On the Time-Domain Response of Havriliak-Negami Dielectrics

We apply a combination of asymptotic and numerical methods to study electromagnetic pulse propagation in the Havriliak-Negami permittivity model of fractional relaxation. This dielectric model contains the Cole-Cole and Cole-Davidson models as special cases. We analytically determine the impulse response at short and long distances behind the wavefront, and validate our results with numerical methods for performing inverse Laplace transforms and for directly solving the time-domain Maxwell equations in such dielectrics. We find that the time-domain response of Havriliak-Negami dielectrics is significantly different from that obtained for Debye dielectrics. This makes possible using pulse propagation measurements in TDR setups in order to determine the appropriate dielectric model, and its parameters, for the actual dielectric whose properties are being measured.

[1]  W. Coffey,et al.  Microscopic models for dielectric relaxation in disordered systems. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  W. Marsden.  I and J , 2012 .

[3]  Jeong-Ki Pack,et al.  Dispersive effect of UWB pulse on human head , 2007, EMC 2007.

[4]  F. Barnes,et al.  Handbook of biological effects of electromagnetic fields , 2007 .

[5]  Peter G. Petropoulos,et al.  The wave hierarchy for propagation in relaxing dielectrics , 1995 .

[6]  R. Hilfer,et al.  H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  R. W. Lau,et al.  The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. , 1996, Physics in medicine and biology.

[8]  T. M. Roberts.  Measured and predicted behavior of pulses in Debye- and Lorentz-type materials , 2004, IEEE Transactions on Antennas and Propagation.

[9]  R. Cole,et al.  Dielectric Relaxation in Glycerine , 1950 .

[10]  K. Cole,et al.  Dispersion and Absorption in Dielectrics II. Direct Current Characteristics , 1942 .

[11]  Kremer,et al.  Scaling of the alpha relaxation in low-molecular-weight glass-forming liquids and polymers. , 1991, Physical review letters.

[12]  Everett G. Farr,et al.  Ultra-Wideband Antennas and Propagation. Volume 4: Impulse Propagation Measurements of Water, Dry Sand, Moist Sand, and Concrete. , 1997 .

[13]  Tapani Repo,et al.  Application of Impedance Spectroscopy for Selecting Frost Hardy Varieties of English Ryegrass , 1996 .

[14]  Dispersive effect of UWB pulse on human head , 2007, 2007 18th International Zurich Symposium on Electromagnetic Compatibility.

[15]  Matthew F. Causley,et al.  Incorporating the Havriliak-Negami dielectric model in the FD-TD method , 2011, J. Comput. Phys..

[16]  R. Cole,et al.  Dielectric Relaxation in Glycerol, Propylene Glycol, and n‐Propanol , 1951 .

[17]  P. Petropoulos.  On the time-domain response of cole-cole dielectrics , 2005, IEEE Transactions on Antennas and Propagation.

[18]  M. Kelbert,et al.  Pulses and Other Wave Processes in Fluids , 1996 .

[19]  Peter G. Petropoulos,et al.  Asymptotics and energy estimates for electromagnetic pulses in dispersive media , 1996 .

[20]  J. Garnier,et al.  Fractional precursors in random media , 2010 .

[21]  S. Havriliak,et al.  A complex plane representation of dielectric and mechanical relaxation processes in some polymers , 1967 .

[22]  K. Cole,et al.  Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics , 1941 .

[23]  Lloyd N. Trefethen,et al.  Parabolic and hyperbolic contours for computing the Bromwich integral , 2007, Math. Comput..