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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

NJIT

**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.