Anderson localization in the subwavelength regime

TL;DR

This paper demonstrates how high-contrast resonators with random parameters can reproduce Anderson localization features, revealing the role of hybridized subwavelength modes and long-range interactions in wave localization.

Contribution

It introduces a first-principles asymptotic model using generalized capacitance matrices to explain Anderson localization in complex resonator systems.

Findings

Resonator scattering reproduces Anderson localization features.

Hybridization of subwavelength modes causes energy level repulsion.

Phase transition with eigenmode symmetry swapping leads to strong localization.

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 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.