Nonlinear Effects in Reduced-Dimensional Structures: From Wave Guide Arrays to Slow Light -- Nonlinear Effects in One-Dimensional Photonic Lattices -- Nonlinear Optical Waves in Liquid Crystalline Lattices -- Nonlinear Optics and Solitons in Photonic Crystal Fibres -- Spatial Switching of Slow Light in Periodic Photonic Structures -- Nonlinear Effects in Multidimensional Lattices: Solitons and Light Localization -- to Solitons in Photonic Lattices -- Complex Nonlinear Photonic Lattices: From Instabilities to Control -- Light Localization by Defects in Optically Induced Photonic Structures -- Polychromatic Light Localisation in Periodic Structures -- Periodic Structures for Matter Waves: From Lattices to Ratchets -- Bose-Einstein Condensates in 1D Optical Lattices: Nonlinearity and Wannier-Stark Spectra -- Transporting Cold Atoms in Optical Lattices with Ratchets: Mechanisms and Symmetries -- Atomic Bose-Einstein Condensates in Optical Lattices with Variable Spatial Symmetry -- Symmetry and Transport in a Rocking Ratchet for Cold Atoms -- Metamaterials: From Linear to Nonlinear Features -- Optical Metamaterials: Invisibility in Visible and Nonlinearities in Reverse -- Nonlinear Metamaterials -- Circuit Model of Gain in Metamaterials -- Discrete Breathers and Solitons in Metamaterials.

Optical information processing of the future is associated with a new generation of compact nanoscale optical devices operating entirely with light. Moreover, adaptive features such as self-guiding, reconfiguration and switching become more and more important. Nonlinear devices offer an enormous potential for these applications. Consequently, innovative concepts for all-optical communication and information technologies based on nonlinear effects in photonic-crystal physics and nanoscale devices as metamaterials are of high interest. This book focuses on nonlinear optical phenomena in periodic media, such as photonic crystals, optically-induced, adaptive lattices, atomic lattices or metamaterials. The main purpose is to describe and overview new physical phenomena that result from the interplay between nonlinearities and structural periodicities and is a guide to actual and future developments for the expert reader in optical information processing, as well as in the physics of cold atoms in optical lattices.