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Transport and Anderson localization in disordered two-dimensional photonic lattices

Nature volume 446, pages 52–55 (2007)Cite this article

Abstract

One of the most interesting phenomena in solid-state physics is Anderson localization, which predicts that an electron may become immobile when placed in a disordered lattice1. The origin of localization is interference between multiple scatterings of the electron by random defects in the potential, altering the eigenmodes from being extended (Bloch waves) to exponentially localized2. As a result, the material is transformed from a conductor to an insulator. Anderson’s work dates back to 1958, yet strong localization has never been observed in atomic crystals, because localization occurs only if the potential (the periodic lattice and the fluctuations superimposed on it) is time-independent. However, in atomic crystals important deviations from the Anderson model always occur, because of thermally excited phonons and electron–electron interactions. Realizing that Anderson localization is a wave phenomenon relying on interference, these concepts were extended to optics3,4. Indeed, both weak5,6,7,31 and strong8,9,10,11 localization effects were experimentally demonstrated, traditionally by studying the transmission properties of randomly distributed optical scatterers (typically suspensions or powders of dielectric materials). However, in these studies the potential was fully random, rather than being ‘frozen’ fluctuations on a periodic potential, as the Anderson model assumes. Here we report the experimental observation of Anderson localization in a perturbed periodic potential: the transverse localization of light caused by random fluctuations on a two-dimensional photonic lattice. We demonstrate how ballistic transport becomes diffusive in the presence of disorder, and that crossover to Anderson localization occurs at a higher level of disorder. Finally, we study how nonlinearities affect Anderson localization. As Anderson localization is a universal phenomenon, the ideas presented here could also be implemented in other systems (for example, matter waves), thereby making it feasible to explore experimentally long-sought fundamental concepts, and bringing up a variety of intriguing questions related to the interplay between disorder and nonlinearity.

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Figure 1: Transverse localization scheme.
Figure 2: Experimental results for propagation in disordered lattices.
Figure 3: Results of numerical simulations of linear propagation in disordered lattices.
Figure 4: Numerical (top row) and experimental (bottom row) results, showing the effects of nonlinearity on Anderson localization.

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Acknowledgements

We are indebted to our colleagues B. Shapiro and E. Akkermans for discussions on Anderson localization. This research was supported by the Israeli Science Foundation, by the German-Israeli DIP Project, and by the Russell Berrie Nanotechnology Institute at the Technion, Israel.

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Authors and Affiliations

  1. Physics Department, Technion—Israel Institute of Technology, Haifa 32000, Israel,

    Tal Schwartz, Guy Bartal, Shmuel Fishman & Mordechai Segev

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  1. Tal Schwartz
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Correspondence to Mordechai Segev.

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Supplementary information

Supplementary Information

This file contains Supplementary Discussion, Supplementary Experimental Methods, Supplementary Figure 1 with Legend, Supplementary Numerical Methods and additional references. Supplementary Discussion is shown as Supplementary Information A. Supplementary Information B describes the experimental setup and the generation of a z-invariant disordered lattice and includes Supplementary Figure 1 showing a schematic diagram of the system. Supplementary Information C describes the numerical simulations used and contains a discussion on the estimated values of the mean free path and localization length. (PDF 1074 kb)

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Schwartz, T., Bartal, G., Fishman, S. et al. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007). https://doi.org/10.1038/nature05623

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