Band structure of photonic crystals and optical Bloch oscillations

The light Bloch oscillations in the array of the coupled waveguides are investigated using the multiple-scattering formalism based on the electrodynamics of continua approach. The axes of the waveguides are parallel and belong to the same plane. Each waveguide is supposed to be an infinite homogeneous cylinder. A special case when the refractive index of the waveguides increases steadily in the lateral direction. To describe the path of the light beam, the local isofrequency curve is calculated. It is found that the beam path represents the Bloch oscillation - a spatial periodic light motion in the array. The results obtained possess a good correspondence with the experimental data available.