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Coupled-mode theory for spatial gap solitons in optically induced lattices
Boris A Malomed1, Thawatchai Mayteevarunyoo, Elena A Ostrovskaya
1Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
Summary
We developed models for spatial gap solitons in photonic lattices, finding stable solutions for stationary and moving solitons. Interactions between these solitons are mostly elastic, with inelastic collisions near instability borders.
Area of Science:
- Nonlinear Optics
- Photonic Lattices
- Soliton Physics
Background:
- Photonic lattices are crucial for controlling light propagation.
- Spatial gap solitons are localized light structures in such lattices.
- Nonlinear photorefractive crystals offer unique properties for soliton formation.
Purpose of the Study:
- To derive and analyze coupled-mode equations for spatial gap solitons.
- To investigate stationary and moving (tilted) solitons in 1D and quasi-1D photonic lattices.
- To explore the stability and interactions of these solitons.
Main Methods:
- Derivation of coupled-mode equations incorporating saturable nonlinearity and four-wave-mixing.
- Analytical solutions for stationary gap solitons in 1D systems.
- Numerical solutions for quasi-1D systems and tilted solitons.
- Direct simulations for stability analysis and interaction studies.
Main Results:
- Implicit analytical solutions for stationary gap solitons in 1D.
- Numerical solutions for quasi-1D and tilted solitons, confirming stability.
- Identification of a nontrivial instability border and two disjointed stability regions in Q1D.
- Observation of predominantly elastic collisions between tilted solitons.
Conclusions:
- The derived models accurately describe spatial gap solitons in nonlinear photonic lattices.
- Stable stationary and moving solitons exist, with complex stability boundaries.
- Soliton interactions are generally elastic, highlighting their robustness.