Transmission and reflection of normally incident, pulsed electromagnetic plane waves upon a Lorentz half-space

Abstract

One-dimensional propagation of a normally incident, pulsed electromagnetic plane wave upon an isotropic, spatially homogeneous, Lorentz half-space is investigated analytically. Fourier integral representations of the time-dependent reflected and transmitted fields are obtained for an arbitrary incident pulse, and detailed examinations of these fields are made when the incident field is a finite-cycle-sine function. The inversion integral for the time-dependent reflected field is expressed in terms of the pole contribution and branch-cut integrals, whereas the uniform asymptotic methodology of Oughstun Sherman [J. Opt. Soc. Am. A6, 1394 (1989)] is applied to the transmitted field. Only the contribution from the distant saddle points to the transmitted field is studied in detail. An example is provided that shows that the effects of including the reflection and transmission coefficients may not be ignored when microwave or optical pulses are launched across the interface. Specifically, for Brillouin’s choice of the medium’s physical parameters, the reflected field has a peak value that is 21% of the incident field’s amplitude and that corresponds to a 21% decrease in the main signal (pole contribution) of the transmitted field when the transmission coefficient is unity. This study extends past analytical formulations of the one-dimensional problem by conducting an in-depth analysis of the reflected field for a normally incident finite-cycle-sine wave and by addressing how inclusion of frequency-dependent transmission and reflection coefficients affects the fields. In particular, situations for which the effect of the frequency-dependent transmission and reflection coefficients is significant are discussed. Finally, the analysis of the reflected field should be useful for diagnostic purposes.