Spatial optical solitons in waveguide arrays

We overview theoretical and experimental results on spatial optical solitons excited in arrays of nonlinear waveguides. First, we briefly summarize the basic properties of the discrete nonlinear Schrödinger (NLS) equation frequently employed to study spatially localized modes in arrays, the so-called discrete solitons. Then, we introduce an improved analytical model that describes a periodic structure of thin-film nonlinear waveguides embedded into an otherwise linear dielectric medium. Such a model of waveguide arrays goes beyond the discrete NLS equation and allows studying many new features of the nonlinear dynamics in arrays, including the complete bandgap spectrum, modulational instability of extended modes, different types of gap solitons, the mode oscillatory instability, the instability-induced soliton dynamics, etc. Additionally, we summarize the recent experimental results on the generation and steering of spatial solitons and diffraction management in waveguide arrays. We also demonstrate that many effects associated with the dynamics of discrete gap solitons can be observed in a binary waveguide array. Finally, we discuss the important concept of two-dimensional (2-D) networks of nonlinear waveguides, not yet verified experimentally, which provides a roadmap for the future developments of this field. In particular, 2-D networks of nonlinear waveguides may allow a possibility of realizing useful functional operations with discrete solitons such as blocking, routing, and time gating.