Waveform Parameter Estimation and Dispersive Material Characterization

Abstract

The re∞ection of short duration electromagnetic pulses from dielectric media is of interest in diverse technological applications, e.g., geophysics, material science and biomedical engineering. In this paper, the time domain pulse re∞ection from a dispersive lossy dielectric half space is investigated. The properties of a half space are described in frequency domain by the Debye and Cole-Cole models, respectively. The two models are commonly used to capture the relaxation-based dispersive properties. First, transient re∞ected pulses are analyzed and waveform parameters are estimated. Then, based on the estimation, the relationships between the waveform parameters of re∞ected pulses and the properties of dispersive material as well as incident angles are discussed. Meanwhile, the results obtained with the Debye model are compared to those obtained with the Cole-Cole model. The application of these results to material characterization and diagnosis is explored. There is excellent agreement between our results and those in the literature, which validates the correctness and efiectiveness of this work. Our technique is based on the numerical inversion of the Laplace transform, leads to good accuracy, and has a simple algorithm, short calculation time, small required memory size, readily controlled error and wide range of applicability. The knowledge of material properties is required in various technological flelds, such as geophysics, material science and biomedical engineering. The characterization of bulk materials would be the most direct way to acquire this knowledge and greatly helpful to understand the underlying physics at the microscopic level, which is much more complicated in comparison with the existing formula- tions of the bulk efiects. A typical approach to bulk material characterization is to examine re∞ected electromagnetic pulses from the interface between free space and the investigated material. Many kinds of materials show the relaxation-based dispersive properties that are commonly captured by the Debye (1) and Cole-Cole (2) models. The transient analysis of pulses re∞ected from a dispersive interface can be conducted in frequency domain flrst. Then the results in time domain may be ob- tained by carrying out a numerical Fourier transform of the frequency domain response. However, this is very time consuming since a wide frequency range needs to be considered. Furthermore, it is preferable to solve the problems directly in time domain under certain circumstances. The flnite difierence time domain (FDTD) technique can be applied to this problem, but computation costs can be high under some conditions. Rothwell (3) worked out the time domain re∞ection coe-cients of a Debye half space for both horizontal and vertical polarizations that involve exponential and modifled Bessel functions and require convolution operations to evaluate. To our knowledge, the time domain re∞ection coe-cient of a Cole-Cole half space for any polarization has been not avail- able so far. It is the purpose of this paper to develop a new technique for transient analysis of pulse re∞ection from Debye and Cole-Cole media, and apply this technique to waveform parameter estimation and material characterization. This technique is based on the numerical inversion of the Laplace transform and has several signiflcant advantages.