Disorder-induced localization of light in one- and two-dimensional photonic lattices

We study Anderson localization of light in one-dimensional (1D) and 2D photonic lattices. The influence of nonlinearity and disorder on Anderson localization in both systems is studied numerically. A sharp difference between localization in the linear and the nonlinear regimes is observed. Localization in the linear regime is more pronounced in the 2D lattice than in the 1D lattice. In the nonlinear regime, the coexistence of nonlinearity and disorder leads us to different conclusions. There are different nonlinear regimes in which 1D localization is more pronounced than 2D localization.