Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices

Abstract

We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one-dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly measured. Nonlinear perturbations enhance localization in one type and induce delocalization in the other. In a complementary approach, we study the evolution on short time scales of delta-like wave packets in the presence of disorder. A transition from ballistic wave packet expansion to exponential (Anderson) localization is observed. We also find an intermediate regime in which the ballistic and localized components coexist while diffusive dynamics is absent. Evidence is found for a faster transition into localization under nonlinear conditions.

Mobility transition from ballistic to diffusive transport in non-Hermitian lattices

“…Today, disorder is explored in many disciplines, such as optics 5 , solid-state physics 6 , acoustics 7 and matter waves 8,9 . In particular, optical systems attracted much interest, and so far numerous sub-ballistic transport phenomena based on disorder have been observed; these include the Anderson localization 5,10,11 , quantum decoherence 12 , Levy flights 13 and anomalous diffusion 14 .…”

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

“…Two-dimensional superlattices have successfully been implemented in directwritten waveguide systems 54 and a disorder could be introduced to them at ease by randomly exchanging the lattice ordering in both dimensions. Also, the interplay of non-linearities and disorder, which has proven to host a variety of interesting phenomena in non-relativistic systems 19,50,55 , is yet to be investigated in the relativistic context. A commonly considered non-linear Dirac equation contains an additional interaction term of third order in the spinor 56 , which can be implemented by a Kerr non-linearity in waveguide lattices 57 .…”

“…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].…”