Waves on Wednesday Seminar Series

Wednesday, February 23,  2005, 10:00 am
Cullimore 611
New Jersey Institute of Technology


EMP Propagation in the Cole-Cole Dielectric Model: Asymptotics and Numerics

Peter Petropoulos

Department of Mathematical Sciences


Abstract (in HTML)

We investigate time-domain electromagnetic pulse propagation in a dispersive lossy dielectric half-space whose properties are described in the frequency-domain by the Cole-Cole model $\epsilon(\omega)=\epsilon_{\infty}+\frac{\epsilon_s-\epsilon_{\infty}} {1+(i\omega\tau)^{\alpha}}$, $0<\alpha <1$. With asymptotic techniques we calculate the small-depth impulse response and determine it is infinitely smooth at the wavefront. This result contrasts the case of the Debye medium ($\alpha=1$) in which the wavefront supports discontinuities that decay exponentially with depth. Then, with asymptotic and numerical methods we investigate the large-depth impulse response. We find that while the saddle-point method accurately predicts the space-time location of the peak of the response it is of limited applicability in the full determination of such response. Significantly, we find the peak of the response for $0<\alpha<1$ arrives earlier than in the case of $\alpha=1$. Our asymptotic results are validated with independent results obtained numerically.