论文信息 - FDTD Modeling of Wave Propagation in Cole-Cole Media With Multiple Relaxation Times

FDTD Modeling of Wave Propagation in Cole-Cole Media With Multiple Relaxation Times

A finite-difference time-domain (FDTD) method for simulating wave propagation in Cole-Cole dispersive media with multiple relaxation times is presented. The main difficulty that the proposed method circumvents is the presence of fractional derivatives in the time-domain representation of the polarization relation. The latter is approximated by a set of auxiliary differential equations using Pad approximants, where each approximant corresponds to a single relaxation time of the Cole-Cole model. The auxiliary differential equations are discretized by means of central differences and are further employed within a conventional FDTD scheme. The efficiency of the proposed method is demonstrated by simulating the propagation of a wideband Gaussian pulse that excites a one-dimensional Cole-Cole medium with two relaxation times.

I.T. Rekanos | T.G. Papadopoulos

[1] Bernard Jecko,et al. Application of fractional derivatives to the FDTD modeling of pulse propagation in a Cole–Cole dispersive medium , 1996 .

[2] F. Teixeira. Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media , 2008, IEEE Transactions on Antennas and Propagation.

[3] Ichiro Fukai,et al. A finite-difference time-domain formulation for transient propagation in dispersive media associated with Cole-Cole's circular arc law , 1990 .

[4] R. Luebbers,et al. Debye Function Expansions of Complex Permittivity Using a Hybrid Particle Swarm-Least Squares Optimization Approach , 2007, IEEE Transactions on Antennas and Propagation.

[5] M. Lindstrom,et al. A large-scale study of the ultrawideband microwave dielectric properties of normal breast tissue obtained from reduction surgeries , 2007, Physics in medicine and biology.

[6] K. B. Oldham,et al. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[7] Jian Li,et al. A New FDTD Formulation for Wave Propagation in Biological Media With Cole–Cole Model , 2006, IEEE Microwave and Wireless Components Letters.

[8] M.-R. Tofighi,et al. FDTD Modeling of Biological Tissues Cole–Cole Dispersion for 0.5–30 GHz Using Relaxation Time Distribution Samples—Novel and Improved Implementations , 2009, IEEE Transactions on Microwave Theory and Techniques.