Multiple Bragg wave coupling in photonic band-gap crystals

We report angle and polarization resolved reflectivity from strongly photonic fcc crystals consisting of air spheres in titania. For a $30°$ range of angles of incidence, multiple peaks with distinct polarization dependence are observed that clearly reveal avoided crossing behavior. Calculated photonic dispersion curves show that the multiple peaks result from band repulsion of Bloch states due to simultaneous Bragg diffraction by (111) and (200) planes. Our results demonstrate that many-wave coupling leads to substantial deviations from simple Bragg diffraction, with significantly flattened bands, a requirement for the appearance of complete photonic band gaps.