We review recent advances related to nonlinear propagation in periodic structures, where the refractive index varies along one or two directions, i.e. gratings and planar photonic crystals. I will present recent experiments showing how periodic media have been used for pulse compression and the generation of slow Bragg solitons. I then present recent nonlinear experiments performed in photonic crystal waveguides that demonstrate the strong reinforcement of nonlinear third-order optical phenomena with slow light with applications to optical switching, quantum light sources and broadband frequency conversion.
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