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Algebraic bright and vortex solitons in defocusing media
Olga V Borovkova1, Yaroslav V Kartashov, Boris A Malomed
1ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, Castelldefels 08860, Spain. Olga.Borovkova@icfo.es
Optics Letters
|August 18, 2011
Summary
Spatially inhomogeneous nonlinear landscapes support various bright solitons. Soliton energy flow converges when nonlinearity growth rate exceeds dimensionality, ensuring stability for fundamental solitons and certain multipoles/vortices.
Area of Science:
- Nonlinear optics
- Mathematical physics
- Condensed matter theory
Background:
- Investigating stable soliton solutions in nonlinear media is crucial for understanding wave propagation.
- Previous studies often focused on homogeneous nonlinearities, limiting the types of stable solitons observed.
Purpose of the Study:
- To explore the existence and stability of bright solitons in spatially inhomogeneous defocusing nonlinear landscapes.
- To analyze the conditions under which energy flow converges and different soliton types remain stable.
Main Methods:
- Analytical and numerical methods were employed to study nonlinear landscapes with peripheral nonlinearity growth.
- The nonlinearity coefficient was modeled as (1+|r|(α)), where |r| is the radial distance and α is the growth rate.
- Stability analysis was performed for fundamental, higher-order, and vortex solitons.
Main Results:
- One- and two-dimensional fundamental, higher-order, and vortex bright solitons with algebraically decaying tails were demonstrated.
- Soliton energy flow convergence was observed when the nonlinearity growth rate (α) exceeded the dimensionality (D).
- Fundamental solitons exhibited unconditional stability, while multipoles and vortices showed stability for sufficiently large nonlinearity growth rates.
Conclusions:
- Spatially inhomogeneous nonlinear landscapes offer a versatile platform for generating and controlling various bright soliton types.
- The condition α>D is critical for ensuring the convergence of energy flow and the stability of complex soliton structures.
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