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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

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Published on: July 29, 2013

Delocalization induced by nonlinearity in systems with disorder.

Ignacio García-Mata¹, Dima L Shepelyansky

¹Laboratoire de Physique Théorique, UMR 5152 du CNRS, Université Toulouse III, 31062 Toulouse, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 28, 2009

Summary

Nonlinearity causes spreading in Anderson localization in disordered lattices, with algebraic growth observed up to 10^9 time units. Localization persists below a critical nonlinearity threshold.

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Area of Science:

Condensed matter physics
Quantum mechanics
Statistical physics

Background:

Anderson localization describes the suppression of wave function propagation in disordered systems.
Nonlinearity can significantly alter the behavior of localized states.

Purpose of the Study:

To numerically investigate the impact of nonlinearity on Anderson localization in 1D and 2D lattices.
To characterize the time evolution and scaling of wave packet spreading under nonlinear conditions.

Main Methods:

Numerical simulations of wave propagation in disordered lattices.
Analysis of the time-dependent number of populated sites.
Calculation of the exponent nu governing algebraic spreading.

Main Results:

Moderate nonlinearity induces algebraic spreading of the wave packet, with the number of populated sites growing as t^nu.
The exponent nu was found to be approximately 0.15-0.2 for d=1 and 0.25 for d=2.
Anderson localization is preserved below a critical nonlinearity strength up to simulation times of 10^9.

Conclusions:

Nonlinearity fundamentally modifies Anderson localization, leading to a novel spreading regime.
The observed spreading exponent aligns with theoretical predictions.
Further investigation into nonlinear field perturbation effects on fidelity decay is warranted.