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Finite-dimensional model for defect-trapped light in planar periodic nonlinear structures.

Alejandro B Aceves1, Tomás Dohnal

  • 1Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA.

Optics Letters
|September 27, 2006
PubMed
Summary

We developed a model to understand how 2D gap solitons interact with defects in photonic gratings. This model accurately describes energy trapping in defect modes, crucial for photonic device applications.

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Area of Science:

  • Nonlinear optics
  • Condensed matter physics
  • Photonics

Background:

  • 2D gap solitons (GSs) are fundamental nonlinear wave solutions in periodic photonic structures.
  • Bragg resonant nonlinear gratings support gap solitons through strong light-matter interactions.
  • Localized defects in gratings can significantly alter soliton dynamics and energy localization.

Purpose of the Study:

  • To investigate the dynamics of 2D gap solitons in the presence of localized defects within Bragg resonant nonlinear gratings.
  • To develop and validate a simplified model for the energy trapping mechanism at defects.
  • To understand the interaction between gap solitons and defect modes.

Main Methods:

  • Derivation of a finite-dimensional model based on the interaction of linear defect modes.
  • Numerical simulations of 2D gap soliton propagation in gratings with defects.
  • Comparison of the finite-dimensional model predictions with full numerical simulations.

Main Results:

  • The finite-dimensional model accurately approximates the dynamics of defect-trapped states.
  • Resonant energy transfer from gap solitons into defect modes is the primary trapping mechanism.
  • The model shows good agreement with full dynamics for moderate energy trapping regimes.

Conclusions:

  • A reduced-order model effectively captures the essential physics of gap soliton energy trapping at defects.
  • This work provides a valuable tool for designing and analyzing photonic devices with defect-engineered soliton behavior.
  • Understanding these dynamics is key for applications in optical switching, signal processing, and energy localization in photonic systems.