Nonlinear guided waves and spatial solitons in a periodic layered medium

We overview the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by a sequence of linear and nonlinear layers. First, we consider a single layer with a cubic nonlinear response (a nonlinear waveguide) embedded into a periodic layered linear medium, and describe nonlinear localized modes (guided waves and Bragg-like localized gap modes) and their stability. Then, we study modulational instability as well as the existence and stability of discrete spatial solitons in a periodic array of identical nonlinear layers, a one-dimensional nonlinear photonic crystal. Both similarities and differences with the models described by the discrete nonlinear Schrodinger equation (derived in the tight-binding approximation) and coupled-mode theory (valid for the shallow periodic modulations) are emphasized.