Critical scaling of polarization waves on a heterogeneous chain of resonators

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.

Section on singularity spectrum included

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