We present an overview of the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by linear and nonlinear waveguides. First we consider a single layer with a cubic nonlinear response (a nonlinear slab waveguide) embedded in 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 model of nonlinear photonic crystals. We emphasize both similarities to and differences from the models described by the discrete nonlinear Schrödinger equation, which is derived in the tight-binding approximation, and the coupled-mode theory, which is valid for shallow periodic modulations.
© 2002 Optical Society of America
Andrey A. Sukhorukov and Yuri S. Kivshar, "Nonlinear guided waves and spatial solitons in a periodic layered medium," J. Opt. Soc. Am. B 19, 772-781 (2002)