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Related Concept Videos

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.
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: 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: Jun 11, 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

Beyond Gaussians-diffraction of complex light: tutorial.

Travis M Crumpton, Luat T Vuong

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |June 10, 2026
    PubMed
    Summary
    This summary is machine-generated.

    We introduce Dirichlet energy (U~D) to quantify how complex light beams spread due to diffraction. This new metric, U~D, predicts the diffraction length of structured light, offering insights into light propagation.

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    Area of Science:

    • Optics and Photonics
    • Quantum Optics
    • Mathematical Physics

    Background:

    • Complex light beams undergo significant changes during propagation due to linear diffraction.
    • Characterizing the rate of diffraction for structured light is crucial for understanding light-matter interactions and optical system design.

    Purpose of the Study:

    • To introduce and validate Dirichlet energy (U~D) as a novel metric for characterizing the diffraction of complex light.
    • To establish a relationship between Dirichlet energy and the diffraction length of structured light beams.

    Main Methods:

    • Beam profiles were characterized using Dirichlet energy (U~D).
    • The metric's properties (translation-invariance, structure-information) were analyzed during propagation.
    • The scaling of diffraction length (L_df) with U~D was investigated.

    Main Results:

    • Dirichlet energy (U~D) was found to be a translation-invariant and structure-informed metric.
    • U~D remains constant during beam propagation in vacuum.
    • The diffraction length of structured light was shown to scale proportionally to U~D (L_df ∝ U~D).

    Conclusions:

    • Dirichlet energy (U~D) provides a robust method for quantifying the asymptotic rate of diffraction for complex light.
    • This metric offers a self-consistent framework for analyzing the propagation dynamics of structured light, including Laguerre-Gaussian vortex and fractal beams.