Gaussian Intensity Distribution Research Articles

Second-order statistical characteristics of a radially polarized Gaussian Schell-model beam with elliptical optical vortex phase in a turbulent atmosphere

Abstract Based on the extended Huygens-Fresnel integral method, we have derived analytical formulae for the cross-spectral density matrix of a radially polarized Gaussian Schell-model beam with elliptical optical vortex phase (i.e., partially coherent radially polarized elliptical vortex (PCRPEV) beam) propagating through atmospheric turbulence, and have investigated the evolution laws of statistical characteristics such as the average intensity, degree of coherence (DOC), and degree of polarization (DOP) of the PCRPEV beam in turbulence. The results indicate that atmospheric turbulence causes the average intensity distribution of the PCRPEV beam to split and rotate during propagation, ultimately degenerating into a Gaussian-like distribution. Moreover, the PCRPEV beam with lower ellipticity, larger coherence length, and higher topological charge degenerates into a Gaussian-like beam at a slower rate in turbulence. Additionally, we also find that DOC distribution is related to topological charge, meaning that it can provide a new way to measure topological charge. In addition, we simulate the propagation of the PCRPEV beam through atmospheric turbulence using the complex screen and the multi-phase screens methods to verify the theoretical results. The research indicates that the simulation results are essentially consistent with the theoretical findings. These outcomes hold significant relevance for the advancement of free-space optical communication and remote sensing technologies.

Crystallization behavior of amorphous GST films under an ultrafast laser irradiation

The crystallization behaviors of amorphous Ge2Sb2Te5 films induced by an ultrafast laser with a time-shaping Gaussian intensity distribution have been studied. The crystalline regions were characterized using optical microscopy, scanning electron microscopy, atomic force microscopy, and Raman spectroscopy. It is found that the region ablated by a single pulse undergoes recrystallization, with a reflectivity higher than that of the non-ablated crystalline region. While preserving the integrity of the film, the diameter of the region with high and uniform reflectivity induced by burst mode is twice that of a single pulse, and the reflectivity is 3 % higher than the 31 % achieved with a single pulse. Additionally, the energy window for laser-induced crystallization expands with an increasing number of burst pulses; specifically, it increases by approximately 2.4 times when the number of sub-pulses is 4 or 5. The Raman results at low pulse energy show a high peak intensity at the 105 cm−1 in related to the vibrations of Te-rich tetrahedra, indicating that the degree of crystallinity in the burst mode region is superior to that achieved with single pulse irradiation. Furthermore, the blue shift of this Raman peak with increased pulse energy further supports that burst mode provides sufficient time for nucleation growth. This work offers insights into achieving more controllable crystallization, which can enhance its applications in phase change memory and other reconfigurable devices.

Unraveling the propagation dynamics of radially polarized anomalous vortex beams in turbulent maritime atmospheres

Based on the unified theory of coherence-polarization, we utilize the extended Huygens-Fresnel principle to derive analytical expressions for the average intensity distribution of a radially polarized anomalous vortex beam (RPAVB) propagating through non-Kolmogorov maritime atmospheric turbulence. The hollow structure of the RPAVB can be sustained over long distances by manipulating the self-focusing point position, which depends on the initial beam parameters. This manipulation effectively mitigates the effect of maritime atmospheric turbulence. Additionally, the RPAVB undergoes a transition into a Gaussian form at significant distances, which can be intentionally slowed down by increasing the beam order, topological charge, beam width, or reducing the turbulent strength.

Generation of the flat-top beam using convolutional neural networks and Gerchberg-Saxton algorithm

Abstract Laser technology has made rapid progress in recent years and has been widely used in various fields such as medicine, biology, military, and materials science. However, the limitations of traditional Gaussian intensity distribution of the laser beams in applications have prompted the emergence and development of flat-top beam shaping technology, which has received widespread attention. Here, we introduce a new method for generating flat-top beams that combines the traditional Gerchberg-Saxton algorithm with convolutional neural networks, using spatial light modulators to achieve flat-top beam shaping. A comparative analysis was conducted by comparing the root mean square error and diffraction efficiency of the generated flat-top beam with the results obtained using only the traditional Gerchberg-Saxton algorithm. Compared with the traditional Gerchberg-Saxton algorithm, the method proposed in this paper can generate a flat-top beam with smaller differences from the target light intensity and higher energy utilization, providing new possibilities for the application of laser technology.

Compact Partially End-Pumped Innoslab Laser Based on Micro-Cylindrical Lens Array Homogenizer

We demonstrate a compact, partially end-pumping Innoslab laser based on a micro-cylindrical lens array homogenizer. A dimension of 12 × 0.4 mm2 flat-top pumping line with a Gaussian intensity distribution across the line was simulated by the ray tracing technique. The rate equations considering the asymmetric transverse spatial distributions are theoretically developed. The simulation results are in good agreement with the experimental results. Preliminary data shows that for a pump power of 260 W, a maximum pulse energy of 15.7 mJ was obtained with a pulse width of 8.5 ns at a repetition frequency of 1 kHz. The beam quality M2 factors in the unstable and stable directions were 1.732 and 1.485, respectively. The technology has been successfully applied to temperature and humidity profiling lidar and ozone lidar and has been productized, yielding direct economic value.

Laser powder bed fusion of pure copper using ring-shaped beam profiles

Additive manufacturing of copper using laser powder bed fusion (PBF-LB/M) enables the production of highly complex components. However, processing of copper by means of near-infrared laser radiation is challenging due to its absorptivity of only 5%–20%. Using a keyhole welding process with a Gaussian intensity distribution increases the absorptivity up to 53% due to multireflection. This enables the production of components with a density larger than 99.5% and electrical conductivity larger than 90% of the International Annealed Copper Standard (IACS), but this type of welding leads to keyhole porosity due to keyhole instabilities. One way of counteracting is the use of a heat conduction welding process. However, due to the Gaussian intensity distribution, it is not possible to supply sufficient energy to eliminate lack-of-fusion porosity and concurrently avoid the formation of a keyhole. Ring-shaped beam profiles have proven their advantages in stabilizing the PBF-LB/M process with a tendency toward higher laser power, but pure copper has not yet been processed in this way. Therefore, this study investigates the potential of three ring-shaped beam profiles to produce specimens with a density of more than 99.5% and their respective electrical conductivity using a laser power of up to 1300 W. In order to understand the underlying welding process, the weld geometry of single-tracks is analyzed. Specimens with a density of up to 99.77% and an electrical conductivity of up to 101.62% IACS are produced, whereby the material properties and welding regime depend on the selected ring-shaped beam profile.

Sheet conductance of laser-doped layers using a Gaussian laser beam: an effective depth approximation

Laser doping of silicon with pulsed and scanned laser beams is now well-established to obtain defect-free, doping profile tailored, and locally selectively doped regions with a high spatial resolution. Picking the correct laser parameters (pulse power, pulse shape, and scanning speed) impacts the depth and uniformity of the melted region geometry. This work performs laser doping on the surface of single crystalline silicon, using a pulsed and scanned laser profile with a Gaussian intensity distribution. A deposited boron oxide precursor layer serves as a doping source. Increasing the local inter-pulse distance xirr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_\ ext {irr}$$\\end{document} between subsequent pulses causes a quadratic decrease of the sheet conductance Gsh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_\ ext {sh}$$\\end{document} of the doped surface layer. Here, we present a simple geometric model that explains all experimental findings. The quadratic dependence stems from the approximately parabolic shape of the individual melted regions directly after the laser beam has hit the Si surface. The sheet resistance depends critically on the intersection depth dch\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d_\ ext {ch}$$\\end{document} and the distance xirr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_\ ext {irr}$$\\end{document} of overlap between two subsequent, neighboring pulses. The intersection depth dch\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d_\ ext {ch}$$\\end{document} quadratically depends on the pulse distance xirr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_\ ext {irr}$$\\end{document} and therefore also on the scanning speed vscan\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$v_\ ext {scan}$$\\end{document} of the laser. Finally, we present a simple model that reduces the complicated three dimensional, laterally inhomogeneous doping profile to an effective two-dimensional, homogeneously doped layer which varies its thickness with the scanning speed.

In-situ electron beam characterization for electron beam powder bed fusion

Electron beam powder bed fusion is an advanced additive manufacturing technology that utilizes an electron beam to fabricate complex metallic components layer by layer. It is well known, that the beam profile is one of the most important key ingredients for successful processing. Surprisingly, the beam profile during the process is almost unknown until today. The state of the art in beam characterization comprises pre-processes applying different beam measurement devices which ensure a beam profile evaluation at one or a small number of fixed locations on the build area. To the knowledge of the author, there exist no technique to measure the beam profile in-situ during manufacturing at arbitrary locations on the build area.This study presents a groundbreaking method for an in-situ measurement technique of the beam profile for electron beam powder bed fusion. The method exploits electron optical images of a sintered powder bed after preheating. After converting the image into the frequency space by a Fourier transformation, the beam profile is reconstructed. In this work we demonstrate the feasibility on a focused electron beam with an elliptical Gaussian intensity distribution. This real-time assessment capability, completed within seconds, marks a significant advancement in the field of electron beam powder bed fusion, promising to improve manufacturing outcomes through enhanced process optimization and beam profile monitoring.

Manifestation of the normal intensity distribution law (NIDL) in the rovibrational emission spectrum of hydroxyl radical

The latest experimental [Noll et al. Atmos. Chem. Phys. 20, 5269 (2020)] and theoretical [Brooke et al. J. Quant. Spectr. Rad. Transfer 168, 142 (2016)] data on the OH emission intensities are analysed with use of the NIDL. It is found that the calculated intensities of the Δ v > 6 transitions should not be trusted. The analysis of the OH data revealed that the NIDL theory is not applicable to the satellite bands. The effect of small reduced mass previously discovered in H 2 [Ushakov et al. J. Mol. Spectrosc. 399, 111863 (2024)], causing the NIDL straight-line slope to be larger than the one associated with the repulsive branch of the potential, is demonstrated in OH, and the same should be true of all the diatomic hydrides. We performed ab initio calculations of the OH repulsive branch and compared it with the one of Brooke et al. and the other due to Varandas and Voronin [Chem. Phys. 194, 91 (1995)]. We found that the ab initio PEF closely follows the Varandas-Voronin potential in the repulsive region important for calculating the overtone intensities [Medvedev, J. Chem. Phys. 137, 174307 (2012)].

Effect of steady-state thermal blooming on partially coherent radially polarized beams propagating in the atmosphere

We undertake a computational study of the steady-state thermal blooming effect on a special class of partially coherent vector beams, called partially coherent radially polarized (PCRP) beams, propagating through the atmosphere. A computational propagation model that is based on a multi-phase screen method is established to simulate partially coherent vector beams. With the use of this model, the propagation properties of PCRP beams with different initial powers and spatial coherence widths are studied in detail, including average intensity distribution, r.m.s. beam width, and polarization. Our results unveil that PCRP beams can effectively reduce or overcome the negative effects caused by thermal blooming when the initial coherence width falls below a certain threshold. Further, it is shown that the spatial distribution of degree of polarization (DOP) is significantly affected by the thermal blooming during beam propagation, whereas the global DOP (integrating the DOP over a beam’s cross-section) is not.

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.

Unveiling Spatiotemporal Diffusion of Hot Carriers Influenced by Spatial Nonuniform Hot Phonon Bottleneck Effect in Monolayer MoS2.

The exceptional semiconducting properties of two-dimensional (2D) transition metal dichalcogenides (TMDs) have made them highly promising for the development of future electronic and optoelectronic devices. Extensive studies of TMDs are partly associated with their ability to generate 2D-confined hot carriers above the conduction band edges, enabling potential applications that rely on such transient excited states. In this work, room-temperature spatiotemporal hot carrier dynamics in monolayer MoS2 is studied by transient absorption microscopy (TAM), featuring an initial ultrafast expansion followed by a rapid negative diffusion, and ultimately a slow long-term expansion of the band edge C-excitons. We provide direct experimental evidence to identify the abnormal negative diffusion process as a spatial contraction of the hot carriers resulting from spatial variation in the hot phonon bottleneck effect due to the Gaussian intensity distribution of the pump laser beam.

Transient pump-probe analysis of pump-induced lensing in laser amplifiers.

Understanding of pump-induced lensing in laser amplifiers is essential for the optimized design of high-power lasers with high spatial quality, but there is usually incomplete knowledge of the interplay between thermal and population induced lensing mechanisms, lensing under lasing and non-lasing conditions, and transient lensing effects under pulsed operation. This paper provides quantitative insight of pump-induced lensing effects by using experimental transient pump-probe measurements in an alexandrite laser amplifier end-pumped by a short pulse pump beam with Gaussian spatial intensity distribution. Lensing results are presented showing a large difference in lensing under both non-lasing and lasing conditions and distinction of the population lens and thermal lens contributions from their different response time. Different pump beam sizes are used to show the variation of the relative strength of the lensing mechanisms. Comparison of experimental results with the analytical transient theory developed in this paper for the Gaussian pump beam gives excellent agreement and quantitative information on the thermal and population contributions to the amplifier lens. This paper provides a methodology for quantitative investigation of pump-induced lensing in general laser amplifier systems, and potentially other classes of optical materials with residual optical absorption.

Evolution properties of partially coherent electromagnetic elliptical vortex beam propagating through atmospheric turbulence

We obtained the analytical formulas of partially coherent electromagnetic elliptical vortex beam (PCEEVB) propagating through atmospheric turbulence with the help of the extended Huygens–Fresnel principle and explored the normalized average intensity distribution of PCEEVB in turbulence. It is worth noting that the PCEEVB appears new characteristics such as self-rotating, self-splitting, and self-healing in turbulence. It can be also found that the number of peaks caused by splitting of beams is relevant to the topological charge n. What’s more, reducing the ellipticity, magnifying the topological charge, and increasing the initial coherent length δ 0 can improve the anti-turbulence ability of PCEEVB in turbulence. The multi-phase screen simulation results are consistent with the theoretical results. Our results will have significant implications for laser communications, laser radar, and laser remote sensing.

The influence of laser beam shaping on surface roughness, surface figure and mid-spatial frequency of fused silica glass in CO2 laser smoothing

CO2 laser with Gaussian and top-hat laser intensity distribution, were utilized to process fused silica with 50 mm diameter in raster scanning path to explore the evolution of surface roughness, waviness and surface figure. The results show that surface roughness can be decreased to < 10 nm with both Gaussian and top-hat CO2 laser smoothing; Top-hat laser will cause higher PSD2 value compared with Gaussian, but Gaussian has led to added mid-spatial frequency at 0.4395 mm−1 (2.28 mm) with 75 % overlap rate (raster scanning distance is 2.327 mm); The surface profile of fused silica has evolved from the initial convex to concave profile after being irradiated by both CO2 lasers. From experiments, improper overlap rate will cause greater distortion, and higher power density can result in serious damage to the PV value of surface figure.

Multimode beam propagation through atmospheric turbulence

The investigation focuses on studying the propagation characteristics of multimode lasers in the turbulent amosphere. By employing the Huygens-Fresnel integral, we develop analytical formulations for various propagation parameters. These include the average intensity distribution, kurtosis parameter, beam spread, and the average transmittance of multimode beams in turbulent atmosphere. Our findings reveal that as the propagation distance or the structure constant of the atmosphere increases, i.e., turbulence becomes stronger, the kurtosis parameter and the beam spread increase. The multimode beam exhibits a Gaussian like intensity profile when the propagation distance is significantly increased or when the structure constant becomes sufficiently large. For the case of the Gaussian beam, the kurtosis parameter is found to be 3. The multimode beam's kurtosis parameter rises as the turbulence becomes stronger and eventually approaches 3. Raising the mode content leads to a rise in the average transmittance; however, it leads to a decline in the Kurtosis parameter and the beam spread.

Exploring the intensity, distribution and evolution of teleconnections using climate network analysis.

Teleconnections refer to long-range climate system linkages occurring over typically thousands of kilometers. Generally speaking, most teleconnections are attributed to the transmission of energy and propagation of waves although the physical complexity and characteristics behind these waves are not fully understood. To address this knowledge gap, we develop a climate network-based approach to reveal their directions and distribution patterns, evaluate the intensity of teleconnections, and identify sensitive regions using global daily surface air temperature data. Our results reveal a stable average intensity distribution pattern for teleconnections across a substantial spatiotemporal scale from 1948 to 2021, with the extent and intensity of teleconnection impacts increasing more prominently in the Southern Hemisphere over the past 37 years. Furthermore, we pinpoint climate-sensitive regions, such as southeastern Australia, which are likely to face increasing impacts due to global warming. Our proposed method offers new insights into the dynamics of global climate patterns and can inform strategies to address climate change and extreme events.

Soft x-ray Ar + 8 laser excited by low-voltage capillary discharge.

We demonstrated the operation of a 46.9-nm capillary discharge Ar + 8-laser excited by electrical pulses at a very low voltage (35 - 45 kV), which is approximately two times lower than previously reported. The decrease in pulse voltage not only allows for further reduction in the size of the laser's excitation part, but also a principal shift to the experimental methods, techniques, and technologies used in ordinary pulsed gas lasers operating in the ultraviolet, visible, and infrared regions of the spectra. In an argon-filled alumina capillary with an inner diameter of 3.1 mm and a length of 22 cm, laser pulses with an energy of 4 µJ and a duration of 1.6 ns were generated. The laser produces a beam with a Gaussian intensity distribution and an FWHM divergence of 1.9 mrad. The results could be particularly useful in the development of compact, practical soft x-ray capillary lasers for use in small laboratories at educational and research institutions.

Transmission Characteristics and Spatial Coherence of Partially Coherent Light-Emitting Diode Array in the Ocean

Underwater LED light sources are commonly implemented in array configurations with a wide-angle field of view, primarily catering to high-speed communication within a few meters. To increase transmission distance and mitigate oceanic turbulence effects, this paper focuses on the spatial coherence analysis of narrow-beam partially coherent light-emitting diode (PCLED) arrays, examining their average light intensity distribution, beam width, and spatial coherence during oceanic transmission. Based on the extended Huygens–Fresnel integral, the optical field models and spatial characteristics of the radial PCLED array are derived under oceanic conditions, considering parameters such as water attenuation coefficient, kinetic energy dissipation rate, temperature dissipation rate, temperature-to-salinity ratio, as well as the radial filling factor and the sub-beam spatial coherence length of the light source at different transmission distances. The simulations show that, as the spatial coherence length of the sub-beam decreases from hundreds to a few micrometers, the combining distance of the beam arrays also decreases. This reduction in coherence results in the average light intensity distribution degrading into a Gaussian-like distribution, with a significant five-fold decrease in peak intensity. Furthermore, the width of the array spreads, starting from distances of 7 m and 0 m, respectively. The radial PCLED beam array, with its sub-beam spatial coherence length inside micrometers, possesses inherent characteristics that suppress turbulence effects and has future extensive possibilities in the ocean.

Absorption Line Oscillator Strengths for the C 2Π(0)-A 2Σ+(0) Band of Nitric Oxide

We have determined absorption oscillator strengths for rotational transitions of the C 2Π(0)-A 2Σ+(0) band of NO, which has been detected in the upper atmosphere of Venus. The molecular quantum defect orbital method has been used in the calculation of the electronic transition moment and the Rydberg–valence interaction between the C 2Π(v = 0) and the B 2Π (v = 7) states has been considered. Considerable deviations from normal intensity distribution of the rotational lines have been found at J ≤ 5.5. As far as we know, the present line f-values are reported here for the first time. These data may be useful in the interpretation of the observations obtained by the Visible and Infrared Thermal Imaging Spectrometer instrument on the Venus Express spacecraft.