The goal of this study is to conduct an analytical study of the properties (permittivity and permeability or refractive index) of a dispersive time-dependent linear isotropic medium interacting with electromagnetic fields. It is found that the permittivity and permeability of the time-dependent dispersive medium may either have an exponential profile or a sinusoidal profile. The permittivity and permeability can vanish or can be negative as in metamaterials. Therefore, the refractive index can vanish, so the electromagnetic wave can propagate at an infinite speed (c ≫ 3·10⁸ m/s). It is also shown that the permittivity and permeability can simultaneously be negative as in left-handed metamaterials (LHM). The general electric field and magnetic field solutions are derived, and the electric and magnetic flux densities are evaluated. The wave dispersion relation is also analysed. The obtained solutions can be used to validate experimental results by applying the initial and boundary conditions which are appropriate to the experimental setup. ε
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