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.Comment: 20 pages (LaTeX) with 12 figures (EPS
