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Related Concept Videos

Gauss's Law01:07

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
Gauss's Law in Dielectrics01:17

Gauss's Law in Dielectrics

Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
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...
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...
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,...

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Related Experiment Video

Updated: May 30, 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

Gaussian content as a laser beam quality parameter.

Shlomo Ruschin1, Elad Yaakobi, Eyal Shekel

  • 1Department of Physical Electronics, School of Electrical Engineering Faculty of Engineering, Tel-Aviv University, Tel-Aviv, Israel. ruschin@eng.tau.ac.il

Applied Optics
|August 12, 2011
PubMed
Summary
This summary is machine-generated.

We introduce Gaussian content (GC) as a new laser beam quality parameter. This metric, based on Gaussian overlap, is useful for applications focusing on coherence properties and beam coupling.

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Area of Science:

  • Optics and Photonics
  • Laser Physics
  • Quantum Optics

Background:

  • Accurate characterization of laser beams is crucial for various optical applications.
  • Existing quality parameters may not fully capture coherence properties relevant for specific applications.
  • The need for a parameter that quantifies the 'Gaussian-ness' of a laser beam, especially concerning its coherence.

Purpose of the Study:

  • To propose and define a new quality parameter for laser beams, termed Gaussian content (GC).
  • To establish the mathematical framework and calculation procedures for GC.
  • To demonstrate the utility of GC in practical laser applications, particularly those involving coherence and beam coupling.

Main Methods:

  • Defining Gaussian content (GC) as the overlap integral between a given laser field and an optimally defined Gaussian.
  • Deriving mathematical formulas for GC calculation for various beam profiles.
  • Applying GC to analyze the coherent combination of laser arrays and diode laser to single-mode fiber coupling.
  • Experimentally measuring GC and verifying its conservation during beam propagation.

Main Results:

  • The mathematical definition and calculation procedures for GC are established.
  • GC is shown to be a valuable parameter for characterizing laser beams, especially regarding coherence.
  • Application examples demonstrate GC's relevance in coherent beam combination and fiber coupling.
  • Experimental validation confirms the measurement and propagation conservation of GC.

Conclusions:

  • Gaussian content (GC) offers a valuable, optional metric for laser beam quality assessment.
  • GC is particularly suited for applications sensitive to beam coherence and optimal coupling.
  • The proposed parameter is experimentally validated, confirming its practical applicability.