Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak–Negami Media

Fractional Calculus Based FDTD Modeling of Layered Biological Media Exposure to Wideband Electromagnetic Pulses

“…The system is irradiated by a plane wave propagating along the z-direction with the electric field linearly polarized along the x-axis. In particular, the excitation signal is a sinusoidally time-modulated Gaussian pulse having the same parameters reported in [22]. The chosen time and spatial steps are ∆t = 0.3 ps and ∆z = 0.1 mm, respectively.…”

“…Despite its simplicity, it was proven that this simple planar model produces SAR values very close to those obtained by using more complex ones [31]. Moreover, it has been demonstrated that the developed fractional derivative-based FDTD scheme allows an accurate space-time evaluation of electromagnetic field profiles in a broad frequency range [22][23][24][25][26]. The reflection and transmission of a electromagnetic wave at the tissue interface depends on the frequency, permittivity and conductivity of the involved biological materials.…”

“…In order to evaluate the electromagnetic field propagation inside the layered structure involving HN dielectric materials, the FDTD scheme proposed in [22][23][24][25][26] has been used. In particular, it implements a more general series representation of the Riemann-Liouville fractional derivative operator, and it takes into account multiple relaxation times, as well as ohmic losses occurring in common biological media displaying different dispersion mechanisms.…”

“…Moreover, the conventional total field/scattered field approach and the Courant stability criterion are considered. Thus, applying a second order accurate finite-difference scheme and the procedure detailed in [22][23][24][25][26] for the finite-difference discretization, the FDTD update equations for the electric field, E, the magnetic field H and the auxiliary displacement current density, J i , can be calculated within the HN media and UPML regions. In particular, by considering the standard Cartesian Yee cell grid for the FDTD scheme and applying the central difference discretization, a second order O (∆z) 2 truncation error is achieved.…”

Time-domain simulation for fractional relaxation of Havriliak-Negami type

“…The observation of experimental data has however showed that a pure Debye relaxation, in which the memory of the excitation is instantaneously lost, is rather uncommon in practice and several phenomena exhibit deviations from exponential decaying; this is the case, for instance, of electric polarization in non-standard media such as amorphous polymers or biological tissues (see, for instance, [2]- [4]). …”