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Related Concept Videos

Symmetry Elements in a Crystal01:27

Symmetry Elements in a Crystal

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
Determination of Crystal Structures01:29

Determination of Crystal Structures

In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...

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Related Experiment Video

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

Published on: September 26, 2014

Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method.

Po-jui Chiang1, Chin-ping Yu, Hung-chun Chang

  • 1Graduate Institute of Electro-Optical Engineering, National Taiwan University, Taipei, Taiwan 106-17, Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
Summary

A new multidomain pseudospectral method accurately calculates band diagrams for 2D photonic crystals. This advanced technique ensures reliable numerical convergence for photonic crystal analysis.

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Last Updated: Jul 16, 2026

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

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Published on: September 26, 2014

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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

Area of Science:

  • Computational physics
  • Materials science
  • Optics

Background:

  • Photonic crystals offer unique light manipulation properties.
  • Accurate calculation of band diagrams is crucial for designing photonic crystal devices.
  • Existing methods may face challenges with complex geometries and accuracy.

Purpose of the Study:

  • To propose a novel, accurate, and numerically convergent method for calculating 2D photonic crystal band diagrams.
  • To address challenges associated with curved interfaces and ensure field continuity.

Main Methods:

  • Utilizes a multidomain Chebyshev collocation method to approximate spatial derivatives.
  • Converts the Helmholtz equation into a matrix eigenvalue problem solved via the shift inverse power method.
  • Employs multidomain division and imposes field continuity conditions for complex permittivity profiles.

Main Results:

  • Demonstrates excellent numerical convergence and accuracy for both transverse-electric and transverse-magnetic waves.
  • Successfully analyzes various photonic crystal structures, including those with curved interfaces.
  • Shows extremely high accuracy in the analysis of mini band gaps.

Conclusions:

  • The proposed multidomain pseudospectral method provides a robust and accurate approach for 2D photonic crystal band structure calculations.
  • The method's effectiveness is validated across different wave polarizations and complex structural designs.
  • Offers a reliable tool for the advancement of photonic crystal research and applications.