Beam Divergence Research Articles

Efficiency-enhanced TM-mode gyrotron with down-taper interaction structure

Recent advancements have shown that transverse magnetic (TM)-mode gyrotrons are feasible under specific conditions, yet their capabilities remain insufficiently explored. This article systematically investigates a W-band TM11-mode gyrotron within the down-tapered structure(s) to uncover its limitations and underlying physics. 2D interaction-efficiency maps are scanned as functions of the tube's geometrical parameters or beam parameters under magnetic-field tuning. An oversized tube integrated with short two-stage down tapers enhances the output efficiency of the fundamental axial mode and effectively alleviates the axial-mode competition. The peak electron-beam efficiency of the TM11 mode exceeds 50% with an idealized cold beam. The 3D particle-in-cell simulations are utilized to validate the real-time scheme including multiple transverse modes. Incorporating realistic beam spread, the first-harmonic TM11 mode effectively suppresses the second-harmonic and third-harmonic transverse electric modes with a maximum steady output of 130 kW, corresponding to an interaction efficiency of 37%. Complex dynamics regarding the mode-competing and mode-forming processes are revealed and discussed. This study not only facilitates the exploration of TM-mode gyrotrons but also provides insights into the harmonic gyrotron using the axis-encircling electron beam, where TM modes have more chances to be excited and dominate oscillations.

Ionization loss spectra of high-energy protons in an oriented crystal at various incidence angles with respect to a crystalline plane

The ionization energy loss distributions (spectra) of high-energy protons in oriented silicon crystals are considered on the basis of computer simulation. Evolution of the spectra with the change of the angle θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} between the particle momentum and the crystal (110) plane is investigated. It is shown that both the most probable and the average energy loss change non-monotonically with the increase of θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document}. While at small θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} these losses are lower than their values in a disoriented crystal, at larger θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} they can be higher than these values. The dependence of the most probable energy loss on θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} contains a discontinuity, which however might be challenging to register experimentally. Additionally, the influence of dechanneling and the incident beam divergence on the spectra of planar channeled protons is demonstrated.

200 mm optical synthetic aperture imaging over 120 meters distance via macroscopic Fourier ptychography

Fourier ptychography (FP) imaging, drawing on the idea of synthetic aperture, has been demonstrated as a potential approach for remote sub-diffraction-limited imaging. Nevertheless, the farthest imaging distance is still limited to around 10 m, even though there has been a significant improvement in macroscopic FP. The most severe issue in increasing the imaging distance is the field of view (FoV) limitation caused by far-field conditions for diffraction. Here, we propose to modify the Fourier far-field condition for rough reflective objects, aiming to overcome the small FoV limitation by using a divergent beam to illuminate objects. A joint optimization of pupil function and target image is utilized to attain the aberration-free image while estimating the pupil function simultaneously. Benefiting from the optimized reconstruction algorithm, which effectively expands the camera’s effective aperture, we experimentally implement several FP systems suited for imaging distances of 12 m, 65 m, and 120 m with the maximum synthetic aperture of 200 mm. The maximum synthetic aperture is thus improved by more than one order of magnitude of the state-of-the-art works from the furthest distance, with an over fourfold improvement in the resolution compared to a single aperture. Our findings demonstrate significant potential for advancing the field of macroscopic FP, propelling it into a new stage of development.

Near-infrared double-layer cascaded metasurface for beam shaping

The vast applicability of collimated flat-topped beam shapers, predominantly constructed from traditional lens elements, is met with challenges when the scale is less than wavelength. Metasurfaces have an excellent ability for optical manipulation, which can provide a promising approach to flat optics. Here, a metasurface-based Gaussian beam shaper is designed to combine the transmission phase principle with geometric transformation methods, which can reshape a 1550 nm Gaussian beam into a flat-topped beam with a uniformity of 84.39%. Furthermore, a cascaded metasurface beam shaper design is proposed to address the significant divergence in the flat-topped beam obtained from the single-layer metasurface. Simulation results indicate the output beam exhibits both uniform intensity and phase distributions over a considerable transmission distance, effectively minimizing the divergence of the output beam. This research has potential applications in various fields, such as optical antennas, fiber optics, and other optical systems.

Simulation Study of High-Precision Characterization of MeV Electron Interactions for Advanced Nano-Imaging of Thick Biological Samples and Microchips.

The resolution of a mega-electron-volt scanning transmission electron microscope (MeV-STEM) is primarily governed by the properties of the incident electron beam and angular broadening effects that occur within thick biological samples and microchips. A precise understanding and mitigation of these constraints require detailed knowledge of beam emittance, aberrations in the STEM column optics, and energy-dependent elastic and inelastic critical angles of the materials being examined. This simulation study proposes a standardized experimental framework for comprehensively assessing beam intensity, divergence, and size at the sample exit. This framework aims to characterize electron-sample interactions, reconcile discrepancies among analytical models, and validate Monte Carlo (MC) simulations for enhanced predictive accuracy. Our numerical findings demonstrate that precise measurements of these parameters, especially angular broadening, are not only feasible but also essential for optimizing imaging resolution in thick biological samples and microchips. By utilizing an electron source with minimal emittance and tailored beam characteristics, along with amorphous ice and silicon samples as biological proxies and microchip materials, this research seeks to optimize electron beam energy by focusing on parameters to improve the resolution in MeV-STEM/TEM. This optimization is particularly crucial for in situ imaging of thick biological samples and for examining microchip defects with nanometer resolutions. Our ultimate goal is to develop a comprehensive mapping of the minimum electron energy required to achieve a nanoscale resolution, taking into account variations in sample thickness, composition, and imaging mode.

Experimental study on beam focusing of ionic liquid electrospray thruster with focus structure

The application of Ionic Liquid Electrospray Thrusters (ILETs) in micro/nanosatellites is very promising. However, the divergent beam of ILETs significantly affects their performance, including thrust, specific impulse, lifetime, propulsion efficiency, and more. Therefore, in order to improve the performance of ILETs, it is essential to optimize the beam. In this study, a focus structure was designed and fabricated. A series of beam focusing experiments were performed using a conical porous tungsten emitter and the ionic liquid EMI-BF4 as a propellant. The operational state of ILETs was demonstrated, with over 95 % of the beam composed of ions. After configuring the focus structure, the electric field in the emission region is weakened by the focus electrode, which has a certain negative effect on the starting voltage and emission current. Analysis of the beam focusing results showed that the focus structure reduced the beam divergence half-angle (half-angle) from 40° to 11° and concentrated the beam current within a half-angle of 7.3°. By estimating the thrust and specific impulse of the thruster, it was found that the focus structure could maximize the specific impulse by up to 22.4 % at the same voltage and increase it by approximately 23 % at the same power-to-thrust ratio. This focus structure demonstrated excellent focusing effect on a single conical emitter, making this research valuable as a reference for designing a focus structure for other types of emitters.

Dual-spherical-wave optical scanning holographic microscopy with resolution enhancement and an extended depth of field

Conventional optical scanning holographic microscopy (OSHM) is realized by using a plane wave and a spherical wave as the illumination. The resolution of the conventional OSHM is limited by the numerical aperture of the spherical wave and cannot exceed the Rayleigh limit. In this paper, the OSHM by using dual spherical waves as the illumination is studied. The model of a Gaussian wave, together with the constraints on the signal strength and the visibility, are considered in the analysis of the dual-spherical-wave (DS) OSHM. For an object located at the symmetry plane of the DS-OSHM, the resolution can slightly exceed the Rayleigh limit, and the depth of field (DoF) is extended significantly. For a transparent object, the noise in the DS-OSHM is less than that of the conventional OSHM, thanks to the highly divergent scanning beam. If the object is off the symmetry plane, the resolution is still enhanced, but the extension of the DoF is limited. In addition, a clear reconstructed image will be observed not only at the original object plane, but also at its mirror plane. To the best of our knowledge, this phenomenon is reported for the first time.

Semiconductor laser collimation and shaping design based on the combination of a rotationally symmetrical lens and a cylindrical lens

A dual-lens collimation and shaping system which is composed of a rotationally symmetric lens and an aspherical cylindrical lens is proposed in this paper. The system design method is discussed in detail, and the divergent elliptical laser beams are finally converted into collimated circular beams. The simulation results show that the maximum divergence angle of the beams can be collimated to 2.58 µrad, the standard deviation of the edge beam radius samples (SDRS) can be decreased from the original 4.227 to 0.135 mm, and the ratio of beam waist (RBW) drops from 1.554 to 1.0093 in the case of the output beam radius of 40 mm. The effects of transmission distance, astigmatism, wavelength deviation, light source offset, and lens offset on the collimation shaping effect are discussed. The collimation system can be widely used in long-distance optical communication systems and the design method in this paper can provide some new ideas for optical design researchers.

On the possibility of long‐distance transmission of OAM beam in rectangular tunnels

AbstractThis letter explores the possibility of long‐distance transmission of an orbital angular momentum (OAM) beam through rectangular tunnels. Theoretical analysis reveals that the OAM beam propagating in the tunnel with square cross section fulfills the conditions for axial propagation and exhibits azimuth symmetry. In comparison with free‐space OAM generation, we draw the conclusion that long‐distance transmission of OAM beams is achievable in the tunnels with square cross section. The validity of our conclusion is further substantiated through numerical experiments. Simulation results demonstrate that the first‐order OAM beam radiated by a uniform circular antenna array exhibits favorable helical phase distribution and the circular symmetry of the amplitude distribution in the tunnel beyond the Rayleigh distance. However, these characteristics degrade with increasing mode order and propagation distance, because the increase of high‐order OAM beam divergence angle and propagation distance will exacerbate the impact of multipath effects in the tunnel environment.

Adaptive Beam Divergence, and Intensity Decay Compensation in OCT for Enhanced Tissue Imaging

Adaptive Beam Divergence, and Intensity Decay Compensation in OCT for Enhanced Tissue Imaging

High birefringent slotted core slotted cladding porous core PCF for THz waveguide

A novel design featuring a porous core photonic crystal fiber (PC-PCF) is proposed in this paper for terahertz (THz) waveguide application. This work uses finite element method (FEM) and a boundary condition related to perfectly matched layer (PML) for analyzing the guiding properties. This methodology is supported by a fiber type featuring a slotted core and slotted cladding, utilizing Zeonex as the material. It offers high birefringence valued at 0.0978, small confinement loss of 10−14 dB/cm, a meager amount of effective material loss (EML) valued at 0.011697 dB/cm and a very high core power fraction (CPF) of 67.156%. Additionally, it shows a flattened pattern of dispersion measuring 0.4 ± 0.2 ps/THz/cm at an extensive frequency range of 0.5 THz to 2 THz. Other significant waveguide properties: effective refractive index, numerical aperture (NA), V-parameter, effective area, spot size, and beam divergence of the suggested fiber are numerically analyzed and conferred thoroughly. Regarding its mode of operation, the proposed fiber primarily functions in multimode, but it can also operate in single mode for higher porosity levels and lower core diameters. This unique characteristic renders the proposed PC-PCF structure well-suited for a broad range of applications, offering versatility as to its mode of operation.

Multi-Fresnel-Lens Pumping Approach for Simultaneous Emission of Seven TEM00-Mode Beams with 3.73% Conversion Efficiency

TEM00-mode operation is a requirement in many laser-based applications due to the small divergence and high-power density of the emitted laser beam. A solar laser scheme was designed and numerically studied with the goal of increasing the solar-to-laser power conversion efficiency in the TEM00-mode operation. The collection and primary concentration of sunlight was performed via twelve sets of folding mirrors and Fresnel lenses, toward a laser head composed of a fused silica torus volume and seven Ce:Nd:YAG rods, in a side-pump configuration. With this scheme, TEM00-mode laser power totaling 212.39 W could potentially be produced from seven beams, with six of them being 32.60 W each and with Mx2 = 1.00, My2 = 1.01 quality factors. Notably, 35.40 W/m2 collection efficiency and, most importantly, 3.73% solar-to-laser power conversion efficiency were numerically achieved. The latter efficiency value represents a 1.81-time improvement over the experimental record, established with a prototype that had a single Ce:Nd:YAG rod in an end-side pump configuration.

Design and experimental validation of an aspheric multi-lenticular plano-convex lens for VCSEL beam collimation

In this work, we propose a design method of an aspheric lens that achieves collimation for a VCSEL laser beam. The designed lens features a planar front surface and an aspheric back surface of which the profile is mathematically characterized and precisely determined based on the proposed method. The method is derived from a basic geometric-optics analysis and construction approach. The collimating effect of the lens was first analyzed in simulation and then validated in experimental measurement. The experimental results show that the collimator lens transforms the input VCSEL laser beam divergence angle from 25° (436.33 mrad) to an output angle of 3.6906 mrad.

Quantitative detection of axial defects in pipelines based on modified multi-mode total focusing method (MTFM)

The axial defects in pipelines are hard to detect effectively with the conventional multi-mode total focusing method (MTFM). The inner and outer curved surfaces of pipelines induce beam divergence, reducing focusing performance and introducing imaging distortion and errors. In this paper, the MTFM employed for inspecting flat plates is modified in consideration of the influences of pipe curvature on the ray paths of direct, half-skip and full-skip mode waves. The corresponding travel times are recalculated and used for performing delay-and-sum (DAS) beamforming, achieving the profile reconstruction and quantitative detection of axial defects. The simulation and experiments were implemented on the carbon steel pipeline with 100 mm outer radius and 20 mm wall thickness. The phased array (PA) probe with 32 elements and 5 MHz central frequency and the 55° curved wedge were adopted to detect the inner-wall axial defects in pipeline. The profiles of the planar defects with a length of 5 mm and orientation angles of −45°∼45° were well reconstructed by modified MTFM, and the measurement errors of flaw lengths, orientation angles and tip depths were no more than 16.6 %, 5.1° and 4.0 % after correction, respectively. Further simulated and experimental results indicate that the internal axial defects can also be detected and quantified by modified MTFM. Finally, the influences of pipe curvature on modified MTFM are discussed by simulation.

Optical beam spread in seawater

We study the spatial and angular distribution of light in a narrow stationary beam propagating in a medium like seawater. For a power-law parametrization of the seawater phase function, using radiative transfer analysis, we derive analytical expressions that determine the radiance distribution in the medium. Both the case of intermediate source–receiver distances, where absorption only begins to affect spreading of the beam, and the asymptotic regime of beam propagation are examined. For the main characteristics of the radiance distribution (the total power, the variance of the angular and radial distributions), scaling relations involving the inherent optical parameters of seawater are found. To validate the expressions obtained we carry out Monte Carlo simulation for commonly adopted seawater scattering models (of Petzold and Morel et al) and their analytical parameterizations. For optical parameters typical to seawater, the predicted analytical laws are in excellent agreement with the results of the Monte Carlo computations.

Polarization purity and dispersion characteristics of nested antiresonant nodeless hollow-core optical fiber at near- and short-wave-IR wavelengths for quantum communications

Advancements in quantum communication and sensing require improved optical transmission that ensures excellent state purity and reduced losses. While free-space optical communication is often preferred, its use becomes challenging over long distances due to beam divergence, atmospheric absorption, scattering, and turbulence, among other factors. In the case of polarization encoding, traditional silica-core optical fibers, though commonly used, struggle with maintaining state purity due to stress-induced birefringence. Hollow core fibers, and in particular nested antiresonant nodeless fibers (NANF), have recently been shown to possess unparalleled polarization purity with minimal birefringence in the telecom wavelength range using continuous-wave (CW) laser light. Here, we investigate a 1-km NANF designed for wavelengths up to the 2-μm waveband. Our results show a polarization extinction ratio between ~−30 dB and ~−70 dB across the 1520 to 1620 nm range in CW operation, peaking at ~−60 dB at the 2-μm design wavelength. Our study also includes the pulsed regime, providing insights beyond previous CW studies, e.g., on the propagation of broadband quantum states of light in NANF at 2 μm, and corresponding extinction-ratio-limited quantum bit error rates (QBER) for prepare-measure and entanglement-based quantum key distribution (QKD) protocols. Our findings highlight the potential of these fibers in emerging applications such as QKD, pointing towards a new standard in optical quantum technologies.

Hitless two-dimensional focal plane switch array based on Mach-Zehnder interferometer-embedded micro-ring resonators

Empowered by compact micro-ring (MRR) arrays, wavelength-division-multiplexing (WDM)-based focal plane switch array (FPSA) chip is a promising solution for light detection and ranging (LiDAR) due to its parallelism and high-level integration. However, an MRR channel with a shifting central wavelength may interrupt another channel by dropping an optical signal with an unexpected wavelength, which causes discontinuous beam scanning. To overcome this bottleneck, we propose and fabricate a hitless two-dimensional (2-D) FPSA chip based on a 2 × 8 Mach-Zehnder interferometer-embedded micro-ring resonator (MZER) array. The FPSA chip realizes a beam divergence of 0.18° × 0.05°, a field of view (FoV) of 9.07° × 6.42° with single-ended emission, and a FoV of 10.75° × 6.42° with dual-ended field-of-view splicing technology. Besides, we demonstrate the hitless function of our FPSA chip by performing continuous wavelength sweeping and further applying it to a free-space optical communication link. The experimental results validate the feasibility of our proposed hitless FPSA chip, which efficiently prevents signal interruptions during beam steering.

Scaling laws for high energy Gaussian beams propagation through the atmosphere.

In order to meet the requirements of rapid evaluation of high-energy lasers for practical applications, this paper constructs scaling laws for Gaussian beams propagation through the atmosphere. Firstly, the beam spreading due to single effects including diffraction, optical turbulence and thermal blooming is scaled to identify suitable scaling factors. Then, the scaling functions of the effective radius with multi-effect interaction are established step by step, and the scaling exponents are fixed by genetic algorithm. Finally, the scaling laws of the far-field mean intensity of high-energy laser propagating through atmosphere are constructed. Comparison with the simulations in given scenarios reveals the mean relative error of the scaled mean intensity.

Multi-objective design optimization and physics-based sensitivity analysis of field emission electric propulsion for CubeSat platforms

Field-emission electric propulsion is an electrostatic space electric propulsion technology that offers various advantageous features including efficient design, high specific impulse, and versatile thrust capabilities ranging from micro-Newton to milli-Newton levels. These characteristics make this type of propulsion a promising technology for small satellite platforms, enabling precise attitude control, orbit maintenance, and de-orbiting through ionization and acceleration of a liquid metal propellant. The growing demand for small propulsion systems in CubeSat platforms has spurred significant progress in modeling and characterizing field emission electric propulsion thrusters to enhance their overall performance. However, little study has been conducted to investigate the effect of geometric configurations on electric fields or expelled ion trajectories for design optimization. In this study, multi-objective design optimization is performed by incorporating electrostatic simulation coupled with an analytical performance model into evolutionary algorithms based on prediction from surrogate modeling, aiming to optimize the thruster emission design to maximize thruster performance. Physical insights into the key design factors influencing the performance of field emission electric propulsion have been gained by probing into the interaction between ion particles and electric field behavior within the thruster. It has been found that the length of the emitter tip has a significant effect on plume divergence, i.e., a longer emitter tip under the influence of electric field at higher emitter current tends to result in lower initial acceleration of emitted ions and subsequently wider spread or divergence of the ion beam. A shorter emitter tip, on the other hand, generates a sharper E-field gradient, resulting in a more focused and narrower ion beam. Additionally, sensitivity analysis has identified the mass flow rate and potential distributions as the most influential design factors on performance due to the active roles they play in the performance generation process.

Bound state in the continuum enabled ultralong silicon ridge waveguide grating antennas for integrated LiDAR applications.

As a novel method for solid-state light detection and ranging (LiDAR), optical phased arrays (OPAs) cater to the growing market requirement for mass-produced chip-scale beam steering devices. Waveguide grating antennas (WGAs) with low loss, high efficiency and large emitting aperture are strongly desirable to achieve low beam divergence and high resolution for OPAs. In this paper, we report two kinds of silicon ridge-waveguide-based WGAs with ultra-sharp instantaneous field-of-view (IFOV) for LiDAR applications. The ridge-concave WGA (RCC-WGA) and ridge-convex WGA (RCV-WGA) are designed on account of both sides of ridge area have relatively weak mode field distribution. Lateral quasi-bound state in the continuum (L-BIC) is utilized to further suppress side scattering and improve the emission efficiency. The RCC-WGAs and RCV-WGAs are fabricated on silicon-on-insulator (SOI) platform with 220 nm device layer and foundry compatible etching depths. The measured losses are as low as 2.64 and 2.40 dB/mm at 1550 nm wavelength. The antenna length can up to 6 mm, with theoretical beam divergences of 0.0195° and 0.0175° at the wavelength of 1550 nm, while the experimental results are 0.0251° and 0.0237°, respectively. The proposed low-beam-divergence WGAs are promising in high resolution solid-state LiDAR applications.