Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Gauss's Law01:07

Gauss's Law

8.9K
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.
8.9K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

8.9K
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,...
8.9K
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

8.7K
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...
8.7K
Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

2.4K
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...
2.4K
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

9.0K
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...
9.0K
Plane Electromagnetic Waves I01:30

Plane Electromagnetic Waves I

4.6K
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...
4.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Regenerative polymer-based modalities for diabetic foot ulcers: From material design to clinical translation.

Nanomedicine : nanotechnology, biology, and medicine·2026
Same author

Fungal-induced rapid agarwood formation in Aquilaria malaccensis with resin quality equivalent to natural agarwood.

Microbiological research·2026
Same author

Predictive validity of daily sequential organ failure assessment (SOFA)-2 score for 30-day mortality.

Critical care (London, England)·2026
Same author

Half-integer thermal conductance in integer quantum Hall states.

Nature communications·2026
Same author

Automated Calculation of Sequential Organ Failure Assessment (SOFA) Score in the Intensive Care Unit: Algorithm Development, Validation, and Association With 30-Day Mortality.

Acta anaesthesiologica Scandinavica·2026
Same author

Critical Illness-Associated Hyperglycemia and New-Onset Diabetes: A Retrospective Cohort Study.

Critical care medicine·2025

Related Experiment Video

Updated: Nov 25, 2025

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

22.2K

Focused Gaussian beam in the paraxial approximation.

Ankur Das, Navid Soltani, Mario Agio

    Optics Letters
    |December 16, 2020
    PubMed
    Summary

    Researchers derived analytical expressions for focused Gaussian beams using the paraxial approximation. The study highlights the importance of higher-order Bessel functions in defining the electric field within the focal region.

    Area of Science:

    • Optics and Photonics
    • Electromagnetism
    • Mathematical Physics

    Background:

    • Focused Gaussian beams are crucial in various optical and photonic applications.
    • Understanding beam behavior in the focal region is essential for device design and performance.

    Purpose of the Study:

    • To derive analytical expressions for a focused Gaussian beam within the paraxial approximation.
    • To investigate the influence of the lens filling factor on the focused beam characteristics.
    • To elucidate the role of higher-order Bessel functions in shaping the electric field at the focus.

    Main Methods:

    • Derivation of analytical expressions for a focused Gaussian beam.
    • Application of the paraxial approximation.
    • Analysis of arbitrary lens filling factors.

    More Related Videos

    Femtosecond Laser Filaments for Use in Sub-Diffraction-Limited Imaging and Remote Sensing
    06:16

    Femtosecond Laser Filaments for Use in Sub-Diffraction-Limited Imaging and Remote Sensing

    Published on: April 25, 2019

    7.8K
    Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
    10:39

    Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

    Published on: October 11, 2016

    9.9K

    Related Experiment Videos

    Last Updated: Nov 25, 2025

    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

    22.2K
    Femtosecond Laser Filaments for Use in Sub-Diffraction-Limited Imaging and Remote Sensing
    06:16

    Femtosecond Laser Filaments for Use in Sub-Diffraction-Limited Imaging and Remote Sensing

    Published on: April 25, 2019

    7.8K
    Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
    10:39

    Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

    Published on: October 11, 2016

    9.9K
  • Investigation of higher-order Bessel functions.

    • Main Results:

    • Obtained analytical expressions for focused Gaussian beams under paraxial conditions.
    • Demonstrated the impact of the lens filling factor on beam focusing.
    • Identified the significant contribution of higher-order Bessel functions to the focal electric field.

    Conclusions:

    • The derived analytical expressions provide a valuable tool for analyzing focused Gaussian beams.
    • Higher-order Bessel functions play a key role in accurately describing the electric field in the focal region.
    • This research contributes to a deeper understanding of beam propagation and focusing in optical systems.