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Related Concept Videos

Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Gauss's Law: Planar Symmetry01:27

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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...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
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Related Experiment Video

Updated: May 21, 2026

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

Novel coordinate system for Gaussian beam reflection.

Jie Yuan1, Meixiong Chen, Zhenglong Kang

  • 1Department of Optoelectronic Engineering, College of Opto-electric Science and Engineering, National University of Defense Technology, Changsha Hunan 410073, China. jieyuan@nudt.edu.cn

Optics Letters
|June 5, 2012
PubMed
Summary
This summary is machine-generated.

A new coordinate system simplifies Gaussian beam reflection analysis. This method enhances laser resonator design and beam propagation studies, overcoming limitations of traditional approaches.

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Area of Science:

  • Optics and Photonics
  • Laser Physics

Background:

  • Gaussian beam propagation is crucial in laser resonator design.
  • Traditional coordinate systems present challenges in analyzing complex resonators.
  • Accurate modeling of beam reflection is essential for optical system performance.

Purpose of the Study:

  • To introduce a novel coordinate system for Gaussian beam reflection.
  • To demonstrate the system's utility in analyzing laser resonators, particularly nonplanar ring resonators.
  • To highlight the limitations of conventional coordinate systems.

Main Methods:

  • Developed a new coordinate system based on Gaussian beam reflection.
  • Utilized reflection from a spherical mirror to define the coordinate system.
  • Analyzed coordinate rotation using a segment of a general resonator.
  • Applied the system to nonplanar ring resonators.

Main Results:

  • The novel coordinate system effectively describes Gaussian beam reflection.
  • Coordinate rotation was detailed using a general resonator segment.
  • The system's application was demonstrated in nonplanar ring resonators.
  • Experimental validation confirmed the system's efficacy.

Conclusions:

  • The proposed coordinate system offers advantages over traditional methods.
  • It simplifies the analysis of Gaussian beam propagation in complex resonators.
  • This novel system is valuable for designing laser resonators and analyzing beam propagation.