Slowing down and reflection of waves in truncated periodic media

We consider wave propagation and scattering governed by one dimensional 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 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. I. Introduction This paper is designed to provide a mathematical foundation for studying the processes of slowing down of the wave packets in periodic media. The problem of creating compact and efficient optical delay devices has been very actively discussed in literature for the last several years, but it has not yet been solved technologically. Such devices can find many applications, for example in synchronizing the work of very fast optical elements and much slower electronics. Several different mechanisms to slow down the propagation of wave packets have been considered Most of them are based on a use of periodic media with a flat dispersion relation ω = ω(k) in some region. For such media, the derivative k ′ (ω) is very big, and the group velocity V g (ω) =