Spatial and temporal localization of light in two dimensions

Multiple scattering of waves has been the subject of intense debates and proliferic studies in the context of disorder-induced Anderson localization [1]. However, despite several decades of research, the mere existence of Anderson localization of light [2] and its relation to another long predicted phenomenon, namely Dicke super- and subradiance [3], are still not clearly understood. As most experiments are typically performed in a three dimensional setting, models have also been focused on such 3D configurations. However, both numerical and fundamental aspects of localization strongly depend on the dimension of the explored system. For this reason, we have focused our efforts on a 2D system. Two-dimensional set-up can be obtained, e.g., with a disordered arrangement of scatterers in microwave cavities, in photonic crystals, near surface plasmons or with laser-cooled atoms located in an off-resonance optical cavity. The main advantage of that the reduced dimensionality also allows for a direct comparison between two regimes of scattering, one corresponding to a scalar model of light, the other one corresponding to a vectorial model of light, where the polarization of the wave needs to be taken into account. Then we are able to switch between the scalar or vectorial regime, between the presence or the absence of polarization degrees of freedom, and the presence or the absence of near field terms, making it an ideal tool to investigate the role of polarization in localization and subradiance. Performing scaling analysis we observe in both cases long lived atomic modes of the scattering, yet only the scalar case exhibits Anderson localized modes. Investigating the reasons for the absence of localization in cold atoms ensambles, it appears that both the coupling of polarization and the presence of near field terms are able to prevent long lifetimes and Anderson localization. We finally show that, albeit extremely long mode lifetimes are present only in localization regime, this lifetimes and their localization length are uncorrelated [4].
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[1] P. W. Anderson, Physical Review. 109, 1492 (1958).

[2] S. E. Skipetrov, I. M. Sokolov, Physical Review Letters 112, 023905 (2014).

[3] R. H. Dicke, Physical Review. 93, 99 (1954).

[4] C. E. M?ximo, N. Piovella, Ph. W. Courteille, R. Kaiser, R. Bachelard. To be submitted.