Uniform in Time Asymptotic and Numerical Methods for Propagation in Dielectric Exhibiting Fractional Relaxation and Efficient and Accurate Impedance Boundary Conditions for High-Order Numerical Schemes for the Time-Dependent Maxwell Equations
Abstract
In this paper we examine the small- and large-depth response of a Cole-Cole dielectric half-space subjected to a prescribed incident pulse; the case of delta-function incidence is employed to determine and analyze the resulting impulse response. Our purpose is to contrast our findings to the corresponding ones obtained for the Debye model in order to ascertain whether the time-domain waveforms obtained in a TDR experiment could serve as a means for selecting the most appropriate frequency-domain model for the experimentally obtained dielectric data. Our approach involves both asymptotic and numerical methods. We find that the Cole-Cole model's impulse response is in find that the Cole-Cole model's impulse response is infinitely smooth at the wavefront (small-depth), and determine its shape. It follows that sawtooth and square-pulse waveforms, and all other realistic waveforms, become smooth after travelling a brief time in any Cole-Cole model. This is in contrast to the case of the Debye impulse response which is discontinuous at the wavefront.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 14, 2008
- Accession Number
- ADA479286
Entities
People
- Peter G. Petropoulos
Organizations
- New Jersey Institute of Technology