Transport and Anderson localization in disordered two-dimensional photonic lattices

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(1). 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(2). 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(3,4). Indeed, both weak(5-7,31) and strong(8-11) 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.