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Related Concept Videos

Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
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...
Maxwell's Equation Of Electromagnetism01:29

Maxwell's Equation Of Electromagnetism

James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is represented by...
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of the problem,...

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Related Experiment Video

Updated: Jun 19, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Vector-beam solutions of Maxwell's wave equation.

D G Hall

    Optics Letters
    |October 30, 2009
    PubMed
    Summary

    Vector Bessel-Gauss beams describe the complete transverse electric field, extending beyond scalar solutions like Hermite-Gauss and Laguerre-Gauss modes. These novel vector beams offer a more comprehensive description of light fields.

    Area of Science:

    • Optics and Photonics
    • Electromagnetism
    • Mathematical Physics

    Background:

    • Hermite-Gauss and Laguerre-Gauss modes are standard paraxial solutions to the scalar Helmholtz equation.
    • These modes represent linearly polarized fields or single Cartesian components of vector fields.
    • The scalar nature limits their ability to describe the full transverse electric field.

    Purpose of the Study:

    • To introduce and analyze a family of localized vector Bessel-Gauss beam solutions.
    • To demonstrate that these vector beams can describe the entire transverse electric field.
    • To connect recently reported solutions to this broader family of vector beam modes.

    Main Methods:

    • Solving the vector wave equation in the paraxial limit.
    • Developing localized Bessel-Gauss beam solutions.

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    Generation and Coherent Control of Pulsed Quantum Frequency Combs
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    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

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    09:04

    Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

    Published on: February 23, 2018

    Generation and Coherent Control of Pulsed Quantum Frequency Combs
    06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

  • Analyzing the mathematical properties of these vector modes.

    • Main Results:

    • A family of localized vector Bessel-Gauss beam solutions exists.
    • These vector beams fully describe the transverse electric field.
    • Two recently published beam solutions are identified as members of this family.

    Conclusions:

    • Vector Bessel-Gauss beams provide a more complete description of paraxial light fields than scalar modes.
    • This family of solutions offers a unified framework for understanding certain vector beam properties.
    • The findings advance the understanding of structured light and electromagnetic field descriptions.