This paper proposes a radial dependent dispersive finite-difference time-domain method for the modelling of electromagnetic cloaking structures. The permittivity and permeability of the cloak are mapped to the Drude dispersion model and taken into account in dispersive FDTD simulations. Numerical simulations demonstrate that under ideal conditions, objects placed inside the cloak are `invisible to external electromagnetic fields. However for the simplified cloak based on linear transformations, the back scattering has a similar level to the case of a PEC cylinder without any cloak, rendering the object still being `visible. It is also demonstrated numerically that the simplified cloak based on high-order transformations can indeed improve the cloaking performance.
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