Slowdown of the wave packages in finite slabs of periodic medias

Abstract

A simple mathematical model is provided for a description of wave propagation through finite slabs of periodic media. The model concerns the devices of CROW (coupled resonators optical waveguide) type which are widely discussed in physical literature in the last several years. An incident pulse is considered, whose frequency is distributed in a small neighbourhood of a singular frequency for which the dispersion relation of the medium is very flat, and the group velocity (for the infinite medium) is small. It is proved that only a small part of the energy of the pulse propagates with the speed of light. Another part of the energy propagates with the group velocity. The price to pay for this slowdown is the reflection of the majority of the energy of the incident pulse.