Critical scaling of polarization waves on a heterogeneous chain of resonators

TL;DR

This paper investigates the critical scaling and localization transition of electromagnetic polarization waves in a disordered chain of resonators, highlighting the effects of long-range interactions and non-Hermiticity.

Contribution

It reveals the critical scaling behavior and localization transition in a one-dimensional resonator chain due to long-range dipole interactions and non-Hermitian effects.

Findings

Critical scaling observed in eigenvalue spectrum due to Anderson transition.

All eigenmodes are localized for parallel polarization with inverse squared coupling.

Comparison shows non-Hermiticity and coupling modulation significantly affect localization.

Abstract

The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the eigenvalue spectrum due to the disorder-induced Anderson transition. This localization transition (in a formally one-dimensional system) is attributed to the long-range dipole-dipole interaction, which decays inverse linearly with distance for polarization perpendicular to the chain. For polarization parallel to the chain, with inverse squared long range coupling, all eigenmodes are shown to be localized. A comparison with the results for Hermitian power-law random banded matrices and other intermediate models is presented. This comparison reveals the significance of non-Hermiticity of the model and the periodic modulation of the coupling.