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The third test case pertains the pulse propagation inside a dispersive medium described by both the linear and exponential filling factor functions having f(0) = 0.
In our problem, the interface exists not only in the plasma-vacuum interface, but also in the inside of the inhomogeneous plasma cylinder which is the interface of two dispersive mediums.
The standard FDTD notation for the dispersive medium based on ADE method can be found in [21].
But if the dispersive medium shows appreciable conductivity, the plates charge up, resulting in electrode polarization, which masks the dielectric relaxation effect.