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Related Concept Videos

Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
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Updated: May 23, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
07:42

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

Spatial solitons under competing linear and nonlinear diffractions.

Y Shen1, P G Kevrekidis, N Whitaker

  • 1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 3, 2012
PubMed
Summary
This summary is machine-generated.

This study presents a new model for spatial solitons in nonlinear photonic crystals, analyzing their stability and interactions. It reveals how nonlinear diffraction influences soliton behavior, leading to merging or collapse.

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Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
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Published on: January 3, 2016

Area of Science:

  • Nonlinear optics
  • Mathematical physics

Background:

  • The nonlinear Schrödinger (NLS) equation is a fundamental model in optics.
  • Understanding spatial solitons in nonlinear media is crucial for optical technologies.

Purpose of the Study:

  • To introduce a generalized NLS model incorporating nonlinear diffraction.
  • To analyze the stability and interactions of spatial solitons within this new model.

Main Methods:

  • Variational approximation (VA)
  • Exact analytical solutions
  • Numerical computations
  • Vakhitov-Kolokolov (VK) criterion

Main Results:

  • Exact analytical prediction of the soliton stability border and maximum power.
  • Observation of collapse effects beyond a critical point.
  • Numerical simulations showing soliton merging into robust or collapsing pulsons based on nonlinear diffraction strength.

Conclusions:

  • The generalized NLS model accurately describes spatial solitons near the supercollimation point.
  • Nonlinear diffraction plays a key role in determining soliton stability and interaction outcomes.