By recasting the definition of the dielectric constants in terms of currents, as well as using atomistic simulations and analytical derivations, we show that the dielectric permittivity can be negative at an ultrashort timescale, under perfect screening conditions and for very different materials and switching mechanisms, in line with recent experiments and modelings. In particular, we found that this effect can be due to a previously overlooked phenomenon of postswitching polarization oscillations. We also derived practical analytical formulas that can be experimentally checked.