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Published on: November 30, 2012
Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity
Rodrigo A Vicencio1, Magnus Johansson
1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany. rodrigov@mpipks-dresden.mpg.de
Summary
Localized modes in 2D nonlinear Schrödinger lattices exhibit mobility, with stability exchanging between different solution families. A Peierls-Nabarro barrier governs the energy needed to initiate movement of these discrete spatial solitons.
Area of Science:
- Nonlinear Optics
- Condensed Matter Physics
- Mathematical Physics
Background:
- Localized modes, such as discrete spatial solitons, are crucial in nonlinear optical systems.
- Understanding their mobility is key for applications in optical waveguide arrays and photorefractive crystals.
- The behavior of these solitons is governed by the two-dimensional nonlinear Schrödinger equation with saturable nonlinearity.
Purpose of the Study:
- To investigate the mobility of localized modes in 2D nonlinear Schrödinger lattices with saturable nonlinearity.
- To analyze the stability and exchange of stability among different families of stationary solutions.
- To determine the Peierls-Nabarro barrier for mobile discrete spatial solitons.
Main Methods:
- Numerical analysis of exact stationary solutions for localized modes.
- Investigation of solution stability through bifurcation analysis.
- Calculation of the Peierls-Nabarro barrier for mobile solitons.
Main Results:
- Three families of stationary solutions (single-site, two-site, and four-site peaks) were identified.
- A repeated exchange of stability was observed between these solution families as power varied.
- Symmetry-broken intermediate solutions emerged at bifurcation points, and good mobility was found for lower nonlinearity parameters.
Conclusions:
- The mobility of localized modes in 2D nonlinear Schrödinger lattices is dependent on power and nonlinearity.
- The Peierls-Nabarro barrier quantifies the energy required for soliton mobility.
- These findings are relevant for controlling light propagation in discrete optical systems.
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