Self-trapping of light and nonlinear localized modes in 2D photonic crystals and waveguides

We overview our recent results on the nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we describe the existence domains for nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.