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Related Concept Videos

Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

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...
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

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.
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Scanning Electron Microscopy

A scanning electron microscope (SEM) is used to study the surface features of a sample by using an electron beam that scans the sample surface in a two-dimensional manner. Typically, areas between ~1 centimeter to 5 micrometers in width can be imaged. SEM can be used to image bacteria, viruses, tissues as well as larger samples like insects. Conventional SEM gives a magnification ranging from 20X to 30,000X and spatial resolution of 50 to 100 nanometers.
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Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Deflection of a Beam

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.
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Related Experiment Video

Updated: Jun 20, 2026

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
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Z-scan experiment with anisotropic Gaussian Schell-model beams.

Yongxin Liu1, Jixiong Pu, Hongqun Qi

  • 1Department of Electric Science & Technology, Huaqiao University, Quanzhou, Fujian 362021, China.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|September 2, 2009
PubMed
Summary

This study enhances z-scan experiments using anisotropic Gaussian Schell-model (AGSM) beams. Increasing the e factor and spatial coherence improves sensitivity for nonlinear optical measurements.

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Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Published on: October 11, 2016

Area of Science:

  • Nonlinear Optics
  • Laser Physics
  • Optical Metrology

Background:

  • The z-scan technique is a standard method for measuring nonlinear optical properties of materials.
  • Anisotropic Gaussian Schell-model (AGSM) beams offer unique properties for beam shaping and propagation.
  • Understanding beam characteristics is crucial for optimizing experimental sensitivity.

Purpose of the Study:

  • To theoretically analyze the z-scan experiment utilizing AGSM beams.
  • To investigate the influence of beam anisotropy and spatial coherence on z-scan transmittance.
  • To identify methods for enhancing the sensitivity of z-scan measurements.

Main Methods:

  • Derivation of the cross-spectral density for AGSM beams after lens propagation.
  • Theoretical simulation of z-scan experiment results based on derived expressions.
  • Analysis of the impact of the e factor (beam width ratio) and spatial coherence on transmittance.

Main Results:

  • The on-axis z-scan transmittance is shown to increase with higher e factors.
  • Enhanced spatial coherence in both x and y orientations leads to larger transmittance changes.
  • A direct correlation was found between increased e factor/coherence and improved z-scan sensitivity.

Conclusions:

  • The sensitivity of the z-scan experiment can be significantly improved by increasing the e factor of AGSM beams.
  • Augmenting the spatial degree of coherence also enhances the experiment's sensitivity.
  • These findings provide a pathway for more precise nonlinear optical characterization.