Wave propagators for transient waves in periodic media

One-dimensional propagation of transient EM-waves in periodic media is studied. The media are periodic in the direction of propagation and can be of finite or infinite length. Wave propagators, that map a transient field from one point in the medium to another, are introduced. A number of useful relations for the propagators are presented. Some of these relations are used in the determination of explicit expressions for the short time behavior of a transient wave as it propagates in a periodic medium. The theory is exemplified by several numerical examples