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Related Concept Videos

Beams01:30

Beams

1.8K
Beams are integral components of structural engineering and construction, designed to support loads applied at various points along their length. These long, straight members can be classified based on geometry, cross-section, support type, and equilibrium condition.
Based on geometry, beams can be straight, tapered, or curved. Straight beams are the most common type and have a constant cross-section throughout their length. Tapered beams, on the other hand, have a varying cross-section along...
1.8K
Deflection of a Beam01:19

Deflection of a Beam

715
Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
715
Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

452
In the design of a supported timber beam subjected to a distributed load, both the beam's physical dimensions and the timber's characteristics, such as its grade and species, are critical. These factors determine the allowable stress values, which are crucial for calculating the necessary beam depth to ensure structural integrity and safety.
The design begins with analyzing the beam as a free body to identify moments and force balances, thereby determining support reactions. Next, the...
452
Principal Stresses in a Beam01:11

Principal Stresses in a Beam

713
In prismatic beams subject to arbitrary transverse loading, It is essential to analyze the interaction between shear forces and bending moments in order to understand stress distribution and ensure structural integrity. The highest normal or bending stress occurs at the outer fibers of the beam, decreasing linearly to zero at the neutral axis. In contrast, shear stress peaks at the neutral axis and diminishes toward the outer surfaces.
Analyzing principal stresses is crucial, especially in...
713
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

409
The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...
409
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

424
Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...
424

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Updated: Jan 27, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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High-power vortex beam generation enabled by a phased beam array fed at the nonfocal-plane.

Tianyue Hou, Yuqiu Zhang, Qi Chang

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    Generating high-power vortex beams using phased arrays is challenging due to phase control issues. This study introduces a novel non-focal-plane method for accurate phase extraction, enabling efficient vortex beam generation.

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    Area of Science:

    • Optics and Photonics
    • Laser Physics
    • Beam Shaping Technology

    Background:

    • High-power vortex beams are crucial for optical communication, nonlinear frequency conversion, and laser processing.
    • Phased arrays offer a method for generating high-power vortex beams by controlling individual beamlets.
    • Current methods using focal plane intensity profiles struggle with accurate phase control for vortex beam generation.

    Purpose of the Study:

    • To address the limitations of focal plane methods in generating vortex beams.
    • To introduce and analyze a novel cost function extraction method at a non-focal-plane.
    • To enable efficient generation of vortex beams with various topological charges.

    Main Methods:

    • Numerical simulation to analyze a new cost function extraction concept.
    • Development of a non-focal-plane approach for phase control signal extraction.
    • Application to generating vortex beams, including Bessel-Gaussian beams.

    Main Results:

    • Demonstrated the feasibility of extracting cost functions at a non-focal-plane.
    • Showcased the efficiency of the new method for generating vortex beams.
    • Validated the method for different topological charges, including second-order Bessel-Gaussian beams.

    Conclusions:

    • The non-focal-plane cost function extraction method overcomes limitations of traditional focal plane approaches.
    • This technique provides an efficient pathway for generating vortex beams via coherent beam combining.
    • The proposed concept offers a valuable reference for practical implementation of advanced vortex beam generation.