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Updated: May 19, 2026
09:19
Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
Published on: July 29, 2013
Universal mechanism for Anderson and weak localization.
Marcel Filoche1, Svitlana Mayboroda
1Physique de la Matière Condensée, Ecole Polytechnique, Centre National de la Recherche Scientifique, 91128 Palaiseau, France. marcel.filoche@polytechnique.edu
Summary
This study reveals a universal mechanism behind Anderson localization and weak localization in vibrating systems. This mechanism unifies various localization phenomena by partitioning systems into subregions based on a hidden geometric landscape.
Area of Science:
- Physics
- Wave Phenomena
- Condensed Matter Physics
Background:
- Stationary wave localization occurs in diverse systems (mechanical, optical, quantum) due to disorder or complex geometry.
- Anderson localization is a key example, explaining metal-insulator transitions, but a unified understanding is lacking.
Purpose of the Study:
- To demonstrate a single, universal mechanism underlying both Anderson and weak localization.
- To establish a unified theoretical framework for various wave localization phenomena.
Main Methods:
- Analysis of the interplay between the wave operator and system geometry.
- Identification of a hidden landscape partitioning the system into weakly coupled subregions.
- Solving a specific boundary problem to characterize the landscape and coupling strengths.
Main Results:
- Both Anderson and weak localizations stem from the same universal mechanism.
- This mechanism partitions systems into subregions defined by the valleys of a hidden geometric landscape.
- The landscape's properties rigorously predict localization behavior and eigenmode energies.
Conclusions:
- Anderson localization is a specific instance of weak localization within a rough landscape.
- The developed theory provides a unified perspective on wave localization across different systems and dimensions.
- Geometric properties of the hidden landscape are crucial for understanding and predicting localization.
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