  We demonstrate that high transmission through sharp bends in photonic crystal
waveguides can be described by a simple model of the Fano resonance where the
waveguide bend plays a role of a specific localized defect. We derive effective
discrete equations for two types of the waveguide bends in two-dimensional
photonic crystals and obtain exact analytical solutions for the resonant
transmission and reflection. This approach allows us to get a deeper insight
into the physics of resonant transmission, and it is also useful for the study
and design of power-dependent transmission through the waveguide bends with
embedded nonlinear defects.
