Direct observation of a localization transition in quasi-periodic photonic lattices

The localization of waves in non-periodic media is a universal phenomenon, occurring in a variety of different quantum and classical systems, including condensed-matter, Bose-Einstein condensates in optical lattices, quantum chaotic systems, sound waves and light. A localization phase transition is expected to occur in three dimensional disordered systems as the strength of disorder crosses a critical value. Recently, a crossover from an extended to a localized phase has been observed in low-dimensional photonic lattices and Bose-Einstein condensates. Other experiments studied the critical behaviour near the transition in three dimensions via transmission measurements. However, no direct observation of a localization transition for light has been reported. In 1979 Aubry and Andre predicted that for a certain class of quasi-periodic potentials, a localization phase transition can occur already in one-dimension. This strongly correlated potential is markedly different from the disordered case were the potential is uncorrelated. Here we report an experiment that realizes the Aubry-Andre model in quasi-periodic photonic lattices. We observe the signature of a localization phase transition by directly measuring the expansion rates of initially narrow wave packets propagating in the lattice. Below the transition point, all the modes of the system are extended and therefore an initially narrow wave-packet eventually spreads across the entire lattice. Above the critical point, all modes are localized and expansion is suppressed. In addition, we study the effect of weak nonlinear interactions on light propagation below and above the transition.