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This paper presents a time-domain technique to compute the electromagnetic field and to reconstruct an unknown 1-D slab of finite length characterized by a permittivity profile. The modeling tool is divided into a forward and an inverse solver. The forward solver computes the internal electromagnetic field of a known slab, whereas the inverse scheme solves an inverse scattering problem by reconstructing the permittivity profile of an unknown slab. Both the solvers have been found to have the ability to deal with different types of slabs and incident transient electromagnetic pulses. They have been validated against synthetic data and also been applied to measured time domain reflectometry (TDR) data.