Uniform Beam Research Articles

Large angle and high uniform diffractive laser beam splitter with divergent spherical wave illumination

Splitting angle, generally limited by the feature size of diffractive optical element (DOE), is one of the significant metrics of the diffractive laser beam splitter. In this study, we realize large angle and high uniform split beams by using a divergent spherical wave front incidence. For designing this diffractive beam splitter, the Gerchberg-Saxton (GS) optimization algorithm which is known as a widely used method in DOE design is modified. Meanwhile, a negative feedback method is proposed to further improve the uniformity in experiment to compensate the incident wavefront distortion. Finally, a phase-only spatial light modulator (SLM) was used to test the feasibility and adaptiveness of our design strategy. In the experiment, we achieved several kinds of beam splitters and the uniformities are all better than 3.0% which the uniformity is measured by the peak-to-valley (PV) ratio.

Simple and robust approach to uniform laser beam splitting with a spatial light modulator

A simple and robust approach to laser beam splitting employing a spatial light modulator is presented. A weighted, one-dimensional Gerchberg-Saxton algorithm with a target intensity distribution consisting of separated pixels is employed. The resulting phase is a Fourier series and thus a strictly periodical grating. The orthogonal superposition of these gratings enables two-dimensional beam arrays with high uniformity. The approach is not prone to numerical artifacts generating speckles. Due to the strict periodic nature of the grating, the split beam uniformity is hardly affected by misalignment, beam quality, or high laser input power. The diffraction efficiency is high.

Investigations on opportunities and challenges of brilliant high-power laser beam welding with 24 kW and adjustable power distribution for different materials

Solid-state laser beam sources offer the possibility of generating high-brilliance laser beams with low expansion and high usable intensity at the focal point. New approaches include beam shaping with the use of core and ring fiber and, therefore, variable power distribution in the laser beam focal point and material interaction area. Particularly, high-power laser beam welding benefits from beam shaping because of the stabilizing effect on the weld pool. Furthermore, the technical progress achieved with regard to beam quality also allows one to achieve high Rayleigh lengths and, therefore, a more uniform beam diameter over the whole material thickness. In this study, investigations on high-power laser beam welding with a 24 kW disk laser beam source are conducted for three different materials (mild steel, aluminum alloy, and copper), which are of high interest for welding in different sectors. The influence of power distribution between the core and the ring as well as welding speed on weld geometry (depth and width), weld pool stability, and the resulting weld seam quality is investigated. It is shown that the welding process cannot just be scaled up in comparison with welding with lower laser beam power but has its own challenges. It is possible that high welding depths (12 mm for copper, more than 12 mm is possible for aluminum, and 25 mm for mild steel) could be achieved in one pass. To achieve this, aluminum needs the lowest energy per unit length per mm of sheet thickness and copper the highest.

Development of Kagome-based functionally graded beams optimized for flexural loadings

This study is concerned with the development of an innovative beam geometry based on a tessellation of Kagome unit cells and the improvement of its geometry with the aim of increasing its flexural properties. This aspect was achieved by generating a functionally graded metamaterial structure based on a novel approach that considers the well-established analytical beam theory models as the basis of for the optimization of the structural parameters of the unit cells at an individual level. The starting premise is that the optimal strut thickness variation with the height of the beam will cause the material to yield uniformly in the critical cross-section. Preliminary studies were conducted in order to numerically determine the variation of the stiffness and the strength of the Kagome structure with the thickness of its struts. Considering the equivalent stress distribution during bending in the critical cross-section, an optimal variation of the stiffness with the height of the beam was evaluated. Based on these results, different values for the strut diameter were imposed at corresponding coordinates relative to the neutral axis, assuring a continuous transition across the height of the beam. The flexural properties of the developed functionally graded structure were evaluated using finite element analyses and determined superior characteristics when compared with the data obtained from simulations performed on an uniform Kagome beam with of the same mass. The investigated structures were manufactured through stereolithography and subjected to three-point bending tests, the results being in agreement with the numerical data, thus validating the design.

Bandgap estimation and broadening of piezoelectric metamaterial beams undergoing longitudinal vibration

Abstract In the realm of acoustic metamaterials, two crucial challenges have attracted significant interests: (1) How to predict the bandgap range fast and accurately? (2) How to achieve a broader bandgap at a relatively low cost? This paper addresses these challenges by analyzing a type of piezoelectric metamaterial beams comprising unit cells with sub-cells undergoing longitudinal vibration. The longitudinal bandgap estimation relationship based on the effective medium theory is proposed for the first time to estimate the bandgap range of piezoelectric metamaterial beams with unit cells containing sub-cells, and verified with the transfer matrix method. Moreover, novel methods are introduced to construct graded piezoelectric metamaterial beams by combining different sub-cells within a single cell. The proposed graded piezoelectric metamaterial beams occupy significantly less space than conventional graded counterparts and exhibit wider longitudinal bandgaps compared to uniform piezoelectric metamaterial beams.

Modeling and optimization of acantilevered energy harvester partially covered by a macro fiber vomposite patch

Piezoelectric energy harvesters (PEH) are recognized as smart structural devices, offering researchers an innovative approach to estimate the energy harvested from real vibration sources. This work presents linear analytical methods for predicting the energy harvested from an unimorph cantilevered beam with a proof mass, with a substrate partially covered by a Macro Fiber Composite (MFC) patch. In order to enhance a PEH that can generate more density of electrical power, a new framework for MFC harvesters with discontinuous geometries using Euler-Bernoulli assumptions is proposed. The length of the harvester can be divided into three parts of uniform beams followed by applying appropriate continuity conditions. Mixing rules are used to derive the equivalent properties of the MFC patch which is considered as five layers. The active layer contains a piezoceramic macro fibers embedded within an epoxy matrix, which is fully covered by electrode and Kapton layers. The excitation of the system is assumed to be at its base. The proposed method is validated through experimental comparison issued from the literature. The results indicate that the location of the MFC patch has a significantly affect to the density of electrical power, the optimal resistance and the natural frequencies.

A Method of Realizing Adaptive Uniform Illumination by Pyramid Prism for PA-LiDAR

In this paper, we propose a simple method to generate the uniform illumination using a pyramid prism for Plane Array Laser Imaging Detection and Ranging (PA-LiDAR). The principle of the pyramid prism shaping the Gaussian beam to form a uniform beam was analyzed theoretically. By changing the parameters of the pyramid prism and laser beam, the profile distribution of the output beam can be easily adjusted. Based on the operation mode and illumination requirements of PA-LiDAR, we have developed a set of LiDAR prototypes using a pyramid prism and carried out experimental research on these prototypes. The simulation and experimental results demonstrated that this method can achieve a uniform illumination beam with excellent propagation properties for meeting the technical requirements of PA-LiDAR. This method of uniform illumination has the advantages of being simple, flexible, easily adjustable and convenient to operate.

Energy absorption of auxetic honeycomb with graded beam thickness based on Bezier curve

In order to improve the energy absorption and lightweight of the structure, a novel auxetic honeycomb with graded beam thickness based on Bezier curve (BZH) is proposed on the basis of the double arrow negative Poisson ratio honeycomb. The finite element model of BZH under axial compression is established, and its accuracy is verified by experiments. Compared with a honeycomb of uniform beam thickness (DUH) of the same mass, the thickness of the beam becomes thicker in the middle and thinner on both sides, which causes the BZH to produce more plastic hinges when compressed, and the energy absorption is increased by 12 %. By parameter analysis of beam thickness distribution trend, the mechanical properties of BZH can be effectively controlled. A theoretical model of BZH under quasi-static compression is also established and the BZH configuration is optimized by proxy modeling technique and NSGA-II algorithm. The results show that the SEA of the optimized structure is increased from 5.23 kJ·kg-1 to 6.17 kJ·kg-1, and the energy efficiency is reduced from 3.44 kN to 2.96 kN. Therefore, auxetic honeycomb with graded beam thickness based on Bezier curve has great potential in the field of energy absorption.

A Novel Topology of a 3 × 3 Series Phased Array Antenna with Aperture-Coupled Feeding.

This paper presents a novel 3 × 3 phased array antenna optimized for 4 GHz operation, achieving a realized gain of 13.2 dBi and enabling 30-degree beam steering with a minimal capacitance variation of 1.5 pF. The design features a series aperture-coupled feeding mechanism that not only reduces the antenna's size but also simplifies the fabrication process, making the device both cost-effective and compact. Integrating cost-efficient quadrature-hybrid phase shifters and novel power splitters with cascaded quadrature hybrids ensures uniform power distribution and precise beam steering. The innovative use of these components addresses common challenges in phased array systems, such as space constraints, high costs, and complex power distribution.

Shape optimization of a non-uniform piezoelectric bending beam for human knee energy harvester

Abstract Scavenging energy from the human body to provide a sustainable source for electronic devices has gained significant attention. Recently, scientists have focused on harnessing biomechanical energy from human motion. This study was dedicated to developing and optimizing a non-uniform piezoelectric bending beam-based human knee energy harvester. The bimorph non-uniform piezoelectric bending beam consisted of a non-uniform carbon fiber substrate and piezoelectric macro fiber composites. Compared to the uniform piezoelectric bending beam, the non-uniform piezoelectric beam can optimize the shape to improve the average strain, thus improving the energy harvesting efficiency. In this study, eight shape functions, including ellipse, sin, tanh, exponential function, parabola, trigonometric line, and bell curves, were investigated and optimized. The bell curve bending beam was selected and fabricated due to its good performance. Then, a benchmark platform was developed to test the deflection curve and reaction force when the nonuniform bending beam was compressed. Finally, to validate the design, experimental testing on three subjects was conducted when they were equipped with the harvester and walked on a treadmill. Testing results indicated that the non-uniform bending beam-based energy harvester can improve the energy harvesting efficiency by 28.57% compared to the uniform beam-based energy harvester. The output power can reach 18.94 mW when walking at 7.0 km h−1.

Utilizing an aspheric lens and compound ellipsoidal cavity for a laser uniform illumination system

To achieve uniform laser illumination of an active imaging system with a small aperture diameter and large field angle, we have developed what we believe to be a novel structure for achieving uniform beam shaping that integrates a laser source, an aspheric lens, and a composite ellipsoidal cavity to enable active laser illumination. Through an aspheric lens, the fundamental mode Gaussian beam is transformed into double Gaussian and flat-top radiation at the target plane. The double Gaussian radiation is further reflected by a complex ellipsoidal cavity, where it is evenly distributed into equal radiation flux. This flux combines with the flat-top radiation, resulting in a uniform distribution at the target plane. The parameters of the complex ellipsoidal cavity are determined using an equalization algorithm. After combining the transmission for flat-top shaping by the aspheric lens and secondary reflection shaping by the composite ellipsoidal cavity, we achieved an aperture measuring 29.7 mm with an aperture angle of 84.0°, at a distance of 2 m from the target plane, with a diameter of 3.6 m, resulting in uniformity reaching 92.7%. RMS and MT/R determine the effectiveness of the compound ellipsoidal cavity design, depending on the maximum reflection angle and transmission angle. MT/R is inversely proportional to the maximum reflection angle, while RMS is directly proportional to the transmission angle. By setting the maximum reflection angle to 32.0° and the transmission angle to 8.0°, we were able to achieve a minimum root-mean-square focusing radius of 108.6 µm along with a minimum effective MT/R ratio of 1.07. The overlap degree between transmission and reflection directly impacts the target plane’s uniformity, adjusted through a defined adjustment factor. Optimizing this factor to 0.9 maximizes the uniformity of the target plane.

Modeling and analysis of a flexible spinning Euler-Bernoulli beam with centrifugal stiffening and softening: A linear fractional representation approach with application to spinning spacecraft

The derivation of a linear fractional representation (LFR) model for a flexible, spinning and uniform Euler-Bernoulli beam is accomplished using the Lagrange technique, fully capturing the centrifugal force generated by the spinning motion and accounting for its dependence on the angular velocity. This six degrees of freedom (DOF) model accounts for the behavior of deflection in the moving body frame, encompassing the bending, traction and torsion dynamics. The model is also designed to be compliant with the Two-Input-Two-Output Port (TITOP) approach, which offers the possibility to model complex multibody mechanical systems, while keeping the uncertain nature of the plant and condensing all the possible mechanical configurations in a single LFR. To evaluate the effectiveness of the model, various scenarios are considered and their results are tabulated. These scenarios include uniform beams with fixed root boundary conditions for different values of tip mass, root offset and angular velocity. The results from the analysis of the uniform cantilever beam are compared with solutions found in the literature and obtained from a commercial finite element software. Ultimately, this paper presents a multibody model for a spinning spacecraft mission scenario. A comprehensive analysis of the system dynamics is conducted, providing insights into the behavior of the spacecraft under spinning conditions.

Free vibration analysis of an O-pattern graphene reinforced axial functionally graded polymer matrix nano-composite non-uniform beam

Recently, the demand for nanocomposites in the form of functionally graded materials (FGM) has increased because of their improved weight-to-stiffness ratios, less delamination effects, and ability to have desired qualities at the right location. Additionally, compared to typical composites, static qualities like strength and elasticity are superior. In this research work, a model for an axially graphene-reinforced functionally graded polymer matrix nanocomposite non-uniform beam is prepared, to obtain the dynamic behavior of the beam in form of its Natural Frequencies. Along the length of the beam, the graphene Nano reinforcement is dispersed in an epoxy polymer matrix as “O” pattern using a function. Material modulus at each location of the beam is modelled using Halpin-Tsai micromechanics theory, the mass density and Poisson’s Ratio of the beam are determined using rule of mixture. The geometry non-uniformity of the beam is modelled using an exponential function. Using MATLAB software code, simulation and parametric analysis of the beam are performed for various slenderness ratios and varied boundary conditions. The non-uniform beam result is obtained after the result for a uniform beam is used to validate it. In result it is analyzed that for the particular geometric and reinforcement configuration of the beam, as the non-uniformity in the beam geometry is increases, the fundamental frequency decreases, and the slenderness ratio has also the same effect on its fundamental frequency.

Collaborative optimization of phase and amplitude of composite signals for acousto-optic beam splitting technology.

Multi-frequency acousto-optic beam splitting plays a significant role in many laser applications due to its advantages of inertia free, fast refreshing speed and high-precision controllable light intensity and direction. How to reduce the intermodulation distortion and improve the uniformity of the beam splitting intensity has become an intensive issue. This paper proposes the collaborative optimization method to co-optimize of the phase and amplitude of acousto-optic device multi-frequency composite signals, which can eliminate the nonlinear distortion of the amplification of multi-frequency composite signals and increase the energy utilization rate and accuracy of intensity control for each sub-beam. A closed-loop control system for 2D acousto-optic beam splitting is constructed. The uniform array beam splitting with a mean square deviation of less than 0.02 and no spurious points, beam splitting with a controllable intensity distribution, and beam splitting with a controllable beam spacing distribution are realized. And the 2D diffraction efficiency reaches 63.5%. This provides a superior solution for beam splitting applications with an arbitrary number of beam splitting, intensity distribution, and spacing distribution.

Implementation of variable cross-section curved beam in train-turnout dynamic interactions

The abundance of variable cross-section curved rails in railway turnouts emphasizes the necessity of intricately modeling them, which facilitates a more accurate evaluation of train-turnout interactions. This study presents a general formulation for analyzing both free and forced vibrations of a variable cross-section curved Timoshenko beam and its implementation in train-turnout dynamic interactions. First, the natural frequencies and mode shapes for in-plane and out-of-plane free vibrations of the beam are determined through eigenvalue analysis, taking into careful consideration the characteristics of variable cross-section and curvature. Then, the forced vibration solution is derived using modal superposition and orthogonality. Furthermore, comparative analyses using finite element method (FEM) validate the natural frequencies and dynamic responses of a beam under various boundary conditions, confirming the reliability and accuracy of the proposed method. Finally, the developed beam model is then applied to simulate the switch rail and point rail under train-turnout interactions, revealing the differences from existing methods that modeled these components as uniform cross-section straight beams. Numerical analyses provide new insights by comparing wheel-rail forces and rail acceleration. Considering curve and variable cross section characteristics could contribute to a more accurate evaluation of train-turnout dynamic interactions.

Laser-driven acceleration of a 94.8 MeV uniform proton beam enhanced by a thin axial absorber rod

Laser-based proton accelerators offer promising advantages for many sensitive applications due to their compact size. However, achieving uniform beams with a narrow energy spread remains a challenge. Here, a beamline simulation is performed using the racein and codes to optimize the spectral and spatial characteristics of a laser-driven proton beam. This beamline, comprised of four magnetic quadrupoles and equipped with a thin axial absorber rod in conjunction with an energy selection aperture for narrowing the energy spread, a carbon scatterer foil for beam spot smoothing, and an angular selection aperture for beam collimation, effectively transports a selected proton beam energy within the range of 50–250 MeV. In this work, laser-accelerated protons with a wide energy spread were transported through the proposed beamline, which was optimized for 109 MeV protons. The protons emerged well-collimated with a significantly narrowed energy spread of 94.8±3.9 MeV (a reduction from the intended 109 MeV due to passage through the scatterer) and a homogenized, 11 mm diameter beam spot while maintaining a transmission efficiency above 2.2%. Published by the American Physical Society 2024

Terahertz tunable three-dimensional photonic jets

Highly localized electromagnetic field distributions near the “shadow-side” surface of certain transparent mesoscale bodies illuminated by light waves are called photonic jets. We demonstrated formation of three-dimensional (3D) tunable photonic jets in terahertz regime (terajets, TJs) by dielectric micro-objects -including spheres, cylinders, and cubes-coated with a bulk Dirac semimetal (BDS) layer, under uniform beam illumination. The optical characteristics of the produced TJs can be modulated dynamically through tuning the BDS layer’s index of refraction via changing its Fermi energy. It is demonstrated that the Fermi energy of BDS layer has a significant impact on tuning the optical characteristics of the produced photonic jets for both TE and TM polarizations. A notable polarization dependency of the characteristics of the TJs was also observed. The impact of obliquity of the incident beam was studied as well and it was demonstrated that electromagnetic field distributions corresponding to asymmetric photonic jets can be formed in which the intensity at the focal region is preserved in a wide angular range which could find potential application in scanning devices. It was found that the maximum intensity of the TJ occurs at a non-trivial morphology-dependent source-angle.

Nonlinear design, analysis, and testing of a single-stage compliant orthogonal displacement amplifier with a single input force for microgrippers

To achieve dexterous and stable micro/nanomanipulation, a large grasping stroke, compact design, and parallel grasping are required for microgrippers; thus, a single-stage compliant orthogonal displacement amplifier (CODA) with a single input force would be an ideal transmission mechanism. However, the existing small-deflection-based design schemes cannot adapt to large deflections or shearing effect, thereby affecting the orthogonal movement transformation accuracy. This study proposed, analyzed, and experimentally investigated a nonlinear design scheme for a single-stage CODA with a single input force. First, the nonlinear design principle is described qualitatively. By combining closed-form analytical modelling, finite element analysis, and numerical fitting, the nonlinear extent of a pre-set variable cross-sectional beam in the CODA is formulated. By utilizing the beam constraint model and small-deflection-based modelling, the nonlinear extent of the undetermined uniform straight beam in the CODA is derived. Based on the design principle and nonlinear models, a nonlinear design scheme is proposed quantitatively. Finite element simulations and experimental tests are conducted to verify the proposed scheme, and the limitations of our previous study are revealed.

Large size shielded metal-ceramic cathodes

The technology for manufacturing large size shielded metal-ceramic cold cathodes is described. It has been shown that the use of a shielded metal-ceramic cathode allows to significantly increase the impedance of the vacuum diode and to form an electron beam of constant cross-sectional size or of the required size (up to 400 mm wide) with a fairly uniform electron beam current density distribution (≤15%).It has been found that the emission decline of the shielded metal-ceramic cathode, like that of the metal-dielectric cathode operating at a high repetition rate (≥100 pps), is significant at the beginning of the process and then slows down, allowing continuous operation for up to 40 h. Both cathodes require periodic cleaning of the plates, which is more difficult for metal-ceramic plates.At the same time, a metal-ceramic cathode works better at low vacuum, allowing twice as much current to be generated (in the same geometry) as a metal-dielectric cathode, while reducing the accelerating voltage by ∼15%. However, metal-ceramic plates are about 100 times more expensive to manufacture than dielectric plates for a metal-dielectric cathode.Therefore, the choice of cathode type for vacuum diode accelerators is not a trivial problem, but depends on many factors that must be taken into account in each case and for each radiation technology.

Modal characteristics of functionally graded porous Timoshenko beams with variable cross-sections

The study focuses on the free vibration analysis of beams composed of functionally graded porous materials and characterized by a variable cross-section along their length. A broad range of beams is examined encompassing various tapered configurations, porosity profiles, and porosity content. The equations of motion are derived using Hamilton’s principle within the framework of Timoshenko beam theory. These equations are solved semi-analytically using the differential transform method, which has been adapted to incorporate various boundary conditions such as clamped–clamped, clamped–free, clamped–pinned, and pinned–pinned constraints within a general formulation of the beam eigenvalue problem. To validate the proposed solution technique, computed natural frequencies are compared with existing literature results for tapered inhomogeneous beams and uniform porous beams. Notably, new results are obtained for tapered porous beams. In this regard, a comprehensive parametric study explores the influence of various factors on the natural frequencies and mode shapes of functionally graded porous beams with variable cross-sections. These factors include the type of porosity profiles, a range of porosity parameters, cross-section taper ratios, and specific boundary conditions. The findings deepen our understanding of the modal characteristics of functionally graded porous beams, providing valuable guidance for engineering design and structural optimization in relevant applications. Additionally, they may serve as benchmarks for other researchers.