Self-collimation and focusing effects in zero-average index metamaterials.

One dimensional photonic crystals combining positive and negative index layers have shown to present a photonic band gap insensitive to the period scaling when the volume average index vanishes. Defect modes lying in this zero-n gap can in addition be obtained without locally breaking the symmetry of the crystal lattice. In this work, index dispersion is shown to broaden the resonant frequencies creating then a conduction band lying inside the zero-n gap. Self-collimation and focusing effects are in addition demonstrated in zero-average index metamaterials supporting defect modes. This beam shaping is explained in the framework of a beam propagation model by introducing an harmonic average index parameter.