Longitudinal waves prevent Anderson localization of light
Résumé
A wave propagating in a medium exhibiting strong random variations (disorder) of its properties may experience a peculiar interference phenomenon known as Anderson localization and manifesting itself in a complete halt of long-range transport of wave energy [1]. Anderson localization leads to a metal-insulator transition in three-dimensional (3D) disordered conductors at low temperatures when charge carriers reveal their quantum-mechanical nature [1], to suppression of sound transmission through strongly disordered elastic media [2], and to arrest of expansion of a Bose-Einstein condensate in a random optical potential [3]. The phenomenon is believed to be ubiquitous for all waves but attempts to observe it in experiments with light in 3D media ran into multiple difficulties [4]. We have discovered that the vector character of electromagnetic waves prevents Anderson localization of light in a simple model of resonant point-like scatterers in 3D, suggesting a fundamental reason for the failure of experiments [5]. Here we propose an extension of the self consistent theory of localization that incorporates the vector character of light and, in particular, ensures proper treatment of longitudinal electromagnetic excitations that arise in the presence of disorder [6]. We show that including longitudinal excitations in the theory has dramatic consequences and that the interference between transverse and longitudinal waves eliminates the localization transition predicted by the very same theory for scalar or purely transverse electromagnetic waves. Comparison of theoretical predictions with ab-initio numerical simulations shows that when the Ioffe-Regel parameter kl decreases below 1, the photon diffusion coefficient D grows instead of vanishing. This is in contrast to the behavior found for scalar or purely transverse waves. In addition, D depends on the sign of detuning, being larger for blue than for red detuning, which signals that the single parameter kl is not sufficient to characterize the strength of scattering for light. Our recent results suggest that the same mechanism of suppression of Anderson localization is also at work in random ensembles of small dielectric scatterers [7]. 1. P.W. Anderson, Phys. Rev. 109, 1492 (1958) 2. H. Hu et al., Nat. Phys. 4, 945 (2008) 3. F. Jendrzejewski et al., Nat. Phys. 8, 398 (2012) 4. S.E. Skipetrov and J.H. Page, New J. Phys. 18, 021001 (2016) 5. S.E. Skipetrov and I.M. Sokolov, Phys. Rev. Lett. 112, 023905 (2014) 6. B.A. van Tiggelen and S.E. Skipetrov, Phys. Rev. B 103, 174204 (2021) 7. A. Yamilov et al., Nat. Phys. 19, 1308 (2023)