The richness of the dispersion relation of electromagnetic bandgap materials

We review several effects that arise from the richness of the dispersion relation of the electromagnetic bandgap materials (EBGMs). Indeed, EBGMs could simulate homogenous material whose optical index is lower than one or even negative (at least for the refraction). We take advantage of this property to design a lens with very short focal length or to confine emission in a narrow lobe. It is also shown how one can take advantage of the rapidly varying properties of the EBGMs near a band edge to design a prism whose dispersion is greater than any conventional prism or grating.