Related Experiment Video
Updated: Jul 19, 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
Gap solitons in quasiperiodic optical lattices
Hidetsugu Sakaguchi1, Boris A Malomed
1Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
Summary
Researchers constructed stable 1D and 2D solitons in quasicrystal potentials. These solitons exhibit mobile and elastic collision properties, with stable fundamental and vortical solitons found in 2D models.
Area of Science:
- Nonlinear physics
- Condensed matter physics
- Mathematical physics
Background:
- Gross-Pitaevskii equations describe Bose-Einstein condensates and nonlinear optics.
- Quasicrystal potentials introduce unique, non-periodic structures.
- Solitons are self-reinforcing wave packets that maintain their shape.
Purpose of the Study:
- To construct and analyze families of solitons in 1D and 2D Gross-Pitaevskii equations.
- To investigate soliton behavior in the presence of quasicrystal potentials.
- To determine the stability and properties of these solitons.
Main Methods:
- Analytical and numerical methods were used to construct soliton solutions.
- The Gross-Pitaevskii equation with repulsive nonlinearity and quasicrystal potential was solved.
- Stability analysis was performed for the obtained soliton families.
Main Results:
- Stable 1D solitons were found in three band gaps for weak potentials, exhibiting elastic collisions.
- In strong potentials, multiple types of 1D solitons were identified, including stable and unstable species.
- Both fundamental and vortical solitons were found to be stable in the 2D quasicrystal model (fivefold optical lattice).
Conclusions:
- Quasicrystal potentials support stable and mobile solitons in both 1D and 2D systems.
- The dimensionality and potential strength significantly influence soliton properties and stability.
- The findings contribute to understanding nonlinear wave phenomena in complex potentials.
Related Concept Videos
01:28Standing 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:
02:32The 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...
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...
01:12Bewley Lattice Diagram
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
01:01Energy Bands in Solids
Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
Band Formation:
When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states that no two...
Band Formation:
When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states that no two...
02:18Network Covalent Solids
Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...