An Auxiliary Differential Equation Method for FDTD Modeling of Wave Propagation in Cole-Cole Dispersive Media

A method for modeling time-domain wave propagation in dispersive Cole-Cole media is presented. The Cole-Cole model can describe the frequency dependence of the electromagnetic properties of various biological tissues with great accuracy over a wide frequency range and plays a key role in microwave medical imaging. The main difficulty in the time-domain modeling of Cole-Cole media is the appearance of fractional time derivatives. In the proposed method a Padé approximation is employed resulting in auxiliary differential equations of integer order. A finite-difference time-domain method is developed to solve the differential equations obtained. The comparison of analytical and calculated relative complex permittivity values over wideband frequency domain proves the validity of the method.