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Related Concept Videos

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,...
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...
Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
Plane Electromagnetic Waves I01:30

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...
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.

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Related Experiment Video

Updated: Jun 9, 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

Beam quality changes in Hermite-Gauss mode fields propagating through Gaussian apertures.

J Serna, P M Mejías, R Martínez-Herrero

    Applied Optics
    |September 8, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study analyzes how Hermite-Gauss laser modes maintain their beam quality when passing through Gaussian apertures. Understanding this is crucial for laser system design and performance optimization.

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    Related Experiment Videos

    Last Updated: Jun 9, 2026

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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    Published on: August 12, 2013

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    Published on: October 11, 2016

    Area of Science:

    • Optics and Photonics
    • Laser Physics

    Background:

    • Hermite-Gauss (HG) modes are fundamental solutions in laser resonators.
    • Gaussian apertures are common optical elements that can affect laser beam propagation.

    Purpose of the Study:

    • To investigate the impact of Gaussian apertures on the beam quality of HG laser modes.
    • To provide insights into the propagation characteristics of HG modes through limiting optical elements.

    Main Methods:

    • Theoretical analysis of HG mode propagation.
    • Mathematical modeling of beam transformation through Gaussian apertures.

    Main Results:

    • The beam quality parameter M² of HG modes changes predictably with aperture size.
    • Specific HG modes exhibit distinct degradation patterns.

    Conclusions:

    • Gaussian apertures significantly influence HG mode beam quality.
    • The findings are essential for designing laser systems requiring precise beam characteristics.