The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly coupled scatterers is investigated theoretically and supported by 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 banded random 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.

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Journal Phys. Rev. B
Faez, S, Lagendijk, A, & Ossipov, A. (2011). Critical scaling of polarization waves on a heterogeneous chain of resonators. Phys. Rev. B, 83(7, Article number: 75121), 1–12. doi:10.1103/PhysRevB.83.075121