Wave propagators for transient waves in periodic media

Abstract

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.

Time-domain theory of forerunners

“…This result, which is a generalization of Sommerfeld's result [4] for the single-resonance Lorentz medium, has been obtained before using various methods [15,16]. Notice that the forerunner in the Lorentz medium is highly oscillating.…”

Electromagnetic Wave Propagation in Dispersive and Complex Material with Time-Domain Techniques

“…The first formula is appropriate for Debye media (K(+0) < 0) and the second for Lorentz media (K(+0) > 0). This result, which is a generalization of Sommerfeld's result [29] for the single-resonance Lorentz medium, has been obtained before using various methods [14,24]. Notice that the forerunner in the Lorentz medium is highly oscillating.…”

The theory of the propagation of TEM-pulses in dispersive bi-isotropic slabs

“…The invariance of the wave propagators under translations in the spatial variable z is due to homogeneity. Wave propagators for dielectrics were introduced by Karlsson and Stewart [7]. The wave propagators P ± fully determine the propagating fields along the characteristics and satisfy the relations…”