Pulsed Reflection and Transmission for a Dispersive Half Space

One-dimensional propagation of a normally incident, pulsed finite-cycle sine, electromagnetic plane wave on an isotropic, spatially homogeneous, Lorentz half space is investigated analytically. Detailed examinations of the reflected and transmitted fields are made. The inversion integral for the time-domain reflected field is expressed in terms of pole contributions and branch-cut integrals, which are computed numerically whereas the uniform asymptotic methodology of Oughstun and Sherman is applied to the transmitted field. Only the contributions from the distant saddle points to the transmitted field are studied thoroughly. An example is provided that shows that the reflection and transmission coefficients may not be ignored. Specifically, for Brillouins choice of the mediums physical parameters, the reflected field has a peak value that is 21 of the incident fields amplitude and that corresponds to a 21 decrease in the main signal pole contributions of the transmitted field when the transmission coefficient is unity. This work generalizes past formulations by accounting for reflection from the medium and by addressing how inclusion of frequency-dependent transmission and reflection coefficients affects the fields.