Slow light enhanced nonlinear optics in periodic structures

We review recent advances related to slow light in periodic structures, where the refractive index varies along one or two directions, i.e. gratings and planar photonic crystals. We focus on how these geometries are conducive to enhancing the nonlinear interaction between light and matter. We describe the underlying theory developed for shallow gratings, but whose conclusions can be extended to planar photonic crystal waveguides, in particular the enhancement of third-order nonlinear processes with slow light. We review some experiments showing how gratings have been used for pulse compression and the generation of slow gap solitons. We then present recent nonlinear experiments performed in photonic crystal waveguides that demonstrate the strong reinforcement of nonlinear third-order optical phenomena with slow light. We discuss the challenges associated with slow light in these 2D structures and their unique advantage-dispersion engineering-for creating broadband nonlinear devices for all-optical signal processing. By breaking down the relation between dispersion and group velocity imposed in gratings, these structures also offer new opportunities for generating soliton-like effects over short length scales, at low powers and with short pulses.