Anderson localization of light in photonic lattices for dimensional crossover

Abstract

We study Anderson localization of light in a photonic lattice in which the dimension is gradually changing from one to two. The influence of nonlinearity and disorder effects on Anderson localization in such a transitional system is investigated numerically. A sharp difference between localization in the linear and nonlinear regimes is demonstrated. In the linear regime, localization is more pronounced in two dimensions, whereas in certain nonlinear regimes it is more pronounced in one dimension. We also find that the localization in the intermediate cases of crossover is less pronounced than in both the pure one-dimensional and two-dimensional cases in the linear regime, whereas in the nonlinear regime this depends on the strength of the nonlinearity. We find two different localization lengths in the system with dimensionality crossover.