Transport and Anderson localization in disordered two-dimensional photonic lattices

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 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.

The random mass Dirac model and long-range correlations on an integrated optical platform

“…If that region is large enough and the disorder conditions are homogeneous across it, such a spatial average will be entirely equivalent to an ensemble average over many realizations of the same disorder on a smaller region 48 . This equivalence is commonly exploited in the optical observation of Anderson localization 18,49,50 and has recently been empirically verified 51 .…”

“…We fabricated 65 waveguide lattices with s ¼ 0.9 k, each comprising N ¼ 23 cells and a kink, randomly positioned on the interval kA [2,18] according to the triangular probability distribution P(k)p(18 À k). The upper limit is chosen such that the right-hand boundary at n ¼ N ¼ 23 does not have any significant influence on the gap state.…”

“…Disorder effects have been widely investigated in the context of non-relativistic physics, modelled by a Schrödinger equation with a disordered potential and leading to the famous Anderson localization [16][17][18][19][20] . The major difference between non-relativistic and relativistic disordered systems lies in the number of occurring length scales and the nature of the resulting correlations.…”

Universal scheme to generate metal–insulator transition in disordered systems

“…Another seminal work along this direction is the scaling theory of localization [5], which indicates that all electronic states are exponentially localized in low-dimensional noninteracting systems even for infinitesimal disorder and become localized in three-dimensional (3D) systems with sufficiently large disorder strength. In fact, Anderson localization is a universal wave phenomenon and has been observed experimentally in a wide variety of systems, including light [6][7][8][9], microwaves [10], acoustic waves [11,12], and matter waves [13][14][15][16][17].…”

Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal

“…section reveals two aspects of transport characteristics in the quasicrystal. An average intensity profile close to the Gaussian shape corresponds to diffusive transport 26 26 . The intensity profile for the diamond structure is quite distinct from those of the quasicrystal (Fig.…”