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Related Concept Videos

Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
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Prismatic Beams: Problem Solving

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Deflection of a Beam01:19

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Standing Waves in a Cavity01:28

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
Beams with Symmetric Loadings01:15

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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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Related Experiment Video

Updated: Jun 26, 2026

Preparation of Free-Surface Hyperbolic Water Vortices
04:35

Preparation of Free-Surface Hyperbolic Water Vortices

Published on: July 28, 2023

Hollow vortex beams.

Shunichi Sato1, Yuichi Kozawa

  • 1Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai, Japan. sato@tagen.tohoku.ac.jp

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|December 26, 2008
PubMed
Summary
This summary is machine-generated.

Researchers analytically discuss hollow beam formation for radially and azimuthally polarized vortex beams with arbitrary topological charge under strong focusing. The study provides expressions for focused vector-vortex beams, detailing their hollow beam formation capability.

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Last Updated: Jun 26, 2026

Preparation of Free-Surface Hyperbolic Water Vortices
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Area of Science:

  • Optics and Photonics
  • Electromagnetism
  • Laser Physics

Background:

  • Vortex beams, characterized by helical phase fronts, are crucial in optical manipulation and communication.
  • Controlling the polarization and phase of light is essential for advanced optical applications.
  • Strong focusing of light beams can lead to unique intensity and polarization distributions.

Purpose of the Study:

  • To analytically investigate the formation of hollow beams from radially and azimuthally polarized vortex beams.
  • To derive expressions for the electric fields of focused vector-vortex beams.
  • To determine the parameters influencing hollow beam formation, specifically the topological charge and Bessel function order.

Main Methods:

  • Analytical treatment of vector diffraction theory under strong focusing conditions.
  • Derivation of electric field expressions for focused vector-vortex beams.
  • Analysis of Bessel functions of the first kind to understand hollow beam formation.
  • Investigation of vortex beams formed by linear combinations of radial and azimuthal polarization.

Main Results:

  • Analytical expressions for the electric fields of focused vector-vortex beams were obtained.
  • The order of the Bessel function of the first kind was identified as a key factor in hollow beam formation.
  • The study confirmed the ability to form hollow beams with arbitrary topological charge.
  • Intensity profiles across the focus were calculated and presented for various vortex beam configurations.

Conclusions:

  • Hollow beam formation is analytically demonstrated for radially and azimuthally polarized vortex beams under strong focusing.
  • The topological charge and Bessel function order precisely control the hollow beam characteristics.
  • The findings provide a theoretical framework for designing and generating tailored optical beams for advanced applications.