Superluminal integrated waveguides

We consider a planar dielectric waveguide with a very sharp thin slab of distinct refractive index immersed on it. We obtain the band structure of this integrated waveguide as function of the contrast index, and show that there are propagating modes whose transverse distribution of their amplitudes is both oscillating and exponentially decaying. The oscillating modes exhibit the usual dispersion relation of a standard waveguide, while the evanescent modes give place to a different dispersion relation which does not have cut-off frequency and whose group velocity is superluminal. Thus, this guide allows us for a sub-wavelength propagation regime, as observed in certain metamaterials waveguides.