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) over bar 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) over bar 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. (C) 2011 Optical Society of America