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

Keywords: wave-guides; breathers; existence; solitons; states; bends

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