Self-guiding in two-dimensional photonic crystals.

Dielectric periodic media can possess a complex photonic band structure with allowed bands displaying strong dispersion and anisotropy. We show that for some frequencies the form of iso-frequency contours mimics the form of the first Brillouin zone of the crystal. A wide angular range of flat dispersion exists for such frequencies. The regions of iso-frequency contours with near-zero curvature cancel out diffraction of the light beam, leading to a self-guided beam.