Fractional-Calculus-Based FDTD Algorithm for Ultra-Wideband Electromagnetic Pulse Propagation in Complex Layered Havriliak-Negami Media

A novel finite-difference time-domain algorithm for modeling ultra-wideband electromagnetic pulse propagation in layered multi-relaxed Havriliak-Negami media is presented. The proposed scheme is based on a general, yet computationally efficient, series representation of the fractional derivative operator associated with the permittivity function describing the frequency dispersion properties of the dielectric material. Dedicated uniaxial perfectly matched layer boundary conditions are derived and implemented in combination with the basic time-marching scheme. Moreover, a total field/scattered field formulation is adopted in order to analyze the material response under plane-wave excitation. Compared to alternative numerical methodologies available in the scientific literature, the proposed technique features a significantly enhanced robustness and accuracy which are essential for solving complex electromagnetic propagation problems typically encountered in bio-engineering applications.