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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...

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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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Published on: September 26, 2014

Two-dimensional disordered lattice solitons.

Nikolaos K Efremidis¹

¹Department of Applied Mathematics, University of Crete, Heraklion, Crete, Greece. nefrem@tem.uoc.gr

|March 3, 2009

Summary

We studied optical solitons in disordered lattices, finding they originate from linear modes. Soliton behavior, including localization, depends on lattice properties and power, with highly confined solitons existing in all waveguides.

Area of Science:

Nonlinear optics
Condensed matter physics
Photonics

Background:

Optical solitons are self-reinforcing light waves.
Disordered lattices present complex environments for wave propagation.
Understanding soliton behavior in such systems is crucial for optical technologies.

Purpose of the Study:

To investigate families of optical solitons in 2D disordered lattices.
To analyze the relationship between linear modes and soliton formation.
To explore how nonlinearity and lattice properties influence soliton localization.

Main Methods:

Identification of linear modes and their band structure.
Introduction of Kerr nonlinearity to study soliton families.
Analysis of soliton delocalization via resonant interactions.

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Examination of highly confined solitons in individual waveguides.

Main Results:

Soliton families were found to originate from the system's linear modes.
Soliton localization is dependent on the eigenvalue of the supporting linear mode.
Increasing power can lead to soliton delocalization through resonant interactions.
Highly confined solitons exist in every waveguide for both positive and negative nonlinearity.

Conclusions:

The study establishes a clear link between linear modes and nonlinear soliton formation in disordered lattices.
Soliton dynamics are tunable via power and are influenced by resonant interactions with the lattice.
The existence of highly confined solitons offers potential for robust optical signal control.