Long-range interaction and nonlinear localized modes in photonic crystal waveguides

Nonlinear photonic crystals and nonlinear waveguides embedded into photonic structures with periodically modulated dielectric constant are used for the generation and observation of nonlinear localized modes. The effectivity of the waveguides is nonlocal and has been described by a nonlinear lattice model with long-range coupling and nonlocal nonlinearity. A theory of nonlinear localized modes that can be excited in photonic crystal waveguides of different geometry has been developed. The existence of such modes for the frequencies in the photonic band gaps has been predicted for 2D and 3D photonic crystals with Kerr nonlinearity.