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

We develop the theory of nonlinear localized modes (intrinsic localized mod es or discrete breathers) in two-dimensional (2D) photonic crystal waveguid es. We consider different geometries of the waveguides created by an array of nonlinear dielectric rods embedded into an otherwise perfect linear 2D p hotonic crystal, and demonstrate that the effective interaction in such wav eguides is nonlocal, being described by a nonlinear lattice model with long -range coupling and nonlocal nonlinearity. We reveal the existence of diffe rent types of nonlinear guided mode that are also localized in the waveguid e direction, and describe their unique properties, including bistability.