Open access
Date
2024Type
- Journal Article
ETH Bibliography
yes
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Abstract
In this paper, we use recent breakthroughs in the study of coupled subwavelength resonator systems to reveal new insight into the mechanisms responsible for the fundamental features of Anderson localization. The occurrence of strong localization in random media has proved difficult to understand, particularly in physically derived multi-dimensional models and systems with long-range interactions. We show here that the scattering of time-harmonic waves by high-contrast resonators with randomly chosen material parameters reproduces the characteristic features of Anderson localization. In particular, we show that the hybridization of subwavelength resonant modes is responsible for both the repulsion of energy levels as well as the widely observed phase transition, at which point eigenmode symmetries swap and very strong localization is possible. We derive results from first principles, using asymptotic expansions in terms of the material contrast parameter and obtain a characterization of the localized modes in terms of generalized capacitance matrices. This model captures the long-range interactions of the wave-scattering system and provides a concise framework to explain the exotic phenomena that are observed. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000654285Publication status
publishedExternal links
Journal / series
Communications in Mathematical PhysicsVolume
Pages / Article No.
Publisher
NatureFunding
200307 - Mathematics of dielectric artificial media (SNF)
863179 - Bio-Inspired Hierarchical MetaMaterials (EC)
Related publications and datasets
Is new version of: http://hdl.handle.net/20.500.11850/552817
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ETH Bibliography
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