Slowing down and reflection of waves in truncated periodic media

We consider wave propagation and scattering governed by 1-D Schrödinger operators with truncated periodic potentials. The propagation of wave packets with narrow frequency supports is studied. The goal is to describe potentials for which the group velocity (for a periodic problem) is small and the transmission coefficient for the truncated potential is not too small, i.e. to find media where a slowing down of the wave packets coexists with a transparency.