Localization and trapping of light in one- and two-dimensional nonlinear periodic structures

Novel photonic crystals have been proposed and built where the phenomenon of light localization occurs. This localization takes many forms, including discrete and continuous gap solitons, trapping via defect modes, localization due to randomness, just to name some. In this paper we discuss pulse dynamics in nonlinear one-dimensional fiber Bragg gratings and two-dimensional periodic waveguides. Here, gap solitons propagate and are trapped into defect via resonant interactions. A third case we consider is that of light propagation in nonlinear fiber arrays where we add randomness that model imperfections in the separation between fibers. The model which describes the dynamics is the discrete nonlinear Schroedinger equation with random coupling coefficients. The question we address is whether light localization as a balance of discrete diffraction and nonlinearity is robust when random effects are present.