  We study the ultrafast Kerr effect and high-harmonic generation in type-II
superconductors by formulating a new model for a time-varying electromagnetic
pulse normally incident on a thin-film superconductor. It is found that type-II
superconductors exhibit exceptionally large $\chi^{(3)}$ due to the progressive
destruction of Cooper pairs, and display high-harmonic generation at low
incident intensities, and the highest nonlinear susceptibility of all known
materials in the THz regime. Our theory opens up new avenues for accessible
analytical and numerical studies of the ultrafast dynamics of superconductors.
