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High-order-mode soliton structures in two-dimensional lattices with defocusing nonlinearity
P G Kevrekidis1, H Susanto, Z Chen
1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
Summary
This study explores high-order-mode solitons in defocusing nonlinear waveguide lattices. Unlike focusing cases, these structures exhibit different stability, with dipole solitons becoming unstable.
Area of Science:
- Nonlinear Optics
- Soliton Physics
- Condensed Matter Physics
Background:
- Discrete solitons are localized states in periodic nonlinear media.
- High-order-mode solitons have been studied primarily in self-focusing nonlinearities.
- Defocusing nonlinearities present unique challenges for soliton stability.
Purpose of the Study:
- To investigate the existence and stability of high-order-mode solitons (dipole, quadrupole, vortex) in 2D defocusing nonlinear lattices.
- To compare the stability regimes of these solitons with those in self-focusing systems.
- To provide insights into nonlinear periodic systems like Bose-Einstein condensates.
Main Methods:
- Theoretical analysis of a generic envelope nonlinear lattice model.
- Numerical simulations to determine soliton existence and stability boundaries.
- Examination of specific soliton structures like dipole, quadrupole, and vortex modes.
Main Results:
- Existence and stability regimes for dipole, quadrupole, and vortex solitons in 2D defocusing lattices were identified.
- High-order-mode soliton stability in defocusing lattices differs significantly from self-focusing cases.
- Dipole solitons, stable in focusing regimes, were found to be unstable in the defocusing regime.
Conclusions:
- The stability of high-order-mode solitons is highly dependent on the nonlinearity type (focusing vs. defocusing).
- Defocusing nonlinearities introduce distinct stability characteristics for localized states in waveguide lattices.
- Findings are relevant for understanding nonlinear phenomena in systems like Bose-Einstein condensates in optical lattices.
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