A method for modeling reflectionless conductive dispersive slabs is presented. The slabs are impedance matched to the surrounding half-spaces and are temporally dispersive with a spatially varying impedance. It is shown that the effects from the variation of the impedance can be matched by the temporal dispersive effects and the conductivity so that for a normally incident plane wave the slab does not reflect any field regardless of the shape of the incident transient field. The problem of finding reflectionless media is formulated as an inverse problem where the constitutive relation is to be determined as a function of depth given a reflection kernel which is zero. The inverse problem is solved by a time domain Green functions technique
