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Transport and Anderson localization in disordered two-dimensional photonic lattices

机译：无序二维光子晶格中的输运和安德森局部化

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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 lattice. 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 localized. 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 optics. Indeed, both weak and strong 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.
机译：固态物理学中最有趣的现象之一是安德森局部化，它预测电子在置于无序晶格中时可能会变得不动。定位的起源是由于电势中的随机缺陷而导致的电子多次散射之间的干扰，从而将本征模从扩展（布洛赫波）改变为指数定位。结果，材料从导体转变为绝缘体。安德森的工作可以追溯到1958年，但从未在原子晶体中观察到强的局部化，因为局部化仅在电势（周期性晶格和叠加在其上的涨落）与时间无关时才会发生。然而，在原子晶体中，由于热激发的声子和电子-电子相互作用，总是会出现与安德森模型的重要偏离。意识到安德森定位是一种依赖于干涉的波动现象，因此这些概念扩展到了光学。实际上，传统上通过研究随机分布的光学散射体（通常是电介质材料的悬浮液或粉末）的传输特性，通过实验证明了弱和强的局域效应。但是，在这些研究中，电势是完全随机的，而不是像安德森模型所假设的那样，是周期性电势的“冻结”波动。在这里，我们报告在扰动的周期性电势中的安德森定位的实验观察：由二维光子晶格上的随机波动引起的光的横向定位。我们证明了在存在障碍的情况下弹道运输是如何扩散的，并且与安德森本地化的交叉发生在较高的障碍水平上。最后，我们研究了非线性如何影响安德森局部化。由于安德森本地化是一种普遍现象，因此此处介绍的思想也可以在其他系统中实现（例如，物质波），从而使探索实验性的，长期寻求的基本概念成为可能，并提出了许多与之相关的有趣问题。无序与非线性之间的相互作用。

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