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Related Concept Videos

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:
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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...
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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...
Modes of Standing Waves: II01:04

Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.

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Related Experiment Video

Updated: Jun 22, 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

Coupled mode theory for photonic crystal cavity-waveguide interaction.

Edo Waks, Jelena Vuckovic

    Optics Express
    |June 6, 2009
    PubMed
    Summary

    We developed a new theory for optical cavities interacting with waveguides, accounting for waveguide dispersion. This model accurately predicts cavity quality factor (Q) except when dispersion distorts spectra, leading to overestimated Q values.

    Area of Science:

    • Photonics
    • Optical Engineering
    • Condensed Matter Physics

    Background:

    • Optical cavities coupled to waveguides are fundamental in integrated photonics.
    • Understanding their interaction is crucial for device design and performance prediction.
    • Waveguide dispersion effects can significantly alter light propagation and cavity coupling.

    Purpose of the Study:

    • To develop a coupled mode theory for optical cavity-waveguide interactions including waveguide dispersion.
    • To analytically solve for add and drop spectra under linear dispersion.
    • To numerically investigate spectral distortions in the nonlinear dispersion regime.

    Main Methods:

    • Derivation of a coupled mode theory incorporating waveguide dispersion.
    • Analytical solution for add and drop spectra in the linear dispersion limit.

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    Fabrication of 1-D Photonic Crystal Cavity on a Nanofiber Using Femtosecond Laser-induced Ablation
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    Fabrication of 1-D Photonic Crystal Cavity on a Nanofiber Using Femtosecond Laser-induced Ablation

    Published on: February 25, 2017

    Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
    12:18

    Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

    Published on: August 5, 2013

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    Last Updated: Jun 22, 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

    Fabrication of 1-D Photonic Crystal Cavity on a Nanofiber Using Femtosecond Laser-induced Ablation
    13:02

    Fabrication of 1-D Photonic Crystal Cavity on a Nanofiber Using Femtosecond Laser-induced Ablation

    Published on: February 25, 2017

    Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
    12:18

    Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

    Published on: August 5, 2013

  • Numerical solution of coupled mode equations for band-edge interactions.

    • Main Results:

    • The theory accurately predicts cold cavity quality factor (Q) for weak interactions in the linear dispersion limit.
    • Numerical simulations reveal spectral distortions due to the density of states at the band edge.
    • These distortions can lead to overestimations of cavity Q by more than an order of magnitude.

    Conclusions:

    • The derived coupled mode theory provides a robust framework for analyzing optical cavity-waveguide systems.
    • Nonlinear dispersion effects, particularly at band edges, necessitate careful interpretation of spectral measurements.
    • Accurate Q factor determination requires accounting for dispersion-induced spectral distortions.