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Self-trapping of light and nonlinear localized modes in two-dimensional photonic crystals

We develop a theory of nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we demonstrate that it provides an accurate method for investigating the existence and properties of localized defect modes. Using this technique, we describe the existence of 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.