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Updated: Apr 27, 2026
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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
Published on: July 29, 2013
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Topological approximation of the nonlinear Anderson model.
Alexander V Milovanov1, Alexander Iomin2
1ENEA National Laboratory, Centro Ricerche Frascati, I-00044 Frascati, Rome, Italy Space Research Institute, Russian Academy of Sciences, 117997 Moscow, Russia and Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany.
Summary
We investigated Anderson localization with nonlinear interactions, finding quadratic nonlinearity uniquely enables abrupt transitions. This transition resembles percolation on a Bethe lattice, with subdiffusive wave spreading and a critical exponent of 1/3.
Area of Science:
- Condensed Matter Physics
- Nonlinear Dynamics
- Quantum Chaos
Background:
- Anderson localization describes wave function confinement in disordered systems.
- Nonlinear interactions significantly alter localization dynamics, leading to complex behaviors like chaos and Lévy flights.
Purpose of the Study:
- To analyze Anderson localization phenomena under arbitrary power nonlinearity in nonlinear Schrödinger models.
- To identify distinct dynamical regimes and transitions based on nonlinearity type and phase space topology.
Main Methods:
- Analysis of nonlinear Schrödinger models with varying power nonlinearities.
- Characterization of phase space topology and resonance overlap.
- Description of localization-delocalization transitions using percolation theory on an infinite Cayley tree (Bethe lattice).
Main Results:
- Quadratic nonlinearity uniquely facilitates abrupt localization-delocalization transitions.
- Wave field spreading near criticality is subdiffusive, with a power-law growth of the second moment (t^{1/3}).
- Superquadratic nonlinearity exhibits self-organized criticality, automatically developing percolation points.
Conclusions:
- The study reveals diverse localization-delocalization behaviors driven by nonlinearity type.
- Quadratic nonlinearity is crucial for abrupt transitions, while superquadratic nonlinearity demonstrates self-organized criticality.
- The findings provide a theoretical basis for understanding transport properties in complex, many-body systems.
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