Related Experiment Video
Updated: May 12, 2026
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
Selection rule for Dirac-like points in two-dimensional dielectric photonic crystals
1Department of Physics, South China University of Technology, Guangzhou 510641, China.
Optics Express
|April 3, 2013
Summary
We found a simple rule to predict Dirac-like points in photonic crystals. This rule uses mode-coupling integrals or Bloch state symmetry, simplifying the discovery of these important optical features.
Area of Science:
- Condensed matter physics
- Photonics
- Materials science
Background:
- Dirac-like points in photonic crystals are crucial for unique light manipulation.
- Predicting their existence often requires complex simulations.
- A simplified prediction method is highly desirable.
Purpose of the Study:
- To develop a general selection rule for identifying Dirac-like points in 2D dielectric photonic crystals.
- To provide a method for quick and conclusive prediction of Dirac-like points.
- To establish a rule applicable across various photonic crystal designs.
Main Methods:
- Derivation of the selection rule using perturbation theory.
- Analysis of mode-coupling integrals between degenerate Bloch states.
- Examination of Bloch state symmetry as an alternative prediction criterion.
Main Results:
- A non-zero mode-coupling integral between degenerate Bloch states guarantees a Dirac-like point.
- The selection rule can be determined from Bloch state symmetry alone.
- The rule is independent of wave polarization, lattice structure, and material composition.
Conclusions:
- A robust and universally applicable selection rule for Dirac-like points has been established.
- This rule significantly simplifies the prediction and design of photonic crystals with Dirac-like points.
- The findings facilitate the exploration of novel photonic devices and functionalities.
Related Concept Videos
01:26Imperfections 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...
01:27Electrostatic 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.
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.
01:25Imperfections 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...
01:28Magnetostatic Boundary Conditions
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
02:58Crystal 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...
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...
01:31Dielectric Polarization in a Capacitor
The presence of a dielectric medium in a capacitor not only changes the voltage and capacitance but also affects the electric field. In general, dielectrics can be of two types: polar and nonpolar. In a polar dielectric, the positive and negative charges in the molecules are separated by a distance and hence have a permanent dipole moment. In contrast, no such charge separation exists in a nonpolar dielectric, however the nonpolar molecules get polarized in the presence of an external electric...