Delocalization transition for light in two dimensions

TL;DR

This paper predicts a localization-delocalization transition for light in a 2D waveguide with randomly placed atoms, driven by atomic density and near-field interactions, challenging the common belief of inevitable localization in 2D.

Contribution

It introduces the concept of a transition driven by atomic density and near-field interactions, contrary to the traditional view of inevitable localization in 2D systems.

Findings

A localization-delocalization transition occurs at a critical atomic density.

The transition is driven by near-field dipole-dipole interactions.

Critical exponent of the transition estimated as approximately 1.4.

Abstract

Common belief, confirmed by existing experiments, is that arbitrarily weak disorder should lead to spatial localization of eigenmodes of scalar wave equations when wave propagation is two-dimensional (2D). We predict that contrary to this belief, a localization-delocalization transition can take place for light scattered by two-level atoms placed at random positions in the middle plane of a parallel-plate 2D waveguide fed by its fundamental transverse-magnetic (TM) mode (electric field polarized perpendicular to the waveguide and atomic planes). This transition, driven by near-field dipole-dipole interactions between atoms, occurs upon increasing the areal number density of atoms beyond some critical value. A finite-size scaling analysis of the transition yields an estimate of its critical exponent ${\nu}$ = 1.4 $\pm$ 0.2.