An area of intense research is that of photonics, where light propagation features are controlled by clever engineering of periodic optical structures. Perhaps the best known photonic devices are the fiber Bragg grating and photonic crystal fibers. In both cases there is plenty of experimental work that illustrates the rich dynamics that emerges when linear periodic properties combine with nonlinear intensity dependent effects. Phenomena such as slow gap soliton dynamics in fibers and supercontinuum generation in photonic crystal fibers have been observed only when periodicity and nonlinearity are present.

In this work we consider optical pulse dynamics in two nonlinear periodic geometries: a two dimensional nonlinear waveguide Bragg grating and a periodic array of nonlinear optical fibers. What we will show in the first case is the existence of nontrivial optical bullet dynamics such as light trapping, bending and switching. The second geometry presents a unique nonlinear system to study light localization in a discrete disordered system. This disorder is due to manufacturing imperfections resulting in unequal spacing between neighbor fibers. Our results will show how discrete linear diffraction, random coupling modeled as linear multiplicative noise and self-focusing nonlinearity compete to either enhance or deter spatial localization.