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Keywords = large-angle beam deflection

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7 pages, 837 KB  
Communication
Dielectric Catenary Metasurface for Broadband and High-Efficiency Anomalous Reflection
by Xinjian Lu, Wenxin Li, Guiyong Chen, Bo Liu, Xin Xie, Zhongming Zang, Kuo Hai and Zhu Li
Photonics 2025, 12(7), 684; https://doi.org/10.3390/photonics12070684 - 7 Jul 2025
Viewed by 412
Abstract
This paper proposes a broadband and high-efficiency anomalous reflection device based on a dielectric catenary metasurface, addressing the bottleneck problems of low efficiency and narrow bandwidth in traditional discrete metasurfaces. By designing a silicon-based equal-strength catenary structure, the efficient control of circularly polarized [...] Read more.
This paper proposes a broadband and high-efficiency anomalous reflection device based on a dielectric catenary metasurface, addressing the bottleneck problems of low efficiency and narrow bandwidth in traditional discrete metasurfaces. By designing a silicon-based equal-strength catenary structure, the efficient control of circularly polarized light beams within a wide angular range in the infrared band has been achieved. Simulation results show that the designed metasurface exhibits excellent beam steering performance when the deflection angle reaches 65°. Furthermore, to characterize the diffraction efficiency of the metasurface within a large angular range, the results indicate that under oblique incidence (0–60°), the diffraction efficiency of the ±1st order exceeds 80%, and the undesired higher-order diffractions are significantly suppressed. This ultrahigh working efficiency is attributed to the nearly perfect polarization conversion and continuous phase profile of the dielectric catenary structure. By combining catenary optics with the low-loss properties of the dielectric material, this design provides a new solution for the design of efficient, broadband, and wide-angle planar optical devices. Full article
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22 pages, 3922 KB  
Article
Research on the Dynamic Characteristics of a Typical Medium–Low-Speed Maglev Train–Bridge System Influenced by the Transverse Stiffness of Pier Tops
by Yanghua Cui, Xiangrong Guo, Hongwei Mao and Jianghao Liu
Appl. Sci. 2025, 15(12), 6628; https://doi.org/10.3390/app15126628 - 12 Jun 2025
Viewed by 506
Abstract
With the continuous development of maglev transportation technology, medium–low-speed maglev trains have been widely implemented in many countries. However, due to the limitations of existing specifications, the stiffness limit values of the large-span main girders used in medium–low-speed maglev trains have not been [...] Read more.
With the continuous development of maglev transportation technology, medium–low-speed maglev trains have been widely implemented in many countries. However, due to the limitations of existing specifications, the stiffness limit values of the large-span main girders used in medium–low-speed maglev trains have not been unified. To address this issue, this study takes a specific bridge on a dedicated maglev line as an example and uses self-developed software to model the vehicle–bridge dynamic system. The natural vibration characteristics and vehicle–bridge coupling vibration response of the bridge are calculated and analyzed. Based on this, the influence of pier top stiffness on the dynamic characteristics of a typical medium–low-speed maglev train–bridge system under different working conditions is investigated, with a focus on the lateral line stiffness at the pier top. The results show that vehicle speed has no significant effect on the lateral displacement of the main girder, the lateral displacement of the pier top, the lateral acceleration of the pier top, and the transverse and longitudinal angles of the beam end, and no obvious regularity is observed. However, in the double-track operating condition, the vertical deflection of the main girder is significantly higher than that in the single-track operating condition. As the lateral linear stiffness at the pier top increases, the fundamental frequency of the bridge’s lateral bending vibration gradually increases, while the fundamental frequency of longitudinal floating gradually decreases. The lateral displacements, including those of the main girder, pier top, and beam ends, all decrease, whereas the lateral and vertical vibration accelerations of the main girder and the train are less affected by the lateral stiffness at the pier top. Full article
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27 pages, 16018 KB  
Article
Investigation of Structural Nonlinearity Effects on the Aeroelastic and Wake Characteristics of a 15 MW Wind Turbine
by Zhenju Chuang, Lulin Xia, Yan Qu, Wenhua Li and Jiawen Li
J. Mar. Sci. Eng. 2025, 13(1), 116; https://doi.org/10.3390/jmse13010116 - 10 Jan 2025
Cited by 4 | Viewed by 1419
Abstract
As wind turbines increase in size, blades become longer, thinner, and more flexible, making them more susceptible to large geometric nonlinear deformations, which pose challenges for aeroelastic simulations. This study presents a nonlinear aeroelastic model that accounts for large deformations of slender, flexible [...] Read more.
As wind turbines increase in size, blades become longer, thinner, and more flexible, making them more susceptible to large geometric nonlinear deformations, which pose challenges for aeroelastic simulations. This study presents a nonlinear aeroelastic model that accounts for large deformations of slender, flexible blades, coupled through the Actuator Line Method (ALM) and Geometrically Exact Beam Theory (GEBT). The accuracy of the model is validated by comparing it with established numerical methods, demonstrating its ability to capture the bending–torsional coupled nonlinear characteristics of highly flexible blades. A bidirectional fluid–structure coupling simulation of the IEA 15MW wind turbine under uniform flow conditions is conducted. The effect of blade nonlinear deformation on aeroelastic performance is compared with a linear model based on Euler–Bernoulli beam theory. The study finds that nonlinear deformations reduce predicted angle of attack, decrease aerodynamic load distribution, and lead to a noticeable decline in both wind turbine performance and blade deflection. The effects on thrust and edgewise deformation are particularly significant. Additionally, nonlinear deformations weaken the tip vortex strength, slow the momentum exchange in the wake region, reduce turbulence intensity, and delay wake recovery. This study highlights the importance of considering blade nonlinear deformations in large-scale wind turbines. Full article
(This article belongs to the Topic Wind, Wave and Tidal Energy Technologies in China)
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13 pages, 7666 KB  
Article
Polarization-Insensitive Metasurface with High-Gain Large-Angle Beam Deflection
by Huanran Qiu, Liang Fang, Rui Xi, Yajie Mu, Jiaqi Han, Qiang Feng, Ying Li, Long Li and Bin Zheng
Materials 2024, 17(23), 5688; https://doi.org/10.3390/ma17235688 - 21 Nov 2024
Cited by 1 | Viewed by 1457
Abstract
Metasurfaces have shown great potential in achieving low-cost and low-complexity signal enhancement and redirection. Due to the low transmission power and high attenuation issues of current high-frequency communication technology, it is necessary to explore signal redirection technology based on metasurfaces. This paper presents [...] Read more.
Metasurfaces have shown great potential in achieving low-cost and low-complexity signal enhancement and redirection. Due to the low transmission power and high attenuation issues of current high-frequency communication technology, it is necessary to explore signal redirection technology based on metasurfaces. This paper presents an innovative metasurface for indoor signal enhancement and redirection, featuring thin thickness, high gain, and wide-angle deflection. The metasurface integrates the design principles of a Fabry–Perot cavity (FPC) theory with a Phase Gradient Partially Reflective Metasurface (PGPRM). Its unit is a fishnet structure with a substrate only 1/33 λ thin. Based on the precise phase control of the dual-layer PGPRM (with an inter-layer distance of 8 mm), the proposed metasurface can obtain phase coverage as small as 78° while achieving high-gain beam deflection as large as 47°. Simulation results show that within the band 8.6–9.2 GHz (6.7%), a single-layer metasurface can deflect the beam to 29° with a maximum gain of 16.9 dBi. In addition, it is also 360° polarization-insensitive in the xoy plane at 9 GHz with large-angle deflection characteristic retained. Moreover, cascading PGPRM can effectively improve the beam deflection angle. After analysis, the scheme with a double-layer spacing of 8 mm was ultimately selected. Simulation results show a double-layer metasurface can deflect the beam to 47° with a maximum gain of 16.4 dBi. This design provides an efficient and cost-effective solution for large-angle beam deflection with gain enhancement for indoor wireless communication. Full article
(This article belongs to the Special Issue Advances in Metamaterials: Structure, Properties and Applications)
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15 pages, 5298 KB  
Article
Deformation and Fracture Mechanisms of Thick Hard Roofs in Upward Mining Coalfaces: A Mechanical Model and Its Validation
by Wei Zhang, Linchao Cao, Dongsheng Zhang, Yang Hu, Jingyu Chang and Zhenying Zhang
Appl. Sci. 2024, 14(22), 10278; https://doi.org/10.3390/app142210278 - 8 Nov 2024
Cited by 2 | Viewed by 1008
Abstract
The safety and efficiency of underground coal mining are threatened by thick hard roofs characterized by large overhang areas, problematic spontaneous caving, and high dynamic load upon their breakage. In this study, a mechanical model of the bearing capacity of thick hard roofs [...] Read more.
The safety and efficiency of underground coal mining are threatened by thick hard roofs characterized by large overhang areas, problematic spontaneous caving, and high dynamic load upon their breakage. In this study, a mechanical model of the bearing capacity of thick hard roofs in upward mining coalfaces associated with mining activities is built based on bending theories for beams with single generalized displacement and the elastic foundation beam theory. Using this method, we analyze the deformation and fracture mechanisms of a thick hard roof during upward mining. We further derive the mechanical equations of rotational angle, bending moment, shear force, and deflection of the free overhang and coal-bearing zone in the thick hard roof and an equation for calculating the limiting span. The mechanical behaviors of the thick hard roof bearing state are analyzed under different parameters. The results show that the foundation coefficient, roof thickness, and angle of upward mining have little influence on the roof bending moment but are positively correlated to the limiting span. Roof load and overhang length have a significant influence on the roof bending moment. They are negatively and positively correlated with the limiting span, respectively. Finally, a case study is performed on the Ш601 upward mining coalface in the Zhuzhuang Coal Mine. The distribution characteristics of the bending moment of the thick hard roof at different extraction stages are analyzed. At each stage, the limiting spans of the thick hard roof upon breaking were calculated as 13.18, 18.82, and 22.50 m, respectively, being close to the on-site measured periodic weighting lengths of 13.33, 19.33 m, and 22.67 m. This close fit proves the feasibility and accuracy of the developed mechanical model. The present study offers theoretical guidance for estimating the weighting length of thick hard roofs in coalfaces and for engineering technology control in similar scenarios. Full article
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22 pages, 30308 KB  
Article
Bending Behaviour and Failure Modes of Non-Glue-Laminated Timber Beams Composed of Wooden Dowels and Self-Tapping Screws
by Yu-Hsiang Yeh and Yi-Chi Yeh
Buildings 2024, 14(2), 394; https://doi.org/10.3390/buildings14020394 - 1 Feb 2024
Cited by 5 | Viewed by 2232
Abstract
The purpose of this research is to compare the bending behaviour of non-glue-laminated timber beams and glulams by full-scale four-point bending tests. The focus is on the non-glue beams laminated by different materials or techniques and then to determine their bending stiffness and [...] Read more.
The purpose of this research is to compare the bending behaviour of non-glue-laminated timber beams and glulams by full-scale four-point bending tests. The focus is on the non-glue beams laminated by different materials or techniques and then to determine their bending stiffness and failure modes. The laminating efficiency of various materials or techniques is underlined. The manufacturing process concerning non-glue-laminated timber beams has to be determined. As structural elements with large dimensions, such components require adaptable laminating and producing techniques. While the beams composed of wooden dowels refer to the dowel-laminated timber (DLT), those made of self-tapping screws (STSs) can be simply related to nail-laminated timber (NLT) products. Then, a full-scale four-point bending test was carried out to appraise 26 laminated beams, including non-glue- and glue-laminated timber. The results of the test demonstrated that the material, the spacing and the angle of the transversal fasteners significantly influence bending behaviour. The bending stiffness of the beams laminated by STSs was about 7.86% higher than the value of the beams with wooden dowels, although the tendency of each pair of beams did not remain convergent. Reducing the interval of the fasteners can considerably increase the bending stiffness of the beams. Fasteners inserted at 45 degrees, or in a so-called V-type pattern, contribute to improving bending stiffness, and both wooden dowels and STSs reveal the same tendency. At this angle, STSs demonstrate better laminating efficiency than wooden dowels. The STS beams’ bending stiffness was about 48.6% of that determined for glulams. On the contrary, in beams with 135-degree fasteners, or, namely, an A-type pattern, inserted fasteners possessed lower bending stiffness than in those with 90-degree fasteners. In addition to the considerable bending stiffness, the STS beams revealed a stable response as far as their load-deflection curves were concerned. A comparison of experimental and theoretical results contributes to verifying the feasibility as well as the weakness of two analytic methods. The predicting capacity of the associated equations needs to be improved, particularly for the withdrawal resistance and connecting effect of inclined STSs. Full article
(This article belongs to the Special Issue Properties of Wood and Bamboo Used in Construction)
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8 pages, 993 KB  
Communication
Dynamic Tunable Deflection of Radiation Based on Epsilon-Near-Zero Material
by Lin Cheng, Kun Huang, Yu Wang and Fan Wu
Photonics 2023, 10(6), 688; https://doi.org/10.3390/photonics10060688 - 14 Jun 2023
Cited by 1 | Viewed by 1893
Abstract
Epsilon-near-zero nanoantennas can be used to tune the far-field radiation pattern due to their exceptionally large intensity-dependent refractive index. In this study, we propose a hybrid optical antenna based on indium tin oxide (ITO) to enable optical tuning of the deflection of radiation, [...] Read more.
Epsilon-near-zero nanoantennas can be used to tune the far-field radiation pattern due to their exceptionally large intensity-dependent refractive index. In this study, we propose a hybrid optical antenna based on indium tin oxide (ITO) to enable optical tuning of the deflection of radiation, specifically a hybrid structure antenna of ITO and dielectric material, which makes the deflection angle changes 17 as incident intensities increase. Moreover, by employing an array of ITO or hybrid nanodisks, we can enhance the unidirectionality of the radiation pattern, resulting in a needle-like shape with an angular beam width α< 8 of the main lobe. The deflection angle of the radiation pattern response with the needle-like lobe paves the way for further studies and applications in beam steering and optical modulation where dynamic control of the nanoantennas is highly desirable. Full article
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12 pages, 4331 KB  
Article
Airborne Quantum Key Distribution Performance Analysis under Supersonic Boundary Layer
by Huicun Yu, Bangying Tang, Haolin Ding, Yang Xue, Jie Tang, Xingyu Wang, Bo Liu and Lei Shi
Entropy 2023, 25(3), 472; https://doi.org/10.3390/e25030472 - 8 Mar 2023
Cited by 6 | Viewed by 2283
Abstract
Airborne quantum key distribution (QKD) that can synergize with terrestrial networks and quantum satellite nodes is expected to provide flexible and relay links for the large-scale integrated communication network. However, the photon transmission rate would be randomly reduced, owing to the random distributed [...] Read more.
Airborne quantum key distribution (QKD) that can synergize with terrestrial networks and quantum satellite nodes is expected to provide flexible and relay links for the large-scale integrated communication network. However, the photon transmission rate would be randomly reduced, owing to the random distributed boundary layer that surrounding to the surface of the aircraft when the flight speed larger than Mach 0.3. Here, we investigate the airborne QKD performance with the BL effects. Furthermore, we take experimental data of supersonic BL into the model and compare the airborne QKD performance under different conditions. Simulation results show that, owing to the complex small-scale turbulence structures in the supersonic boundary layer, the deflection angle and correspondingly drifted offset of the beam varied obviously and randomly, and the distribution probability of photons are redistributed. And the subsonic and supersonic boundary layer would decrease ~35.8% and ~62.5% of the secure key rate respectively. Our work provides a theoretical guidance towards a possible realization of high-speed airborne QKD. Full article
(This article belongs to the Collection Quantum Information)
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18 pages, 4312 KB  
Article
Super-Resolution and Wide-Field-of-View Imaging Based on Large-Angle Deflection with Risley Prisms
by Chao Gui, Detian Wang, Xiwang Huang, Chunyan Wu, Xin Chen and Huachuan Huang
Sensors 2023, 23(4), 1793; https://doi.org/10.3390/s23041793 - 5 Feb 2023
Cited by 10 | Viewed by 3279
Abstract
A novel single camera combined with Risley prisms is proposed to achieve a super-resolution (SR) imaging and field-of-view extension (FOV) imaging method. We develop a mathematical model to consider the imaging aberrations caused by large-angle beam deflection and propose an SR reconstruction scheme [...] Read more.
A novel single camera combined with Risley prisms is proposed to achieve a super-resolution (SR) imaging and field-of-view extension (FOV) imaging method. We develop a mathematical model to consider the imaging aberrations caused by large-angle beam deflection and propose an SR reconstruction scheme that uses a beam backtracking method for image correction combined with a sub-pixel shift alignment technique. For the FOV extension, we provide a new scheme for the scanning position path of the Risley prisms and the number of image acquisitions, which improves the acquisition efficiency and reduces the complexity of image stitching. Simulation results show that the method can increase the image resolution to the diffraction limit of the optical system for imaging systems where the resolution is limited by the pixel size. Experimental results and analytical verification yield that the resolution of the image can be improved by a factor of 2.5, and the FOV extended by a factor of 3 at a reconstruction factor of 5. The FOV extension is in general agreement with the simulation results. Risley prisms can provide a more general, low-cost, and efficient method for SR reconstruction, FOV expansion, central concave imaging, and various scanning imaging. Full article
(This article belongs to the Section Optical Sensors)
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8 pages, 1700 KB  
Communication
Grating-like Terahertz Metasurface for Large-Deflection-Angle Beam Manipulations
by Yuan Fu, Xiaojian Fu, Lei Shi and Tie Jun Cui
Appl. Sci. 2022, 12(23), 12322; https://doi.org/10.3390/app122312322 - 2 Dec 2022
Cited by 6 | Viewed by 2931
Abstract
Multifunctional terahertz beam manipulations have attracted much attention because of the potential for wide-scale applications in terahertz imaging, communications, etc. In this work, a grating-like terahertz reflective-type metasurface is designed for terahertz beam manipulations on the basis of a frequency-scanning mechanism. The theoretical [...] Read more.
Multifunctional terahertz beam manipulations have attracted much attention because of the potential for wide-scale applications in terahertz imaging, communications, etc. In this work, a grating-like terahertz reflective-type metasurface is designed for terahertz beam manipulations on the basis of a frequency-scanning mechanism. The theoretical calculation based on the grating principle has predicted that the metasurface grating can steer the deflected beam from 59.5° to 47.3° as the frequency of the perpendicularly incident terahertz wave changes between 0.87 and 1.02 THz. The large-deflection-angle frequency-scanning performance is validated by both numerical simulations and experimental tests. The metasurface grating developed in this work possesses the potential for applications in terahertz beam steering and beam-splitting devices. Full article
(This article belongs to the Special Issue Progress and Application of Electromagnetic Materials)
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15 pages, 3510 KB  
Article
Finite Element Analysis and Reinforcement of Steel Crane Beam under Eccentric Track Loading
by Chunting Lu, Zheng Yang, Pengfei Li, Xiangwei Zhang, Jie Huang and Ling Wang
Machines 2022, 10(9), 783; https://doi.org/10.3390/machines10090783 - 7 Sep 2022
Cited by 4 | Viewed by 3071
Abstract
The crane track of a steel structure workshop was installed eccentrically, and the crane operation caused a large deflection of the crane beam, requiring reinforcement measures. The finite element model of the crane beam was established by Midas Gen finite element software, and [...] Read more.
The crane track of a steel structure workshop was installed eccentrically, and the crane operation caused a large deflection of the crane beam, requiring reinforcement measures. The finite element model of the crane beam was established by Midas Gen finite element software, and the maximum stress, deflection, and the stress amplitude of 9 m and 12 m steel crane beam under different track eccentricity values were analyzed. The results show that when there is no brake truss, the maximum stress and deflection of the crane beam will increase greatly under the action of eccentric loading. On the contrary, a brake truss can effectively reduce the adverse effect of eccentric loading; the fatigue strength of crane beam cannot be controlled under eccentric rail loading. The reason why steel crane beam is sensitive to track eccentricity is that its torsional stiffness is too small. As a reinforcement measure, welding angle steel or steel plate lower on the crane beam flange, forming a box section, can effectively increase the torsional stiffness of the crane beam; the residual stress can then be effectively reduced by applying intermittent welding and reinforcement using the same material. Full article
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24 pages, 1361 KB  
Article
Explicit Solutions to Large Deformation of Cantilever Beams by Improved Homotopy Analysis Method I: Rotation Angle
by Yinshan Li, Xinye Li, Shuhao Huo and Chen Xie
Appl. Sci. 2022, 12(13), 6400; https://doi.org/10.3390/app12136400 - 23 Jun 2022
Cited by 5 | Viewed by 2993
Abstract
An improved homotopy analysis method (IHAM) is proposed to solve the nonlinear differential equation, especially for the case when nonlinearity is strong in this paper. As an application, the method was used to derive explicit solutions to the rotation angle of a cantilever [...] Read more.
An improved homotopy analysis method (IHAM) is proposed to solve the nonlinear differential equation, especially for the case when nonlinearity is strong in this paper. As an application, the method was used to derive explicit solutions to the rotation angle of a cantilever beam under point load at the free end. Compared with the traditional homotopy method, the derivation includes two steps. A new nonlinear differential equation is firstly constructed based on the current nonlinear differential equation of the rotation angle and the auxiliary quadratic nonlinear differential equation. In the second step, a high-order non-linear iterative homotopy differential equation is established based on the new non-linear differential equation and the auxiliary linear differential equation. The analytical solution to the rotation angle is then derived by solving this high-order homotopy equation. In addition, the convergence range can be extended significantly by the homotopy–Páde approximation. Compared with the traditional homotopy analysis method, the current improved method not only speeds up the convergence of the solution, but also enlarges the convergence range. For the large deflection problem of beams, the new solution for the rotation angle is more approachable to the engineering designers than the implicit exact solution by the Euler–Bernoulli law. It should have significant practical applications in the design of long bridges or high-rise buildings to minimize the potential error due to the extreme length of the beam-like structures. Full article
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13 pages, 2059 KB  
Article
MEMS-Scanner Testbench for High Field of View LiDAR Applications
by Valentin Baier, Michael Schardt, Maximilian Fink, Martin Jakobi and Alexander W. Koch
Sensors 2022, 22(1), 39; https://doi.org/10.3390/s22010039 - 22 Dec 2021
Cited by 5 | Viewed by 4332
Abstract
LiDAR sensors are a key technology for enabling safe autonomous cars. For highway applications, such systems must have a long range, and the covered field of view (FoV) of >45° must be scanned with resolutions higher than 0.1°. These specifications can be met [...] Read more.
LiDAR sensors are a key technology for enabling safe autonomous cars. For highway applications, such systems must have a long range, and the covered field of view (FoV) of >45° must be scanned with resolutions higher than 0.1°. These specifications can be met by modern MEMS scanners, which are chosen for their robustness and scalability. For the automotive market, these sensors, and especially the scanners within, must be tested to the highest standards. We propose a novel measurement setup for characterizing and validating these kinds of scanners based on a position-sensitive detector (PSD) by imaging a deflected laser beam from a diffuser screen onto the PSD. A so-called ray trace shifting technique (RTST) was used to minimize manual calibration effort, to reduce external mounting errors, and to enable dynamical one-shot measurements of the scanner’s steering angle over large FoVs. This paper describes the overall setup and the calibration method according to a standard camera calibration. We further show the setup’s capabilities by validating it with a statically set rotating stage and a dynamically oscillating MEMS scanner. The setup was found to be capable of measuring LiDAR MEMS scanners with a maximum FoV of 47° dynamically, with an uncertainty of less than 1%. Full article
(This article belongs to the Section Sensing and Imaging)
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11 pages, 2952 KB  
Article
A Broadband High-Diffraction-Efficiency Electro-Optic Bragg Deflector Based on Monolithic Dual-Grating Periodically-Poled Lithium Niobate
by An-Chung Chiang, Yuan-Yao Lin, Shou-Tai Lin and Yen-Yin Lin
Photonics 2021, 8(7), 242; https://doi.org/10.3390/photonics8070242 - 28 Jun 2021
Viewed by 2425
Abstract
Electro-optic (EO) Bragg deflectors have been extensively used in a variety of applications. Recent developments show that bandwidths and deflection efficiencies, as well as angular bandwidths, would significantly limit the utilization of EO Bragg deflectors, especially for applications which need strong focusing, such [...] Read more.
Electro-optic (EO) Bragg deflectors have been extensively used in a variety of applications. Recent developments show that bandwidths and deflection efficiencies, as well as angular bandwidths, would significantly limit the utilization of EO Bragg deflectors, especially for applications which need strong focusing, such as intra-cavity applications. In this paper, we introduce a broadband EO Bragg deflector based on periodically-poled lithium niobate with a monolithic dual-grating design. We analyzed the deflection properties of this device by using a modified coupled wave theory and showed that this device can be still efficient for a small beam radius under strong focusing, whereas a single-grating one becomes very inefficient. Using a 1064-nm laser beam with a 100-μm beam radius, we obtained a 74% deflection efficiency with a 190-V bias voltage with a 0.5-mm-thick and 7.5-mm-long dual-grating sample. The acceptance angle for the Bragg condition of this device is as large as a few tens of mrad. The potential bandwidth of this device exceeds 500 nm if the proper operation region is chosen. Full article
(This article belongs to the Special Issue Electro-Optic Modulator)
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36 pages, 806 KB  
Article
On the Generation of Harmonics by the Non-Linear Buckling of an Elastic Beam
by Luiz M. B. C. Campos and Manuel J. S. Silva
Appl. Mech. 2021, 2(2), 383-418; https://doi.org/10.3390/applmech2020022 - 15 Jun 2021
Cited by 2 | Viewed by 3916
Abstract
The Euler–Bernoulli theory of beams is usually presented in two forms: (i) in the linear case of a small slope using Cartesian coordinates along and normal to the straight undeflected position; and (ii) in the non-linear case of a large slope using curvilinear [...] Read more.
The Euler–Bernoulli theory of beams is usually presented in two forms: (i) in the linear case of a small slope using Cartesian coordinates along and normal to the straight undeflected position; and (ii) in the non-linear case of a large slope using curvilinear coordinates along the deflected position, namely, the arc length and angle of inclination. The present paper starts with the exact equation in a third form, that is, (iii) using Cartesian coordinates along and normal to the undeflected position like (i), but allowing exactly the non-linear effects of a large slope like (ii). This third form of the equation of the elastica shows that the exact non-linear shape is a superposition of linear harmonics; thus, the non-linear effects of a large slope are equivalent to the generation of harmonics of a linear solution for a small slope. In conclusion, it is shown that: (i) the critical buckling load is the same in the linear and non-linear cases because it is determined by the fundamental mode; (ii) the buckled shape of the elastica is different in the linear and non-linear cases because non-linearity adds harmonics to the fundamental mode. The non-linear shape of the elastica, for cases when powers of the slope cannot be neglected, is illustrated for the first four buckling modes of cantilever, pinned, and clamped beams with different lengths and amplitudes. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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