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Related Concept Videos

Imperfections in Crystal Structure: Point, Line and Plane Defects01:25

Imperfections in Crystal Structure: Point, Line and Plane Defects

A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...
Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
Imperfections in Crystal Structure: Non-Stoichiometric Defects01:29

Imperfections in Crystal Structure: Non-Stoichiometric Defects

Non-stoichiometric defects refer to a type of defect in the crystal structure of a compound where the ratio of its constituent elements deviates from the ideal stoichiometric ratio. There are two main types of non-stoichiometric defects: metal excess defects and metal deficiency defects.Metal excess defects occur when there is a slight surplus of metal ions than what is required by the stoichiometric ratio of the compound. For example, heating a sodium chloride crystal in sodium vapor results...
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:
Crystallographic Point Groups01:29

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...
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Related Experiment Video

Updated: Jun 22, 2026

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

Computing Photonic Crystal Defect Modes by Dirichlet-to-Neumann Maps.

Shaojie Li, Ya Yan Lu

    Optics Express
    |June 25, 2009
    PubMed
    Summary

    We present an efficient numerical method for calculating defect modes in 2D photonic crystals. This approach utilizes Dirichlet-to-Neumann (DtN) maps for faster computation of defect mode frequencies.

    Area of Science:

    • Photonics
    • Computational Physics
    • Materials Science

    Background:

    • Photonic crystals offer unique light manipulation properties.
    • Efficient computation of defect modes is crucial for designing photonic devices.
    • Existing methods can be computationally intensive.

    Purpose of the Study:

    • To develop an efficient numerical method for computing defect modes in two-dimensional photonic crystals.
    • To leverage Dirichlet-to-Neumann (DtN) maps for improved computational efficiency.
    • To enable faster design and analysis of photonic crystal-based devices.

    Main Methods:

    • The method is based on Dirichlet-to-Neumann (DtN) maps of defect and normal unit cells.
    • The DtN map relates the wave field on a cell's boundary to its normal derivative.

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    Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

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    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

    Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
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    Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

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    Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
    10:35

    Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

    Published on: September 26, 2014

  • Defect mode frequencies are determined by the singularity of a small matrix derived from a linear system on discretized cell edges.

    • Main Results:

    • An efficient numerical method for computing defect modes in 2D photonic crystals is developed.
    • The method's computational efficiency is enhanced by using DtN maps.
    • The singularity condition of a small matrix accurately determines defect mode frequencies.

    Conclusions:

    • The developed numerical method provides an efficient way to compute defect modes in 2D photonic crystals.
    • The use of DtN maps significantly improves computational speed.
    • This method facilitates the design and analysis of advanced photonic devices.