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Статья

Fractional-Calculus-Based FDTD Algorithm for Ultrawideband Electromagnetic Characterization of Arbitrary Dispersive Dielectric Materials

IEEE Transactions on Antennas and Propagation. 2016. No. 8. P. 3533-3544.
Caratelli D., Mescia L., Bia P., Stukach O.

A novel finite-difference time-domain algorithm
for modeling ultrawideband electromagnetic pulse propagation
in arbitrary multirelaxed dispersive media is presented. The
proposed scheme is based on a general, yet computationally
efficient, series representation of the fractional derivative operators
associated with the permittivity functions describing the
frequency dispersion properties of a given 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 with alternative
numerical methodologies available in the scientific literature,
the proposed technique features a significantly enhanced accuracy
in the solution of complex electromagnetic propagation
problems involving higher order dispersive dielectrics, such as
the ones typically encountered in geoscience and bioengineering
applications.