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 mode (electric field polarized perpendicular to the waveguide and to the atomic plane). 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 $\nu =1.4\pm 0.2$.

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• Anderson localization
• Light propagation in random media
• Atomic ensemble
• Random & disordered media
• Discrete dipole approximation
• Finite-size scaling