Nonlinear transmission and light localization in photonic-crystal waveguides

We study light transmission in two-dimensional photonic-crystal waveguides with embedded nonlinear defects. First, we derive effective discrete equations with long-range interaction for describing the waveguide modes and demonstrate that they provide a highly accurate generalization of the familiar tight-binding models that are employed, e.g., for the study of coupled-resonator optical waveguides. Using these equations, we investigate the properties of straight waveguides and waveguide bends with embedded linear and nonlinear defects. We emphasize the role of evanescent modes in the transmission properties of such waveguides and demonstrate the possibility of the nonlinearity-induced bistable (all-optical switcher) and unidirectional (optical diode) transmission. Additionally, we demonstrate adaptability of our approach for investigation of multimode waveguides by the example of the bound states in their constrictions.