Electromagnetic Pulse Propagation across a Planar Interface Separating Two Lossy, Dispersive Dielectrics

  • John A. Marozas
  • Kurt E. Oughstun


Our understanding of the dynamics of pulse propagation in a homogeneous, isotropic, locally linear, temporally dispersive lossy medium is a fundamental problem in electromagnetic wave theory1–6. As a plane wave pulse propagates through a dispersive, lossy medium, each spectral component propagates with its own characteristic phase velocity v p (ω) = ω/β(ω) and is attenuated at a rate that is characterized by its own attenuation coefficient \(\alpha \left( \omega \right) = \Im \left\{ {\tilde k(\omega )} \right\}\), where \(\tilde k(\omega ) = \beta \left( \omega \right) + i\alpha \left( \omega \right)\) is the complex wavenumber of a time-harmonic plane wave of angular frequency ω. The relative phases and amplitudes of the spectral components of the initial pulse then change by differing amounts as the propagation distance increases, thereby giving rise to the observed distortion of the propagated pulse. The seminal analysis of dispersive pulse propagation in a linear dielectric filling the half-space z ≥ 0 was provided by Sommerfeld1 and Brillouin2,4 in 1914 using the asymptotic method of steepest descents. The recent analysis of Oughstun and Sherman7–9 using modern asymptotic expansion techniques has resulted in significant quantitative improvements in the entire description of the propagated field as well as a correct description of the signal velocity in causally dispersive media. This analysis has also led to a clear physical interpretation of the dynamical pulse evolution in a given dispersive medium in terms of the frequency dispersion of the attenuation coefficient and the energy transport velocity for a time-harmonic field9–11.


Dispersive Medium Transmitted Field Fresnel Reflection Coefficient Precursor Field Complex Wavenumber 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • John A. Marozas
    • 1
  • Kurt E. Oughstun
    • 1
  1. 1.College of Engineering and MathematicsUniversity of VermontBurlingtonUSA

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