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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...
Equations of Wave Motion01:02

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
The de Broglie Wavelength02:32

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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...
Propagation Speed of Electromagnetic Waves01:30

Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:
Electromagnetic Waves in Matter01:30

Electromagnetic Waves in Matter

Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, or glass.
Consider the electromagnetic wave passing through a dielectric medium. In such a case, Maxwell's equations get modified. In Ampere's law, ε0 , the dielectric permittivity of free space is replaced with ε, the permittivity of dielectric. Also, the vacuum permeability μ0 is replaced by the permeability of the medium, μ.
Furthermore, the...

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Related Experiment Video

Updated: Jun 16, 2026

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
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Optical fiber eigenvalue equation: plane wave derivation.

J D Love, A W Snyder

    Applied Optics
    |February 19, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study derives the eigenvalue equation for optical waveguides using basic plane wave principles. The method applies to both step and parabolic refractive index profiles, simplifying analysis.

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    Area of Science:

    • Optics and Photonics
    • Waveguide Theory

    Background:

    • Optical waveguides are crucial components in integrated optics and telecommunications.
    • Accurate modeling of waveguide behavior is essential for device design and performance prediction.

    Purpose of the Study:

    • To derive the asymptotic form of the eigenvalue equation for circular optical waveguides.
    • To demonstrate a simplified approach using fundamental wave concepts.

    Main Methods:

    • Application of plane wave concepts, including phase changes, Fresnel's, and Snell's laws.
    • Analysis of optical waveguides with circular cross-sections.
    • Treatment of both step-index and parabolic refractive index profiles.

    Main Results:

    • Successful derivation of the asymptotic eigenvalue equation for optical waveguides.
    • Demonstration that fundamental optical laws are sufficient for this derivation.
    • Validation of the method for different refractive index profiles.

    Conclusions:

    • A simplified, yet accurate, method for analyzing optical waveguides has been developed.
    • The derived eigenvalue equation provides insights into waveguide behavior.
    • This approach offers a valuable tool for optical waveguide design and research.