Finite-dimensional model for defect-trapped light in planar periodic nonlinear structures
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Updated: Jul 19, 2026

Comprehensive Characterization of Extended Defects in Semiconductor Materials by a Scanning Electron Microscope
Published on: May 28, 2016
Alejandro B Aceves1, Tomás Dohnal
1Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA.
Abstract:
We study the dynamics of 2D gap solitons (GSs) in Bragg resonant nonlinear (photonic) gratings in the presence of localized defects. Previous work [Stud. Appl. Math.115, 209 (2005)] explains the mechanism of trapping the GS-carried energy at a defect via a resonant energy transfer from the GS into defect modes. We derive a finite-dimensional model that describes the evolution of the defect-trapped state as an interaction of linear defect modes and show that this model approximates the full dynamics very well in the regime when moderate amounts of GS energy are trapped.
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In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.