of the efforts towards improved PRV measurements, we have taken an existing atmospheric trace gas retrieval algorithm (GFIT) and have successfully adapted it to fit the telluric absorption features in stellar spectra down to the spectral noise level (typically ∼1%). We have established a stellar spectral fitting processing pipeline, Stellar-GFIT, to analyze a series of stellar spectra observed by two spectrographs, PARVI (1.1–1.76 μm) commissioned at the Palomar Observatory (Palomar Mountain, CA) and iSHELL (1–5 μm) deployed on the IRTF (Mauna Kea, HI). For this, we have (1) implemented a Gaussian instrumental line shape function, (2) generated atmospheric models (consisting of temperature, pressure, and volume mixing ratios of all the known trace gases) for the particular observation sites and times, (3) employed the most up-to-date spectroscopic parameters in the target spectral regions, and finally (4) developed a series of spectral fitting intervals of ∼60 cm−1 width, i.e., micro-windows, customized to the individual orders of each spectrograph. Stellar-GFIT is also capable of handling non-telluric features, such as transitions from a gas cell placed in the starlight beam and stellar features if a model spectrum template is available for the target star. We present spectrum fits from the observations of various target stars and discuss the performance and advantages of our novel approach. One of the major strengths of Stellar-GFIT is an ability to adjust the abundance of atmospheric trace gases simultaneously with determining the stellar doppler shift, mitigating any adverse impacts of short-timescale variations of water vapor.

The Ensemble Tangent Linear Model Applied to a Cloud Physics Parameterization

Abstract An Ensemble Tangent Linear Model (ETLM) is applied to a cloud physics scheme used in the Navy Global Environmental Model (NAVGEM). The ensemble is created using 3-hour forecasts from the Ensemble Transform method used in the NAVGEM data assimilation system. The model states are saved before and after applying the cloud physics parameterization (which includes condensation/evaporation of cloud ice and cloud liquid water and stratiform precipitation), and these states are used to construct linearized model tendencies for temperature, specific humidity, cloud liquid water, and cloud ice water. We examine separately the application of the ETLM to cloud physics components that are explicitly local versus non-local. For the local components, an ETLM is built using a single grid point. ETLMs from 50 to 1000 members are tested, and skillful forecasts can be obtained for both local and non-local physics even with a moderate sized ensemble (e.g., 100 members). At 1000 members, the globally-averaged forecast error reductions (relative to persistence errors) are ∼40% for temperature, water vapor, and cloud liquid water and ∼30% for cloud ice. When initial perturbations are reduced by a factor of 0.1, the error reductions increase to ∼65% for all variables. For physics with non-local components (stratiform precipitation) the covariances that comprise the ETLM are localized with a Schur product matrix using a Gaussian localization shape with tunable length. The optimal lengths increased with ensemble size from ∼2-3 km for 50 members to ∼10 km for 1000 members. ETLMs for “all cloud physics” are also constructed and evaluated.

Stability and Preservation of Fuzzy Membership Functions in Adaptive Gaussian Derivative Filters

This paper examines the stability and preservation of fuzzy membership functions in Gaussian filters, particularly focusing on the Adaptive Gaussian Derivative (AGD) filter. Gaussian filters are essential for smoothing and noise reduction in image processing. The AGD filter, which adapts based on local image statistics, outperforms traditional methods. Key concepts like fuzzy sets, Boundary Input Boundary Output (BIBO) stability, and convolution are defined, and the mathematical formulation of the Gaussian and its derivative is presented. The AGD filter's BIBO stability ensures bounded outputs for bounded inputs, guaranteeing consistent behavior. It also preserves fuzzy membership function properties, maintaining convexity and boundedness through linearity and continuity. Frequency response analysis using Fourier Transform confirms the AGD filter retains the Gaussian shape in the frequency domain, preserving image smoothness. Theorems and proofs validate the AGD filter's stability and its capability to preserve fuzzy membership functions, ensuring reliable processing in applications such as medical image analysis. These properties make the AGD filter a robust tool for advanced image processing tasks.

Development and validation of a three-dimensional wind-turbine wake model based on high-order Gaussian function

Under natural conditions, the wake velocity distribution approximates top-hat shape in the near wake center, and a Gaussian shape in the far wake. To improve the prediction accuracy of the wake distribution, this paper proposes a three-dimensional high-order Gaussian linear entrainment wake model by modifying the wake velocity distribution with high-order Gaussian function. Field tests and wind tunnel tests are then conducted. The obtained results show that the proposed model can accurately describe the radial and vertical spatial distributions of the wake flow. Under different wind speeds, the maximum and minimum radial relative errors are respectively 7.29% and 1.4%, while the maximum and minimum vertical relative errors are respectively 7.64% and 3.87%. This demonstrates that the proposed model can accurately predict the velocity distribution in the whole wake region. The proposed model is simple, has low cost, and exhibits high accuracy. Thus, it can be used in wind farm layout optimization and wake control.

Spatial distribution of self-seeded air lasers induced by the femtosecond laser filament plasma

The femtosecond laser filament-induced air laser plays a significant role for the remote sensing of air pollutants. The spatial distributions of air laser intensity were investigated experimentally in previous studies. However, the mechanism of the air laser propagation properties inside the filament plasma has not been quite clear yet. Moreover, few studies have been dedicated to the reproduction of the air laser profile from nitrogen molecules propagating in the filament plasma based on the numerical simulation method. In this study, the lasing action of the air laser from the transition of the first negative (0,0) band of nitrogen ions at 391 nm was simulated during the femtosecond laser filamentation. The beam profile of the air laser changes from a Gaussian or super-Gaussian shape to an outer ring structure by increasing the filament length or nitrogen ion density, which is in accord with the previous experimental result. A multiple-diffraction effect has been proposed to clarify the mechanism of the outer rings beam pattern formation, which is induced by the dynamical interaction between the lasing effect and diffraction effect of the air laser propagating inside the filament plasma. In addition, the amplified air laser power as a function of both the filament length and nitrogen ion density was investigated. Our study would pave the way to improve the energy conversion efficiency and directivity of remote air lasers, which would be significant for remote sensing applications.

Inhomogeneous broadening effects on bistable behavior in a hybrid optomechanical system

Optical bistability is investigated for optomechanical system composed of an ensemble of inhomogeneously broadened two-level atoms embedded between the two mirrors of the optical cavity, that is subjected to two input (strong and probe) fields. We consider two types of inhomogeneous broadened distributions, namely, Lorentzian and Gaussian line shapes. The first order harmonic components of the output fields (due to the presence of probe field) show reversed and knotted bistability shapes simultaneously with the standard bistable shape of the fundamental component of the field at frequency ωc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{c}$$\\end{document}. The inhomogeneous broadened line width for both Lorentzian and Gaussian distribution affects the dispersive switching of the system, as well as the bistable behavior. Locations of the maxima of photon numbers associated with higher harmonics of the output fields are identified with respect to the probe field frequency.

Turbulent structure and circulation inside different planar contractions

We study the turbulent circulation and coherent vortical structures for flow through three separate two-dimensional planar 4:1 contractions, where the turbulence is subjected to different rates of mean strain. We use four high-speed video cameras for Lagrangian particle tracking velocimetry, to measure time-resolved velocity fields in volumes inside the contractions. We identify the coherent vortical structures and quantify their alignment with the mean strain. The intermediate strain contraction shows the strongest alignment. We also compute circulations around square loops in three perpendicular planes, to form a “circulation vector,” whose instantaneous alignment mirrors that of the coherent structures, with strong inhomogeneities between circulation components at the exit of the contractions. The circulation probability density functions show extended exponential tails for the smallest loops, with more Gaussian shapes in the inertial range.

Effect of Nitrogen on the Structure and Composition of Primordial Organic Matter Analogs.

Organic molecules are ubiquitous in primitive solar system bodies such as comets and asteroids. These primordial organic compounds may have formed in the interstellar medium and in protoplanetary disks (PPDs) before being accreted and further transformed in the parent bodies of meteorites, icy moons, and dwarf planets. The present study describes the composition of primordial organics analogs produced in a laboratory simulator of the PPD (the Nebulotron experiment at the CRPG laboratory) with nitrogen contents varying from N/C < 0.01 to N/C = 0.63. We present the first Fourier transform ion cyclotron resonance mass spectrometry analysis of these analogs. Several thousands of molecules with masses between m/z 100 and 500 are characterized. The mass spectra show a Gaussian shape with maxima around m/z 250. Highly condensed polyaromatic hydrocarbons (PAH) are the most common compounds identified in the samples with lower nitrogen contents. As the amount of nitrogen increases, a dramatic increase of the chemical diversity is observed. Nitrogen-bearing compounds are also dominated by polyaromatic hydrocarbons (PANH) made of 5- and 6-membered rings containing up to four nitrogen atoms, including triazine and pyrazole rings. Such N-rich aromatic species are expected to decompose easily in the presence of water at higher temperatures. Pure carbon molecules are also observed for samples with relatively small fractions of nitrogen. MS peaks compatible with the presence of amino acids and nucleobases, or their isomers, are detected. When comparing these Nebulotron samples with the insoluble fraction of the Paris meteorite organic matter, we observe that the samples with intermediate N/C ratios bracketing that of the Paris insoluble organic matter (IOM) display relative proportions of the CH, CHO, CHN, and CHNO chemical families also bracketing those of the Paris IOM. Our results support that Nebulotron samples are relevant laboratory analogs of primitive chondritic organic matter.

Evaluating wind-farm power generation using a new direct integration of axisymmetric turbine wake

Engineering wake models enable fast calculation of wind-farm power generation including wake-turbine interactions, which is critical for annual energy yield calculations and for farm optimisation either at the design phase or during operation. The operating point of a turbine is determined based on its rotor-averaged wind speed, which is impacted by upstream wakes. The rotor-averaged deficit is typically calculated numerically by using a set of averaging points across the rotor disk, for which a Gaussian shape function is commonly evaluated. This numerical approach can have uncertainty based on the distribution of the averaging points. Also, a large number of averaging points can increase computational cost, which is detrimental for studies that rely on many individual calculations of farm power generation, e.g. layout optimisation. To avoid these drawbacks, we present a novel analytical solution to the circular-disk integration of a two-dimensional axisymmetric Gaussian function depicting upstream wakes for an arbitrary lateral offset between the rotor and the wake source. The analytical expression is compared against numerical averaging of an upstream wake, and is applied to the Horns Rev 1 wind farm showing excellent accuracy. Wind-farm layout optimisation models, especially methods based on gradient-descent optimisation, can benefit from the presented expression significantly, as this provides an analytically differentiable formulation for the rotor-averaged wind speed.

Tunable temporal dynamics of dipole response in graphene-wrapped core–shell nanoparticles

The investigation on the temporal dynamics of graphene-wrapped core–shell nanoparticles under the illumination of a Gaussian impulse have been carried out. By altering the graphene layers and the aspect ratio of the core–shell structure, we can adjust the resonant modes into typical cases in regime of terahertz. Accordingly, different scenarios for the temporal evolution are detected, which include two kinds of ultrafast oscillation with exponential decay tendency, pure exponential decay, and Gaussian shape, when the pulse duration of the incident pulse is much shorter than, similar to, and much longer than the localized surface plasmon lifetime. To one's interest, when the coupling between two resonant modes exists, one predicts the long-periodic oscillation, whose period is just the difference between the frequencies of the resonant modes. Hence, the intrinsic properties of the ultrafast oscillation can be hardly influenced by the input signals. Further quantitative calculation demonstrate that the periods of the ultrafast oscillations can be tuned by different physical mechanisms, which are, respectively, based on the self-interacting correction of a single resonance and the strong coupling between the resonant modes in frequency domain. Our results may be applicable in the fields of optical sensors, optical information processing, and other nanophotonic devices.

Polarization singularities for shaping of vector flat-top beams in utilization for high-power laser micromachining of various materials

Structured light is desired in the micromachining of various materials. As the latest ultrashort laser sources increase the average power by increasing the repetition rate, the efficiency of the process becomes crucial in laser micromachining. The standard Gaussian beam shape, because of its slow ascending/descending slope, is not the most efficient beam, neither in precise energy deposition nor in heat management. Flat-top beams are required for precise and even energy distribution and are used in laser ablation or thin-film removal. We look at a rather abstract concept of polarization singularities and investigate them to create a vector flat-top beam. For this purpose, we devise a beam-shaping method based on the volumetric birefringent nano gratings which allow the generation of high-energy polarization singularities. By tuning the input beam waist, we have generated three most common laser micromachining beam profiles (Gaussian, Flat-top, and ring- or doughnut-shaped). The resulting high-quality and high-energy polarization singularities allow us to systematically demonstrate their use in transparent and opaque material micromachining, as well as the usual application for flat-top beams of thin-film removal.

Effects of Beam Mode on Hole Properties in Laser Processing

The laser beam mode affects the power density distribution on the irradiated target, directly influencing the product quality in laser processing, especially the hole quality in laser drilling. The Gaussian beam shape, Mexican-Hat beam shape, Double-Hump beam shape, and Top-Hat beam shape are four typical laser beam modes used as a laser heat source and introduced into our proficient laser-drilling model, which involves complex physical phenomena such as heat and mass transfer, solid/liquid/gas phase changes, and two-phase flow. Simulations were conducted on an aluminum target, and the accuracy was verified using experimental data. The results of the simulations for the fundamental understanding of this laser–material interaction are presented in this paper; in particular, the hole shape, including the depth–diameter ratio and the angle of the cone, as well as spatter phenomena and, thus, the formed recast layer, are compared and analyzed in detail in this paper. This study can provide a reference for the optimization of the laser-drilling process, especially the selection of laser beam mode.

Large deviations of the argument of the Riemann zeta function

AbstractLet . We prove an unconditional lower bound on the measure of the sets for . For , our bound has a Gaussian shape with variance proportional to . At the endpoint, , our result implies the best known ‐theorem for that is due to Tsang. We also explain how the method breaks down for given our current knowledge about the zeros of the zeta function. Conditionally on the Riemann hypothesis, we extend our results to the range .

Spectral and Imaging Observations of a C2.3 White-Light Flare from the Advanced Space-Based Solar Observatory (ASO-S) and the Chinese Hα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha $\\end{document}Solar Explorer (CHASE)

Solar white-light flares are characterized by an enhancement in the optical continuum, which are usually large flares (X- and M-class flares). Here, we report a small C2.3 white-light flare (SOL2022-12-20T04:10) observed by the Advanced Space-based Solar Observatory and the Chinese Hα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha $\\end{document}Solar Explorer (CHASE). This flare exhibits an increase of ≈ 6.4% in the photospheric Fe i line at 6569.2 Å and ≈ 3.2% in the nearby continuum. The continuum at 3600 Å also shows an enhancement of ≈ 4.7%. The white-light bright kernels are mainly located at the flare ribbons and co-spatial with nonthermal hard X-ray sources, which implies that the enhanced white-light emissions are related to nonthermal electron-beam heating. At the bright kernels, the Fe i line displays an absorption profile that has a good Gaussian shape, with a redshift up to ≈ 1.7 km s−1, while the Hα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha $\\end{document} line shows an emission profile having a central reversal. The Hα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha $\\end{document} line profile also shows a red or blue asymmetry caused by plasma flows with a velocity of several to tens of km s−1. It is interesting to find that the Hα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha $\\end{document} asymmetry is opposite at the conjugate footpoints. It is also found that the CHASE continuum increase seems to be related to the change in the photospheric magnetic field. Our study provides comprehensive characteristics of a small white-light flare that help understand the energy release process of white-light flares.

Temporal dynamics of surface phonon polaritons in polar dielectric nanoparticles with nonlocality

Surface phonon polaritons (SPhPs) supported by polar dielectrics have been a promising platform for nanophotonics in mid-infrared spectral range. In this work, the temporal dynamic behavior of polar dielectric nanoparticles without (or with) spatial dispersion/nonlocality driven by the ultrashort Gaussian pulses is carried out. We demonstrate that three possible scenarios for the temporal evolutions of the dipole moment including ultrafast oscillations with the decay, exponential decay, and keeping a Gaussian shape exist, when the pulse duration of the incident field is much shorter than, similar to, and much longer than the localized SPhP lifetime. Once the nonlocal effect is considered, the oscillation period becomes large slightly, and the exponential decay turns fast. Furthermore, nonlocality-induced novel temporal behavior is found such as the decay with long-period oscillations when the center frequency of the incident pulse lies at the frequency of adjacent longitudinal resonant modes. The positive and negative time-shifts of the dielectric response reveal that the excitation of the dipole moment will be delayed or advanced. These temporal evolutions can pave the way towards potential applications in the modulation of ultrafast signals for the mid-infrared optoelectronic nanodevices.

Extremely low coercivity of powder Co-rich amorphous alloy obtained by gas atomisation

A novel Co-base soft magnetic powder with ultra-low coercivity was produced by inert gas atomisation. The as-atomised powder is fully amorphous owing to its high glass forming ability and the proper selection of atomisation conditions; it exhibits a very low coercivity (0.130 Oe) mainly due to the low magnetostriction coefficient of Co-based alloys. After production, the powder was annealed at different temperatures between 300 and 600 ºC for 30 minutes. Crystallisation started at around 575 ºC, which is the temperature of the first exothermic peak detected by differential scanning calorimetry. Annealing the powder at temperatures below 550 ºC develops only structural relaxation of the amorphous structure. The smallest coercivity (0.056 Oe) was found in the sample annealed at 400 ºC. On the other hand, an increment of the coercivity of four orders of magnitude occurred after full crystallisation at 600 ºC (394.320 Oe). From the analysis of the curves of anisotropy field distribution, it can be concluded that this Co-base alloy shows lower average anisotropy field, a more gaussian shape and a wider distribution than Fe-base alloys. This is explained by a lower magnetoelastic anisotropy and a more homogeneous distribution of the magnetic anisotropy. The powder exhibits a spherical shape that makes it very suitable as ferromagnetic phase to manufacture powder cores with extremely low hysteresis loss for medium-high frequency applications.

Energy efficiency of Gaussian and ring profiles for LPBF of nickel alloy 718

Additive manufacturing (AM) has the potential for improving the sustainability of metal processing through decreased energy and materials usage compared to casting and forging. Laser powder bed fusion (LPBF) of high-temperature alloys such as nickel alloy 718 is one of the key modalities supporting this effort. One of the major drawbacks to LPBF is its slow build speed on the order of 5–10 cubic centimeters per hour print speed. This experimental study investigates how to increase the productivity of the LPBF process by switching from a traditional Gaussian laser shape to a ring laser shape using a nLight multi-modal laser. The objective is to increase productivity, reducing energy consumption and time, without sacrificing mechanical properties by switching to the ring laser thereby improving the sustainability of LPBF. Results include measuring the energy consumption of an Open Additive LPBF system during 718 printing and comparing the microstructure and mechanical properties of the two different lasers.

A new method for instrumental profile reconstruction of high-resolution spectrographs

Context. Knowledge of the spectrograph’s instrumental profile (IP) provides important information needed for wavelength calibration and for the use in scientific analyses. Aims. This work develops new methods for IP reconstruction in high-resolution spectrographs equipped with astronomical laser frequency comb (astrocomb) calibration systems and assesses the impact that assumptions on the IP shape have on achieving accurate spectroscopic measurements. Methods. Astrocombs produce ≈ 10 000 bright, unresolved emission lines with known wavelengths, making them excellent probes of the IP. New methods based on Gaussian process regression were developed to extract detailed information on the IP shape from these data. Applying them to HARPS, an extremely stable spectrograph installed on the ESO 3.6m telescope, we reconstructed its IP at 512 locations of the detector, covering 60% of the total detector area. Results. We found that the HARPS IP is asymmetric and that it varies smoothly across the detector. Empirical IP models provide a wavelength accuracy better than 10m s−1 (5m s−1) with a 92% (64%) probability. In comparison, reaching the same accuracy has a probability of only 29% (8%) when a Gaussian IP shape is assumed. Furthermore, the Gaussian assumption is associated with intra-order and inter-order distortions in the HARPS wavelength scale as large as 60 m s−1. The spatial distribution of these distortions suggests they may be related to spectrograph optics and therefore may generally appear in cross-dispersed echelle spectrographs when Gaussian IPs are used. Empirical IP models are provided as supplementary material in machine readable format. We also provide a method to correct the distortions in astrocomb calibrations made under the Gaussian IP assumption. Conclusions. Methods presented here can be applied to other instruments equipped with astrocombs, such as ESPRESSO, but also ANDES and G-CLEF in the future. The empirical IPs are crucial for obtaining objective and unbiased measurements of fundamental constants from high-resolution spectra, as well as measurements of the redshift drift, isotopic abundances, and other science cases.