TY - JOUR
T1 - On the time-domain response of Cole - Cole dielectrics
AU - Petropoulos, Peter G.
N1 - Funding Information:
Manuscript received November 5, 2004; revised July 13, 2005. This work was supported in part by the Air Force Office of Scientific Research (AFOSR), Air Force Materiel Command, USAF under Grant FA9550-05-1-0162. The author is with the Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2005.858837
PY - 2005/11
Y1 - 2005/11
N2 - 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 ε(ω) = ε ∞ + (εs - ε ∞)/(1 + (iωτ)α), 0 < α < 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 (α = l) 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 approximation of such response for times past the arrival of the peak. Significantly, we find the peak of the response for 0 < α < 1 arrives earlier than in the case of α = 1. Our asymptotic results are validated with independent results obtained numericall.
AB - 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 ε(ω) = ε ∞ + (εs - ε ∞)/(1 + (iωτ)α), 0 < α < 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 (α = l) 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 approximation of such response for times past the arrival of the peak. Significantly, we find the peak of the response for 0 < α < 1 arrives earlier than in the case of α = 1. Our asymptotic results are validated with independent results obtained numericall.
KW - Cole - Cole dielectric model
KW - Debye dielectric model
KW - Dispersive dielectrics
KW - Maxwell's equations
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U2 - 10.1109/TAP.2005.858837
DO - 10.1109/TAP.2005.858837
M3 - Article
AN - SCOPUS:28644436825
SN - 0018-926X
VL - 53
SP - 3741
EP - 3746
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 11
ER -