  We study the electric permittivity of the QED vacuum in the presence of a
strong constant electric field, motivated by the analogy between the
dynamically-assisted Schwinger effect in strong-field QED and the Franz-Keldysh
effect in semiconductor physics. We develop a linear-response theory based on
the non-equilibrium in-in formalism and the Furry-picture perturbation theory,
with which and also utilizing the Kramers-Kr\"onig relation, we calculate the
electric permittivity without assuming weak fields and low-frequency probes. We
discover that the electric permittivity exhibits characteristic oscillating
dependence on the probe frequency, which directly reflects the change of the
QED-vacuum structure by the strong field. We also establish a quantitative
correspondence between the electric permittivity and the number of
electron-positron pairs produced by the dynamically-assisted Schwinger effect.
