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Related Concept Videos

Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.
Gauss's Law in Dielectrics01:17

Gauss's Law in Dielectrics

Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
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...
Standing Waves in a Cavity01:28

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
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...
Susceptibility, Permittivity and Dielectric Constant01:26

Susceptibility, Permittivity and Dielectric Constant

When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of the bound and free charge densities, while the total charge density can also be written in terms of the total electric field. The bound charge density can be measured in terms of polarization, leading to the relationship between electric displacement and polarization.

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Related Experiment Video

Updated: Jun 16, 2026

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
11:08

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

Published on: November 30, 2012

Explicit general eigenvalue solutions for dielectric slab waveguides.

J F Lotspeich

    Applied Optics
    |February 6, 2010
    PubMed
    Summary
    This summary is machine-generated.

    A new formula simplifies calculating TE eigenmode propagation constants in dielectric slab waveguides. This method avoids complex eigenvalue equations with high accuracy, improving waveguide design.

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    Area of Science:

    • Optics and Photonics
    • Materials Science

    Background:

    • Dielectric slab waveguides are fundamental in integrated optics.
    • Calculating eigenmode propagation constants typically involves solving transcendental equations.

    Purpose of the Study:

    • To develop a general formula for TE eigenmode propagation constants in dielectric slab waveguides.
    • To provide a convenient alternative to transcendental eigenvalue equations.
    • To present a method for deriving TM eigenvalues with high accuracy.

    Main Methods:

    • Developed an explicit formula for TE eigenmode propagation constants.
    • The formula incorporates guide layer thickness, operating wavelength, and refractive indexes.
    • A method for TM eigenvalue derivation was also presented.

    Main Results:

    • The formula provides general solutions for TE eigenmode propagation constants.
    • Maximum error for TE modes is less than 0.6%.
    • TM eigenvalues can be derived with an accuracy of approximately 99% or better.

    Conclusions:

    • The developed formula offers a significant simplification for analyzing dielectric slab waveguides.
    • This approach circumvents complex transcendental equations, facilitating practical applications.
    • The method enhances the accuracy and efficiency of waveguide design and analysis.